Welcome to Alan Thompson's General Mathematics Quiz Sheets Links: Matching Items in Printable Format.

Topic Preview Gateway Page.

 This page is a gateway to other pages, as well as a comprehensive listing of the topics covered, the questions and their matched answers.

 By using CTRL-F various terms or words can be found so that the most useful topic can be located amongst the preview sheets.

 Links to each printable topic quiz can be found both near the top of this page, and between the preview sheets.

 Each topic has matching items statements to assist in gaining familiarisation with General Mathematics terms.


  

1. Link to all the topic question pages, with answers beside the questions, located further down on this webpage.

   Preview Topic Tests on this webpage.


2. Link to individual topic links for printable, 2 page sheets: questions followed by answers, all on separate web pages.

These links are below on this webpage. Note the links are also between between the preview topics located further down this webpage.

  Question/Answer single topic sheet links below


  

3. Link to the complete set of 43 topic question papers with answers collated onto separate consecutive pages, all on a single webpage.

   Question Sheets collated with Answer Sheets, all 43 topics.


  

4. Link to all the questions-only pages (no answers provided), all on a single webpage.

   Question Sheets only, all 43 topics.


  

5. Link to all the answers-only pages, in topic groups of 3, all on a single webpage.

   Answers only webpage, all 43 topics


  

6. Link to Preview sheets: all the question pages with-answers beside the questions. This is located on a separate webpage.

   Preview: Answers and Questions on the same page, all 43 topics.


 Further instructions for finding a suitable topic to print, or a set of answers, accompanies each of the pages indicated in 3 to 6 above.

 Essentially, once a page has loaded, find a topic with CTRL-F, and print by selecting a suitable area (with mouse) and then right click on the selected area to print.

Warning: using Ctrl-P can result the printing of the entire set of question/answer/question and answer sheets, up to around 46 pages depending on which web page you are viewing. Unfortunately, suitable pagination is not available.

  For suitable pagination it is best to access the separate topics from this webpage either via the topic index links immediately below, or via the links located between the preview pages further below.

 The site is set up like this so that you can navigate to the desired topic without relying on specific topic headings which often don't explain fully the contents of the topic.



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The following links open Printable Single Topic pages.

 These pages are composed of a page of matching items and a page with the answers. Using CTRL-P or right-click-mouse (then select print from pop-up menu), will lead to a 2 page print out. Questions on the first page. Answers on the second page.


    Worksheet   1    Probability 1

    Worksheet   2    Probability 2

    Worksheet   3    Probability 3 Arrangements

    Worksheet   4    Probability 4 Arrangements

    Worksheet   5    Statistics 1

    Worksheet   6    Statistics 2

    Worksheet   7    Statistics 3

    Worksheet   8    Statistics 4

    Worksheet   9    Statistics 5

    Worksheet  10   Statistics 6

    Worksheet  11   Statistics 7

    Worksheet  12   Statistics 8

    Worksheet  13   Statistics 9

    Worksheet  14   Statistics 10

    Worksheet  15   Financial Maths 1

    Worksheet  16   Financial Maths 2

    Worksheet  17   Financial Maths 3

    Worksheet  18   Financial Maths 4

    Worksheet  19   Financial Maths 5

    Worksheet  20   Financial Maths 6

    Worksheet  21   Financial Maths 7

    Worksheet  22   Financial Maths 8

    Worksheet  23   Financial Maths 9

    Worksheet  24   Algebra 1

    Worksheet  25   Algebra 2

    Worksheet  26   Algebra 3

    Worksheet  27   Algebra 4

    Worksheet  28   Algebra 5

    Worksheet  29   Algebra 6

    Worksheet  30   Algebra 7

    Worksheet  31   Measurement, Trigonometry, Geometry, Time 1

    Worksheet  32   Measurement, Trigonometry, Geometry, Time 2

    Worksheet  33   Measurement, Trigonometry, Geometry, Time 3

    Worksheet  34   Measurement, Trigonometry, Geometry, Time 4

    Worksheet  35   Measurement, Trigonometry, Geometry, Time 5

    Worksheet  36   Measurement, Trigonometry, Geometry, Time 6

    Worksheet  37   Measurement, Trigonometry, Geometry, Time 7

    Worksheet  38   Measurement, Trigonometry, Geometry, Time 8

    Worksheet  39   Measurement, Trigonometry, Geometry, Time 9

    Worksheet  40   Measurement, Trigonometry, Geometry, Time 10

    Worksheet  41   Measurement, Trigonometry, Geometry, Time 11

    Worksheet  42   Measurement, Trigonometry, Geometry, Time 12

    Worksheet  43   Measurement, Trigonometry, Geometry, Time 13



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  Questions: Sheet 1 Probability 1

  1   certain this is said of an event that has a probability of 1
  2   impossible this is said of an event that has a probability of 0
  3   frequency how often an event occurs
  4   probability the degree of likelihood of an event occurring on a scale of 0 to 1
  5   event the outcome of an experiment that we are interested in
  6   fifty-fifty describing two events have equal chance of occurring, probability = 1/2
  7   unlikely this is said of an event that has a small probability of occurring
  8   likely this is said of an event that has a high probability of occurring
  9   probable term describing where there is a very high chance of an event occurring
10   improbable term describing where there is a very low chance of an event occurring
11   general knowledge this is needed in order for a person to be able to describe the chances of an event occurring
12   sample space this is a list of all the possible outcomes of a probability experiment
13   number of elements this quantity in a sample space is the total number of possible outcomes
14   distinct elements possible outcomes in a sample space listing that are completely different
15   favourable outcomes the elements from a sample space that meet the requirements for a particular event to occur
16   multi-stage event situation where there is more than one part to a probability experiment
17   S = { , , , } sample space answer format
18   E = { , , , } elements in a sample space that fit particular criteria format
19   equally likely outcomes will be this if selection is random for one event



  Probability 1Two page printable: Student Answer Sheet followed by the Answers


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  Questions: Sheet 2 Probability 2

  1   tree diagram a diagram showing a branching for every stage of a probability experiment and the possible outcomes (and probabilities) at each stage
  2   follow branches once a probability tree diagram is drawn, this is done to find the sample spaces that occur
  3   once this is how often a tree diagram must branch for every stage of a multistage probability experiment
  4   use tree diagram a suitable technique used in any example where there is more than one stage to a probability experiment
  5   tree diagram this tool is useful in checking whether or not a series of random events result in outcomes that are equally likely
  6   fundamental counting principle the total number of ways that a succession of independent choices can be made is found by multiplying the number of ways each single choice is made
  7   independent choices the fundamental counting principle can be used to find the total possible choices if those choices are …
  8   ability this is one of the other factors that make outcomes to be not equally likely e.g., winners of a race
  9   relative frequency number of times an event has occurred/(divided by) number of trials
10   relative frequency this is used to estimate the probability of an event as a decimal or a percentage
11   P(event) probability of an event, number of favourable outcomes/total number of outcomes
12   sample space a list of all the possible outcomes in a probability experiment
13   event space a list of all favourable outcomes in a probability experiment
14   percent probability find probability as a fraction and then convert to percentage by multiplying by 100
15   decimal probability find probability as a fraction and then convert to decimal by dividing the numerator by the denominator
16   probability range from zero to one, from impossible to certain to occur
17   complement of an event the event that describes all other possible outcomes to the probability experiment
18   probability sum P(event) + P(complementary event) = 1
19   P(event) equals 1 - P(complementary event)



  Probability 2Two page printable: Student Answer Sheet followed by the Answers


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  Questions: Sheet 3 Probability 3 Arrangements

  1   ordered arrangements a random sequenced selection of items, solved by x! (i.e. x factorial) or, n x (n-1) x (n-2)...... x 1
  2   ordered selection number of first choices that can be made times number of second choices that can be made times... x! (i.e. x factorial), a permutation
  3   unordered arrangements these selections have no set order e.g. representative team selection, no ranking
  4   ordered selections these selections have a definite order like first, second, third; captain, vice-captain
  5   unordered selection a random unsequenced selection of items, solved by dividing the number of ordered selections by the number of possible arrangements of those selected
  6   unordered selection a random selection of items solved by x!/y!: n x (n-1) x (n-2) ... x 1 divided by m x (m-1) x ( m-2) x ... x 1; i.e. ordered selections divided by possible arangements
  7   probability tree tree diagram using probability of events on the branches especially in situations where each event has a different probability
  8   probability formula P(event) = number of favourable outcomes per total number of possible outcomes
  9   unordered selection probability calculate the number of ordered selections that can be made (x!) and divide it into number of arrangements of the selected (y!)
10   at least one questions asking for this are solved using the complementary event method: P(event) = 1 - P(not event)
11   one this is the sum of the probability of an event and its complement
12   probability changes this is a reason for reading a question carefully and applying the information to a probability tree diagram
13   add probabilities this is done if an outcome can be obtained in more then one way as observed with a probability tree, process used between branches of the probability tree
14   multiply probabilities this mathematical operation is performed on probabilities linked along branches of a probability tree
15   permutation an arrangement of a set of objects into a sequence or order from which selections are made one at a time, the number of which can be found with x!



  Probability 3 ArrangementsTwo page printable: Student Answer Sheet followed by the Answers


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  Questions: Sheet 4 Probability 4 Arrangements

  1   expected outcomes this is found by multiplying the number of times a trial is repeated by the probability of an event
  2   average expected outcome where probability multiplied by trials results in a fraction or decimal and yet only whole units are possible (by rounding)
  3   expected referring to outcomes, meaning that a number of outcomes is predicted but may not actually occur
  4   financial expectation average return in a financial (gambling) situation where probability of a positive result is known
  5   financial result money returned by a particular outcome in gambling
  6   financial expectation multiply the financial result of each outcome by the probability of each outcome and add the results
  7   negative financial outcome financial loss is indicated by this
  8   positive financial outcome financial gain is indicated by this
  9   two-way table a two-dimensional grid that shows the outcome of an experiment in terms of two variables, e.g. medical tests which indicate positive results, false positive results, negative results and false negative results
10   rows part of a two-way table that displays the numbers of things with and without a condition
11   columns part of a two-way table that displays information about accuracy with regards to the numbers displayed for things with and without a condition
12   percentage accuracy of tests can be expressed in this form from a two-way table
13   probability an expression of the amount of certainty about the accuracy of tests, as determined from numbers in a two-way table
14   same total relationship between the sum of a two-way table rows and the sum of the two-way table columns. Used to determine missing information
15   probability a use of a completed two-way table to determine the chances of a particular outcome, e.g. a true positive result vs a false positive result



  Probability 4 ArrangementsTwo page printable: Student Answer Sheet followed by the Answers


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  Questions: Sheet 5 Statistics 1

  1   trends and conclusions reasons for analysing data, useful information that can be obtained from data
  2   external source place where data is found by researching the information available from other people, e.g. stock exchange tables
  3   internal source place where data is found by collecting it yourself, e.g. by observation and survey questioning
  4   observation method of obtaining internally sourced data in which a response is NOT required from people, data is obtained by watching and noting
  5   questioning method of obtaining internally sourced data in which a response IS required from people, data is obtained by filling in forms, surveys
  6   open ended type of question that makes analysis of internally sourced data difficult because of the wide range of responses obtained
  7   closed type of question that makes analysis of internally sourced data easier because there is a limited range of responses
  8   research method by which externally sourced data is obtained, using facts and figures supplied by other people
  9   table form the usual first form into which collected data is organised so that it can be easily analysed to find trends and draw conclusions
10   gate post tally method in which every fifth item counted is used to cross off 4 tallies, for easier counting of 5s, in frequency tables
11   category arbitrary division ranges that enable data to be more easily analysed, e.g. income range $0 to $120 divided into 6 equal sub-ranges: $0 to $20, $21 to $40, ….
12   tally a single stroke given for each occurrence of an item in a tally and gatepost column of a frequency table
13   graph most common way of displaying data for easier interpretation and understanding
14   column style of graph drawn when we wish to show quantity, categories being written on the horizontal axis and frequencies on the vertical axis
15   sector style of graph that is used when we want to compare quantities, related to the angles in a circle (fractions of 360o), requiring a key, a pie chart
16   statistical inquiry process being carried out when data is studied to find out what it means, produces conclusions about the data
17   quality control one of the uses to which companies put data analysis, to see if their products meet certain minimum standards



  Statistics 1Two page printable: Student Answer Sheet followed by the Answers


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  Questions: Sheet 6 Statistics 2

  1   privacy an issue related to information that people consider they should not provide in surveys, e.g. income, voting intentions
  2   ethical an issue related to uses to which information is put, e.g. selling data to other organisations that survey respondents my not wish to have access to their details
  3   privacy guarantees a way of ensuring that the data collected is retained by the person collecting the data and not passed on
  4   anonymous surveys a way of ensuring that the data collected cannot be linked to a particular person
  5   data grouping a way of ensuring specific details cannot be revealed, even with identified respondents to a survey
  6   sample a portion of the total population that is surveyed so that the results can be extended (extrapolated) to be related to the whole population
  7   target population the actual group of people who are to be surveyed, chosen at random or systematically
  8   database an organised set of data on a population
  9   census survey in which the entire population is counted and or questioned, in Australia this happens every 5 years
10   sampling a practical, economical, fast, and relatively accurate way of obtaining a target population for a survey
11   random sample a target population that has been chosen by a method in which luck is the only factor in deciding which members are to participate
12   stratified sample a target population for a survey chosen so that it has similar characteristics to the entire population (percentage proportion composition) e.g. pro rata student survey based on school year and the number of students in each year group, otherwise chosen at random
13   systematic sample a target population for a survey chosen according to some organised pattern
14   bias this occurs when the sample chosen for a survey is more likely to be of one opinion rather than representing the total population
15   categorical data data which is not numerical and can be grouped, e.g. types of cars, order does not matter
16   quantitative data data that can be measured and given a numerical value, order does matter
17   discrete data quantitative data that has only exact values, usually integers e.g. number of cars of each colour



  Statistics 2Two page printable: Student Answer Sheet followed by the Answers


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  Questions: Sheet 7 Statistics 3

  1   continuous data quantitative data that can have any value within certain limits, e.g. height, temperature, can be measured to various levels of accuracy
  2   unitary method a calculation method using ratio and percentage to determine the actual numbers represented by various fractions or percentages of a population
  3   capture-recapture a technique used to estimate populations that cannot be easily counted, involves capturing, tagging, releasing and recapturing and using percentage to determine the whole population
  4   percentage tagged in capture-recapture method of estimating population, this quantity equals (number tagged/number caught) x 100, on the second capture only
  5   unitary percentage method in capture-recapture, the percentage tagged in second capture is assumed equivalent to the percentage of the whole population represented by the tagged of the first capture; hence this method can be used to determine the whole population
  6   sample selection survey preparation needs to account for population characteristics such as age, sex, religion, socio-economic and ethnic backgrounds which all need to be in the same proportion as the whole population if the survey is to be related to the whole population
  7   frequency tables method used to tabulate data that allows ease in tallying of quantitative data
  8   score a term that can be used to describe each piece of data
  9   grouped continuous data being listed as a series of sub-ranges or classes
10   ungrouped discrete data being listed as separate categories
11   class centre used with grouped data to show the middle of the sub-ranges of continuous data being recorded
12   frequency total number of times a score (or class, or category) occurs
13   column headings for a frequency table, that involves grouped data classes: score, class centre, tally, frequency
14   dot plot a graph that is used to display a set of scores on a number line as a series of dots above the number line
15   sector graph also called a pie chart, used to compare quantities by dividing a circle in proportion to their frequencies
16   line graph a graph used to compare the change in one quantity with the change in another, suitable for continuous quantitative data
17   bar graph graph suitable for categorical data, in which horizontal rectangles are drawn from the vertical axis



  Statistics 3Two page printable: Student Answer Sheet followed by the Answers


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  Questions: Sheet 8 Statistics 4

  1   column graph graph suitable for categorical data, in which vertical rectangles are drawn from the horizontal axis
  2   radar charts a circular line graph that is useful for showing data trends that repeat in a cyclic manner e.g. annual average temperature
  3   misrepresentation this can be done to information shown graphically by adjusting the scale to magnify differences to appear as definite trends
  4   statistics graphs frequency histogram and frequency polygon: most useful when displaying or quantitative data
  5   histogram a graph that is similar to a column graph but in which there are no gaps left between the columns, used in analysing frequency
  6   only gap the first half unit space before the first column on a frequency histogram is left as this because the horizontal axis divisions are based on class centres
  7   one colour this is used if a frequency histogram is shaded because the joined columns are essentially representing different levels of the same thing
  8   vertical axis this is the axis used to represent frequency on a frequency histogram
  9   centre place under each column where the labels appear on a frequency histogram, e.g. data labels (ungrouped data) and class centre (grouped data)
10   frequency histogram a column graph showing frequency on the vertical axis and data category on the horizontal axis
11   frequency polygon a line drawn through the centres of the tops of the columns of a frequency histogram, commencing at zero and ending half a column away from the last column
12   cumulative frequency a running total of the frequencies column in a frequency table or graph, found by adding successively the frequency of each data category
13   no gap this is achieved on a cumulative frequency graph by leaving no half column space before the first column
14   cumulative frequency histogram a column graph showing cumulative frequency on the vertical axis and data category on the horizontal axis
15   cumulative frequency polygon a line drawn through the right hand corners of the tops of the columns of a cumulative frequency histogram, commencing at zero (bottom left of first column), ending at the top (right hand corner) of the last column
16   range the difference between the highest and lowest score: highest score - lowest score
17   interquartile range difference between upper and lower quartiles: upper quartile score - lower quartile score



  Statistics 4Two page printable: Student Answer Sheet followed by the Answers


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  Questions: Sheet 9 Statistics 5

  1   lower quartile lowest 25% of the scores
  2   upper quartile the highest 25% of the scores
  3   median middle score (for an odd number of scores) or the average of the two middle scores (for an even number of scores) found when scores are arranged in ascending order
  4   ascending order way in which scores have to be arranged in order to find lower and upper quartiles, and the median
  5   use of median finding upper and lower quartile after dividing the scores into two groups after having arranged them in ascending order
  6   decile a band of 10% of all scores, calculated in the same way as quartiles, using appropriate percentage on the vertical scale of a cumulative frequency graph
  7   finding quartiles use to which cumulative frequency polygons (drawn on cumulative frequency histograms) are put as the vertical axis can easily be divided into quartiles
  8   stem-and-leaf plots a method of displaying a data set where the first part of a number is written in the stem and the second part is written in the leaves, giving a graphical representation of data spread
  9   key 3|4 = 34% an example of what must always be provided with a stem-and-leaf plot so that the values in the stem and leaf have quantitative meaning
10   use of stem-and-leaf plot finding quartiles, medians, deciles etc, because the actual data scores are recorded in the diagram in sequence
11   five-number summary a series of numbers that represent the following: lower extreme, lower quartile, median, upper quartile, and the upper extreme ,of a set of data scores
12   box-and-whisker plots a graphical display of a five-number summary, drawn to scale so a box represents the interquartile range and median, and the whiskers represent the range
13   scaled number line a box-and-whisker plot is drawn next to this so that the distribution of data can be easily determined, when comparing more than one data set
14   mean sum of all scores divided by the number of scores, the average of a set of quantitative data
15   central tendency a method for describing a typical score of a data set, measured by mean, median and mode
16   typical score a data score that represents the full range of data scores in a set of data, expressed as mean, median or mode
17   Σ(f×x) / Σ(f) method used to calculate the mean of a set of data scores from a frequency table or a frequency histogram: sum of (frequency x scores) per sum of (frequencies)



  Statistics 5Two page printable: Student Answer Sheet followed by the Answers


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  Questions: Sheet 10 Statistics 6

  1   class centres these are used when finding (f×x) / Σ(f) during calculation of mean from data that had been grouped into ranges
  2   f×x a column that can be added to a frequency table to facilitate the calculation of total score for determining mean
  3   standard deviation a calculated measure of the spread of data, two types are used: population and sample
  4   population standard deviation σn: the function used to find the spread of data when statistical analysis is done on the entire population, giving a slightly lower value compared to the sample version
  5   sample standard deviation σn-1 or sn: the calculator function used to find the spread of data when statistical analysis is done on a sample of the population, giving a slightly higher value compared to the population version
  6   M+ the button used on a calculator for the input of class centre x frequency
  7   clear stats memory this MUST be done before input of statistical data to a calculator
  8   ogive another term for the cumulative frequency polygon
  9   cumulative frequency column this is added to a frequency distribution table so that the median can be easily determined
10   ogive or the cumulative frequency polygon, can be is used to determine the median and quartiles for a set of grouped data by drawing horizontal lines to it
11   mode the score with the highest frequency
12   summary statistic a number such as mean, median and mode, which describes a data set
13   mean problem extreme scores can bias the mean
14   median this statistic summary is used when the mean is not a good measure of central tendency of a data set e.g. outliers skewing the mean
15   outlier an observation to lies an abnormal distance from other values in a data set
16   mode this statistic summary is used to measure central tendency of a discrete data set when the mean and median may have very little meaning
17   discrete data the mode is the best measure of central tendency for this type of data because the values are not not part of a continuum



  Statistics 6Two page printable: Student Answer Sheet followed by the Answers


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  Questions: Sheet 11 Statistics 7

  1   measures of location in statistics, mean and median and mode are ways of showing the central values of a data set
  2   measure of spread range, interquartile ranges and standard deviation are ways of showing the spread of a data set
  3   outlier a score in a data set that is either much less or much greater than others, and which make the mean no longer typical of the data set
  4   skewness the distribution of a set of scores in a data set, related to whether the mean (or median or mode) are high, central or low on the range
  5   normal distribution this is when a data set of scores is symmetrically distributed about the mean
  6   positive skew when the majority of the scores are at the lower end of a distribution, due to (mean - median (or mode)) being greater than zero
  7   negative skew when the majority of the scores are at the higher end of a distribution, due to (mean - median (or mode)) being less than zero
  8   symmetrical data this situation results in the mean and median being the same score, while the mode may be the same, or at the two extreme ends of the range
  9   symmetrical data data set in which the frequencies of scores are equally distributed about the mean and median
10   small size of the standard deviation (σ) when the data are clustered around the mean
11   area chart a graph showing more than one data set by placing each set successively on top of the previous set, so that the area in each section allows for comparison of quantities
12   same display a way of comparing more than one set of data by using the same axes of a graph, stem-and-leaf plot, radar chart, area chart, box-and-whisker plot
13   same scale two box-and-whisker plots are placed on this so that the two data sets can be compared
14   two-way tables tabulated data that allows the data to be compared when there are two variables
15   continuous variables quantities describing traits of individuals in a population such as height and mass which have a symmetrical frequency distribution



  Statistics 7Two page printable: Student Answer Sheet followed by the Answers


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  Questions: Sheet 12 Statistics 8

  1   z-score standardised score, indicating the position of a particular score in relation to the mean, = (x - mean)/σ
  2   z-score the distance a score is from the mean in terms of the standard deviation of the normal distribution that the score is part of
  3   bell-shaped curve shape of the graph of a normally distributed data set, resulting in mean, median and mode being equal
  4   equal mean, median, and mode are this, when they represent a data set that has a normal distribution which results in a bell-shaped curve
  5   one standard deviation in any normal distribution, 68% of the values will lie within this range from either side of the mean
  6   two standard deviations in any normal distribution, 95% of the values will lie within this range from either side of the mean
  7   three standard deviations in any normal distribution, 99.7% of the values will lie within this range from either side of the mean
  8   z-score of -1 to +1 in any normal distribution, 68% of the values will lie within this range
  9   z-score of -2 to +2 in any normal distribution, 95% of the values will lie within this range
10   z-score of -3 to +3 in any normal distribution, 99.7% of the values will lie within this range
11   z-score of > 0 in any normal distribution, 50% of the scores, the top half of the scores
12   z-score of < 0 in any normal distribution, 50% of the scores, the bottom half of the scores
13   very probably term describing the chances of a score being within a z-score of -2 to +2
14   almost certainly term describing the chances of a score being within a z-score of -3 to +3
15   problem suspected term describing a score that likes outside a z-score of -3 to +3



  Statistics 8Two page printable: Student Answer Sheet followed by the Answers


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  Questions: Sheet 13 Statistics 9

  1   scatterplots graphical representation of data showing single visible points for each data point
  2   independent variable variable placed on the horizontal axis of graphs such as scatterplots
  3   dependent variable variable placed on the vertical axis of graphs such as scatterplots
  4   dependent variable the variable that responds to chances in the independent variable
  5   independent variable the variable that is deliberately controlled by an investigator in an experiment
  6   scatterplots style of graph used when the plotted points show a trend rather than a distinct line; used to compare two variables
  7   linear relationship straight line relationship between a dependent variable and an independent variable in a graph such as a scatterplot
  8   non-linear relationship curved line relationship between a dependent variable and an independent variable in a graph such as a scatterplot
  9   no relationship this is indicated when the points plotted on a scatterplot do not appear to form either a straight line (linear) or curved line (non-linear relationship
10   line of best fit a line drawn on a scatterplot that passes through or is close to as many points as possible
11   median regression line a line of best fit that is extrapolated to make predictions about data
12   extrapolate to extend a graph (line of best fit, median regression line) so as to make predictions about future trends
13   on or close location of two points with respect to a median regression line (line of best fit), and being used to find its slope by calculating rise/run, on a scatterplot
14   equation y = mx + b, used to make predictions beyond data, produced by finding m (slope) and b (y-intercept), for a median regression line on a scatterplot
15   predictions these can be made from the equation of a median regression line about the variables concerned



  Statistics 9Two page printable: Student Answer Sheet followed by the Answers


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  Questions: Sheet 14 Statistics 10

  1   correlation a statement reflecting the relationship between two variables
  2   positive correlation when one variable increases with another
  3   negative correlation when one variable decreases with another
  4   perfect positive correlation scatterplot description in which the points line up to form a straight line with positive slope, coefficient (m) of +1
  5   perfect negative correlation scatterplot description in which the points line up to form a straight line with negative slope, coefficient (m) of -1
  6   correlation coefficient a figure between -1 and +1 which indicates the strength of a correlation between two variables in a scatterplot
  7   no correlation points on a scatterplot showing no relationship between two variables, coefficient (m) of -0.25 to +0.25
  8   strong positive correlation points on a scatterplot close to the median regression line with a positive slope, coefficient of 0.75 to 1
  9   moderate positive correlation points on a scatterplot with an intermediate spread from the median regression line with a positive slope, coefficient of 0.5 to 0.75
10   weak positive correlation points on a scatterplot with a wide spread from the median regression line with a positive slope, coefficient of 0.25 to 0.5
11   strong negative correlation points on a scatterplot close to the median regression line with a negative slope, coefficient of -0.75 to -1
12   moderate negative correlation points on a scatterplot with an intermediate spread from the median regression line with a negative slope, coefficient of -0.5 to -0.75
13   weak negative correlation points on a scatterplot with a wide spread from the median regression line with a negative slope, coefficient of -0.25 to -0.5
14   causality the determination of whether one variable causes another: both, one, or neither may be caused by the other
15   reasonable expectation a moderate positive or negative correlation can lead to this conclusion about the relationship between two variables (from correlation on a scatterplot)



  Statistics 10Two page printable: Student Answer Sheet followed by the Answers


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  Questions: Sheet 15 Financial Maths 1

  1   wage money earned at an hourly rate, calculated by multiplying the hourly rate by the number of hours worked during the week
  2   hours worked quantity that can be calculated by dividing the wage by the hourly rate
  3   allowance an amount paid for working under unfavourable conditions, calculated and then added to the normal pay
  4   casual rate of pay this rate of pay is higher than for the workers receiving it to compensate for having no holidays and receiving no sick leave
  5   commission an amount earned by a person, paid as a percentage of the value of sales made
  6   sliding scale a series of commissions paid as a percentage of value of sales, each portion calculated separately and then added together
  7   retainer a fixed payment made to people working for a commission, whether or not they make any sales
  8   payment by piece payment to an employee for the amount of work completed (piecework)
  9   piecework work condition in which an employee is paid for the amount of work completed (payment by piece)
10   overtime money paid when a wage earner works more than the regular hours each week
11   penalty rate a higher hourly rate of pay given to employees for working overtime, e.g. time and a half
12   time and a half a rate of pay in which an employee is paid 1.5 times the usual rate of normal pay e.g. for working on Saturday
13   double time a rate of pay in which an employee is paid 2 times the usual rate of normal pay e.g. for working on Sunday
14   total pay sum of normal pay, time and a half pay, and double pay
15   gross pay pay before any deductions are made, such as tax, union fees
16   net pay the pay received after deductions have been take out, net pay = gross pay - deductions
17   deductions amounts that are calculated as a percentage of gross earnings on an annual basis and then taken out in equal weekly or fortnightly amounts



  Financial Maths 1Two page printable: Student Answer Sheet followed by the Answers


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  Questions: Sheet 16 Financial Maths 2

  1   annual leave loading an amount that employees are often paid when they take their annual leave, 17.5% of 4 weeks pay
  2   bank fees costs levied by banks for the use of their facilities to collect, store and transfer money, e.g. charges a transaction
  3   budgeting adding up expenditure and comparing it with income
  4   budget to allocate money to cover expenses, by comparing income and expenditure
  5   balance condition of a budget when income equals expenditure
  6   weekly/fortnightly annual expenses need to be converted to this before placing in the expenditure column of a budget to be compared to weekly/fortnightly wages
  7   unspent money this should be set aside as savings in a budget to bring the budget into balance
  8   household bills these need to be read and understood before you can manage a budget
  9   youth allowance a benefit paid to people generally between the ages of 18 and 21 who are in full time education or looking for work (the latter, up to 24 years), in low income families
10   pension various benefits paid to people who are aged (over 66 years and 6 months), disabled (unable to work), single parenting
11   Jobseeker a benefit paid to people over 21 years who are looking for work
12   Austudy a benefit paid to people over 25 years who are in full time study
13   Abstudy a benefit paid to Aborigines and Torres Strait Islanders to assist with education in low income families
14   interest an amount paid by a borrower for the use of money or by a bank for the use of a customers savings
15   simple interest interest is calculated by using only the initial investment, SI = Prn, principal × interest × number of years
16   principal the initial amount of an investment
17   investment bonds government or semi-government vehicles for investment to raise money for capital works, paid at simple interest rates paid at varying intervals
18   debentures means by which private companies raise capital from investors, interest paid at varying intervals



  Financial Maths 2Two page printable: Student Answer Sheet followed by the Answers


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  Questions: Sheet 17 Financial Maths 3

  1   simple interest graphs a method that can be used to compare different interest rates on the one set of axes, (interest paid vs years), slope = interest rate
  2   compound interest interest added to the principal and this new balance is used to calculate the next interest payment A = P(1+r)n
  3   compounded value the amount to which the initial investment grows when the interest is added to the principle for subsequent interest calculations (future value)
  4   future value the amount to which the initial investment grows when the interest is added to the principle for subsequent interest calculation (compounded value)
  5   compounding period time over which interest is earnt to be added to the principal for the purposes of compounding: yearly, monthly etc
  6   actual interest rate this is found by converting the annual interest rate to monthly by allowing for the compounding period
  7   compound value interest factor (CVIF) the compounded value that $1 will amount to under a certain investment, obtained from tables showing interest rate per period vs period
  8   present value (PV) the value of an investment at a given starting time, like now
  9   compounded value (CV) the value of an investment at the end of a compounding period: CV = PV x CVIF (present value x compounded value interest factor)
10   time to reach a certain value the CVIF (compound value interest factor) can be used to calculate this: CV = PV x CVIF or CVIF = CV/PV, and then using CVIF tables to locate the periods from the value
11   exponential graph type of graph produced when future value (compound interest) is presented graphically because of the use of an indice in the formula: A = P(1 + r)n
12   linear graph type of graph produced when simple interest is presented graphically because of the direct relationship between SI and P: SI = Prn
13   compare investments this process is made easier by drawing the graphs of several investments on the one set of axes
14   compound interest graph to obtain information for this type of graph, we need to subtract the principal from the future value after calculating the future value for each period
15   shares portions of a company sold to investors so that the company can use the money raised for expansion. Can be bought and sold like commodities
16   advance calculation advantage of investing money in banks and financial institutions, because of the application of an interest rate which known at the time of the initial investment
17   risk and no fixed return disadvantages of investing in a company by purchasing shares of the company.



  Financial Maths 3Two page printable: Student Answer Sheet followed by the Answers


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  Questions: Sheet 18 Financial Maths 4

  1   part owner an investor who owns shares in a company is this, and, as so, can have a say in the running of the company via shareholder meetings and voting for board members
  2   dividend money earnt from shares as a result of company profits being divided amongst shareholders on the basis of the number of shares owned
  3   increase in value money earnt by shareholders that is derived from the price of the shares on the stock market increasing (capital growth or capital gain)
  4   share risk losses made from selling shares at a prices below the purchase price
  5   developing the company one of the uses of company profits, increasing the value of shares. Some profits are also paid as dividends
  6   dividend yield this is the dividend per share expressed as a percentage of the price of the share. It varies because share prices vary
  7   share performance graphs a graph obtained by plotting and graphing the share price against time (of day, week, month), used to detect trends by drawing a line of best fit
  8   share price trends found by drawing a line of best fit on a share performance graph and extrapolating or interpolating the line
  9   extrapolating extending a graph beyond the information given on a graph to make predictions about future trends in the price of the share
10   interpolating drawing a graph using data found at the end points, filling in data between known data, e.g. drawing a smooth share price curve when only the weekly prices are known
11   inflation the rise of prices within an economy, generally measured as a percentage, reduces the value of money in banks, increases the prices of shares
12   CPI consumer price index, an estimation of inflation in our economy expressed as a percentage
13   future prices these can be estimated by multiplying the present price by the inflation rate (CPI) for one year ahead: = current price x (1 + CPI)
14   compound inflation when future prices are needed for several years ahead, use the compound interest formula: A = P(1 + r)n
15   appreciation the increase in (monetary) value of collectable items such as stamp collections and memorabilia from special occasions, approximate inflation unless the item is rare (faster rate)
16   collectables items that people value because of their aesthetic or sentimental value, e.g. art, stamps, memorabilia from sporting events, medals
17   taxation money collected by the government to pay for government services (hospitals, roads, justice system, sewage, defence)



  Financial Maths 4Two page printable: Student Answer Sheet followed by the Answers


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  Questions: Sheet 19 Financial Maths 5

  1   income tax money paid to government by individuals based on the amount of money earnt
  2   company tax money paid to government by companies based on the amount of profit that is made
  3   gross pay the wage or salary paid by an employer for services (work done)
  4   net pay the amount of money the worker actually receives after deductions such as tax, union fees and superannuation have been taken out
  5   PAYE pay as you earn : term describing workers who have the amount of tax deducted from wages or salaries before they receive their net pay. Also pay as you go
  6   tax return a document each wage earner submits to the taxation office showing gross income, tax deductions and net taxable income for the purpose of calculating tax owing or to be refunded
  7   taxable income the portion of income on which tax is payable, found by taking allowable deductions from gross income
  8   tax deductions allowable amounts that can be taken from gross income for the purpose of calculating taxable income, e.g., work related expenses, charity donations over $2
  9   depreciation loss in value of equipment that is used to earn an income, calculated from percentages applied over successive years (a reverse form of compound interest!)
10   finding taxable income add income from all sources and subtract all tax deductions
11   Medicare levy money paid as part of tax for Australia's national health care scheme e.g. visits to doctors, hospitals; calculated on the basis of 2% of taxable income
12   tax scales used to calculate tax owing on taxable income, shows tax payable on minimum amounts and the rate of tax in the dollar exceeding that amounts
13   group certificate a statement of gross earnings and the amount of PAYE tax instalments paid, given to workers by the employer
14   June 30th the end of the financial year, when a tax return has to be completed and lodged with the taxation office, usually before October 31st
15   tax refund the amount that the tax office returns to a taxpayer if the PAYE tax exceeds the calculated tax due to be paid for a financial year
16   tax brackets grouping of potential taxable incomes each of which has a different rate of taxation
17   calculating tax first determine the appropriate tax bracket on the tax table, and apply the rule for that bracket, e.g. $5,092 plus 32.5 cents for each dollar over $45,000 up to $120,000



  Financial Maths 5Two page printable: Student Answer Sheet followed by the Answers


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  Questions: Sheet 20 Financial Maths 6

  1   tax debt the amount that the tax office bills a taxpayer for if the PAYE tax is less than the calculated tax due to be paid for a financial year
  2   GST goods and services tax (10%), which is added onto the price paid for the goods or services, excluding some basic foods e.g. vegetables, in Australia
  3   VAT value added tax, works in the same way as our GST, but is called this in other countries, e.g. New Zealand; percent rates vary
  4   indirect tax taxes like the GST and VAT which are collected by retailers and service providers when goods and services are bought. The money is then passed onto the tax office
  5   purchase price this is calculated by finding 110% of the pre-tax price. In Australia the advertised price includes the GST of 10%
  6   eleven factor divided into the advertised purchase price of goods in Australia to find the amount of GST being paid for taxable goods
  7   unitary method technique that can be used to calculate GST being added if the percentage is known along with the final purchase price
  8   term of the loan the length of time over which a loan is agreed to be repaid by the borrower
  9   flat rate interest simple interest calculated on the basis of the initial amount borrowed SI = Prn
10   total payments sum of simple interest and principal
11   instalments amount to be repaid each week, fortnight, month, etc., found by dividing the total payments by the number of week, fortnights, months
12   reducing balance loans home loans in which the interest owing is calculated on the basis of the amount of the loan still owing after payments have been made
13   reducible interest interest paid on home loans, based on the interest due on the balance of the loan owing, as it reduces when periodic payments are made
14   monthly interest calculated from the annual interest by dividing by 12, and then used in interest formulas
15   total repaid found by multiplying the monthly payment by the number of repayments
16   each month this is when the interest is calculated and then added to the remaining amount owing prior to subtracting the next instalment, as with variable interest home loan repayments
17   cost of a loan total cost in repaying a loan, including interest, account keeping fees, establishment fees, termination fees, insurances



  Financial Maths 6Two page printable: Student Answer Sheet followed by the Answers


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  Questions: Sheet 21 Financial Maths 7

  1   effective interest rate this is the rate of interest of a flat rate loan converted to the equivalent reducible rate of interest, E = [(1 + r)n - 1]/n
  2   cheaper a home loan is generally this, if you can pay it off faster e.g. with greater than minimum payments, fortnightly instead of monthly payments
  3   credit card accounts a commonly used line-of-credit that involves an instant loan to the card holder from the bank
  4   interest-free period a period of time when money borrowed with a credit card is not charged any interest, interest is then high after that period
  5   lower interest this is generally the case with credit cards that charge interest from the date of commencement of the loan when a purchase is made
  6   daily the period of time that the interest due on a credit card is calculated, based on annual interest/365.25, the amount is then calculated using SI = Prn
  7   repayment plan the way in which a credit card loan is to be paid off, and which is important in deciding which credit card is the cheapest to use
  8   monthly repayment tables instruments used to determine the monthly instalments that are needed to pay off a loan, with interest, years and values per $1000 of loan shown
  9   personal loan money borrowed for the purpose of purchasing a car, boat or holiday package
10   hire purchase money borrowed for a car because the vehicle is being used while the loan is being paid off
11   mortgage loan money borrowed to purchase a house which is used as assurity in case the borrower defaults on the loan
12   loan default situation describing when a mortgage loan borrower becomes unable to pay off a mortgage loan. The lender then takes possession of the house.
13   refinancing changing the loan contract by negotiation between the borrower and lender so that the borrower does not default on the loan
14   foreclosure this occurs when a borrower becomes insolvent and is unable to pay off a loan and the lender then takes possession of the property
15   collateral property or other asset used as an assurity when a loan or mortgage is taken out. If defaulting occurs then the collateral can be taken by the lender to pay for outstanding funds
16   payday loans unsecured short term loans for small amounts of money based on a future salary payday (up to 2 weeks after getting the loan). Interest rates are very high and big default penalties can be incurred
17   BNPL buy now pay later loans offer capacity to pay at time of purchase (loan unsecured) and then repay the provider of the loan later at a time specified by the lender. Up to then interest is low but penalities and extra interest apply if a payment is missed



  Financial Maths 7Two page printable: Student Answer Sheet followed by the Answers


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  Questions: Sheet 22 Financial Maths 8

  1   debit card accounts accounts in which the cardholder accesses saved money (which is basically on loan to banks) through ATMs or EFTPOS
  2   annuity a form of investment involving regular periodic contributions to an account, interest compounding
  3   superannuation a common example of an annuity
  4   fund retirement use to which money accumulated in an annuity (like superannuation) is usually put
  5   end of year this factor needs to be taken into account when using the compound interest formula to calculate the future value of an annuity, the assumed time when money is invested: n = period - 1
  6   compound interest formula A = P(1 + r)n can be used to calculate the future value of an annuity by calculating each years investment separately (n - 1), and adding
  7   future value of an annuity a formula used to find out how much money will have accumulated if a periodic investment (M) is made at the end of each year (n = number of years) and interest is compounded A = M{((1 + r)n - 1)/r}
  8   future value of an annuity a formula that can be used to find how much needs to be contributed to an investment to reach a certain goal M = Ar/((1 + r)n - 1)
  9   compound interest formula formula that can be used to find present value of an annuity, N = A/(1 + r)n (note, N not P)
10   present value of an annuity the single sum investment (N) that would yield the same final annuity value if invested at the same interest rate for the same amount of time: N = A/(1 + r)n
11   present value of an annuity formula used to calculate this, knowing the contribution and interest per period and the number of periods: N = {((1 + r)n - 1)/(r(1 + r)n)}
12   greater financial outcome this is the result of an investment with greater present value compared to one with less present value, calculated with N = {((1 + r)n - 1)/(r(1 + r)n)} or N = A/(1 + r)n
13   future value table a table that shows the future value of an annuity where $1 is invested per interest period
14   present value table a table that shows the present value of an annuity where $1 is invested per interest period
15   saves a calculation this is the function of the future value of an annuity and the present value of an annuity formulas when comparing lump sum compounded interest investment with a periodic payment investment
16   loan repayments these can be calculated by transposing the present value (N or loan) formula to make the periodic payments (M) the equation subject: M = {r(1 + r)n/((1 + r)n - 1)}
17   guess and refine the method used to calculate the amount of time that it will take to repay a loan, by adjusting the value of n in M = {r(1 + r)n/((1 + r)n - 1)}



  Financial Maths 8Two page printable: Student Answer Sheet followed by the Answers


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  Questions: Sheet 23 Financial Maths 9

  1   total loan cost calculated by multiplying the amount of each repayment by the number of repayments made
  2   time to repay loan this can be found from the present value of an annuity formula by substituting various repayment periods until a similar periodic repayment is obtained: M = N{r(1 + r)n/((1 + r)n - 1)}
  3   asset an item that has value to its owner, e.g. car, computer
  4   depreciation the loss of value that an asset undergoes, over a period of time
  5   straight line method this technique is used when calculating depreciation occurring at a constant rate each year, the value can reach zero
  6   S = Vo - Dn straight line depreciation equation, S = salvage value of asset after n periods, Vo = purchase price, and D = amount of depreciation per period
  7   depreciation graph graph with a straight line and a negative slope, used to determine the salvage value of an asset, based on equation: S = Vo - Dn
  8   declining balance method depreciation occurring each year by a percentage of its current value, the value never actually becomes zero
  9   exponential decay term describing the shape of the graph of the salvage value of an asset undergoing declining balance depreciation
10   written off term describing the disposal an asset that has reached zero value
11   zero value of an asset can depreciate to this by the straight line method but not by the declining balance method, even though the asset continues to be used
12   smooth curve shape of the graph for declining value depreciation, which is an example of exponential decay
13   percent depreciation this value taken from 100% is used to find the salvage value of an asset in the declining balance method of depreciation calculation, applied every year in sequence
14   S = Vo(1 - r)n declining balance formula for depreciation, used to calculate salvage value S from purchase price of asset Vo, depreciation rate r and time periods n
15   amount of depreciation this is found by subtracting the salvage value (found with S = Vo(1 - r)n) from the purchase price
16   graphs these can be drawn to compare the value of an asset under different rates of depreciation using the same axes
17   tax deduction the depreciation of an asset used to gain income can be claimed as a taxation deduction and reduce taxable income



  Financial Maths 9Two page printable: Student Answer Sheet followed by the Answers


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  Questions: Sheet 24 Algebra 1

  1   describing sequences state the first term and then describe what is done to it to get the next term
  2   number pattern a sequence of numbers that obey a certain rule, e.g. 9,15,21,27 (T1, T1 + 6, T2 + 6, etc), or: 1,4,16,64 has a common factor of 4: 1, 1 × 4, 4 × 4 etc
  3   subtract process done to a number pattern (sequence) which appears to increase or decrease by a constant amount. The result is added to get the next number; T2 - T1 = T4 - T3; etc
  4   algebraic expression a group of numbers and pronumerals that can be used to describe all the terms of a sequence e.g. -5 + 3n; the pronumeral being replaced by integers
  5   divide process done with consecutive term in a number pattern (sequence) that has terms that appears to be found by multiplying or dividing T2 / T1 = T4 / T3
  6   integer a whole number, e.g. 1, 11, 54
  7   pronumeral a letter that is used to represent a range of numbers
  8   formula an algebraic rule for a calculation, e.g. v = u + at
  9   finding any term the advantage of writing sequences (number patterns) algebraically (no need to write the whole sequence)
10   Tn the n-th term of a number pattern (sequence), where n is a whole number used in an algebraic function describing the term e.g. 2n - 1 or 4n + 3
11   like terms these occur when the same pronumeral occurs, e.g. a + a + a = 3a
12   unlike terms these occur when different pronumerals occur e.g. a + a + a + b + b + b = 3a + 3b
13   adding rule like terms can be added, unlike terms cannot be added
14   subtracting rule like terms can be subtracted, unlike terms cannot be subtracted
15   sign in any expression, this belongs to the term that follows it (represented by the symbols + or -)
16   substitute the process of replacing a pronumeral with a number
17   substitute first when calculating the value of an expression the formula is re-written with known values being used instead of pronumerals before completing the calculation
18   exponent a number or pronumeral to which another number (the base) is raised; an indice, a power



  Algebra 1Two page printable: Student Answer Sheet followed by the Answers


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  Questions: Sheet 25 Algebra 2

  1   power alternative name for an indice, e.g. y raised to the ….... of 3 = y3
  2   indice a number that is used to indicate how many times a base number is multiplied by itself, e.g. in a3 the 3 indicates a × a × a
  3   base number the number to which an indice is a applied, e.g. the a in ax, while the x is the indice
  4   ax × ay = ax+y index law 1: when the same base number is multiplied, add the indices
  5   ax / ay = ax-y index law 2: when the same base number is divided, subtract the indices
  6   (ax)y = axy index law 3, when a base and indice are raised to the power of another indice, multiply the indices
  7   separately the three index laws are considered one at a time for each pronumeral, i.e., …........
  8   add indices process used when two expressions with the same base are being multiplied
  9   subtract indices process used when two expressions with the same base are being divided
10   multiply indices process used when a base is raised by successive powers
11   one (1) result of any number raised to the power of 0 (zero)
12   negative indice a positive indice becomes this if the base as a denominator is changed to being a numerator: 1/a2 becomes a-2/1
13   equation a mathematical sentence in which one expression is shown as being equal to another expression
14   pronumeral value this is being found when we are solving an equation
15   transpose to rearrange an equation so that another pronumeral is the subject of the equation
16   transpose subtracted number to perform this task, add the same number to both sides of the equation
17   transpose added number to perform this task, subtract the same number from each side of the equation
18   transpose dividing number to perform this task, multiply both sides of an equation by the same number



  Algebra 2Two page printable: Student Answer Sheet followed by the Answers


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  Questions: Sheet 26 Algebra 3

  1   transpose multiplying number to perform this task, divide both sides of an equation by the same number
  2   before order for transposing equations: do the added and/or subtracted pronumerals …..... the divided and multiplied pronumerals
  3   after order for transposing equations: do the divided and multiplied pronumerals …....... the added and subtracted pronumerals
  4   equivalent equation this is written out after each step in the solution to ensure nothing is missed
  5   check once you have solved an equation, this is done by substituting your answer for the pronumeral in the original equation
  6   fractions when these are in equations then the lowest common multiple of the denominators is used to multiply the whole equation
  7   function a rule (equation) for a calculation that consists of an independent and a dependent variable
  8   linear function this rule (equation) for a calculation results in a straight line when graph because the variables are directly related
  9   horizontal axis graph axis upon which the independent variable is shown (x axis)
10   vertical axis graph axis upon which the dependent variable is shown (y axis)
11   table of values before plotting points on a graph, this is filled out by substituting into a function a range of values for the independent variable to obtain a range of values of the dependent variable
12   gradient rate of change, vertical rise/horizontal run, increase in the dependent variable for every one unit increase in the independent variable
13   negative gradient rate of change that occurs when the value of the dependent variable decreases as the independent variable increases
14   negative gradient this is the case when the graph of a linear function decreases as we look from left to right
15   intercept place where a line crosses an axis on a graph
16   y-intercept this point on the vertical axis that gives us the value of the dependent variable when the independent variable is equal to zero
17   x-intercept this point on the horizontal axis that gives us the value of the independent variable when the dependent variable is equal to zero
18   function this can be written if the gradient (m) and y-intercept (b) are known using the formula: y = mx + b



  Algebra 3Two page printable: Student Answer Sheet followed by the Answers


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  Questions: Sheet 27 Algebra 4

  1   function this can be written if the gradient (m) and y-intercept (b) are known using the formula: y = mx + b
  2   function graphing this can be done using the y-intercept and using the gradient to identify two other points, the straight line passing through all 3 points
  3   m = (y2-y1)/(x2-x1) formula for calculating the gradient of a straight line graph where two points are known, rise divided by run
  4   counting from y-intercept method of finding two points apart from the y-intercept by using the gradient, so that a line graph for a function can be drawn through the 3 points
  5   coefficient the number written in front of the independent pronumeral in a function, representing gradient
  6   (x, y) rule for naming points on a graph, the gradient can be used to count from the y-intercept and provide points of this nature for plotting to draw a graph
  7   three number of points that need to be plotted to ensure a straight line graph is being drawn
  8   variation this occurs when one quantity is proportional to another
  9   linear function when two quantities vary directly with each other, then the variation can be graphed as this
10   constant of variation this is the gradient of a function describing a variation, in the form of y = ax (a is the gradient)
11   one for the function y = ax, the minimum number of points that are needed to be able to draw a graph of a linear function of a variation because the line is straight and passes through (0, 0)
12   step function this shows the increase in a quantity (on a graph) in steps, a series of horizontal straight lines, e.g. cost of phone calls increasing (suddenly) by 12 cents at the start of a new minute
13   piecewise function this type of function follows different rules for different values of the independent variable, e.g. hourly pay changing when overtime is reached
14   intersection the point where two functions drawn on the one set of axes cross, because the dependent variable for both rules is the same
15   simultaneous equations using two functions to find where they intersect: the point where both conditions hold true at the same time
16   substitution the replacement of pronumerals in and expression with numerical values
17   powers of one linear expressions, those that result in a straight line graph, involve an assumed indice of this nature



  Algebra 4Two page printable: Student Answer Sheet followed by the Answers


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  Questions: Sheet 28 Algebra 5

  1   quadratic expressions that involve indices of powers of two, e.g. y = x2 + 1
  2   cubic expressions that involve indices of powers of three, e.g. y = x3
  3   powers of two quadratic expressions, e.g., area of a square = l2
  4   powers of three cubic expressions, e.g. volume of a sphere = 4/3 πr3
  5   collecting like terms this is what is done when adding and subtracting algebraic expressions
  6   index laws these are used one at a time when multiplying and dividing algebraic expressions
  7   index law 1 ax×ay = ax+y, applied separately to the expressions involved
  8   index law 2 ax/ay = ax-y, applied separately to the expressions involved
  9   index law 3 (ax)y = axy, applied separately to the expressions involved
10   expanding brackets when doing this we multiply every term inside the brackets by what is immediately outside, accounting for its sign
11   negative 1 assumed multiplication factor when expanding a bracketed numerals and pronumerals with no preceding numeral, e.g. -(x - y)
12   formula this is converted to an equation by substitution of values, and then re-organising the expression until the unknown pronumeral is the subject of the equation
13   both sides when re-organising an expression to have a new equation subject, every action is done to …......... e.g. when moving added, subtracted, multiplied, divided, and indexes
14   unknown this is what is being found when solving an equation
15   square root this results in both negative and positive answers, and both should be taken unless the context of the equation means that only the positive should be used, e.g. can't have negative time
16   opposite operation this is done when transposing and solving equations (to both sides) involving indexes, e.g. if the subject is squared, use square root to both sides
17   evaluate use your calculator to find the answer to an equation after known values have been substituted and transposed to provide a single pronumeral as the subject of the equation
18   approximate solution this is obtained for expressions such as 2x = 10, by substitution and testing because there is no simple opposite operation that you can easily use (alternatively you can log both sides for an exact answer: then x log 2 = log 10, and hence x = log 10/log 2)



  Algebra 5Two page printable: Student Answer Sheet followed by the Answers


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  Questions: Sheet 29 Algebra 6

  1   first estimate used to solve equations such as 2x = 10, the answer is found and then further estimates are tried, until an approximate solution is obtained (could log both sides)
  2   scientific notation a shorthand way of writing very large and very small numbers by multiplying by 10x
  3   first digit the decimal point is placed after this and the number is then multiplied by the appropriate power of 10 when writing a number in scientific notation
  4   places moved these are counted when moving a decimal point so that the number of them counted can be used as a power of 10 in scientific notation
  5   large numbers when converting these to scientific notation the decimal point is moved left and the positions (digits) counted for use as a positive power of 10
  6   small numbers when converting these to scientific notation the decimal point is moved right and positions (digits) counted for use as a negative power of 10
  7   three values a table containing at least this amount for both the independent and dependent variables is drawn up prior to graphing a linear function (power of all variables = 1)
  8   parabola the graph of a quadratic function is this shape, y = x2
  9   several points this number of values for both the dependent and the independent variable need to be found (in table form) prior to graphing a quadratic function (y = x2), a smooth curve is drawn
10   concave up this is the general shape of a graph of a quadratic function where the x2 term is positive e.g. y = x2
11   concave down this is the general shape of a graph of a quadratic function where the x2 term is negative e.g. y = -x2
12   minimum point the bottom most point of a quadratic function graph where the x2 component is positive (y = x2), concave up
13   maximum point the top most point of a quadratic function graph where the x2 component is negative (y = -x2), concave down
14   graphing points these are obtained by substituting numerals for pronumerals representing the independent variable in linear and quadratic functions, normally tabulated
15   dependent variable this variable provides the maximum or minimum value at the maximum and minimum points on a quadratic function graph in practical situations
16   y = ax3 general equation of a cubic function, forms a curve, needs several points to be graphed
17   y = a/x general equation of a hyperbolic function, forms a curve, needs several points for graphing
18   y = ax general equation of an exponential function, forms a curve, needs several points for graphing



  Algebra 6Two page printable: Student Answer Sheet followed by the Answers


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  Questions: Sheet 30 Algebra 7

  1   hyperbolic function an expression in the form of y = a/x, forms a curved graph so several points need to first be tabulated
  2   smooth curve shape of the graph drawn for quadratic, cubic, hyperbolic and exponential functions, not just simply joint the dots (of the points)
  3   exponential function an expression in the form of y = ax, forms a curved graph so several points need to first be tabulated
  4   compound interest an example of an exponential function, that can be graphed for comparison purposes: A = P(1 + r)n, which is similar to the form of y = b(ax)
  5   growth function exponential functions are of this nature, e.g., population increase, investment compound interest
  6   depreciation an exponential function that shows decay, due to the interest being less than 1: S = Vo(1 - r)n which is similar to the form of y = b(ax)
  7   variation this occurs when one quantity is proportional to another
  8   cubic variation when one quantity varies as the cube of another, e.g. V = 4/3πr3
  9   quadratic variation when one quantity varies as the square of another, e.g. s = ut + 0.5at2, where s (displacement) varies over t (time), and a is constant (acceleration in this equation)
10   hyperbolic variation when one quantity varies inversely as another e.g. y = 1/x
11   inverse variation the type of variation that occurs when one quantity increases while the other decreases e.g. y = 1/x, the product of the variables is a constant
12   direct variation the type of variation that occurs when one quantity increases while the other increases e.g. y = x, one variable = a constant times the other variable
13   algebraic model this can be used to represent many physical situations by deriving equations of functions
14   proportionality constant a number that a quantity must be multiplied by so that the units of measurement on both sides of an algebraic expression for a variation match up
15   restrictions these may be placed on one or both variables when modelling a situation, e.g. a cinema has a maximum of 120 seats, I = CS where I = income, C = price paid by cinema goers (constant), and S is seats filled, being limited to the range from 0 to 120 only in this case.
16   interpolating drawing a graph using data found at the end points, or, filling in data between known data, e.g. drawing a smooth share price curve when only the weekly prices are known
17   extrapolating extending a graph beyond the information given on a graph to make predictions about future trends in the price of the share
18   calculate constant this is done using information about both variables in a variation so that other points can be found for graphing or calculating (proportionality situations) e.g. N & 1/T i.e. N = k/T where k = NT for each (T,N) point



  Algebra 7Two page printable: Student Answer Sheet followed by the Answers


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  Questions: Sheet 31 Measurement, Trigonometry, Geometry, Time 1

  1   powers of 10 the reason why the metric system is simpler than the imperial system of measurement, it uses this factor
  2   prefix a letter placed in front of the standard unit of measurement signifying the power of 10 being used e.g. in cm c means 10-2, m means metre, called centimetre
  3   length distance between two points, standard unit of metre
  4   mass quantity of matter, standard unit of gram or kilogram depending on use, e.g. mg, kg are based on gram, while t, tonne, is based on kg
  5   capacity space (volume) occupied by an object, a derived unit of cubic metres, or a standard unit of litre (1000 L = 1 m3
  6   time how long a process takes to occur, standard unit of second
  7   mega a million times the standard unit, MJ (mega joules), 106
  8   kilo a thousand times the standard unit km (kilometres), 103
  9   hecto a hundred times the standard unit, hPa (hecto pascals), 102
10   centi a hundredth of a standard unit, cm (centimetre), 10-2
11   milli a thousandth of the standard unit, mg (milligrams), 10-3
12   micro a millionth of the standard unit μg (micrograms or mμ grams), 10-6
13   nano a billionth of the standard unit, nm (nanometres), 10-9
14   minute sixty seconds
15   hour sixty minutes
16   day twenty four hours



  Measurement, Trigonometry, Geometry, Time 1Two page printable: Student Answer Sheet followed by the Answers


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  Questions: Sheet 32 Measurement, Trigonometry, Geometry, Time 2

  1   week seven days
  2   fortnight two weeks
  3   year fifty two weeks or 365.25 days
  4   second standard unit of time upon which the other time measurements are based, a fraction (1/84600 th) of a mean solar day
  5   kilogram standard unit of mass or quantity of matter
  6   litre standard unit of volume or capacity, although volume is often expressed in the derived units of cubic metres: m3
  7   cubic metre derived unit of volume or capacity
  8   metre standard unit of length or the distance between two objects
  9   standard unit the measurement upon which other measurements are based e.g. metre is used as the basis for kilometre, nanometre etc
10   multiply operation used when changing from a larger unit to a smaller unit, e.g., from tonnes to kilogram, multiply by 1000
11   divide operation used when changing from a smaller unit to a larger unit, e.g., from nanometres to metres, divide by one billion (or times by 10-9)
12   large to small unit multiply by the conversion factor, e.g., km to m multiply by 1000
13   small to large unit divide by the conversion factor, e.g., seconds to hour, divide by 60 to get minutes and then divide by 60 to obtain hours
14   approximations all measurements are this, because there is a limit to which readings can be made using measuring devices
15   convenient the degree of accuracy is this, that is we round off to nearest km, m or whatever depending on the overall size of the measurement
16   maximum error when rounding off measurements, this amount is half of the smallest unit provided



  Measurement, Trigonometry, Geometry, Time 2Two page printable: Student Answer Sheet followed by the Answers


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  Questions: Sheet 33 Measurement, Trigonometry, Geometry, Time 3

  1   percentage error calculated from (maximum error × 100)/measurement
  2   half the smallest unit this is the maximum error of a measuring instrument
  3   true accuracy for a measurement, this is found by calculating the percentage error of the measurement
  4   increased accuracy for a measurement, this is obtained by averaging several readings
  5   significant figures the number of non-zero digits at the beginning of a number that we can measure accurately with a measuring device during measurement
  6   zero counts if the non-zero digits of a set of significant figures includes a zero, then this is the case, e.g. 1024 has four significant figures
  7   round off this is done to a number by counting place position of the first non-zero digits, e.g. to the nearest 100
  8   round up rounding done when the digit after the last significant digit is 5 or greater
  9   round down rounding done when the digit after the last significant figure is less than 5
10   scientific notation this is used to write very large or very small numbers correct to the required number of significant figures
11   zeros these are added at the end of a rounded number if there are insufficient digits to complete the required number of significant figures, e.g. 2.00 represents 3 significant figures
12   non-significant zeros zeros before an integer (e.g. 002538 or 0.000728), or zeros after a large number unless otherwise indicated (e.g. 636578000000)
13   significant zeros zeros between integers (e.g. 28019) or zeros written deliberately after a decimal (e.g. 4.30)
14   rate this is a comparison of two quantities of a different type, e.g. 4 runs per over in cricket is the run rate
15   divide in a rate calculation the value of the second quantity is used to do this operation to the first value so that the second value in reality is 1 (dividing the numerator and the denominator by the denominator number maintains the same relationship between the two)
16   converting rates this is done by changing each unit separately, and writing the equivalent rate at each stage, e.g., changing m/s to km/hr



  Measurement, Trigonometry, Geometry, Time 3Two page printable: Student Answer Sheet followed by the Answers


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  Questions: Sheet 34 Measurement, Trigonometry, Geometry, Time 4

  1   ms-1 alternative to writing m/s as a rate of distance change (speed or velocity)
  2   simplified rate quantity obtained by dividing the first quantity by the second quantity
  3   rate questions these need to be read carefully to see whether to multiply or divide, e.g. in recipes quantities for 6 servings given, but need the amounts for 9 servings, therefore multiply each ingredient by 9/6 or 1.5
  4   successive % changes each percentage is applied separately and in sequence when investigating this, because they are percentages of different quantities. E.g. prices increase by 20% and then get discounted by 20% is NOT 0% change
  5   ratio a comparison between two quantities of the same type
  6   same unit before two quantities of the same type can be compared in a ratio they need to be this
  7   simplified ratio this is obtained by dividing each part of a ratio by the highest common factor of the ratio (same factor applied to both sides to maintain the relationship)
  8   value of one share to divide a quantity in a given ratio, we calculate this before calculating for each part of the ratio by adding the ratio parts together and dividing into the quantity e.g. 33 000 divided in ratio of 6:5, divide by 11, then multiply by either 6 or 5
  9   unitary method method used to find the value of a part of a ratio if the ratio and the value of the other part is known, e.g. in ratio 9:10, the 9 ≡ 162 cm, divide both sides by 9 and then times both sides by 10
10   area a measure of the amount of space within a closed shape
11   A = s2 formula for the area of a square
12   A = l × w formula for the area of a rectangle, length times width or length times breadth
13   A = 0.5 × b × h formula for the area of a triangle, half base times perpendicular height
14   A = b × h formula for the area of a parallelogram, base times perpendicular height
15   A = 0.5 × D × d formula for the area of a rhombus, half major diagonal times minor diagonal
16   A = 0.5 × (a + b) × h formula for the area of a trapezium, half the sum of the lengths of the parallel side times the perpendicular height between them



  Measurement, Trigonometry, Geometry, Time 4Two page printable: Student Answer Sheet followed by the Answers


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  Questions: Sheet 35 Measurement, Trigonometry, Geometry, Time 5

  1   square shape for which the following formula is used to calculate area: A = s2
  2   rectangle shape for which the following formula is used to calculate area: A = l × w
  3   triangle shape for which the following formula is used to calculate area: A = 0.5 × b × h
  4   parallelogram shape for which the following formula is used to calculate area: A = b × h, or base times perpendicular height between the base and the side parallel to it
  5   rhombus shape for which the following formula is used to calculate area: A = 0.5 × D × d, or half times the product of the two diagonals
  6   trapezium shape for which the following formula is used to calculate area: A = 0.5 × (a + b) × h, or half the sum of the parallel sides times the perpendicular height between them
  7   traverse survey method used to calculate the area of irregularly shaped blocks of land, enabling the area to be broken into squares, rectangles, triangles, trapeziums, parallelograms and rhombuses
  8   offset perpendicular lines drawn from a traverse of an irregularly shaped block of land to other corners, measured, and forming the sides of triangles or quadrilaterals especially squares, rectangles, parallelograms, rhombi or trapeziums
  9   traverse straight line drawn between two corners of an irregularly shaped block of land, to be used to locate offsets to other corners
10   quadrilaterals two dimensional shapes that have 4 sides, can be used to calculate area of land, especially if they are squares, rectangles, parallelograms, rhombi or trapeziums
11   field diagram a diagram showing the distances along a traverse from a reference point to offsets and the offset distances from the traverse to corners
12   scale diagram this can be drawn from a field diagram using a scale size, e.g. 1 mm to 100 mm
13   solid shapes triangular prism, square pyramid, cube, rectangular prism, cone, cylinder, sphere
14   prism a solid shape where any cross-section parallel to the base is identical to that base
15   pyramid a solid shape with a base and triangular sides that meet in an apex
16   net of a solid the way a shape would look if its faces were unfolded and flattened out



  Measurement, Trigonometry, Geometry, Time 5Two page printable: Student Answer Sheet followed by the Answers


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  Questions: Sheet 36 Measurement, Trigonometry, Geometry, Time 6

  1   vanishing point the place where the parallel sides of solid shapes converge when they are drawn in perspective
  2   perspective drawing diagram of a solid drawn to appear as it would when actually viewed, with parallel sides located on lines meeting at a vanishing point on the horizon
  3   surface area for a solid this is the total area of each face of the shape
  4   SA = 6s,2 formula for the surface area of a cube
  5   SA = 2(lh + lw + wh) formula for the surface area of a rectangular prism
  6   cube solid shape for which the following formula is used to calculate its surface area: SA = 6s2
  7   rectangular prism solid shape for which the following formula is used to calculate its surface area: SA = 2(lh + lw + wh)
  8   volume the amount of space within a solid shape
  9   V = A × h general formula for prism and cylinder volumes, volume = area of the base × height
10   V = s3 formula for the volume of a cube
11   V = l × b × h formula for the volume of a rectangular prism
12   V = πr2h formula for the volume of a cylinder
13   general solid shape for which the following formula is used to calculate its volume: V = A × h, that is area of base times perpendicular height
14   cube solid shape for which the following formula is used to calculate its volume: V = s3
15   rectangular prism solid shape for which the following formula is used to calculate its volume: V = l × b × h
16   scale 1:100 scale often used on plans of buildings which means that the actual building is 100 times as big as the plan drawing



  Measurement, Trigonometry, Geometry, Time 6Two page printable: Student Answer Sheet followed by the Answers


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  Questions: Sheet 37 Measurement, Trigonometry, Geometry, Time 7

  1   cylinder solid shape for which the following formula is used to calculate its volume: V = πr2h
  2   mL this volume capacity unit is the same size as cm3
  3   V = 1/3 Ah formula for volume of a pyramid, one third base area times perpendicular height
  4   V = 1/3 πr2h formula for volume of a cone
  5   V = 4/3 πr3 formula for volume of a sphere
  6   pyramid solid shape for which the following formula is used to calculate its volume: V = 1/3 Ah
  7   cone solid shape for which the following formula is used to calculate its volume: V = 1/3 πr2h
  8   sphere solid shape for which the following formula is used to calculate its volume: V = 4/3 πr3
  9   similarity when two objects are identical in shape, except one is a reduction or an enlargement of the other, e.g. building and its plan
10   similar figures shapes that have the same shape and have corresponding sides in the same proportion or ratio
11   scale factor calculated from the ratio of corresponding sides in similar figures
12   ||| symbol represent "is similar to", e.g. ΔABC is similar to ΔDEF
13   is similar to the symbol ||| represents this when referring to two shapes that have the same corresponding angles but sides of different lengths but corresponding in a common ratio: e.g. triangle ABC ||| triangle DEF
14   equal ratio two shapes are similar if the corresponding sides have this property
15   equal two shapes are similar if the corresponding angles have this property



  Measurement, Trigonometry, Geometry, Time 7Two page printable: Student Answer Sheet followed by the Answers


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  Questions: Sheet 38 Measurement, Trigonometry, Geometry, Time 8

  1   congruent term describing two shapes that are identical in all ways, corresponding sides and corresponding angle equal, scale factor = 1, ΔABC ≡ ΔDEF
  2   similar triangles these can be used to measure the length of objects e.g. height of tree from shadow cast by the tree and a stick of known height
  3   elevations a drawing of what a house will look like from the outside, e.g. from the front, or from the west, drawn to the same scale usually
  4   actual measurement this can be found for a house by measuring the plan size and using the scale and scale factor for calculation
  5   hypotenuse the longest side of a right-angled triangle, the side that is opposite the right-angle
  6   Pythagoras' theorem in any right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the two shorter sides
  7   c2 = a2 + b2 formula for Pythagoras theorem for any right-angled triangle
  8   adjacent one of the shorter sides of a right-angled triangle, the side being closest to the angle being used to identify the side, next to the angle
  9   opposite one of the shorter sides of a right-angled triangle, the side being furthest from the angle being used to identify the side
10   tangent ratio opposite side of a right-angle triangle divided by the adjacent side of the triangle
11   sine ratio opposite side of a right-angle triangle divided by the hypotenuse of the triangle
12   cosine ratio adjacent side of a right-angle triangle divided by the hypotenuse of the triangle
13   trigonometric ratios these are found on the calculator by using the sin, cos and tan functions
14   angles these are found on the calculator by using the sin-1, cos-1 and tan-1 functions
15   degrees mode the mode the calculator must be in when finding trigonometric ratios or angles from such ratios



  Measurement, Trigonometry, Geometry, Time 8Two page printable: Student Answer Sheet followed by the Answers


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  Questions: Sheet 39 Measurement, Trigonometry, Geometry, Time 9

  1   decimal degrees conversion the button on the calculator that does this has written on it o ' "
  2   draw a diagram in tests, problem questions often expect this at the start of the answer, as well as a written answer
  3   SOHCAHTOA acronym for sine = opp/hyp, cos = adj/hyp tan = opp/adj (sock ca toe-a)
  4   angle of elevation angle measured upwards from a horizontal, e.g. looking up to the top of a tree
  5   angle of depression angle measured downwards from a horizontal, e.g., looking down from a cliff
  6   proportional diagrams pictorial representation used to obtain estimates of a distance or angle, also that the accuracy of an answer can be checked
  7   sector the part of a circle between two radii
  8   quadrant a quarter of a circle, sector between two radii at right-angles
  9   A = πr2 formula for finding the area of a circle
10   circle shape for which the following formula is used to calculate area: A = πr2
11   (θ/360) × πr2 formula for find the area of a sector
12   sector shape for which the following formula is used to calculate area: (θ/360) × πr2
13   annulus shape for which the following formula is used to calculate area: A = π(R2 - r2)
14   ellipse shape for which the following formula is used to calculate area: A = πab, where a = semi major axis, b = semi minor axis
15   A = π(R2 - r2) formula for find the area of an annulus (area between two concentric circles)



  Measurement, Trigonometry, Geometry, Time 9Two page printable: Student Answer Sheet followed by the Answers


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  Questions: Sheet 40 Measurement, Trigonometry, Geometry, Time 10

  1   A = πab formula for find the area of an ellipse, a = semi major axis, b = semi minor axis
  2   concentric term describing two circles that have the same centre, forming an annulus
  3   composite shapes term describing a shape that is made of two or more other shapes: area found by adding (or subtracting) component shape areas
  4   Simpson’s rule a method of approximating irregular areas: A = h/3 (df + 4dm + dt)
  5   A = h/3 (df + 4dm + dt) formula used to find the approximate area of irregular areas; Simpson's rule
  6   better estimate this is obtained for the area of an irregular shape when Simpson's rule is used twice by dividing the area into two parts
  7   SA = 2πr2 + 2πrh formula for the surface area of a closed cylinder
  8   SA = 4πr2 formula for the surface area of a sphere
  9   SA = πr2 + 2πrh formula for the surface area of an open cylinder
10   closed cylinder shape for which the following formula is used to calculate area: SA = 2πr2 + 2πrh
11   sphere shape for which the following formula is used to calculate area: SA = 4πr2
12   open cylinder shape for which the following formula is used to calculate area: SA = πr2 + 2πrh
13   composite shapes term describing a shape that is made of two or more other shapes: volume found by adding (or subtracting) component shape volumes
14   compounded what happens to errors in measurement when the measurements are used to calculate area and volume
15   finding volume error calculate the largest possible volume and subtract the smallest possible volume (using lengths + 0.5 smallest unit and then lengths -0.5 of smallest unit)
16   finding area error calculate the largest possible area and subtract the smallest possible area (using lengths + 0.5 smallest unit and then lengths -0.5 of smallest unit)



  Measurement, Trigonometry, Geometry, Time 10Two page printable: Student Answer Sheet followed by the Answers


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  Questions: Sheet 41 Measurement, Trigonometry, Geometry, Time 11

  1   bearing an angle that is used to describe direction
  2   compass bearings N, NE, E, SE, S, SW, W, NW, all separated by an angle of 45o
  3   true bearings angle measured from north in a clockwise direction, from 000o to 360o
  4   draw a diagram a useful technique to enable you to extract information about a question when it involves bearings
  5   written answer this is always given to a problem question
  6   sine rule the ratio of each side of a triangle to the sine on the opposite angle will be equal
  7   a/sin A = b/sin B = c/sin C sine rule: ratio of sides of a triangle to the sine of the opposite angles are equal
  8   written problems begin by drawing a diagram and finish by giving a written answer
  9   inverted the sine rule also works in this form: the ratio of the sines of the angles to their opposite sides (of a triangle) are equal
10   A = 0.5ab Sin C formula for finding the area of a triangle knowing the length of two sides and the included angle
11   triangle shape that the following formula is used to calculate area: A = 0.5ab Sin C
12   cosine rule this allows us to calculate the length of the third side of a triangle when the length of two sides and the included angles are known
13   a2 = b2 + c2 - 2bcCos A cosine rule, used to calculate the length of a side of a triangle when two sides and the included angle are known
14   cosine rule this allows us to calculate the size of an angle in a triangle when the lengths of the three sides are known: a2 = b2 + c2 - 2bcCos A
15   a2 = b2 + c2 - 2bcCos A cosine rule, used to calculate the size of an angle of a triangle when the three sides are known
16   square root don't forget to take this when finding the length of a side using the cosine rule, the final step in the calculation
17   obtuse term describing an angle that is greater than 90,o, resulting in a negative cosine ratio
18   largest angle in any triangle, this is opposite the longest side (useful in solving cosine rule questions)



  Measurement, Trigonometry, Geometry, Time 11Two page printable: Student Answer Sheet followed by the Answers


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  Questions: Sheet 42 Measurement, Trigonometry, Geometry, Time 12

  1   longest side in any triangle, this is opposite the largest angle (useful in solving cosine rule questions)
  2   plane table radial survey an alternative method to offset surveys for finding the area of irregularly shaped fields using radial lines (from a central point to field corners) and known angles between the radial lines
  3   compass radial survey an alternative method to offset surveys for finding the area of irregularly shaped fields using lines (from a central point to field corners) and angles between the radial lines indicated by true bearings
  4   radial survey when radial lines are drawn and measured from a point in the centre of an area
  5   plane table radial survey when radial lines are drawn on a table by sighting each corner of the field and each line length and the angle between lines is measured
  6   compass radial survey when radial lines are drawn on a table by sighting each corner of the field and each line length and true bearing of the lines is measured
  7   circumference distance around a circle found from C = 2 πr or C = πd
  8   C = 2πr or C = πd alternative formulas for finding the circumference of a circle
  9   arc length part of the circumference of a circle, found with l = angle subtended/360 × 2πr
10   great circles the circle of the greatest possible size that lies on the surface of a sphere, e.g., equator, longitudes
11   small circle any circle of smaller size than a great circle around a sphere, e.g. all latitudes apart from the equator
12   latitude the line on the surface of the earth that represents the angular distance either north or south of the equator
13   parallel of latitude small circles parallel to the equator, used to describe how far north or south of the equator a place is in degrees
14   equator the only great circle perpendicular to the earth's axis, the only latitude that is a great circle, and line of reference for all other latitudes
15   Greenwich Meridian the half great circle from the North Pole to the South Pole that is used as a reference for all other half great circles east and west longitudes on the earth, 0o
16   International Date Line based on longitude 180o (east or west), on either side of which the day changes; for convenience the line is bent around some island nations
17   subtracting this operation is done to find the angular distance between two points on the same great circle (meridian of longitude) if the two points lie on the same side of the equator
18   adding this process is done to find the angular distance between two points on the same great circle (meridian of longitude) if the two points lie on opposite sides of the equator



  Measurement, Trigonometry, Geometry, Time 12Two page printable: Student Answer Sheet followed by the Answers


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  Questions: Sheet 43 Measurement, Trigonometry, Geometry, Time 13

  1   nautical mile the arc distance on the surface of the earth along any great circle, subtended by 1 minute angle at the centre of the earth (M)
  2   1 M a nautical mile, conversion factor, equals 1.852 km
  3   earth radius for any great circle on the earth, this is 6400 km, and can be used to calculate any arc distance along any great circle
  4   1 knot speed at sea, which is often given as 1 nautical mile per hour (1 M/hour)
  5   time zones these are calculated by comparison with Greenwich Mean Time for regions around the world
  6   west to east direction of rotation of the Earth on its axis, resulting in the time being later in the day towards the east, or earlier in the day towards the west
  7   add time for place east of Greenwich Mean Time we do this to calculate time zones
  8   subtract time for places west of Greenwich Mean Time we do this to calculate time zones
  9   4 minutes this is the amount of time that one degree of longitude represents
10   1 hour this is the amount of time that 15 degrees of longitude represents
11   subtract a day this needs to be done for time calculation when moving eastward across the International Dateline (Thursday --> Wednesday) e.g. travelling from Australia to S. America
12   daylight saving time a complication that results Australia having 5 time zones during summertime instead of the 3 zones during winter
13   add a day this needs to be done for time calculation when moving westward across the International Dateline (Thursday --> Friday); travelling from S. America to Australia
14   international travel a human activity which requires the calculation of departure and arrival times at different places around the globe
15   time difference this can be found by subtracting the time zones as calculated directly from longitude times from the Greenwich meridian
16   time difference this can be found by finding the longitude difference between two places and then multiplying by 4 minutes for every degree
17   subtract 2 hours going westward from Sydney to Perth you have to do this because it is earlier in the day in Perth compared to Sydney in Winter
18   add 2 hours going eastward from Sydney to New Zealand you have to do this because it is later in day in New Zealand



  Measurement, Trigonometry, Geometry, Time 13Two page printable: Student Answer Sheet followed by the Answers


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Youtube Channel Link.

Alan Thompson's Songs of Bygone Eras on Youtube.



Soundcloud Channel Link.

Alan Thompson's Songs of Bygone Eras on Soundcloud.



Easy access to songs on my Youtube Channel (videos with lyrics) and my SoundCloud Channel (MP3s) via a webpage listing of songs uploaded.

Alan Thompson's Songs of Bygone Eras.






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