TERM

GRADE 12

1

Control Test

2

Paper 1

2 hours

(100 marks)

Paper 2

2 hours

(100 marks)

3

Control Test

Control Test

Paper 1

3 hours

(150 marks)

Paper 2

3 hours

(150 marks)

4

External Examinations

Paper 1

3 hours

(150 marks)

Paper 2

3 hours

(150 marks)

PAPER 1

PAPER 2

Intention

Basic skills’ paper → assesses proficiency of content and/or skills

Applications’ paper → assesses ability to use both mathematical and non- mathematical techniques/considerations to explore familiar and unfamiliar contexts.

Structure and

5 questions

4 or 5 questions

scope of content and/or skills

Four questions deal with contexts relating to each of the topics:

• Finance
• Measurement
• Maps, plans and other representations of the physical world
• Data handling

Fifth question integrates content from across all of these topics.
Likelihood will be examined in the context or one or more of the other questions.
Each question can contain more than one context.

Each question deals with contexts drawing integrated content from across all of the topics:

• Finance
• Measurement
• Maps, plans and other representations of the physical world
• Data handling

Likelihood will be examined in the context or one or more of the other questions.
Each question can contain more than one context.

Level 1

60%

Level 2

35%

25%

Level 3

5%

35%

Level 4

40%

Contexts

Familiar’, i.e. limited to the contexts listed in the CAPS document.

Both ‘familiar’ and ‘unfamiliar’, i.e. not limited to the contexts listed in the CAPS document.

Topic

Weighting (%)

Basic skills topics

Interpreting and communicating answers and calculations

No weighting is provided for these topics. Rather, they will be assessed in an integrated way

throughout the Application Topics.

Numbers and calculations with numbers

Patterns, relationships and representations

Application topics

Finance

35% (±5%)

Measurement

20% (±5%)

Maps, plans and other representations of the physical world

15% (±5%)

Data handling

25% (±5%)

Likelihood

Minimum 5%

The four levels of the Mathematical Literacy assessment taxonomy

GRADE 12

PAPER 1

PAPER 2

OVERALL ALLOCATION

Level 1: Knowing

60% ± 5%

30% ± 5%

Level 2: Applying routine procedures in familiar contexts

35% ± 5%

25% ± 5%

30% ± 5%

Level 3: Applying multi-step procedures in a variety of contexts

5%

35% ± 5%

20% ± 5%

Level 4: Reasoning and reflecting

0

40% ± 5%

20% ± 5%

Question word

What is required of you

Analyse

Separate, examine and interpret

Calculate

This means a numerical answer is required – in general, you should show your working, especially where two or more steps are involved

Classify

Group things based on common characteristics

Compare

Point out or show both similarities and differences between things, concepts or phenomena

Define

Give a clear meaning

Describe

State in words (using diagrams where appropriate) the main points of a structure/process/phenomenon/ investigation

Determine

To calculate something, or to discover the answer by examining evidence

Differentiate

Use differences to qualify categories

Discuss

Consider all information and reach a conclusion

Explain

Make clear; interpret and spell out

Identify

Name the essential characteristics PAY SPECIAL ATTENTION

Label

Identify on a diagram or drawing

List

Write a list of items, with no additional detail

Mention

Refer to relevant points

Name

Give the name (proper noun) of something

State

Write down information without discussion

Suggest

Offer an explanation or a solution

Tabulate

Draw a table and indicate the answers as direct pairs

KEY 

Abbreviation

Meaning

(v)

verb: doing-word or action word, such as “walk”

(n)

noun: naming word, such as “person”

(adj)

adjective: describing word such as

“big”

(adv)

adverb: describing word for verbs, such as “fast”

(prep)

preposition: a word describing a position, such as “on”, “at”

(sing)

singular: one of

(pl)

plural: more than one of

(abbr)

abbreviation

Term

Meaning

A

abbreviate

(v). Make shorter.

account for

(v). Explain why.

adjacent

(adj). Next to something.

analyse

(v). Examine something in detail.

annotated

(adj). Something that has comments or explanations, usually written, added to it.

ante-

(prep). Before (e.g., ante-natal – before birth)

anti-

(prep). Against (e.g., anti-apartheid – against apartheid).

approximate

(v. & adj.). Come close to (v); roughly, almost, not perfectly accurate, close but not exact. The verb is pronounced “approxi-mayt” and the adjective is pronounced “approxi-mitt”.

arbitrary

(adj). Based on random choice; unrestrained and autocratic.

C 

category

(n). Class or group of things.

consecutive

(adj). One after another without any gaps or breaks.

consider

(v). Think about.

contrast

(v). Thow the difference between; (n) something that is very different from what it is being compared with.

conversely

(adv). The opposite of.

D

data (pl), datum (sing)

(n). Information given or found.

deduce

(v). To work something out by reasoning.

deduction

(n). Conclusion or idea that someone has worked out.

define

(v). Give the meaning of a word or words.

definition

(n). The meaning of a word or words.

denote

(v). To refer to or mean something.

determine

(v). Work out, usually by experiment or calculation.

E 

elapse

(v). Pass by or finish, e.g., time.

establish

(v). Show or prove, set up or create.

exceed

(v). Go beyond.

excess

(n). More than necessary.

excluding

(prep). Not including.

exclusive

(adj). Excluding or not admitting other things; reserved for one particular group or person.

exemplar

(n). A good or typical example.

exempt

(v). To free from a duty.

exempt

(adj). Be freed from a duty.

exemption

(n). Being freed from an obligation.

extent

(n). The area covered by something.

F 

factor

(n). A circumstance, fact or influence that contributes to a result; a component or part.

factory

(n). A place where goods are made or put together from parts.

find

(v). Discover or locate.

find

(n). Results of a search or discovery.

finding

(n). Information discovered as the result of an inquiry.

fixed

(adj). Not able to move, attached; or repaired, not broken.

format

(n). Layout or pattern; the way something is laid out.

G 

global

(adj). Found all over the world (globe).

I 

identify

(v). Recognise or point out.

illustrate

(v). Give an example to show what is meant; draw.

imply

(v). Suggest without directly saying what is meant.

indicate

(v). Point out or show.

initial

(n). First.

initiation

(n). The action of beginning something; the action of admitting somebody into a group or organisation.

inter- changeable

(adj). Can be swapped or exchanged for each other.

investigate

(v). Carry out research or a study.

issues

(v). Comes out of.

issues

(n). An important problem or a topic for debate.

M 

magnitude

(adj). Size.

manipulate

(v). Handle or control (a thing or a person).

motivate

(v). Give someone a reason for doing something.

multiple

(adj). Many.

N 

negligible

(adj). Small and insignificant; can be ignored. From “neglect” (ignore).

numerical

(adj). Relating to or expressed as a number or numbers.

numerous

(adj). Many.

O 

obtain

(v). Get.

optimal

(adj). Best; most favourable.

optimum

(adj). Best; (n) the most favourable situation for growth or success.

P 

principal

(n). Head of a school.

principal

(adj). Main or most important.

principle

(n). A basic truth that guides the way a person behaves.

priority

(n). Something that is considered to be more important or comes first.

provide

(v). Make available for use; supply.

Q 

quality

(n). The standard of something compared to other similar things; a characteristic of someone or something.

R 

reciprocal

(adj). Given or done in return.

record

(v). Make a note of something in order to refer to it later (pronounced ree-cord).

record

(n). A note made in order to refer to it later; evidence of something; a copy of something (pronounced rec-cord.

represent

(v). Be appointed to act or speak for someone; amount to.

resolve

(v). Finalise something or make it clear; bring something to a conclusion.

respect

(v). Admire something or someone; consider the needs or feelings of another person.

respectively

(adj). In regards to each other, in relation to items listed in the same order.

S 

simul- taneously

(adv). At the same time.

site

(n). Place.

suffice

(v). Be enough.

surplus

(adj). More than is needed.

survey

(n). A general view, examination, or description of someone or something.

survey

(v). Look closely at or examine; consider a wide range of opinions or options.

T 

tendency

(n). An inclination to do something in a particular way; a habit.

tertiary

(adj). Third level.

truncated

(adj). Cut short.

U 

under- reported

(adj). Not reported enough; there is not enough information.

V  

verify

(v). Show to be true; check for truth; confirm.

vice versa

(adv). The other way round.

versus

(prep). Against. Abbreviated “vs” and sometimes “v”.

A

account

(n. & v.). Finance: A record of income and expenditure. To explain (v), e.g. “Account for why the sky is blue”.

algebra

(n). A mathematical system where unknown quantities are represented by letters, which can be used to perform complex calculations through certain rules.

angel

(n). In Abrahamic religions, a messenger from God. Note the spelling.

angle

(n). The difference in position between two straight lines which meet at a point, measured in degrees. Note the spelling.

annual

(adj). Once every year. (E.g. “Christmas is an annual holiday”).

annum, per

(adv). For the entire year. (E.g. “You should pay R 100 per annum”).

area

(n). Length x breadth (width). In common usage: a place.

asset

(n). Something having value, which can be sold to defray (get rid of) debts. Can refer to physical things such as houses, cars, etc., or to savings and investments.

ATM

(n). Abbreviation: automatic teller machine.

average

(n). Mathematics: The sum of parts divided by the quantity of parts. In common use: neither very good, strong, etc., but also neither very weak, bad, etc; the middle. If you are asked to find the average, you always have to calculate it using the information you have. For example, the average of (1;2;3) is 2, because (1+2+3)/3 = 2. See also mean, median and mode.

axis (sing), axes (pl, pronounced “akseez”)

(n). A line along which points can be plotted (placed), showing how far they are from a central point, called the origin. See origin.
“Vertical axis” or “y-axis” refers to how high up a point is above the origin (or how far below).
“Horizontal axis” or “x-axis” refers to how far left or right a point is away from the origin.

B

bias

(n). To be inclined against something or usually unfairly opposed to something; to not accurately report on something; to favour something excessively.

BMI

(n). Body mass index. Calculated by dividing someone’s weight in kilograms by the square of his or her height in metres. An indication of whether someone is over- or underweight.

BODMAS

(abbr.). Brackets, of/orders (powers, squares, etc), division, multiplication, addition, subtraction. A mnemonic (reminder) of the correct order in which to do mathematical operations.

borrow vs lend

(v). To take something (e.g. money) from someone with their permission for temporary use (borrow). Lend means the opposite: it means to give money to someone for temporary use. Remember: Borrow from, lend to. Can refer to financial transactions. If you take money from a bank, you are the borrower and the bank is the lender.

breadth

(n). How wide something is. From the word “broad”.

budget

(n. & v.). To plan how to spend money (v); a plan of how to spend money (n); an estimate of the amount of money available (n).

C

Cartesian

(adj). Anything believed or proposed by Rene Descartes. In particular, the x-and-y axis coordinate system.

cash

(n). Printed or minted money, money not represented by cheques, cards, etc.

cashier

(n). Person who receives payment.

CFL

(n). Compact Fluorescent Light; a small fluorescent tube curled up inside a standard lightbulb shape.

chance

(n). The same as possibility or likelihood; that something might happen but that it is hard to predict whether it will.

chart

(v). To draw a diagram comparing values on Cartesian axes.

cheque

(n). A bill issued by banks, and filled in by the drawer (the person writing it), to represent an amount owed, usually with place to state who the amount is due to.

circum- ference

(n). The distance around the outer rim of a circle.

compound interest

(n). Interest charged on an amount due, but including interest charges to date. Compare to simple interest.

continuous

(adj). Mathematics: having no breaks between mathematical points; an unbroken graph or curve represents a continuous function. See function.

control

(n. and v.). To ensure something does not change without being allowed to do so (v); an experimental situation to which nothing is done, in order to compare to a separate experimental situation, called the ‘experiment’, in which a change is attempted. The control is then compared to the experiment to see if a change happened.

control variable

(n). A variable that is held constant in order to discover the relationship between two other variables. “Control variable” must not be confused with “controlled variable” (see independent variable).

coordinate

(n). The x or y location of a point on a Cartesian graph, given as an x or y value. Coordinates (pl) are given as an ordered pair (x, y).

correlate

(v). To see or observe a relationship between two things, without showing that one causes the other.

correlation

(n). That there is a relationship between two things, without showing that one causes the other.

correspond

(v). To pair things off in a correlational relationship. For two things to agree or match. E.g. A corresponds to 1, B corresponds to 2, C corresponds to 3, etc.

credit

(n. & v.). To lend someone money
(v); to have a certain amount of money that is not one’s own that was lent to one (n).
Credit limit: how much money you have borrowed or may borrow against.

cubed

(adj). The power of three; multiplied by itself three times.

cubic

(adj). Shaped like a cube; having been multiplied by itself three times.

cylinder

(n). A tall shape with parallel sides and a circular cross-section – think of a log of wood, for example, or a tube. See parallel. The formula for the volume of a cylinder is πr2h.

D

debit

(v. & n.). When someone or an organisation takes money out of your account. Compare to withdraw.

debt

(n). The state of owing money.

deficit

(n). Excess spending, or, the difference between the amount owed and the amount paid; shortfall; the excess of expenditure (spending) or liabilities (debts) over income (earnings) or assets.

denominator

(n). See divisor. In popular speech: a common factor.

depend

(v). To be controlled or determined by something; to require something to happen or exist first.

dependent (variable)

(adj/n). A variable whose value depends on another; the thing that comes out of an experiment, the effect; the results. See also independent variable and control variable. The dependent variable has values that depend on the independent variable, and we plot it on the vertical axis.

deposit

(n). Finance: to place money into an account.

derivation

(n). Mathematics: to show the working of your arithmetic or answer or solution; the process of finding a derivative.

derivative

(n). Mathematics: The rate of change of a function with respect to an independent variable. See independent variable. In common use: something that comes from something else.

diagonal

(adj. & n.). A line joining two opposite corners of an angular shape.

diameter

(n). The line passing through the centre of a shape from one side of the shape to the other, esp. a circle. Formula: d = 2r. See radius, radii, circumference.

difference

(n). Mathematics: subtraction. Informally: a dissimilarity. How things are not the same.

dimension

(n). A measurable extent, e.g. length, breadth, height, depth, time. Physics, technical: the base units that make up a quantity, e.g. mass (kg), distance (m), time (s).

distribution

(n). How something is spread out. Mathematics: the range and variety of numbers as shown on a graph.

divisor

(n). The number below the line in a fraction; the number that is dividing the other number above the fraction line. See numerator, denominator.

domain

(n). The possible range of x-values for a graph of a function. See range.

E

element

(n). Mathematics: part of a set of numbers. Popular use: part of.

elevation

(n). Science: height above the ground or sea level. Architecture: a face of a building as viewed from a certain direction on an architect’s plan of the building. See plan.

eliminate

(v). To remove or get rid of. Mathematics: to cancel a factor out of one side of an equation by dividing by that factor throughout, or by substituting in another formula or value that is equal.

expenditure

(n). How much money, time, or effort has been used on something.

expense

(n). How much something costs in time, money, or effort.

expensive

(adj). Using too much time, money or effort.

exponent

(n). When a number is raised to a power, i.e. multiplied by itself as many times as shown in the power (the small number up above the base number). So, 23 means 2 x 2 x 2. See also cubed.

exponential

(adj). To multiply something many times; a curve representing an exponent.

extrapolation

(n). To extend the line of a graph further, into values not empirically documented, to project a future event or result. In plain language: to say what is going to happen based on past results which were obtained (gotten) by experiment and measurement. If you have a graph and have documented certain results (e.g. change vs time), and you draw the line further in the same curve, to say what future results you will get, that is called ‘extrapolation’. See predict.

F

fraction

(n). Mathematics: Not a whole number; a representation of a division. A part. E.g. the third fraction of two is 0,666 or ²/₃ . meaning two divided into three parts.

frequency

(n). How often.

function

(n). Mathematics: when two attributes or quantities correlate.
If y changes as x changes, then y = f(x). See correlate, graph, Cartesian, axis, coordinate. Also: a relation with more than one variable (mathematics).

fund

(n. & v.). A source of money (n); to give money (v).

G

gradient

(n). A slope. An increase or decrease in a property or measurement. Also the rate of such a change. In the formula for a line graph, y = mx + c, m is the gradient.

graph

(n). A diagram representing experimental or mathematical values or results. See Cartesian.

graphic

(n., adj.). A diagram or graph (n). Popular use: vivid or clear or remarkable (adj.).

graphically

(adv). Using a diagram or graph. Popular use: to explain very clearly.

H

histogram

(n). A bar graph that represents continuous (unbroken) data (i.e. data with no gaps). There are no spaces between the bars. A histogram shows the frequency, or the number of times, something happens within a specific interval or “group” or “batch” of information.

hyperbola

(n). Mathematics: a graph of a section of a cone with ends going off the graph; a symmetrical (both sides the same) open curve.

hypotenuse

(n). The longest side of a right- angled triangle.

I

incline

(n. & v.). Slope. See gradient (n); to lean (v).

independent (variable)

(n). The things that act as input to the experiment, the potential causes. Also called the controlled variable. The independent variable is not changed by other factors, and we plot it on the horizontal axis. See control, dependent variable.

inflation

(n). That prices increase over time; that the value of money decreases over time. General use: the action of getting bigger.

informal sector

(n). Not part of the formal economy; street vendors or home workers; self-employed persons who have not formally registered a corporation or company but are manufacturing or selling items or work.

insufficient

(adj). Not enough.

insurance

(n). Finance: an agreement with an insurance company in which money is paid to guarantee against or compensate for future mishaps or losses. See premium. General use: something that is set up to prevent against future loss or mishap.

interest

(n). Finance: money paid regularly at a particular rate for the use or loan of money. It can be paid by a finance organisation or bank to you (in the case of savings), or it may be payable by you to a finance organisation on money you borrowed from the organisation. See compound interest and simple interest, see also borrow.

intermediate

(adj). A state in between.

interquartile

(adj). Between quartiles. See quartile.

interval

(n). Gap. A difference between two measurements.

inverse

(n). The opposite of. Mathematics: one divided by. E.g. ¹/₂ is the inverse of 2.

invest

(v). To put money into an organisation or bank (e.g. in buying shares) so as to gain interest on the amount at a higher rate. See interest.

investment

(n). Something in which you have invested money (time, or effort, in common usage).

investor

(n). A person who has invested (usually money).

invoice

(n). A formal request for payment (in writing). It will usually state the name of the supplier or vendor (shop); the address of the shop or company that is requesting the amount; the VAT number of the shop; the words “Tax Invoice”; the shop’s invoice number; the date and time of the sale; a description of the items or services bought; the amount of VAT charged (14%); the total amount payable.

K

kWh

(abbr). Unit of power (kilowatt hours) that electricity suppliers charge for. See power, watt. 1000 watts used in 1 hour = 1kWh = 1 unit. So e.g. a 2000 W heater uses 2 units per hour.

L

liability

(n). To owe, or to have something that causes one to be in debt; something that causes you to have to spend money; a legal or financial responsibility.

likely

(adj). To be probable; something that might well happen.

linear

(adj). In a line. Mathematics: in a direct relationship, which, when graphed with Cartesian coordinates, turns out to be a straight line.

logarithm

(n). Mathematics: a quantity representing the power by which a fixed number (the base) must be raised to produce a given number. The base of a common logarithm is 10, and that of a natural logarithm is the number e (2,7183…). A log graph can turn a geometric or exponential relationship, which is normally curved, into a straight line.

longitude

(n). Lines running north to south on the earth, measuring how far east or west one is, in degrees, from Greenwich in the UK. “Longitudinal” (adj) means from north to south, or top to bottom. Running lengthwise. Physics: a wave whose vibrations move in the direction of propagation (travel). Example: sound. Statistics: a study in which information is gathered about the same people or phenomena over a long period of time.

M

magnitude

(n). Size.

manipulate

(v). To change, or rearrange something. Usually in Mathematics it means to rearrange a formula to solve for (to get) an answer.

mean

(n). See average.

mechanical

(n). By means of physical force.

median

(n). Mathematics: the number in the middle of a range of numbers written out in a line or sequence.

member

(n). A part of. Finance: a person or legal entity who is partial owner of a company.

meter

(n). A device to measure something. You might see this spelling used in American books for metre. See metre.

metre

(n). The SI unit of length, 100 cm.

metric

(adj). A measurement system, using a base of 10 (i.e. all the units are divisible by 10). The USA uses something known as the Imperial system, which is not used in science. The Imperial system is based on 12. Examples:

• 2,54 cm (metric) = 1 inch
  (imperial). 1 foot = 12 inches
  = approx. 30 cm; 1 metre
  = 100 cm. 1 Fl.Oz (fluid ounce)
  = approx 30 mℓ.

minimise

(v). To make as small as possible.

minimum

(n). The smallest amount possible.

modal

(adj). Pertaining to the mode, or method. Can mean: about the mathematical mode or about the method used. See mode.

mode

(n). Mathematics: the most common number in a series of numbers. See also mean, median.

model

(n). A general or simplified way to describe an ideal situation, in science, a mathematical description that covers all cases of the type of thing being observed. A representation.

N

numerator

(n). The opposite of a denominator; the number on top in a fraction.

O

optimal

(adj). Best, most.

origin

(n). Mathematics: the centre of a Cartesian coordinate system. General use: the source of anything, where it comes from.

outlier

(n). Statistics: a data point which lies well outside the range of related or nearby data points.

P

parallel

(adj). Keeping an equal distance along a length to another item (line, object, figure). Mathematics: two lines running alongside each other which always keep an equal distance between them.

particular

(adj). A specific thing being pointed out or discussed; to single out or point out a member of a group.

PAYE

(abbr). Pay as you earn, tax taken off your earnings by your employer and sent to the South African Revenue Service before you are paid.

per

(prep). For every, in accordance with.

per annum

(adv). Once per year; for each year.

percent

(adv). For every part in 100. The rate per hundred.

percentile

(n). A division of percentages into subsections, e.g. if the scale is divided into four, the fourth percentile is anything between 75 and 100%.

perimeter

(n). The length of the outer edge; the outer edge of a shape.

period

(n). The time gap between events; a section of time.

periodic

(adj). Regular; happening regularly.

perpendicular

(adj). At right angles to (90˚).

pi

(n). π, the Greek letter p, the ratio of the circumference of a circle to its diameter. A constant without units, value approximately 3,14159.

plan

(n). Architecture: a diagram representing the layout and structure of a building, specifically as viewed from above. More general use: any design or diagram, or any intended sequence of actions, intended to achieve a goal.

plot

(v). To place points on a Cartesian coordinate system; to draw a graph.

policy

(n). Finance: a term referring to an account held with an insurance company; an agreement that the company insures you. General use: a prescribed course of action.

predict

(v). General use: to foresee. Mathematics: see extrapolation.

premium

(n). An amount paid by you to an insurance company for your policy. See policy. General use: expensive or valuable.

probability

(n). How likely something is. See likely. Probability is generally a mathematical measure given as a decimal, e.g. [0] means unlikely, but [1,0] means certain, and [0,5] means just as likely versus unlikely. [0,3] is unlikely, and [0,7] is quite likely. The most common way to express probability is as a frequency, or how often something comes up. E.g. an Ace is 1/13 or 0,077 likely, in a deck of cards, because there are 4 of them in a set of 52 cards.

product

(n). Mathematics: the result of multiplying two numbers.

project

(n. & v.). A project (n., pronounced PRODJ-ekt) is a plan of action or long-term activity intended to produce something or reach a goal. To project (v., pronounced prodj- EKT), is to throw something, or to guess or predict (a projection). To project a result means to predict a result. See extrapolate.

proportion

(n). To relate to something else in a regular way, to be a part of something in relation to its volume, size, etc; to change as something else changes. See correlate and respectively.

Pythagoras’s Theorem

(n). The square on the hypotenuse is equal to the sum of the squares on the other two sides of a right- angled triangle. Where h is the hypotenuse, a is the side adjacent to the right angle, and b is the other side: h2 = a2 + b2.

Q

qualitative

(adj). Relating to the quality or properties of something. A qualitative analysis looks at changes in properties like colour, that can’t be put into numbers. Often contrasted with quantitative.

quantitative

(adj). Relating to, or by comparison to, quantities. Often contrasted with qualitative. A quantitative analysis is one in which you compare numbers, values and measurements.

quantity

(n). Amount; how much.

quartile

(n). A quarter of a body of data represented as a percentage. This is the division of data into 4 equal parts of 25% each. To determine the quartiles, first divide the information into two equal parts to determine the median (Q2), then divide the first half into two equal parts, the median of the first half is the lower quartile (Q1), then divide the second half into two equal parts, and the median of the second half is the upper quartile (Q3). Data can be summarised using five values, called the five number summary, i.e. the minimum value, lower quartile, median, upper quartile, and maximum value.

R

radius (sing), radii (plur)

(n). The distance between the centre of an object, usually a circle, and its circumference or outer edge. Plural is pronounced “ray-dee-eye.”

random

(n). Unpredictable, having no cause or no known cause. Done without planning.

range

(n). Mathematics: the set of values that can be supplied to a function. The set of possible y-values in a graph. See domain.

rate

(n). How often per second (or per any other time period). Finance: the exchange rate or value of one currency when exchanged for another currency; how many units of one currency it takes to buy a unit of another currency. Also “interest rate”, or what percentage of a loan consists of interest charges or fees.

ratio

(n). A fraction; how one number relates to another number; exact proportion. If there are five women for every four men, the ratio of women to men is 5:4, written with a colon (:). This ratio can be represented as the fraction ⁵/₄ or 1¹/₄ or 1,25; or we can say that there are 25% more women than men.

rebate

(n. & v.). To send some money back to a person who has paid too much (v). An amount sent back to someone who has paid too much (n).

receipt

(n). Finance: a piece of paper or other evidence sent to show that an amount was paid and that the person who received it (recipient) wishes to acknowledge (show) that they received (got) it.

receive

(v). To get something.

reception

(n). The process of receiving something. In common use, it can mean to greet people or “receive” them in your house. It can also refer to receiving (getting) a radio or microwave signal, e.g. in a cellphone or radio.

refund

(n). To send back a full payment made by someone who has paid incorrectly. See rebate.

remainder

(n). Leftovers. Mathematics: an amount left over after division which cannot be divided further unless one wishes to have a decimal or fraction as a result, i.e. where the divisor does not exactly divide the numerator by an integer (whole number).

S

scale

(n). A system of measurement, with regular intervals or gaps between units (subdivisions) of the scale.

sector

(n). General use: a subdivision. In Economics or Finance: a part of the economy that is responsible for a particular industry or performs a particular service.

simple interest

(n). Interest charged on the original amount due only, resulting in the same fee every time.

simplify

(v). To make simpler. Mathematics: to divide throughout by a common factor (number or algebraic letter) that will make the equation easier to read and calculate.

solution

(n). Mathematics: the step-by-step displaying of calculations to arrive at answers. Common use: the answer to a problem, in the sense of dissolving (removing) a problem.

solve

(v). To come up with a solution (answer). Show your working.

square

(n). Mathematics: a shape or figure with four equal sides and only right angles; the exponent 2 (e.g. the square of 4 is 42 = 16).

squared

(adj). Having been multiplied by itself, put to the exponent 2. See square.

statement

(n). Finance: a summary of transactions (debits and credits, or payments and receipts) made on an account. See account, debit, credit.

statistics

(n). The mathematics of chance and probability.

subscript

(n). A number placed below the rest of the line, e.g. CO₂.

substitute

(v). To replace.

substitution

(n). The process of substituting. Mathematics: to replace an algebraic symbol in a formula with a known value or another formula, so as to simplify the calculation. See simplify.

subtotal

(n). Finance: the total amount due on a statement or invoice, usually without VAT (tax) charges given. Or: a total for a section of an invoice or statement or series of accounts, but not the total of the whole invoice, statement or account.

sum

(n. & v.). To add things up. Represented by Greek Sigma (s): ∑ or the plus sign (+).

superscript

(n). A number placed above the rest of the line, e.g. πr2.

T

tally

(n). A total count; to count in fives by drawing four vertical lines then crossing through them with the fifth line.

tangent

(n). Mathematics: a straight line touching a curve only at one point, indicating the slope of the curve at that point; the trigonometric function of the ratio of the opposite side of a triangle to the adjacent side of a triangle in a right-angled triangle; a curve that goes off the chart.

tax

(n). A compulsory levy imposed on citizens’ earnings or purchases to fund the activities of government.

taxable

(adj). A service, purchase or item or earning that has a tax applied to it.

transaction

(n). Finance: Exchanging money (payment or receipt); a credit and a debit.

transfer

(n). To move from one place to another. Finance: usually refers to a payment or credit. See credit, debit, transaction.

trends

(n). Mathematics: regular patterns within data.

trigonometry

(n). Mathematics: the relationship and ratios between sides and angles within a right-angled triangle.

U

UIF

(abbr). Unemployment Insurance Fund. A government-run insurance fund which employers and employees contribute to, so that when employees are retrenched they can still collect some earnings.

unit

(n). A subdivision of a scale. See scale.

V

variable

(n. & adj.). A letter used to represent an unknown quantity in algebra (n); a quantity that changes (n); subject to change (adj).

volume

(n). A measure of the space occupied by an object, equal to length x breadth x height.

W

watt

(n). Unit of power or rate of use of energy.

wattage

(n). The amount of power being used, usually rated in kWh. See kWh.

withdraw

(v). To remove. Finance: to take money out of an account that belongs to you. Compare debit.

Y

yard

(n). Old Imperial measurement of length, approximately equal to a metre (1,09 m).

Step 1: Write down the value that you need to find.

Need to find: Area

Step 2: Write down the information that you have. Write down the numbers and the units.

base = 6 cm height = 2 cm

Step 3: Write down the formula that you are going to use.

Area = ½ base × height

Step 4: Write down the formula again, but write the numbers that you know instead of the words or letters.
NB      We call this process substituting.

Area = ½ × 6 cm × 2 cm

Step 5: Now calculate.

= 3 cm × 2 cm

Step 6: Write your answer with the correct units.

= 6 cm²

Step 1: Write down what you need to find.

Need to find: Area and Perimeter. Let’s start with area.

Step 2: Write down the information that you have.

From the diagram:

• base = 110 cm
• height = 1,2 m

The sides of the triangle are at right angles to each other, so one side is the perpendicular height.
^NB    The units of the two lengths are not the same. Always write the values with the same units.
height = 1,2 m = 120 cm (because 100 cm = 1 m)

Step 3: Write down the formula.

Area = base = ½ × height

Step 4: Write down the formula again, but write the numbers that you know instead of the words.

Area = ½ × 110 cm × 120 cm

Step 5: Now calculate.

= 55 cm × 120 cm

Step 6: Write your answer with the correct units.

= 6 600 cm²

Step 7: Calculate the perimeter.

Perimeter = 120 + 163 + 110 = 393 cm

Need to find: Temperature in degree Celsius.

Notes

Information we have: Temperature in degrees Fahrenheit = 67 °F.

°C = (67° – 32°) ÷ 1,8

Replace °F with 67° in the formula:
°C = (°F – 32°) ÷ 1,8.

°C = 35° ÷ 1,8

Remember the order of operations: Calculate the brackets first and then do the division.

°C = 19,444 …°

Round off to two decimal places.

Temperature in degrees Celsius = 19,44 °C

Look at the number in the third decimal place. It is less than 5, so round the second decimal place down.

Need to find: Area

Notes

Information we have: diameter = 40 m; π = 3,142

NB

Always make sure you use the quantity that is written in the formula – radius, not diameter.

Butwe need the radius, which is half of the diameter, so r = 20 m.

A = πr²

A = 3,142 × (20)²

A = πr²  means Area = pi times the radius squared.

A = 3,142 × (20 × 20)

A = 3,142 × 400

A = 1 256,8 m²

Are the units right? Yes, the diameter was given in metres, so the area will be in square metres (m² ).

Step 1

Look at the formula. Which is the quantity that you want to calculate?

Area = length × breadth

Step 2

What do you need to do to get length on its own?
Length is multiplied by breadth. We need to divide by breadth to leave length on its own.
NB     You can only do something to a formula if you do the same to both sides!

Step 3

Divide both sides by breadth:

Area ÷ breadth = length × breadth ÷ breadth

Step 4

Now simplify the formula: area ÷ breadth

= length (because: breadth ÷ breadth = 1)

Step 5

Length =

area ÷ breadth

Step 6

Use the formula to solve the problem by substituting the values for area and breadth.

Selling price

Step 1

Look at the formula. Which is the quantity that you want to calculate?

profit = selling price – cost price
P = SP – CP

Step 2

Substitute the values thatyou have i.e. profit and cost price.

R65 = SP – R121

Step 3

Add cost price to both sides.

R65 + R121 = SP – R121+ R121

Step 4

Now simplify.

R186 = SP (because cost price – cost price = 0)

Step 1

Look at the formula. Which is the quantity that you want to calculate?

number of miles = ⁵/₈ × number of kilometres

Step 2

Number of kilometres is multiplied by ⁵/₈. So we need to multiply by ⁸/₅ because ⁵/₈ × ⁸/₅  = 1.

Step 3

Multiply both sides by ⁸/₅.

number of miles × ⁸/₅ = ⁵/₈ × number of kilometres × ⁸/₅

Step 4

Now simplify the formula:
Move the “× ⁸/₅”.

number of miles  × ⁸/₅ = ⁵/₈ × ⁸/₅ × number of kilometres 

Cancel out: ⁵/₈ × ⁸/₅ = 1.

number of miles  × ⁸/₅ = number of kilometres

Step 5

Now we have number of kilometres = number of miles  × _8

5

Step 6

Use the formula to solve the problem.
You can do this in your head:
30 × 8 = 240
240 ÷ 5 = 48
Or use a calculator: 30 [×] 8
[÷] 5 [=]

number of kilometres = number of miles × ⁸/₅
number of kilometres = 30 × ⁸/₅ = 48 km
Gavin cycled 48 km.

Step 1

Look at the formula. Which is the quantity that you want to calculate?

A = πr ²

Step 2

What do you need to do to get radius on its own on one side of the equation?
There are two things:

• radius is first squared
• then it is multiplied by pi (π)

Step 3

Divide both sides by π

Area ÷ π = πr ² ÷ π

Step 4

When then have
Which we write as:

Area ÷ π = r ²
area = r ²
π

Now take the square root of both sides.

√Area =√r ²
    π

Step 5

Now we have r = √Area
                                π

Step 6

Use the formula to solve the problem, by substituting the given values.
To do this on your calculator: first enter 40 ÷ 3,142 = then press √
Round off to two decimal places

r = √Area
         π
r = √ 40  = 3,568 ...
     3,142
r = 3,57 cm
She needs to make the circle with a radius of 3,57 cm.

Electricity consumption in kWh

50

150

600

1 000

Amount payable in 2011

R27,35

R85,83

R393,67

R728,63

Amount payable in 2012

R28,83

R94,99

R467,43

R888,83

Increase between 2011 and 2012

R1,48

R9,16

R73,67

R160,20

Percentage increase between 2011 and 2012

5,39%

10,67%

18,74%

21,99%

Own an MP3 player

Do not own an MP3 player

Own a cell phone

57

21

Do not own a cell phone

13

9

Own an MP3 player

Do not own an MP3 player

Total

Own a cell phone

57

21

78

Do not own a cell phone

13

9

22

Total

70

30

100