2D

Two dimensional. A flat surface or a measurement in two directions (e.g. area). We call these 2D objects.

3D

Three dimensional. A measurement in three directions (e.g. volume). We call these 3D objects.

acceleration

The acceleration of an object measures the rate of change in its velocity. We use the second derivative [ *f* ''(*t*)] to calculate this.

acute angle

An angle between 0^{o} and 90^{o}.

addition rule (probability)

We can use this for all types of events. However, if the events are mutually exclusive, we do not need the " - P(A and B)" part. This is because P(A and B) = 0 for mutually exclusive events.

additive inverse

When a number is added to its additive inverse the answer is zero.

adjacent angles

Two angles are adjacent if they share the same vertex and have one side in common between them.

algebraic expression

An expression made up of any number of terms seperated from each other by + an -.

algebraic fraction

A fraction which contains variables.

alternate angles

When lines are parallel, we have equal alternate angles. Look for a Z or a N.

alternating series

This is a series in which every term has the opposite sign to the preceding term.

e.g. 1 - 3 + 5 - 4 + 9 . . .

e.g. 1 - 3 + 5 - 4 + 9 . . .

altitude

Perpendicular height of a shape. A triangle has three altitudes.

analytical geometry

This is the branch of mathematics that uses algebra to help in the study of geometry.

angle of depression

Measured from the horizontal downwards.

angle of elevation

Measured from the horizontal upwards.

apex

This is the pointed tip of a cone or pyramid.

arc of a circle

An arc is part of the circumference of a circle.

area

The amount of surface or the size of a surface, measured in square units.

arithmetic sequence

Sequences with a constant first difference i.e. you need to add or subtract the same amount to get the next term.

(e.g. 5 ; 1 ; -3 ; -7 ; . . . )

(e.g. 5 ; 1 ; -3 ; -7 ; . . . )

arithmetic series

You get this when you add the terms of an arithmetic sequence.

(e.g. 5 + 1 - 3 - 7 - . . .)

(e.g. 5 + 1 - 3 - 7 - . . .)

ascending order

From smallest to biggest.

asymptote

A straight line which a graph approaches, but never reaches. In the example below, we have a horizontal asymptote.

axiom

A mathematical fact that is accepted to be true without needing to prove it.

e.g. a tangent to a circle is perpendicular to a radius of that circle, at the point of contact

e.g. a tangent to a circle is perpendicular to a radius of that circle, at the point of contact

axis of symmetry

The line which divides a shape (or graph) so that one half is the mirror image of the other half.

bar graph

Uses horizontal or vertical bars, with spaces in between, to display data.

base of a polygon

Any side of a polygon can be the base(*b*), as long as the height(*h*) is perpendicular to the base.

base of a solid

One of the two identical faces in a prism or the face opposite the apex in a pyramid or cone.

base of an exponent

A number or variable used with an exponent to show a power.

biased sample (statistics)

When everyone does not have an equal chance of being surveyed.

binomial

An algebraic expression with two terms.

bisect

This means to cut something in half.

bivariate data

Involves two variables and is graphically represented using a scatter plot.

(e.g. height and weight of learners)

(e.g. height and weight of learners)

box and whisker diagram (plot)

A graph or diagram that is used to display the five number summary.

broken line graph

A graph where plotted points are joined by line segments.

calculus

Calculus is the study of rate of change, in the same way that geometry is the study of shape and algebra is the study of operations and their applications to solving equations.

capacity

The amount of space inside a container measured in milliletres(*ml*), litres(*l*) or kilolitres(*kl*) and is mostly used for liquids.

Cartesian plane

A plane formed by a horizontal axis (the x-axis) and a vertical axis (the y-axis) intersecting at 0 and is used to locate the position of any point in the plane using two coordinates.

categorical data

Data values which are not numbers. (e.g. colours, type of cars, etc)

certain event (probability)

An event which will definitely happen, i.e. the probability of it happening is equal to 1.

e.g. If event A is getting 1, 2, 3, 4, 5, or 6 when rolling a die, then P(A) = 1

e.g. If event A is getting 1, 2, 3, 4, 5, or 6 when rolling a die, then P(A) = 1

chord

A line segment which connects two points on the circumference of a circle. The longest chord in a circle is the diameter.

class (class interval)

This shows a range or group of data values. (e.g. 1 - 10, 11 - 20, 21 - 30, etc)

class boundary

The begining and the end of a class interval. (e.g. 11 and 20 are the class boundaries of the class interval 11 - 20)

class midpoint

The middle of a class interval in grouped data.

co-interior angles

When lines are parallel, the sum of co-interior angles is 180^{o}. Look for a C or a U.

coefficient

The number which stands in front of the variables in an algebraic term.

collinear

Points are collinear when they lie on the same straight line.

compass directions

North, south, east and west.

complementary angles

The sum of two complementary angles is 90^{o}.

complementary events (probability)

All possible outcomes are in either one of the events (say A and B).

Rule:

P(not A) = 1 - P(A)

or

If A and B are complementary events, then P(B) = 1-P(A) or P(A) = 1 -P(B).

Rule:

P(not A) = 1 - P(A)

or

If A and B are complementary events, then P(B) = 1-P(A) or P(A) = 1 -P(B).

complex numbers

Includes all real and all non-real (imaginary) numbers. We need these numbers to solve an equation like x^{2} = -9.

composite functions

A combination of two functions, where you apply the 1^{st} function to get an answer, and then substitute that answer into the 2^{nd} function, e.g. *f*(*g*(x)).

composite numbers

Numbers with more than 2 factors.

(e.g. 6 = 1 × 6 and 6 = 2 × 3 . This tells us that 6 is a composite number with factors 1, 2, 3 and 6.)

(e.g. 6 = 1 × 6 and 6 = 2 × 3 . This tells us that 6 is a composite number with factors 1, 2, 3 and 6.)

compound interest

This is when you earn interest on interest. Can also be called compound
growth.

Formula: A = P(1 + i)^{n}

Formula: A = P(1 + i)

concavity

A function is concave up where the 2^{nd} derivative is positive and concave down where the 2^{nd} derivative is negative.

concyclic points

Points that all lie on the circumference of the same circle.

cone

A solid with a circular base which comes to a point at the top called the apex.

congruent figures

Figures that have the same size and shape. They are identical.

conjecture

A conclusion based on incomplete evidence.

(e.g. 1 + 4 = 5 and 9 + 16 = 25 are incomplete evidence that the sum of two perfect squares is not a perfect square)

(e.g. 1 + 4 = 5 and 9 + 16 = 25 are incomplete evidence that the sum of two perfect squares is not a perfect square)

consecutive numbers

Numbers which follow one another. (e.g. 34 and 35 are consecutive numbers and 44 and 46 are consecutive even numbers)

consecutive terms

Terms which follow one another in a pattern. T_{1}, T_{2}, and T_{3} are consecutive terms.

constant

A value that does not change or vary.

constant difference

You get this when the differences between consecutive terms in a number pattern are the same.

constant second difference

When the differences between the first differences in a number pattern are the same.

constraints (in linear programming)

These are restrictions and we express them using linear inequalities.

(e.g. a maximum of 12 hours is available for manufacturing or at least 5 units must be sold per day)

(e.g. a maximum of 12 hours is available for manufacturing or at least 5 units must be sold per day)

continuous graph

A graph that can be drawn without lifting your pencil.

convergent series

An infinite series that has a finite sum.

converse of a theorem

A statement formed by interchanging what is given in a theorem and what is to be proven.

correlation coefficient

A number (r) where -1 ≤ r ≤ 1, that measures the strength and direction of the correlation (relationship) between two variables.
e.g. r close to 1 means there is strong positive correlation between the variables
r close to -1 means there is strong negative correlation between the variables
r close to 0 means there is weak or no correlation between the variables

corresponding angles

When lines are parallel, we have equal corresponding angles. Look for a F.

cos (cosine)

The cosine of an angle in a right-angled triangle is equal to the length of the adjacent side divided by the length of the hypotenuse.

cosec

The cosec of an angle in a right-angled triangle is equal to the length of the hypotenuse divided by the length of the opposite side.

cot

The cot of an angle in a right-angled triangle is equal to the length of the adjacent side divided by the length of the opposite side.

counting numbers

The natural numbers and zero: 0, 1, 2, 3, 4, . . .

cube

A solid with six identical square faces.

cube root

The cube root of a number, when multiplied by itself three times, gives the number under the root sign.

cubic function

The highest power of the variable is 3.

e.g.*y* = *x*^{3} + 2*x*^{2} - *x* - 4

e.g.

cubic graph

The graph of a cubic function.

cubic number

A number which can be written as the product of three identical factors.

cumulative frequency

The total of all the frequencies, up to a certain point, in a set of data.

cyclic quadrilateral

A quadrilateral whose 4 vertices all lie on the circumference of the same circle.

cylinder

A solid with two identical circular faces which are perpendicular to a curved surface.

data

Information collected in a statistical survey which can be categorical (e.g.favourite colours, types of cars) or numerical (e.g.length, age, scores).

decagon

A polygon with 10 sides.

decending order

From biggest to smallest.

decreasing

Getting smaller.

decreasing function

When the graph of the function is sloping downwards.

denominator

The bottom part of a fraction.

derivative

Gradient of a function at a certain point.

diagonal

A line segment joining two vertices of a polygon which are not next to each other.

diameter

The distance from a point on the circumference of a circle, through the centre to another point on the circumference.

(diameter = 2 x radius)

(diameter = 2 x radius)

difference

The answer to subtraction.

discrete graph

A graph made up of dots.

dodecahedron

A polyhedron with 12 faces, 20 vertices and 30 edges. The faces are congruent regular pentagons.

domain

The values of *x* for which a function is defined or the set of all possible *x*-values of a function.

edge

Where two faces of a solid meet.

effective interest rate

An interest rate which is compounded annually.

(e.g. 12% p.a. compounded annually)

(e.g. 12% p.a. compounded annually)

enlargement

A transformation which changes the size but not the shape of an object.

equation

A mathematical statement which includes an = sign. The two sides are equal and therefore balanced.

estimated mean

The mean value of grouped data.

event

You can define an event to have specific outcomes.

e.g. let event A be getting an even number when rolling a die

e.g. let event A be getting an even number when rolling a die

exchange rate

The price of one country's money in terms of another country's money. (e.g. R/$: 7.34 means we will pay R7,34 for $1)

experiment (probability)

An activity with outcomes.

e.g. rolling a die

e.g. rolling a die

exponent

Together with its base this makes a power. Also known as an index.

expression

see algebraic expression

extrapolation

This is when you predict or estimate from outside the given range of *x*-values. These predictions are usually poor and unreliable.

face

A flat surface of a solid.

factor theorem

If f(a) = 0 then x – a is a factor of f(x)

or

If f(b/a) = 0 then ax – b is a factor of f(x)

e.g. x + 4 is a factor of f(x) = x2 - 2x - 8 because f(-4) = (-4)2 - 2(-4) - 8 = 0

or

If f(b/a) = 0 then ax – b is a factor of f(x)

e.g. x + 4 is a factor of f(x) = x2 - 2x - 8 because f(-4) = (-4)2 - 2(-4) - 8 = 0

factorial

The product of all the integers from 1 up to the integer in question.

e.g. 5! = 5 x 4 x 3 x 2 x 1

e.g. 5! = 5 x 4 x 3 x 2 x 1

factorise

To write an algebraic expression as a product of its factors.

factors

All natural numbers that can divide exactly into a number.
E.g. Factors of 24: 1 ; 2 ; 3 ; 4 ; 6 ; 8 ; 12 ; 24

feasible region (linear programming)

A region which contains all the points that satisfy a set of constraints.

Fibonacci number pattern

The next number is found by adding the two previous numbers.

five number summary

The minimum value, lower quartile (Q_{1}), median, upper quartile (Q_{3}) and maximum value of a set of data.

formula

A rule using symbols to represent a mathematical or scientific statement.

frequency

The number of times an item or data value occurs.

frequency polygon

A graph which displays grouped data. A frequency polygon is made up of lines which joins the horizontal axis to the data points with coordinates: (midpoint of class ; frequency for that class )

frequency table

A table showing the number of times a data value occurs.

function

A rule where every element in the domain (*x*-values) is linked to only one element in the range (*y*-values).

fundamentel counting principle

If there are **M** ways for an event to occur and **N** ways for a second event to occur, then there are **M x N** ways in which both of them can occur. (NB. this is also true for more than two events)

e.g. If you roll a die (6 outcomes) and flip a coin (2 outcomes), then there are 12 (6 x 2) possible outcomes.

e.g. If you roll a die (6 outcomes) and flip a coin (2 outcomes), then there are 12 (6 x 2) possible outcomes.

future value annuity

When fixed regular payments are made and you get the money in the future. This future value is â€œall the payments plus the interestâ€.

general solution (in trigonometry)

All the possible solutions of a trigonometric equation. We need this because a trig equation has infinitely many solutions.

general term

The general term (T_{n}) is an expression that can be used to calculate any term in a number pattern.

geometric sequence

Sequences with a constant ratio i.e. you need to multiply or divide by the same amount to get the next term.

(e.g. 100 ; 50 ; 25 ; 12,5 ; . . .)

(e.g. 100 ; 50 ; 25 ; 12,5 ; . . .)

geometric series

You get this when you add the terms of a geometric sequence.

(e.g. 100 + 50 + 25 + 12,5 + . . .)

(e.g. 100 + 50 + 25 + 12,5 + . . .)

gradient

This shows the steepness of a line.

grouped data

Data which is grouped together in class intervals. Grouped data is usually displayed on a histogram.

hemisphere

Half a sphere.

heptagon

A polygon with 7 sides.

hexagon

A polygon with 6 sides.

hexahedron (cube)

A polyhedron with 6 faces, 8 vertices and 12 edges. The faces are congruent squares.

hire purchase

A method of buying goods by paying monthly instalments over a period of time.

histogram

A graph which displays grouped data. The height of the bars shows the frequency and there are no gaps between the bars.

horizontal

This is from left to right...like the horizon. A horizontal line is perpendicular to the *y*-axis and parallel to the *x*-axis.

hyperbola

The graph of a function where *x* is in the denominator.

icosahedron

A polyhedron with 20 faces, 12 vertices and 30 edges. The faces are congruent equilateral triangles.

impossible event (probability)

An event which is not possible, i.e. the probability of it happening is equal to 0.

e.g. If event A is getting 7 when rolling a die, then P(A) = 0

e.g. If event A is getting 7 when rolling a die, then P(A) = 0

improper fraction

A fraction in which the numerator (top) is bigger than the denominator (bottom).

inclination angle

This is an angle measured from the *x*-axis in an anti-clockwise direction.

increasing

Getting bigger.

increasing function

When the graph of the function is sloping** **up.

independent events (probability)

Two events are independent if the probability of one event occurring has no influence on the probability of the other event occurring.

e.g. getting heads when tossing a coin and getting a 6 when rolling a die.

Because these are independent events, we can use the product rule as follows: P(H and 6) = P(H) Ã— P(6)

e.g. getting heads when tossing a coin and getting a 6 when rolling a die.

Because these are independent events, we can use the product rule as follows: P(H and 6) = P(H) Ã— P(6)

index

see exponent

inequality

A statement where one quantity is bigger than another quantity. (e.g. *x* > 5 or *x* + 1 < 2)

NB: When solving an inequality, the inequality sign changes direction when multiplying or dividing by a negative number.

NB: When solving an inequality, the inequality sign changes direction when multiplying or dividing by a negative number.

inequality signs

Bigger than or greater than (e.g. 5 > 2).

Smaller than or less than (e.g. 1 < 6).

The open side always point to the bigger value.

Smaller than or less than (e.g. 1 < 6).

The open side always point to the bigger value.

infinity

A quantity without limit. It is a concept, not an actual number.

inflation

This shows the increase (as a percentage) in the cost of goods and services from one year to another.

inflection point

This is the point where a function changes concavity.

integer

Negative whole numbers, zero and positive whole numbers.

interpolation

This is when you predict or estimate from inside the given range of *x*-values. These predictions are usually good and reliable.

interquartile range

The difference between the upper and lower quartiles. IQR = Q_{3} - Q_{1}

intersect

To cross each other. Two lines intersect in one point.

interval notation

A way of showing a set of real numbers. A round bracket means 'excluded' and a square bracket means 'included'. Infinity is always excluded.

inverse function

This is a reflection in the line *y* = *x*. To get the equation of the inverse, you swop the *x*- and *y*-values.

irrational number

A number with non-repeating, never ending decimals. It cannot be written as a fraction.

kite

A quadrilateral with two pairs of equal adjacent sides, but not all four sides have the same length.

LCM

Lowest common multiple. The smallest number into which all the given numbers can divide.

leading coefficient

This the coefficient of the term with the highest degree in a polynomial.

least squares line

see regression line

like terms

Terms with identical variables. We can add and subtract like terms. (e.g. 5*x*^{2}*y* + 3*x*^{2}*y* - *x*^{2}*y* = 7*x*^{2}*y*)

limit

The value that a function approaches as *x* approaches some value.

line of best fit

This is a straight line (linear function) that best represents the data on a scatter plot. The line must go through as many points as possible with roughly the same number of points above and below it.

Also see regression line.

Also see regression line.

linear function

The highest power of the variable is 1. (e.g. y = 3*x* + 1)

linear pattern

The general term of a linear pattern is of the form T_{n} = an + c. A linear pattern has constant differences between consecutive terms.

linear programming

A mathematical method that uses linear inequalities to solve problems involving maximum and minimum quantities.

(e.g. maximum profit and minimum cost)

(e.g. maximum profit and minimum cost)

lower class boundary

The smallest value in a class interval. (e.g. the lower class boundary of 11 - 20 is 11)

many-to-one function

Many elements in the domain are linked to the same element in the range.

On a graph: If you move a vertical line across the graph, the line will cut the graph only once, but if you move a horizontal line across the graph, it will cut the graph more than once.

On a graph: If you move a vertical line across the graph, the line will cut the graph only once, but if you move a horizontal line across the graph, it will cut the graph more than once.

maximum

The biggest value.

mean

One of the measures of central tendency, calculated by dividing the sum of all the data values by the number of data values.

mean point

This is the point on a scatter plot where the *x*-coordinate is the mean of the given *x*-values and the *y*-coordinate is the mean of the given *y*-values.

The mean point always lies on the regression line.

The mean point always lies on the regression line.

measures of central tendency

The mean, median and mode. These are averages which use one value to summarise a set of data.

measures of dispersion

These values tell us how spread out the data is (e.g. range, inter-quartile range and standard deviation).

median

This is a measure of central tendency. The median is the middle value when the data is arranged from smallest to biggest. If there are two middle values, the median is the average of these two values.

median of a triangle

This is the line joining the vertex of a triangle to the midpoint of the opposite side.

midpoint theorem

The line joining the midpoints of two sides of a triangle is parallel to the third side and is equal to half this third side.

minimum

The smallest value.

mixed number

A number which contains a whole number and a proper fraction.

modal class

The class interval with the highest frequency in grouped data.

mode

A measure of central tendency. This is the data value which appears the most often.

monomial

An algebraic expression with only one term.

multiple

To get the multiples of a number, we multiply that number by 1, then 2, then 3, etc.
E.g. Multiples of 5: 5 ; 10 ; 15 ; 20 ; 25 ; . . .

mutually exclusive (probability)

Events which have no common outcomes.

e.g. even and odd numbers are mutually exclusive because numbers cannot be even and odd at the same time

If A and B are mutually exclusive, then P(A and B) = 0.

e.g. even and odd numbers are mutually exclusive because numbers cannot be even and odd at the same time

If A and B are mutually exclusive, then P(A and B) = 0.

natural number

The natural numbers are 1, 2, 3, 4, 5, . . .

negative correlation

One variable on the scatter plot increases as the other variable decreases.

The regression line will have a negative gradient, i.e. the line slopes downwards.

The regression line will have a negative gradient, i.e. the line slopes downwards.

nominal interest rate

Interest rate that is compounded monthly, quarterly, semi-annually, etc. In other words, anything but annually.

(e.g. 12% p.a. compounded monthly)

(e.g. 12% p.a. compounded monthly)

non-real number

Even root of a negative number, also called an imaginary number.

numerator

The top part of a fraction.

obtuse angle

An angle between 90^{o} and 180^{o}.

octagon

A polygon with 8 sides.

octahedron

A polyhedron with 8 faces, 6 vertices and 12 edges. The faces are congruent equilateral triangles.

ogive

A graph in statistics that is used to display cumulative frequency.

one-to-one function

Every element in the domain is linked to a different element in the range.

On a graph: If you move a vertical or a horisontal line across the graph, both will cut the graph only once.

On a graph: If you move a vertical or a horisontal line across the graph, both will cut the graph only once.

ordered pair

The *x*- and *y*-coordinates of any point on the Cartesian plane. These are written inside brackets, with the *x*-coordinate written first.

origin

This is where the *x*- and *y*-axes cross. The coordinates of the origin are (0 ; 0)

outcome

A possible result when doing an experiment in Probability.

e.g. getting 6 when rolling a die

e.g. getting 6 when rolling a die

outlier

Also called an extreme data value. This is a data value which is much bigger or much smaller than the rest of the data.

parabola

This is the graph of a quadratic function.

parallel lines

Lines which are always the same distance apart from each other. They will never meet or cross.

parallelogram

A quadrilateral with both pairs of opposite sides parallel.

pentagon

A polygon with 5 sides.

percentile

Percentiles divide a set of data into 100 equal parts. (e.g. P_{40} is the 40^{th} percentile. It means that about 40% of the data lies below P_{40} and about 60% lies above P_{40})

perimeter

The total distance around a 2D shape.

perpendicular bisector

A perpendicular bisector is a) perpendicular to another line and b) cuts the other line in half.

perpendicular lines

Lines which intersect at 90^{o}.

pi

The ratio of the circumference of a circle to its diameter. π = 3,141592654...

pie chart

A circle graph which is used to compare different categories. Also known as a pie graph.

Platonic solids

These are polyhedra with:

- faces which are congruent regular polygons

- edges which are all the same length

- the same number of edges meeting at each vertex

The 5 Platonic solids are the tetrahedron, the hexahedron (cube), the octahedron, the dodecahedron and the icosahedron.

- faces which are congruent regular polygons

- edges which are all the same length

- the same number of edges meeting at each vertex

The 5 Platonic solids are the tetrahedron, the hexahedron (cube), the octahedron, the dodecahedron and the icosahedron.

polygon

A 2D figure with three or more straight sides.

polyhedra

One polyhedron, many polyhedra.

polyhedron

A 3D object with flat faces where each face is a polygon.

NB: Cylinders, cones and spheres are not polyhedra.

NB: Cylinders, cones and spheres are not polyhedra.

polynomial

An algebraic expression with two or more terms.

population (statistics)

When everyone is surveyed.

positive correlation

Both variables on the scatter plot increase at the same time.

The regression line will have a positive gradient, i.e. the line slopes upwards.

The regression line will have a positive gradient, i.e. the line slopes upwards.

power

A power is a number raised to an exponent.

present value annuity

When regular fixed payments are made and you get the money upfront (now). This present value is “all the payments minus the interest”.

prime factors

Factors which are prime numbers.

e.g. prime factors of 24 = 2 x 2 x 2 x 3 = 2^{3}.3

e.g. prime factors of 24 = 2 x 2 x 2 x 3 = 2

prime number

A number which can only be divided by 1 and itself. The first few prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, ....

prism

A solid in which the base, the top and all cross sections are identical (congruent) polygons.

probability

A measure of the likelihood that a random event will produce a specific outcome.

product

The answer to multiplication.

product rule (probability)

We use this rule with independent events.

proper fraction

A fraction in which the numerator (top) is less than the denominator (bottom).

proportionality theorem

If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides in the same proportion.

pyramid

A 3D solid with a polygon as the base. All the other faces are triangles which meet at a point, the apex.

Pythagoras

The theorem of Pythagoras states that the square of the hypotenuse of a right angled triangle equals the sum of the squares of the other two sides.

quadrant

The Cartesian plane has 4 quadrants. They are the 1^{st}, 2^{nd}, 3^{rd} and 4^{th} quadrants.

quadratic function

The highest power of the variable is 2. (e.g. y = *x*^{2} + *x* - 6)

quadratic pattern

A number pattern which has constant second differences. The general term is of the form: T_{n} = an^{2} + bn + c

quadrilateral

A 2D shape with four sides.

quartiles

The quartiles divide a set of data into 4 equal parts. They are the lower quartile (Q_{1}), the median (M or Q_{2}) and the upper quartile (Q_{3}).

quotient

The answer to division.

radius

The distance from the centre of a circle to its circumference. (diameter = 2 x radius)

random

Random events are unpredictable.

e.g. you cannot predict what number you will get when you toss a die

e.g. you cannot predict what number you will get when you toss a die

random sample (statistics)

When everyone has an equal chance of being surveyed.

range (in algebra)

The values of *y* for which a function is defined or the set of all possible *y*-values of a function.

range (in statistics)

A measure of dispersion (spread) showing the difference between the biggest and smallest data values in a set of data.

rate

A rate compares two different types of measurements.
E.g. A speed of 60 km/h is a rate which compares distance and time

rational number

A number which can be written as a fraction (integer over an integer).

raw data

A list of separate data values.

real number

All the rational and irrational numbers.

reciprocal

Turning a fraction around. A number multiplied by its reciprocal equals 1.

reciprocal trig functions

The reciprocal of sin A is cosec A, the reciprocal of cos A is sec A and the reciprocal of tan A is cot A.

rectangle

A quadrilateral with equal opposite sides and 4 right angles. (A parallelogram with 4 right angles).

recurring decimals

A decimal with digits that repeat 'forever'.These are rational numbers.

reduction formulae (trigonometry)

These are used to reduce (change) angles to acute angles

(e.g. sin 240^{o} = sin (180^{o} + 60^{o}) = -sin 60^{o})

(e.g. sin 240

reflection

A mirror image. Shape and size stay the same.

reflection in x-axis

The sign of *y* changes.

reflection in y-axis

The sign of *x*** **changes.

reflex angle

An angle between 180^{o} and 360^{o}.

regression line

Also known as the **line of best fit** or the **least squares regression line**.

A line drawn through the points on scatter plot to summarise the relationship between the variables being studied.

This line can also be used to make certain predictions and estimations.

A line drawn through the points on scatter plot to summarise the relationship between the variables being studied.

This line can also be used to make certain predictions and estimations.

regular polygon

All the sides and angles are equal.

(e.g. an equilateral triangle has three equal sides and all three angles are 60^{o})

(e.g. an equilateral triangle has three equal sides and all three angles are 60

remainder theorem

If *f*(*x*) is divided by *x* - *a*, then the remainder is *f*(*a*)

or

If*f*(x) is divided by *ax* - *b*, then the remainder is *f*(*b/a*)

e.g. The remainder when*f*(*x*) = *x*^{2} - 2*x* - 8 is divided by *x* + 1 is -5, because *f*(-1) = (-1)^{2} - 2(-1) - 8 = -5

or

If

e.g. The remainder when

representative sample (statistics)

A smaller group which represents the whole population.

residual value

This is the difference between the real (observed) *y*-value for a certain *x*-value and the predicted (use the regression line) *y*-value for that same *x*-value.

revolution

A full turn through 360^{o}.

rhombus

A quadrilateral with parallel opposite sides and 4 equal sides. (A parallelogram with 4 equal sides)

right angle

A 90^{o }angle.

rigid transformation

Any transformation which leaves the shape and size of an object unchanged.

(e.g. Translations, reflections and rotations are all examples of rigid transformations. An enlargement is not a rigid transformation because it changes the size of the object.)

(e.g. Translations, reflections and rotations are all examples of rigid transformations. An enlargement is not a rigid transformation because it changes the size of the object.)

rotation

When an object is rotated aound a fixed point. Shape and size stay the same.

sample (statistics)

When only some people in the population is surveyed.

sample space (probability)

The number of possible outcomes in an experiment.

e.g. n(S) = 6 when rolling a die, because there are 6 outcomes: 1, 2, 3, 4, 5 or 6

e.g. n(S) = 6 when rolling a die, because there are 6 outcomes: 1, 2, 3, 4, 5 or 6

scatter plot (diagram)

A diagram which is used to investigate whether there is any relationship between two variables.

e.g. height and weight of learners (bivariate data)

e.g. height and weight of learners (bivariate data)

scientific notation

A way to write very big or very small numbers. (e.g. 65 000 000 = 6,5 x 10^{7} and 0,000042 = 4,2 x 10^{-5})

sec

The sec of an angle in a right-angled triangle is equal to the length of the hypotenuse divided by the length of the adjacent side.

semi-interquartile range

Half of the interquartile range.

sigma

The sum of.

similar figures

Figures that have the same shape but different size.

simple interest

Interest is calculated on the original amount only. Can also be called simple growth.

Formula: A = P(1 + in)

Formula: A = P(1 + in)

simplify

To write an expression in a simpler form. (e.g. 7*x* - 5*y* - *x* - 2*y* = 6*x* - 7*y*)

simultaneous equations

This is when we use two equations to solve for two unknowns.

sin (sine)

The sine of an angle in a right-angled triangle is equal to the length of the opposite side divided by the length of the hypotenuse.

solid

A 3D shape.

sphere

A perfectly round 3D solid.

square

A quadrilateral with 4 equal sides and 4 right angles.

square number

A number which can be written as the** **product of two identical factors.

square root

The square root of a number when multiplied by itself, gives the original number.

standard deviation

Measure of spread around the mean. Unlike the range, this measure involves all the data values in a set.

stem and leaf diagram

Use this to organise numerical data in statistics. The leaf is the last digit of the number while the stem is all the other digits.

straight angle

An angle of 180^{o}.

sum

The answer to addition.

supplementary angles

The sum of two supplementary angles is 180^{o}.

surd

The square root of a number which is not a perfect square; the cube root of a number which is not a perfect cube; etc.

surface area

Also known as total surface area (TSA). The total area of all the outside surfaces of a 3D solid.

symmetry

Where one half of a shape is the mirror image of the other half. (see axis of symmetry)

tan

The tan of an angle in a right-angled triangle is equal to the length of the opposite side divided by the length of the adjacent side.

tangent (to a circle)

A straight line which touches the circle at just one point. The tangent is perpendicular to the radius (diameter) of the circle.

term

Part of an algebraic expression. Terms are seperated by + and -.

e.g. There are 3 terms in 2*a* - 4*b* + 6 but there is only 1 term in 3(x-2) and in (x-1)(x+3)^{2}

e.g. There are 3 terms in 2

tetrahedron

A polyhedron with 4 faces, 4 vertices and 6 edges. The faces are congruent equilateral triangles.

theorem

A mathematical statement that has been proven to be true. To do this one can use previously proven theorems and/or axioms.

transformation

Moving a shape to a different position. This can be done through a translation, a reflection, a rotation or an enlargement.

translation

Moving a shape up, down, left and/or right without rotating or reflecting it. Shape and size stay the same.

trapezium

A quadrilateral with one pair of parallel sides.

tree diagram

A diagram , made up of branches, that shows all the possible outcomes of an event.

trend line

A line which goes through the data points on a scatter plot. It follows the general trend of the data.

Also known as "the line of best fit".

Also known as "the line of best fit".

trial

This refers to each time you do an experiment in Probability.

e.g. rolling a die 20 times gives 20 trials

e.g. rolling a die 20 times gives 20 trials

trigonometry

The measurement of triangles.

trinomial

An algebraic expression with three terms.

turning point

This is the point where the graph changes from increasing to decreasing or from decreasing to increasing.

undefined number

A number is undefined if its denominator is zero.You may never divide by zero.

ungrouped data

Also known as raw data. A list of separate data values.

unlike terms

Terms with different variables. You may not add or subtract unlike terms. (e.g. 3*x* and 5*y* are unlike terms)

upper class boundary

The biggest value in a class interval. (e.g. the upper class boundary of 11 - 20 is 20)

variable

A letter representing an unknown value.(e.g. *x *and* y*)

variance

This is standard deviation squared. (see standard deviation)

Venn diagram

A diagram which represents the relationship between subsets of some universal set.

vertical

This is from top to bottom. A vertical line is perpendicular to the *x*-axis and parallel to the *y*-axis.

vertically opposite angles

Vertically opposite angles are always equal.

volume

The amount of space occupied by a 3D object.

x - axis

The horizontal axis on the Cartesian plane.

x - intercept

Where the graph crosses the *x*-axis. Also called the root. To find this we put *y* = 0 or *f*(*x*) = 0.

y - axis

The vertical axis on the Cartesian plane.

y - intercept

Where the graph crosses the *y*-axis. To find this we put *x* = 0 or calculate *f*(0).

zero

You may never divide by zero in mathematics, because this gives an undefined answer.