Maths Dictionary

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

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

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

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

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

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

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

An algebraic expression with two terms.

This means to cut something in half.

Involves two variables and is graphically represented using a scatter plot.
(e.g. height and weight of learners) 

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

A graph where plotted points are joined by line segments.

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.

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

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.

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

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

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

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

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

The middle of a class interval in grouped data.

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

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

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

North, south, east and west.

The sum of two complementary angles is 90^o.

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).

Includes all real and all non-real (imaginary) numbers. We need these numbers to solve an equation like  x² = -9. 

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)).

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.)

This is when you earn interest on interest. Can also be called compound growth.
Formula: A = P(1 + i)ⁿ

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

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

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

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

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)

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

Terms which follow one another in a pattern. T₁, T₂, and T₃ are consecutive terms.

A value that does not change or vary.

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

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

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) 

A graph that can be drawn without lifting your pencil.

An infinite series that has a finite sum.

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

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

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

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. 

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.  

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.  

The natural numbers and zero: 0, 1, 2, 3, 4, . . .
We can also call these the Whole Numbers.

A solid with six identical square faces.

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

The highest power of the variable is 3.
e.g. y = x³ + 2x² - x - 4

The graph of a cubic function.

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

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

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

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

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

A polygon with 10 sides.

From biggest to smallest.

Getting smaller.

When the graph of the function is sloping downwards. 

The bottom part of a fraction.

Gradient of a function at a certain point.

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

The distance from a point on the circumference of a circle, through the centre to another point on the circumference.
(diameter = 2 x radius)

The answer to subtraction.

A graph made up of dots.

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

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

Where two faces of a solid meet.

An interest rate which is compounded annually.
(e.g. 12% p.a. compounded annually)

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

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

A triangle with three equal angles and three equal sides. Each angle is 60°.

The mean value of grouped data. 

You can define an event to have specific outcomes.
e.g. let event A be getting an even number when rolling a die

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)

An activity with outcomes.
e.g. rolling a die

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

see algebraic expression

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

A flat surface of a solid.

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

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

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

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

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

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

The minimum value, lower quartile (Q₁), median, upper quartile (Q₃) and maximum value of a set of data.

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

The number of times an item or data value occurs.

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 )

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

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

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.

When fixed regular payments are made and you get the money in the future. This future value is “all the payments plus the interest”.

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

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 ; . . .)

You get this when you add the terms of a geometric sequence.
(e.g. 100 + 50 + 25 + 12,5 + . . .)

This shows the steepness of a line.

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

Half a sphere.

A polygon with 7 sides. 

A polygon with 6 sides.

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

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

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

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

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

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

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

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

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

Getting bigger.

When the graph of the function is sloping up.

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) × P(6)

see exponent

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.

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.

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

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

This is the point where a function changes concavity. 

Negative whole numbers, zero and positive whole numbers.

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

The difference between the upper and lower quartiles. IQR = Q₃ - Q₁

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

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

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

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

A triangle with two equal angles and two equal sides.

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

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

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

see regression line

Terms with identical variables. We can add and subtract like terms. (e.g. 5x²y + 3x²y - x²y = 7x²y) 

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

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.

A line has no starting point or ending point.
e.g. line AB:

A line segment has a specific starting point and a specific ending point.
e.g. line segment AB:

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

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

A mathematical method that uses linear inequalities to solve problems involving maximum and minimum quantities.
(e.g. maximum profit and minimum cost)

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

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.

The biggest value.

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

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

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

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.

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

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.

The smallest value.

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

The class interval with the highest frequency in grouped data.

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

An algebraic expression with only one term.

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 ; . . .

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.

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

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.

Interest rate that is compounded monthly, quarterly, semi-annually, etc. In other words, anything but annually.
(e.g. 12% p.a. compounded monthly)

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

The top part of a fraction.

An angle between 90^o and 180^o.

A triangle with one obtuse angle.

A polygon with 8 sides.

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

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

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.

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

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

A possible result when doing an experiment in Probability.
e.g. getting 6 when rolling a die

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

This is the graph of a quadratic function.

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

A quadrilateral with both pairs of opposite sides parallel.

A polygon with 5 sides.

Percentiles divide a set of data into 100 equal parts. (e.g. P₄₀ is the 40^th percentile. It means that about 40% of the data lies below P₄₀ and about 60% lies above P₄₀)

The total distance around a 2D shape.

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

Lines which intersect at 90^o.

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

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

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.

A 2D figure with three or more straight sides.

One polyhedron, many polyhedra.

A 3D object with flat faces where each face is a polygon.
NB: Cylinders, cones and spheres are not polyhedra.

An algebraic expression with two or more terms.

When everyone is surveyed.

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.

A power is a number raised to an exponent.

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

Factors which are prime numbers.
e.g. prime factors of 24 = 2 x 2 x 2 x 3 = 2³.3

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, ....

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

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

The answer to multiplication.

P(A and B) = P(A) × P(B)  
We use this rule with independent events. 

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

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.

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

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.

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

The highest power of the variable is 2. (e.g. y = x² + x - 6) 

A number pattern which has constant second differences. The general term is of the form: T_n = an² + bn + c

A 2D shape with four sides.

The quartiles divide a set of data into 4 equal parts. They are the lower quartile (Q₁), the median (M or Q₂) and the upper quartile (Q₃).

The answer to division.

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

Random events are unpredictable.
e.g. you cannot predict what number you will get when you toss a die

When everyone has an equal chance of being surveyed.

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

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

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

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

A list of separate data values.

A ray has a specific starting point but no ending point.
e.g. ray AB:

All the rational and irrational numbers.

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

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.

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

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

These are used to reduce (change) angles to acute angles
(e.g. sin 240^o = sin (180^o + 60^o) = -sin 60^o)

A mirror image. Shape and size stay the same.

The sign of y changes.

The sign of x changes.

An angle between 180^o and 360^o.

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.

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

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) = x² - 2x - 8 is divided by x + 1 is -5, because f(-1) = (-1)² - 2(-1) - 8 = -5

A smaller group which represents the whole population.

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.

A full turn through 360^o.

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

A 90^o angle.

A triangle with one 90° angle.

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.)

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

When only some people in the population is surveyed.

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

A triangle with no equal angles or equal sides.

A diagram which is used to investigate whether there is any relationship between two variables.
e.g. height and weight of learners (bivariate data) 

A way to write very big or very small numbers. (e.g. 65 000 000 = 6,5 x 10⁷ and 0,000042 = 4,2 x 10^-5)

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. 

Half of the interquartile range. 

The sum of. 

Figures that have the same shape but different size.

Interest is calculated on the original amount only. Can also be called simple growth.
Formula: A = P(1 + in)

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

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

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.

A 3D shape.

A perfectly round 3D solid. 

A quadrilateral with 4 equal sides and 4 right angles.

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

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

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

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.

An angle of 180^o.

The answer to addition.

The sum of two supplementary angles is 180^o.

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.

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

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

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. 

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

Part of an algebraic expression. Terms are seperated by + and -.
e.g. There are 3 terms in 2a - 4b + 6 but there is only 1 term in 3(x-2) and in (x-1)(x+3)²

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

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

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

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

A quadrilateral with one pair of parallel sides.

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

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".

This refers to each time you do an experiment in Probability.
e.g. rolling a die 20 times gives 20 trials

The measurement of triangles.

An algebraic expression with three terms.

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

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

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

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

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

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

This is standard deviation squared. (see standard deviation)

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

Where 2 lines meet to form an angle.
Plural is vertices.

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

Vertically opposite angles are always equal.

The amount of space occupied by a 3D object.

The horizontal axis on the Cartesian plane.

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

The vertical axis on the Cartesian plane.

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

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