Grade 9 Mathematics — From the Basics Up

Vocabulary flashcards covering core definitions, concepts, and rules from Grade 9 Mathematics.

Number pattern

A list of numbers that follows a rule.

General term ($T_n$)

A formula that can find any number in a pattern at position $n$.

Algebra

Mathematics that uses letters to represent numbers.

Variable

A letter used to represent an unknown number.

Constant

A number on its own in an algebraic expression.

Coefficient

The number placed directly in front of a letter (variable).

Like terms

Terms that contain the same variable raised to the same power, which can be combined.

Simplifying expressions

Making an algebraic expression shorter without changing its value.

Substitution

Replacing a letter in an algebraic expression with a given number.

Product

The answer obtained when numbers or algebraic terms are multiplied together.

Distributive law

The rule where a term outside brackets is multiplied by every term inside the brackets.

Factorising

The process of putting an expression into brackets by finding common factors; the opposite of expanding brackets.

Trinomial

An algebraic expression that contains exactly three terms.

Numerator

The top number of a fraction that indicates how many pieces you have.

Denominator

The bottom number of a fraction that indicates how many equal pieces make up the whole.

Common denominator

A shared denominator required to add or subtract fractions.

Exponent (power)

A number indicating how many times a base is multiplied by itself.

Base

The number that is being multiplied by itself when raised to an exponent.

Equation

A mathematical statement stating that two things are equal.

Gradient ($m$)

A measure of the steepness of a line, calculated as $\frac{\text{change in }y}{\text{change in }x}$.

$y$-intercept ($c$)

The point or vertical coordinate where a line crosses the vertical axis.

Coordinate

A position written as $(x;y)$, where the first value is horizontal and the second is vertical.

Natural numbers

The positive counting numbers, commonly designated in South African school maths as $1;\ 2;\ 3;\ 4;\ 5;\ \ldots$.

Whole numbers

Numbers that include zero and the positive counting numbers ($0;\ 1;\ 2;\ 3;\ 4;\ \ldots$), excluding negative numbers and fractions.

Integers

A number set consisting of negative whole numbers, zero, and positive whole numbers.

Rational numbers

Numbers that can be expressed as a fraction of two integers, where the denominator is not zero.

Irrational numbers

Numbers that cannot be written as a fraction of two integers, having decimal expansions that continue forever without repeating a fixed pattern.

Real numbers

The set comprising all rational and irrational numbers located on an ordinary number line.

Ratio

A mathematical comparison between two or more quantities.

Direct proportion

A relationship where one quantity increases at the same rate as another, described by $y=kx$.

Inverse proportion

A relationship where one quantity increases as the other decreases such that their product remains constant.

Percentage

A proportion or quantity meaning \"out of $100$\".

Discount

An amount of money taken off the original price of an item.

Profit

The positive difference calculated as $\text{selling price}-\text{cost price}$.

Loss

The difference calculated as $\text{cost price}-\text{selling price}$ when an item is sold below cost.

VAT (Value-Added Tax)

A tax added to many goods and services in South Africa, having a standard rate of $15\%$.

Principal ($P$)

The original sum of money deposited, invested, or borrowed.

Simple interest

Interest calculated solely on the original principal amount, represented by $I=\frac{P\times r\times t}{100}$.

Compound interest

Interest earned on both the original principal and on previously accumulated interest, represented by $A=P\left(1+\frac{r}{100}\right)^t$.