Grade 9 mathematics June exam paper KwaZulu-Natal

A rational number can be expressed as a fraction $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$.

A. $\sqrt{2}$ is an irrational number because its decimal representation is non-terminating and non-repeating.
B. $\pi$ is an irrational number because its decimal representation is non-terminating and non-repeating.
C. 0,333... is a repeating decimal, which can be written as $\frac{1}{3}$. This is a rational number.
D. $\sqrt{-4}$ is an imaginary number ($2i$), not a real number, and therefore not a rational number in the set of real numbers.

The correct option is C.

Any non-zero number raised to the power of 0 is 1.

Any number raised to the power of 1 is itself.

The correct option is D.

Multiples of 6: $6, 12, 18, \textbf{24}, 30, ...$

Multiples of 8: $8, 16, \textbf{24}, 32, 40, ...$

The smallest number that appears in both lists is 24.

The correct option is B.

The correct option is B.

$1; 4; 9; 16; ...$

$1 = 1^2$
$4 = 2^2$
$9 = 3^2$
$16 = 4^2$
The sequence consists of perfect squares of consecutive natural numbers.

The next number in the sequence of bases is 5.
The next term is $5^2 = 25$.

The correct option is B.

This is a difference of two squares, which follows the formula $a^2 - b^2 = (a-b)(a+b)$.

Here, $a^2 = x^2$, so $a = x$.
And $b^2 = 4$, so $b = \sqrt{4} = 2$.

The correct option is C.

The correct option is B.

$(-1)^2 = (-1) \times (-1) = 1$
$-2(-1) = 2$

The correct option is C.

In this form, $m$ represents the gradient (slope) of the line, and $c$ represents the y-intercept.

By comparison, the coefficient of $x$ is 2.
Therefore, the gradient $m = 2$.

The correct option is A.

Its equation is of the form $y = mx$.

Substitute $x=1$ and $y=2$ into the equation $y = mx$.

The correct option is B.