Algebraic Manipulation — GCSE Maths practice questions

Question 1

Expand and simplify $2(x + 3) + 4$.

Accepted Answer

$2(x+3)+4 = 2x + 6 + 4 = 2x + 10$.

Answer

$2x + 7$

Answer

$2x + 10$

Answer

$6x + 10$

Answer

$2x + 14$

Question 2

The circumference of a circle is $C = 2\pi r$. Make $r$ the subject.

Accepted Answer

$C = 2\pi r \Rightarrow r = \dfrac{C}{2\pi}$.

Answer

$r = \dfrac{C}{2\pi}$

Answer

$r = 2\pi C$

Answer

$r = \dfrac{2\pi}{C}$

Answer

$r = C - 2\pi$

Question 3

Expand $3(x + 4)$.

Accepted Answer

$3(x+4) = 3\cdot x + 3\cdot 4 = 3x + 12$.

Answer

$3x + 4$

Answer

$3x + 12$

Answer

$x + 12$

Answer

$7x$

Question 4

Expand $2(3x - 5)$.

Accepted Answer

$2(3x-5) = 6x - 10$.

Answer

$6x - 5$

Answer

$5x - 10$

Answer

$6x - 10$

Answer

$6x + 10$

Question 5

Fully factorise $4x - 8$.

Accepted Answer

$	ext{HCF}(4,8)=4$, so $4x - 8 = 4(x - 2)$.

Answer

$4(x - 2)$

Answer

$4(x - 8)$

Answer

$2(2x - 4)$

Answer

$4(x + 2)$

Question 6

Make $x$ the subject of $y = x + 5$.

Accepted Answer

$y = x + 5 \Rightarrow x = y - 5$.

Answer

$x = y - 5$

Answer

$x = y + 5$

Answer

$x = 5 - y$

Answer

$x = \dfrac{y}{5}$

Question 7

Factorise $6x + 9$.

Accepted Answer

$	ext{HCF}(6,9)=3$, so $6x + 9 = 3(2x + 3)$.

Answer

$3(2x + 3)$

Answer

$3(2x + 9)$

Answer

$6(x + 3)$

Answer

$3(6x + 9)$

Question 8

Simplify $\dfrac{x^2}{x}$ (for $x 
eq 0$).

Accepted Answer

$\dfrac{x^2}{x} = x$ for $x 
eq 0$.

Answer

$x$

Answer

$x^2$

Answer

$1$

Answer

$\dfrac{1}{x}$

Question 9

Factorise $x^2 + 5x$.

Accepted Answer

$x^2 + 5x = x(x + 5)$.

Answer

$x(x + 5)$

Answer

$x(x + 5x)$

Answer

$5x(x + 1)$

Answer

$x^2(1 + 5)$

Question 10

Simplify $\dfrac{2x}{6}$.

Accepted Answer

$\dfrac{2x}{6} = \dfrac{x}{3}$.

Answer

$\dfrac{x}{3}$

Answer

$\dfrac{x}{6}$

Answer

$\dfrac{2x}{3}$

Answer

$\dfrac{1}{3}$

Algebraic Manipulation practice questions — GCSE Maths

Problems & worked solutions

Problem 1 — Algebraic Manipulation

Problem 2 — Algebraic Manipulation

Problem 3 — Algebraic Manipulation

Problem 4 — Algebraic Manipulation

Problem 5 — Algebraic Manipulation

Problem 6 — Algebraic Manipulation

Problem 7 — Algebraic Manipulation

Problem 8 — Algebraic Manipulation

Problem 9 — Algebraic Manipulation

Problem 10 — Algebraic Manipulation