Algebraic Manipulation practice questions

Question 1

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

$\dfrac{1}{3}$

Question 2

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 3

Simplify $\dfrac{3x}{x}$ (for $x 
eq 0$).

Accepted Answer

$\dfrac{3x}{x} = 3$ for $x 
eq 0$.

Answer

$3$

Answer

$3x$

Answer

$\dfrac{3}{x}$

Answer

$x$

Question 4

Write $\dfrac{1}{4} + \dfrac{1}{4}$ in its simplest form.

Accepted Answer

$\dfrac{1}{4} + \dfrac{1}{4} = \dfrac{2}{4} = \dfrac{1}{2}$.

Answer

$\dfrac{2}{8}$

Answer

$\dfrac{1}{2}$

Answer

$\dfrac{1}{16}$

Answer

$\dfrac{1}{8}$

Question 5

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 6

Expand $2(3x - 5)$.

Accepted Answer

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

Answer

$6x - 5$

Answer

$5x - 10$

Answer

$6x - 10$

Answer

$6x + 10$

Question 7

Expand $x(x + 7)$.

Accepted Answer

$x(x+7) = x\cdot x + x\cdot 7 = x^2 + 7x$.

Answer

$x^2 + 7x$

Answer

$2x + 7x$

Answer

$x + 7x$

Answer

$x^2 + 7$

Question 8

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 9

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 10

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

$x^2(1 + 5)$

Algebraic Manipulation

Problems & worked solutions

Problem 1 — Simplifying & Algebraic Fractions

Problem 2 — Simplifying & Algebraic Fractions

Problem 3 — Simplifying & Algebraic Fractions

Problem 4 — Simplifying & Algebraic Fractions

Problem 5 — Expanding Brackets

Problem 6 — Expanding Brackets

Problem 7 — Expanding Brackets

Problem 8 — Expanding Brackets

Problem 9 — Factorising

Problem 10 — Factorising

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