Algebraic Manipulation — Honors Math 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

Expand $2(3x - 5)$.

Accepted Answer

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

Answer

$6x - 5$

Answer

$5x - 10$

Answer

$6x - 10$

Answer

$6x + 10$

Question 3

Fully factorise $10ab + 15a$.

Accepted Answer

$10ab + 15a = 5a(2b + 3)$.

Answer

$5a(2b + 3)$

Answer

$5(2ab + 3a)$

Answer

$a(10b + 15)$

Answer

$5a(2b + 15)$

Question 4

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 5

Make $x$ the subject of $y = 3x$.

Accepted Answer

$y = 3x \Rightarrow x = \dfrac{y}{3}$.

Answer

$x = \dfrac{y}{3}$

Answer

$x = 3y$

Answer

$x = y - 3$

Answer

$x = \dfrac{3}{y}$

Question 6

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 7

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 8

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 9

Make $x$ the subject of $y = 2x - 1$.

Accepted Answer

$y = 2x - 1 \Rightarrow y + 1 = 2x \Rightarrow x = \dfrac{y + 1}{2}$.

Answer

$x = \dfrac{y + 1}{2}$

Answer

$x = \dfrac{y - 1}{2}$

Answer

$x = \dfrac{y}{2} + 1$

Answer

$x = 2y + 1$

Question 10

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

$3(6x + 9)$

Algebraic Manipulation practice questions — Honors Math

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