GCSE English and Maths Resits (Grade 4) · Maths

Algebra

37 practice questions, each with the answer and an explanation.

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All 37 questions

Factorise fully $12 x - 18$ .
Solve $5 x - 7 = 3 x + 9$ .
Factorise $x^{2} + 7 x + 12$ .
Work out the value of $3 x^{2} - 2 x$ when $x = - 2$ .
Find the $n$ th term of the sequence $5, 8, 11, 14, \dots$
List the integers that satisfy $7 < 2 x + 1 \leq 15$ .
Use $s = u t + \frac{1}{2} a t^{2}$ to find $s$ when $u = 3$ , $t = 4$ and $a = 2$ .
What is the gradient of a line perpendicular to $y = 2 x + 1$ ?
What is the gradient of the straight line through $(2, 3)$ and $(6, 11)$ ?
Make $x$ the subject of $y = \frac{x + 3}{2}$ .
The perimeter of a rectangle is $P = 2 (l + w)$ . Make $l$ the subject.
Solve $4 (x + 3) = 2 x + 20$ .
Solve $3 x + 2 < 17$ .
A sequence starts at $1$ and each term is double the previous term plus $1$ . What is the fifth term?
Factorise $x^{2} - 49$ .
Pens cost $p$ pence each and notebooks cost $b$ pence each. Which expression is the cost in pence of $4$ pens and $3$ notebooks?
Which expression shows that the sum of any three consecutive whole numbers is a multiple of $3$ ?
Simplify $3 a + 2 b - a + 5 b$ .
Solve $x^{2} - 5 x + 6 = 0$ .
Factorise $2 x^{2} + 7 x + 3$ .
Solve $\frac{x}{3} + 4 = 7$ .
Solve $3 (2 x - 1) = 2 x + 13$ .
Expand $4 (2 x - 3)$ .
Make $t$ the subject of $v = u + a t$ .
Simplify $(2 a^{3} b)^{2}$ .
Expand and simplify $(x - 3)^{2}$ .
A line is parallel to $y = 3 x - 2$ and passes through $(1, 7)$ . What is its equation?
At what value of $x$ does the line $y = 2 x - 3$ cross the $x$ -axis?
Solve the simultaneous equations $3 x + 2 y = 16$ and $5 x - 2 y = 8$ .
Solve $2 x^{2} = 50$ .
Simplify $\frac{x ^{2} + 3 x}{x}$ .
Solve $\frac{x}{2} + \frac{x}{3} = 10$ .
The $n$ th term of a sequence is $7 n - 3$ . Which of these numbers is in the sequence?
Solve the simultaneous equations $2 x + y = 11$ and $x - y = 1$ .
Expand and simplify $(x + 4) (x - 2)$ .
Expand and simplify $3 (x + 2) - 2 (x - 5)$ .
What is the gradient of the line $2 y = 6 x + 4$ ?

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