Printable · GCSE Foundation · ages 14-16

Algebra worksheet — GCSE Foundation

Fifteen questions across the algebra statements at Foundation tier. Choose the non-calculator filter to rehearse Paper 1, which counts for a third of the marks.

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Algebra worksheet — GCSE Foundation

Maths · GCSE Foundation · Algebra · 15 questions

MathsUKwww.geekhero.co.uk

1.The formula for the perimeter of a square is P = 4s, where s is the side length. Make s the subject of the formula.
(a)s = P − 4
(b)s = P + 4
(c)s = P / 4
(d)s = 4P
2.A student is asked whether 3(x − 4) = 3x − 4 is an identity. Which statement gives the correct verdict and reason?
(a)It is an identity, because both sides begin with the term 3x, so they must be equivalent.
(b)It is not even an ordinary equation with a solution: expanding the left-hand side gives 3x − 12, and 3x − 12 = 3x − 4 would require −12 = −4, which is never true.
(c)It is not an identity, because the student forgot to multiply the 4 by 3 on both sides of the equation.
(d)It is not an identity, because the student needs to substitute a specific value of x before comparing the two sides.
3.A straight line passes through the points (2, 7) and (5, 16). Work out the value of y when x = 0.
(a)1
(b)−1
(c)3
(d)4
4.A car's fuel tank contains 50 litres when it starts a journey. After travelling for 2 hours, it contains 38 litres, and fuel is used at a constant rate. Work out the rate at which fuel is used, in litres per hour.
(a)44
(b)19
(c)6
(d)12
5.Solve 2x² = 18.
(a)x = 9 or x = −9
(b)x = 4 or x = −4
(c)x = 6 or x = −6
(d)x = 3 or x = −3
6.The formula for converting a distance in miles, m, to kilometres, k, is k = 8m ÷ 5. Work out k when m = 10.
(a)16
(b)80
(c)18
(d)6.25
7.A straight line passes through the points (2, 5) and (4, 11). Work out the gradient of the line.
(a)8/3
(b)−3
(c)3
(d)1/3
8.Line C passes through (0, 0) and (4, 2). Line D passes through (0, 0) and (2, 2). Write down which of the two lines is the steeper.
(a)There is not enough information
(b)They are equally steep
(c)Line D
(d)Line C
9.Isla says that the lines y = 2x + 1 and y = −2x + 3 are parallel. Write down the statement that gives the correct answer for the correct reason.
y = 2x + 1y = -2x + 3
(a)Yes, because the gradients 2 and −2 add to 0
(b)No, because their gradients are 2 and −2
(c)Yes, because both gradients have size 2
(d)No, because their y-intercepts are 1 and 3
10.The first four terms of a sequence are 6, 13, 20, 27. Work out an expression, in terms of n, for the nth term.
(a)6n + 1
(b)7n
(c)7n − 1
(d)7n + 6
11.A straight line passes through the points (−1, 2) and (3, 14). Work out the equation of the line.
(a)y = 6x − 4
(b)y = x/3 + 13
(c)y = 3x + 5
(d)y = 3x + 23
12.Solve the inequality 2(x − 1) ≤ 8.
(a)x ≤ 4
(b)x ≤ 5
(c)x < 5
(d)x ≤ 3
13.The equation 3(2x − 1) = 4x + 9 is rearranged by expanding the brackets. Which of these is the correctly expanded equation?
(a)5x − 3 = 4x + 9
(b)6x − 3 = 4x + 9
(c)6x − 1 = 4x + 9
(d)6x − 4 = 4x + 9
14.A phone plan costs a fixed £15 per month plus 8p per minute of calls. In one month, Jamal's bill was £23.80. Form an equation using m for the number of minutes, and solve it to find how many minutes Jamal used that month.
(a)485
(b)1.1
(c)297.5
(d)110
15.Write down the gradient of the line with equation y = −x + 3.
y = −x + 3
(a)−3
(b)−1
(c)3
(d)1

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