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.Which expression is equivalent to 7x − 3(2x − 6)?
(a)13x − 18
(b)x − 18
(c)x + 18
(d)x + 6
2.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
3.Grace has t books. Noah has 1 book fewer than Grace. Write down an expression for the number of books Noah has.
(a)t + 1
(b)t − 1
(c)1 − t
(d)t
4.A sequence has the position-to-term rule n² + 2, where n is the position number. Work out the 6th term.
(a)38
(b)36
(c)64
(d)14
5.The first five terms of a quadratic sequence are 2, 5, 10, 17, 26. Work out the next term in the sequence.
(a)28
(b)35
(c)37
(d)39
6.Solve the simultaneous equations 3x + y = 14 and x + y = 6. Work out the value of x.
(a)4.67
(b)−4
(c)2
(d)4
7.Which expression is equivalent to 0.5(4x + 6) − x?
(a)3x + 3
(b)2x + 3
(c)x + 3
(d)x + 6
8.A rule turns each input x into an output y. The inputs are x = −1, 0, 1, 2 and the matching outputs are y = 5, 3, 1, −1. Work out the rule.
(a)y = −2x + 3
(b)y = 2x + 3
(c)y = −2x − 3
(d)y = −x + 4
9.A graph has equation y = x² − 6x + 5. A student says its turning point has x-coordinate 6, because that's the coefficient of x. Which statement corrects the student's mistake?
y = x² − 6x + 5
(a)The student is correct, because the turning point's x-coordinate always equals the coefficient of x.
(b)The turning point has x-coordinate −6, because the sign of the coefficient must be reversed.
(c)The turning point has x-coordinate 5, because that is the larger of the equation's two roots.
(d)The roots of x² − 6x + 5 = 0 are x = 1 and x = 5 (since it factorises to (x − 1)(x − 5)), so by symmetry the turning point has x-coordinate 3, not 6.
10.A straight line has equation y = 2x − 7. Write down the coordinates of the point where the line crosses the y-axis.
y = 2x − 7
(a)(0, 7)
(b)(−7, 0)
(c)(2, −7)
(d)(0, −7)
11.Write down the expression that means the same as m × m × m × n.
(a)3mn
(b)mn³
(c)m³ + n
(d)m³n
12.On Monday, a runner covers 15 km in 2.5 hours. On Tuesday, she covers 12 km in 1.5 hours. Using the formula speed = distance ÷ time, work out on which day she ran faster, and by how much.
(a)Tuesday, by 2 km/h
(b)Tuesday, by 8 km/h
(c)Tuesday, by 3 km/h
(d)Monday, by 2 km/h
13.A square has sides of length y cm. Write down an expression for the perimeter of the square.
(a)2y
(b)y + 4
(c)y²
(d)4y
14.Work out the values of x and y that satisfy both x + y = 10 and x − y = 4.
(a)x = 14, y = −4
(b)x = 7, y = 3
(c)x = 5, y = 5
(d)x = 7, y = 4
15.Solve the inequality x + 5 < 12.
(a)x < 7
(b)x < 17
(c)x > 7
(d)x < −7

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