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.

Non-calculator

VersionsA only A + B A + B + Csame questions, different order

AnswersQuestions only With answer key Key only

CalculatorMixed Non-calculator (Paper 1)Calculator (Papers 2 and 3)

New sheet

Algebra worksheet — GCSE Foundation

Maths · GCSE Foundation · Algebra · Non-calculator · 15 questions

MathsUKwww.geekhero.co.uk

1.The first four terms of a sequence are 4, 6, 8, 10. Work out an expression, in terms of n, for the nth term.
(a)2n + 4
(b)2n
(c)2n + 2
(d)2n − 2
2.A rule turns each input x into an output y. An input of 1 gives an output of 1, an input of 2 gives an output of 4 and an input of 3 gives an output of 9. Work out the rule.
(a)y = 2x
(b)y = 3x
(c)y = x²
(d)y = 3x − 2
3.A rectangular garden has length (x + 7) m and width (x − 7) m. Work out an expression for the area of the garden, giving your answer in its simplest form.
(a)2x
(b)x² + 49
(c)x² − 14x − 49
(d)x² − 49
4.Work out the coordinates of the reflection of (6, −3) in the y-axis.
(a)(−6, −3)
(b)(6, −3)
(c)(−6, 3)
(d)(6, 3)
5.A number machine multiplies its input by 3. The output is 15. Work out the input.
(a)45
(b)12
(c)18
(d)5
6.A straight line has gradient −3 and passes through the point (0, 1). Work out the value of y when x = 2.
(a)7
(b)−5
(c)5
(d)−7
7.A number, n, is doubled and then 7 is subtracted. The result is 15. Form an equation and solve it to find n.
(a)11
(b)4
(c)7.5
(d)22
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.A sequence has the position-to-term rule n² + 1, where n is the position number. Work out how much bigger the 5th term is than the 4th term.
(a)9
(b)7
(c)1
(d)11
10.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.
(a)y = x + 2
(b)y = 2x − 1
(c)y = 2x + 1
(d)y = 2x + 3
11.A quadratic graph y = ax² + bx + c has its turning point on the y-axis. Which statement about its roots must be true?
(a)The two roots must both be positive.
(b)The graph has no roots at all.
(c)The graph must touch the x-axis at exactly one point.
(d)If the graph has two real roots, they are equal and opposite in value, so they sum to zero.
12.A parcel delivery company's cost graph shows the following: the cost is a flat £5 for parcels weighing up to 2 kg, and then rises by £2 for each additional kg above 2 kg. Use the graph to work out the weight of a parcel that costs £17.
(a)8.5 kg
(b)8 kg
(c)6 kg
(d)7.5 kg
13.Which expression means the same as 3 × a × b?
(a)3ab
(b)3a + b
(c)3 + a + b
(d)a³b
14.Solve x² − 6x = 0.
(a)x = 0
(b)x = 3
(c)x = 6
(d)x = 0 or x = 6
15.There are 30 students in a Year 10 maths class. There are 2 more boys than girls. Work out the number of boys and the number of girls.
(a)15 boys and 15 girls
(b)17 boys and 13 girls
(c)14 boys and 16 girls
(d)16 boys and 14 girls

Build your own mix at the worksheet builder.