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.

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 · 15 questions

MathsUKwww.geekhero.co.uk

1.A delivery van's distance-time graph shows the following: it travels 9 km in the first 15 minutes at a steady speed, stops for 45 minutes to unload, then travels a further 21 km in the next 30 minutes, also at a steady speed. Work out the average speed, in km/h, for the whole journey.
(a)36 km/h
(b)39 km/h
(c)40 km/h
(d)20 km/h
2.A distance-time graph shows a car travelling at a constant speed, covering 90 km in 2 hours. Work out the car's speed in km/h.
(a)88 km/h
(b)180 km/h
(c)45 km/h
(d)92 km/h
3.Make b the subject of the formula a = 5b.
(a)b = 5/a
(b)b = a/5
(c)b = 5a
(d)b = a − 5
4.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
5.The height, h metres, of a ball t seconds after a stopwatch is started follows h = (t − 1)(5 − t) for 1 ≤ t ≤ 5, where h = 0 means the ball is at ground level. Work out the two times at which the ball is at ground level.
(a)t = 1 second and t = 4 seconds
(b)t = 1 second and t = −5 seconds
(c)t = 1 second and t = 5 seconds
(d)t = −1 second and t = 5 seconds
6.The graph of y = 24/x is drawn for x > 0. Work out the value of y when x = 6.
(a)y = 18
(b)y = 30
(c)y = 144
(d)y = 4
7.A taxi fare in pounds is given by F = 2.50 + 1.20m, where m is the number of miles travelled. Sam takes a taxi for a journey of 6 miles. Work out the fare.
(a)£7.20
(b)£22.20
(c)£9.70
(d)£10.20
8.A vertical line passes through the point (4, 7). Write down the equation of this line.
(a)y = 7
(b)x = 4
(c)x = 7
(d)y = 4x
9.The graph of y = x² − 7x + 2 crosses the x-axis at two points. One root, read from the graph, is approximately x = 0.30. Using the fact that the sum of the two roots of x² − 7x + 2 = 0 is 7, estimate the other root, correct to 2 decimal places.
y = x² − 7x + 2
(a)x ≈ 6.70
(b)x ≈ 6.30
(c)x ≈ 7.30
(d)x ≈ 0.70
10.To solve 6x − 4 = 2x + 20, Yusuf's first step is to subtract 2x from both sides. Work out what equation this gives.
(a)4x = 20
(b)4x − 4 = 20
(c)4x − 4 = 2x + 20
(d)8x − 4 = 20
11.A rope of length L metres is cut into 6 equal pieces, and 4 metres is then removed from one piece. Write an expression, in metres, for the length of that piece after the cut.
(a)(L − 4)/6
(b)L/6 + 4
(c)4 − L/6
(d)L/6 − 4
12.Solve 6x − 5 = 3x + 13.
(a)18
(b)2
(c)2.67
(d)6
13.Oliver has m stickers and gives 5 of them away. The number he has left is L = m − 5. Work out L when m = 8.
(a)3
(b)40
(c)−3
(d)13
14.Which of these rules generates the sequence 6, 11, 16, 21, …?
(a)6n
(b)5n − 1
(c)5n + 1
(d)n + 5
15.A quadratic curve has a minimum turning point at (3, −4). Which of these statements about the curve must be true?
(a)It does not cross, since the minimum lies below the axis.
(b)It crosses the x-axis, since the minimum is below it.
(c)It touches the x-axis once, at (3, −4).
(d)It is impossible to tell without the full equation.

Build your own mix at the worksheet builder.