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 · Non-calculator · 15 questions

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1.Work out the value of n² − n when n = −3
(a)6
(b)−3
(c)−6
(d)12
2.The cost, in pounds, of hiring a van for d days is given by the formula C = 25 + 18d. A customer's hire cost £133. Work out how many days, d, they hired the van for, by first rearranging the formula to make d the subject.
(a)4.6
(b)7.4
(c)90
(d)6
3.A Fibonacci-type sequence begins 3, 5, 8, 13, ... where each term after the second is the sum of the two terms before it. Work out the 7th term of the sequence.
(a)34
(b)68
(c)55
(d)47
4.The formula for the area of a trapezium is A = (a + b)h / 2, where a and b are the parallel side lengths and h is the height. Make h the subject of the formula.
(a)h = 2A / a + b
(b)h = (a + b) / (2A)
(c)h = A / (a + b)
(d)h = 2A / (a + b)
5.The mean of four numbers is 12.5. Three of the numbers are 8, 15 and 19. Form an equation using n for the fourth number, and solve it to find n.
(a)−4.5
(b)50
(c)29.5
(d)8
6.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
7.A table shows y = x² − 6x + 5 at these points (x, y): (0, 5), (1, 0), (2, −3), (3, −4), (4, −3), (5, 0), (6, 5). Using the symmetry shown, write down the x-coordinate of the turning point.
y = x² − 6x + 5
(a)x = 1
(b)x = 5
(c)x = 6
(d)x = 3
8.Noah says that y = 3 is the solution of the equation y + 10 = 12. Noah is wrong. Work out the correct value of y.
(a)y = 22
(b)y = −2
(c)y = 2
(d)y = 12
9.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
10.Make x the subject of the formula y = x/2 − 5.
y = x
(a)x = (y + 5)/2
(b)x = 2y − 10
(c)x = 2y + 10
(d)x = 2y + 5
11.Yusuf has £40 saved and adds £6 each week. His sister Aisha has £10 saved and adds £11 each week. After how many weeks will they have saved the same amount?
(a)1.76
(b)0
(c)10
(d)6
12.The expression 6n + 15 is written as 3(2n + 5). Which statement is correct?
(a)3 and 2n + 5 are the two terms of 6n + 15
(b)6n and 15 are the factors of 6n + 15
(c)3 and 2n + 5 are both factors of 6n + 15
(d)3 is the only factor of 6n + 15
13.A geometric sequence has first term 5, and each term after that is 3 times the term before it. Work out the first term of the sequence that is greater than 1000.
(a)405
(b)1215
(c)2187
(d)3645
14.Work out the coordinates of the midpoint of the line segment joining (−3, 5) and (7, 9).
(a)(2, 7)
(b)(4, 14)
(c)(5, 2)
(d)(2, 9)
15.Factorise x² − 3x − 10.
(a)(x − 10)(x + 1)
(b)(x − 5)(x + 2)
(c)(x + 5)(x − 2)
(d)(x − 5)(x − 2)

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