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

MathsUKwww.geekhero.co.uk

1.A square tile has an area of 144 cm². Work out the side length of the tile.
(a)12 cm or −12 cm
(b)72 cm
(c)12 cm
(d)36 cm
2.A rule multiplies the input by a fixed number and then adds a fixed number. An input of 1 gives an output of 5, and an input of 3 gives an output of 11. Work out the rule, writing the input as x and the output as y.
(a)y = 3x − 2
(b)y = x + 4
(c)y = 3x + 2
(d)y = 2x + 3
3.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
4.The nth term of a sequence is 2n² + 1. Work out the 4th term of the sequence.
(a)33
(b)65
(c)32
(d)17
5.Solve 6x + 4 = 28
(a)x = 4
(b)x = 144
(c)x = 24
(d)x = 18
6.A hot air balloon is at a height of 20 m and rises at a steady rate. After 4 minutes it is at a height of 52 m. Work out the rate at which the balloon rises, in metres per minute.
(a)8
(b)32
(c)5
(d)13
7.The point D has coordinates (3, −8). Write down the distance of D from the y-axis.
(a)8
(b)3
(c)11
(d)−8
8.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
9.A regular hexagon has sides of length (x + 2) cm. Write down an expression, in terms of x, for the perimeter of the hexagon.
(a)6x + 12
(b)6x + 2
(c)x + 12
(d)8x
10.A cafe sells coffees at £c each and pastries at £p each. Three coffees and two pastries cost £9.60. Two coffees and two pastries cost £7.60. Work out the price of one coffee.
(a)£0.20
(b)£2.00
(c)£3.20
(d)£1.80
11.Make x the subject of the formula y = 5x + 3.
y = 5x + 3
(a)x = (y + 3)/5
(b)x = (y − 3)/5
(c)x = y/5 − 3
(d)x = 5(y − 3)
12.Tom buys 2 notebooks and 6 pencils on Monday, priced at p pence each for a notebook and q pence each for a pencil. On Tuesday he buys 3 more notebooks and 1 more pencil. Write a simplified expression, in pence, for the total amount Tom has spent on notebooks and pencils.
(a)5p + 7q
(b)5p + 6q
(c)2p + 7q
(d)12pq
13.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
14.A plumber charges a £40 call-out fee plus £25 for each hour worked. The total charge, £C, for a job lasting h hours is given by C = 40 + 25h. Work out the charge for a job lasting 3 hours, and name what kind of statement C = 40 + 25h is.
(a)£65, and C = 40 + 25h is an expression
(b)£115, and C = 40 + 25h is a formula
(c)£195, and C = 40 + 25h is a formula
(d)£115, and C = 40 + 25h is an expression
15.Write down the expression that means the same as m² × m × 3.
(a)m⁶
(b)m³
(c)3m²
(d)3m³

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