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.Priya has a budget of £50 for a school trip. The coach costs £14 and each student ticket costs £4. Using the inequality 14 + 4s ≤ 50, work out the greatest number of student tickets, s, she can buy.
(a)16
(b)9
(c)8
(d)12
2.A formula is F = 4s. A pupil says that when s = 5 the value of F is 9, because they added 4 and 5 instead of multiplying. Work out the correct value of F when s = 5.
(a)9
(b)20
(c)45
(d)25
3.Solve 2x − 2 = 2
(a)x = 2
(b)x = 8
(c)x = 0
(d)x = 4
4.The graph of y = x² − 5x + 6 crosses the x-axis at two points. By factorising, work out the x-coordinates of these two points.
y = x² − 5x + 6
(a)x = −1 and x = −6
(b)x = 2 and x = −3
(c)x = 2 and x = 3
(d)x = −2 and x = −3
5.Which of these equations is true for every value of x, making it an identity rather than an equation with just one solution?
(a)5x − 3 = 12
(b)2(x + 3) = 2x + 6
(c)x + 7 = 15
(d)3x = x + 10
6.Work out the value of (x − 4)/2 + 3 when x = 10
(a)0
(b)4.5
(c)6
(d)11
7.A car's speed increases steadily while it accelerates. Its speed v m/s after t seconds is given by v = u + at, where u is the starting speed in m/s and a is the acceleration in m/s². A car starts at u = 4 m/s and accelerates at a = 2 m/s² until it reaches v = 20 m/s. Work out t, the time taken in seconds.
(a)6 s
(b)8 s
(c)32 s
(d)12 s
8.Solve (2x + 1)/3 = 5
(a)7
(b)14
(c)8
(d)2
9.In a shop a shirt costs £x and a pair of trousers costs £(2x + 30). Together the two items cost at least £150. Work out the lowest possible price of the shirt.
(a)£50
(b)£120
(c)£60
(d)£40
10.A rectangular photo has length (x + 3) cm and width x cm. Its area is 40 cm². Work out the value of x.
(a)x = −8
(b)x = 5
(c)x = 5 or x = −8
(d)x = 4
11.A straight line has gradient 3 and passes through the point (1, 4). Work out the equation of the line.
(a)y = x + 3
(b)y = 3x − 1
(c)y = 3x + 1
(d)y = 3x + 4
12.The formula y = x² + 1 gives y in terms of x. Work out the value of y when x = −2.
y = x² + 1
(a)−3
(b)1
(c)5
(d)4
13.A point lies on the y-axis. What can be said about the x-coordinate of that point?
(a)y = 0
(b)x = 0
(c)x = 1
(d)x = y
14.A number machine multiplies its input by 5. Work out the output when the input is −1.
(a)−5
(b)5
(c)4
(d)−6
15.A number machine adds 5 to its input. Work out the output when the input is 0.
(a)5
(b)−5
(c)0
(d)6

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