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.y = 5x − 1. Work out the value of y when x = 3.
y = 5x − 1
(a)14
(b)16
(c)15
(d)10
2.A student says that 5(x + 2) is equivalent to 5x + 2. Which statement explains why the student is wrong?
(a)Addition must always be done before multiplication, so 5(x + 2) equals 5x + 10 only when x = 0.
(b)The bracket must be worked out first using a value of x, so the two expressions can only be compared once x is known.
(c)The 5 must multiply both terms inside the bracket, so 5(x + 2) expands to 5x + 10, which is never equal to 5x + 2 for any value of x.
(d)5(x + 2) means 5 × x + 2, so the student's answer of 5x + 2 is actually correct.
3.A taxi fare, in pounds, for a journey of m miles is given by the formula F = 3 + 2.5m. A journey costs £15.50. Work out the distance travelled, m, by first rearranging the formula to make m the subject, then substituting F = 15.50.
(a)7.4
(b)6.2
(c)3.2
(d)5
4.Solve the simultaneous equations 3x + 2y = 16 and x + y = 7. Work out the value of y.
(a)2
(b)5
(c)9
(d)−5
5.The formula for the profit, £P, made on an item is P = S − C, where S is the selling price and C is the cost price. Make S the subject of the formula.
(a)S = PC
(b)S = P − C
(c)S = P + C
(d)S = C − P
6.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
7.The diagram shows a distance–time graph for a cyclist travelling at a constant speed, for the first 6 minutes of a journey. Distance is in kilometres and time is in minutes. Work out how far the cyclist would travel in 20 minutes at the same speed.
(a)20 km
(b)10 km
(c)40 km
(d)3 km
8.Which expression is equivalent to 3(2x − 5) + 4x?
(a)10x + 15
(b)6x − 15
(c)10x − 15
(d)10x − 5
9.A model rocket's height is given by h = −5t² + 20t, where h is in metres and t is in seconds. A student says the graph of h against t is n-shaped. Which statement gives the correct verdict on the SHAPE and the reason that settles it from the equation?
(a)Yes — the t² coefficient is negative, giving an n-shape.
(b)No — it is U-shaped, since height starts by increasing.
(c)No — the shape comes from the story, not the coefficient.
(d)Yes, but only because the rocket eventually lands.
10.Two brothers have ages that add up to 30. The elder brother is 6 years older than the younger brother. Work out the age of the younger brother.
(a)24
(b)18
(c)15
(d)12
11.Solve the inequality 5x − 3 > 2x + 9.
(a)x > 4
(b)x > 2
(c)x < 4
(d)x > 36
12.A walker's distance-time graph is described as follows: she walks 3 km in the first 15 minutes at a steady speed, rests for 10 minutes, then walks a further 3 km in the next 20 minutes, also at a steady speed. Work out her speed, in km/h, during the first 15 minutes.
(a)12 km/h
(b)9 km/h
(c)8 km/h
(d)0.2 km/h
13.Work out the value of 2x² when x = −3
(a)18
(b)36
(c)−18
(d)−12
14.A company's profit was £2000 in its first year. Each following year, the profit increases by £800. Work out the first year in which the profit is more than £7000.
(a)9
(b)6
(c)7
(d)8
15.Tom is asked to classify the statement 5(2x − 3) = 10x − 15. Which statement about it is correct?
(a)An equation, since it has an equals sign and unknown x.
(b)An identity, since both sides are equal for every x.
(c)A formula, since it relates two different quantities.
(d)An inequality, since the sides are equal sometimes.

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