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.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
2.Solve 2x² = 18.
(a)x = 9 or x = −9
(b)x = 4 or x = −4
(c)x = 6 or x = −6
(d)x = 3 or x = −3
3.Grace says that 2(x + 1) and 2x + 2 always have the same value. Work out the value of both expressions when x = 3.
(a)10
(b)6
(c)8
(d)7
4.A cinema sells adult tickets and child tickets. On one evening, 40 tickets are sold in total. There are 8 more adult tickets sold than child tickets. Work out the number of child tickets sold.
(a)20
(b)32
(c)16
(d)24
5.A straight line has gradient −2 and passes through the point (3, 1). Work out the equation of the line.
(a)y = −2x + 7
(b)y = −2x − 5
(c)y = 2x + 7
(d)y = −2x + 1
6.To solve 5x − 4 = 2x + 8, Chloe's working is shown. Line 1: 5x − 4 = 2x + 8. Line 2: 3x − 4 = 8. Line 3: 3x = 4. Line 4: x = 4/3. Chloe has made a mistake in her working. Which line contains the mistake?
(a)Line 1
(b)Line 2
(c)Line 4
(d)Line 3
7.To rearrange y = 2x − 5 to make x the subject, Sam writes: 'Add 5 to both sides to get y + 5 = 2x, then divide both sides by 2 to get x = (y + 5)/2.' Which statement about Sam's method is correct?
y = 2x − 5
(a)Yes, but step 2 should give x = 2(y + 5)
(b)No; it should be x = (y − 5)/2
(c)Yes; x = (y + 5)/2 is right
(d)No; it should be x = y/2 + 5
8.Write down the coefficient of p in the expression 7 − 4p + 9q.
(a)7
(b)4
(c)9
(d)−4
9.Solve x² + 7x = 0.
(a)x = 0 or x = 7
(b)x = 0 or x = −14
(c)x = 0 or x = −7
(d)x = −7
10.Solve (2x + 1)/3 = 5
(a)7
(b)14
(c)8
(d)2
11.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.
(a)2
(b)3
(c)−6
(d)18
12.Solve the simultaneous equations 5x − 2y = 16 and 3x + 2y = 16. Work out the value of x.
(a)8
(b)4
(c)2
(d)0
13.The formula connecting distance (d), speed (s) and time (t) is d = st. Make s the subject of the formula.
(a)s = t / d
(b)s = d / t
(c)s = d − t
(d)s = dt
14.A coach company charges a booking fee plus a price for each passenger. A booking for 1 passenger costs £9, for 2 passengers costs £15, for 3 passengers costs £21, and for 4 passengers costs £27. Work out an expression, in terms of n, for the cost in pounds of a booking for n passengers.
(a)9n + 6
(b)6n
(c)6n + 9
(d)6n + 3
15.Solve the simultaneous equations 2x + y = 7 and x − y = 2.
(a)x = 1, y = 3
(b)x = 3, y = 2
(c)x = 3, y = 1
(d)x = 3, y = −1

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