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 · 15 questions

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1.A number, w, satisfies the statement "three times w, minus 5, is at least 16". Which of these is the correct inequality for w?
(a)3(w − 5) ≥ 16
(b)3w − 5 ≥ 16
(c)3w − 5 > 16
(d)3w − 5 ≤ 16
2.Which expression is equivalent to 5x − (x + 3)?
(a)4x + 3
(b)6x − 3
(c)4x − 3
(d)5x − 3
3.The diagram shows a straight line passing through the origin, drawn on a numbered grid. Which of these points lies on the line?
(a)(2, 3)
(b)(2, 5)
(c)(2, 6)
(d)(3, 2)
4.Solve 7x − 5 = 3x + 11
(a)−4
(b)1.5
(c)0.6
(d)4
5.A cinema sells adult tickets for £10 and child tickets for £6. A family group buys 9 tickets in total, spending £74. Work out how many adult tickets were bought.
(a)7.4
(b)1.25
(c)5
(d)4
6.The simultaneous equations 2x + 3y = 12 and x − y = 1 are given. Work out the value of y.
(a)y = 2
(b)y = 2.2
(c)y = 3
(d)y = 10
7.Make c the subject of the formula k = 6c.
(a)c = 6k
(b)c = k/6
(c)c = k − 6
(d)c = 6 − k
8.A quadratic graph has roots at x = −3 and x = 5, and it crosses the y-axis at (0, −15). Work out the equation of the curve in the form y = (x − a)(x − b).
(a)y = (x − 3)(x − 5)
(b)y = (x − 3)(x + 5)
(c)y = (x + 3)(x + 5)
(d)y = (x + 3)(x − 5)
9.Which of these numbers is a cube number?
(a)9
(b)27
(c)16
(d)25
10.Solve 3(2x − 1) = 27
(a)4
(b)5
(c)4.5
(d)4 2/3
11.In a sequence, each term is half the term before it. The sequence begins 100, 50, 25. Write down the next term.
(a)0
(b)12.5
(c)12
(d)6.25
12.Solve 2x + 1 = 9
(a)x = 8
(b)x = 16
(c)x = 4
(d)x = 5
13.A box contains 6 chocolates. Write down an expression for the total number of chocolates in c boxes.
(a)6c
(b)6 + c
(c)c ÷ 6
(d)c − 6
14.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
15.A student solves the simultaneous equations 2x + y = 11 and x − y = 1 by elimination, adding the two equations together. Which of these is the correct result of that step?
(a)3x = 12
(b)3x = 10
(c)3x + 2y = 12
(d)x = 12

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