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.Work out the value of 2(x + 2) when x = −5
(a)−3
(b)−1
(c)−6
(d)−8
2.A rectangular garden has length (x + 7) m and width (x − 7) m. Work out an expression for the area of the garden, giving your answer in its simplest form.
(a)2x
(b)x² + 49
(c)x² − 14x − 49
(d)x² − 49
3.The equation 3(2x − 1) = 4x + 9 is rearranged by expanding the brackets. Which of these is the correctly expanded equation?
(a)5x − 3 = 4x + 9
(b)6x − 3 = 4x + 9
(c)6x − 1 = 4x + 9
(d)6x − 4 = 4x + 9
4.Write down the coordinates of the point where the line y = 2x + 4 crosses the y-axis.
y = 2x + 4
(a)(4, 0)
(b)(−2, 0)
(c)(0, 2)
(d)(0, 4)
5.Solve 2x + 1 = 9
(a)x = 8
(b)x = 16
(c)x = 4
(d)x = 5
6.Ethan is 10 years old and his father is 40 years old. Work out how many years ago Ethan's father was seven times as old as Ethan.
(a)24
(b)35
(c)5
(d)30
7.Solve 5x − 9 = 16
(a)1.4
(b)5
(c)25
(d)3.2
8.An arithmetic sequence has first term 40 and common difference −6. Work out the 9th term of the sequence.
(a)−14
(b)−2
(c)−8
(d)88
9.Simplify p + p + p.
(a)p³
(b)3p
(c)3 + p
(d)p
10.A candle is 30 cm tall when lit and burns at a constant rate. After burning for 5 minutes, its height is 20 cm. The height h cm after t minutes is given by h = 30 − mt. Work out the value of m.
(a)2
(b)4
(c)10
(d)0.5
11.Work out the equation of the straight line that passes through (−2, 3) and (4, −9).
(a)y = −2x − 1
(b)y = −2x + 1
(c)y = −(1/2)x + 2
(d)y = 2x + 7
12.Solve 7x − 5 = 3x + 11
(a)−4
(b)1.5
(c)0.6
(d)4
13.The graph of y = x² − 2x − 8 crosses the x-axis at x = −2 and x = 4. Work out the x-coordinate of the turning point of the curve, using the symmetry of the graph.
y = x² − 2x − 8
(a)x = −1
(b)x = 3
(c)x = 2
(d)x = 1
14.The graph of y = 20/x is drawn for x > 0. As the value of x increases, what happens to the value of y?
(a)y stays the same however large x becomes
(b)y decreases towards zero but never reaches it
(c)y increases towards a limit but never reaches it
(d)y decreases at a steady rate and reaches zero
15.The point P has coordinates (0, 12). Write down the axis that P lies on and the y-coordinate of P.
(a)the y-axis, and 0
(b)the x-axis, and 0
(c)the x-axis, and 12
(d)the y-axis, and 12

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