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.Write down the expression that means the same as 3 × y × y.
(a)3y²
(b)3 + y²
(c)y³
(d)(3y)²
2.Solve x² = 49.
(a)x = 7
(b)x = 24.5
(c)x = −7
(d)x = 7 or x = −7
3.Work out the value of n² − n when n = −3
(a)6
(b)−3
(c)−6
(d)12
4.Write down the expression that means the same as 'subtract 5 from n, then divide the result by 2'.
(a)(n − 5)/2
(b)n/2 − 5
(c)2(n − 5)
(d)(5 − n)/2
5.The height, h metres, of a ball t seconds after a stopwatch is started follows h = (t − 1)(5 − t) for 1 ≤ t ≤ 5, where h = 0 means the ball is at ground level. Work out the two times at which the ball is at ground level.
(a)t = 1 second and t = 4 seconds
(b)t = 1 second and t = −5 seconds
(c)t = 1 second and t = 5 seconds
(d)t = −1 second and t = 5 seconds
6.A sequence begins at 50, and each term after that is found by subtracting 8 from the term before it. Priya says the 8th term of the sequence is negative. Is Priya correct?
(a)No: the 8th term is 50 − 8 × 6 = 2, which is positive.
(b)Yes, but the 8th term is 50 − 8 × 8 = −14.
(c)No: repeated subtraction from 50 can never go negative.
(d)Yes: the 8th term is 50 − 8 × 7 = −6, which is negative.
7.The diagram shows the graph of a straight line, drawn on a grid numbered from −5 to 5 on both axes. Which equation could represent the line?
(a) $y = 2 x + 1$
(b) $y = - 2 x - 1$
(c) $y = x - 1$
(d) $y = 2 x - 1$
8.A straight line has equation y = 5x. Work out the value of y when x = 3.
y = 5x
(a)8
(b)3
(c)−15
(d)15
9.Expand 2(x + 12)
(a)2x + 24
(b)2x + 14
(c)24x
(d)2x + 12
10.A rule turns each input x into an output y. The inputs are x = 0, 1, 2, 3 and the outputs are y = 4, 7, 10, 13. Work out the output when x = 5.
(a)19
(b)21
(c)22
(d)16
11.A water butt holds 200 litres and is being drained at a steady 8 litres per minute. Write down the function for the amount of water y, in litres, left after x minutes.
(a)y = 200x − 8
(b)y = −8x − 200
(c)y = 200 − 8x
(d)y = 8x + 200
12.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.
13.The solution to an inequality is n ≤ 5. Write down the largest integer value of n that satisfies this inequality.
(a)5
(b)4
(c)6
(d)−5
14.Solve x² − 100 = 0.
(a)x = 10 or x = −10
(b)x = 10
(c)x = 100 or x = −100
(d)x = 50
15.The point C is 6 units to the right of the origin and 0 units up. Write down the coordinates of C.
(a)(6, 0)
(b)(0, 6)
(c)(0, 0)
(d)(7, 0)

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