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

MathsUKwww.geekhero.co.uk

1.The point A lies on the x-axis. Which statement about A must be true?
(a)y = 0
(b)x = 0
(c)x > 0
(d)x = y
2.A table shows y = x² − 6x + 5 at these points (x, y): (0, 5), (1, 0), (2, −3), (3, −4), (4, −3), (5, 0), (6, 5). Using the symmetry shown, write down the x-coordinate of the turning point.
y = x² − 6x + 5
(a)x = 1
(b)x = 5
(c)x = 6
(d)x = 3
3.The diagram shows part of the graph of a reciprocal function of the form $y = \frac{k}{x}$ , passing through the labelled point. Work out the value of k.
(a)5
(b)6
(c)9
(d)1.5
4.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
5.A hot air balloon is at a height of 20 m and rises at a steady rate. After 4 minutes it is at a height of 52 m. Work out the rate at which the balloon rises, in metres per minute.
(a)8
(b)32
(c)5
(d)13
6.On a map, where each grid unit represents 1 km, Ravi's house is at (−3, 4) and the library is at (6, 4). Work out the distance between Ravi's house and the library.
(a)9 km
(b)0 km
(c)−9 km
(d)3 km
7.Factorise fully 5x + 5y − 5
(a)5(xy − 1)
(b)5(x + y + 1)
(c)5(x + y − 1)
(d)5(x + y − 5)
8.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.
(a)(3, −4)
(b)(−4, 3)
(c)(8, 3)
(d)(−4, −5)
9.Meera writes the statement 3(x + 4) = 3x + 12. Which of these correctly describes what she has written, with a reason?
(a)An identity, true for every value of x
(b)A formula, relating two expressions
(c)An equation, because it has an equals sign
(d)An equation, solved by one value of x
10.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.
(a)7n
(b)12n + 7
(c)7n + 12
(d)7n + 5
11.A plumber charges a £40 call-out fee plus £25 for each hour worked. The total charge, £C, for a job lasting h hours is given by C = 40 + 25h. Work out the charge for a job lasting 3 hours, and name what kind of statement C = 40 + 25h is.
(a)£65, and C = 40 + 25h is an expression
(b)£115, and C = 40 + 25h is a formula
(c)£195, and C = 40 + 25h is a formula
(d)£115, and C = 40 + 25h is an expression
12.Which of these quadratic graphs does NOT cross the x-axis at all?
(a)y = (x − 2)² + 3
(b)y = (x + 4)(x − 1)
(c)y = (x − 2)(x + 3)
(d)y = x² − 9
13.The nth term of a sequence is 2n² + 1. Work out the 4th term of the sequence.
(a)33
(b)65
(c)32
(d)17
14.The braking distance of a car, in metres, is estimated using the formula d = 0.4v² + 6, where v is the speed in mph. A car travelling at 35 mph brakes. Work out the estimated braking distance.
(a)202
(b)490
(c)496
(d)20
15.Solve the inequality x + 5 < 12.
(a)x < 7
(b)x < 17
(c)x > 7
(d)x < −7

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