Algebra worksheet — GCSE Foundation

1.The first four terms of a sequence are 4, 6, 8, 10. Work out an expression, in terms of n, for the nth term.

2.The nth term of a sequence is 2n − 1. Work out the 6th term of the sequence.

3.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?

4.A box holds n pencils. A shop has 6 full boxes and 4 loose pencils. All of these pencils are shared equally between 2 classes. Write down the expression for the number of pencils each class receives.

5.The graph of y = x² − 2x − 8 takes these values: when x = −2, y = 0; when x = −1, y = −5; when x = 0, y = −8; when x = 3, y = −5; when x = 4, y = 0. Use these values to write down the two solutions of x² − 2x − 8 = 0.

6.Explain why the equation 4x + 3 = 4x + 10 has no solution for x.

7.A gardener charges a fixed fee of £15 plus £8 for each hour worked. The total charge, £T, for a job lasting h hours is given by T = 15 + 8h. Work out the charge for a job lasting 4 hours, and identify what kind of statement T = 15 + 8h is.

8.A ball's height, h metres, t seconds after being thrown follows h = (t − 1)(9 − t). Given that the ball is at ground level at t = 1 and t = 9, work out at what time t the ball reaches its maximum height, using symmetry.

9.Two expressions are 6(x − 1) and 6x − 6. A student says these are equivalent for every value of x. Is the student correct?

10.A lift has a weight limit: it must carry no more than 630 kg. Let w be the total weight, in kg, carried by the lift. Which inequality describes this?

11.The first four terms of a sequence are 18, 15, 12, 9. Work out an expression, in terms of n, for the nth term.

12.A taxi charges a £3 fixed fee plus £2 for each mile travelled. Write an expression, in pounds, for the total cost of a journey of n miles.

13.A theatre's front row has 18 seats. Each row behind has 4 more seats than the row in front. Which row has exactly 62 seats?

14.A number, n, is doubled and then 7 is subtracted. The result is 15. Form an equation and solve it to find n.

15.A rectangle has length k cm and width 5 cm less than its length. Write down an expression for the width of the rectangle, in cm.