Algebra worksheet — GCSE Higher

1.Factorise fully 12x² + 18x.

2.A speed-time graph for a car shows the speed increasing steadily from 5 m/s to 17 m/s over 6 seconds. Work out the acceleration of the car, in m/s².

3.Line P has equation y = −2x + 5 and line Q has equation 2y = x + 6. Are lines P and Q perpendicular to each other?

4.A gas company charges a standing charge plus a rate per unit used. The total cost, y in pounds, for using x units is given by y = 0.15x + 20. Work out the cost of using 200 units.

5.Solve 7x − 5 = 3x + 11

6.Which of these is a formula, rather than an expression, an equation, or an identity?

7.For the graph of y = 1/x, where x cannot be zero, which of these statements is correct?

8.Solve 6x − 5 = 3x + 13.

9.The first four terms of a sequence are 11, 18, 25, 32. Ravi thinks the nth term is 7n. Work out the correct expression for the nth term.

10.Harry will spend at most £150 on a party. The cake costs £60 and each helium balloon costs £3. Solve an inequality to find all the possible numbers of balloons, x, that he can buy.

11.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.

12.A car's velocity–time graph is a straight line from (0 s, 4 m/s) rising to (6 s, V m/s), followed by a straight line falling from (6 s, V m/s) to (9 s, 0 m/s). The gradient of the second line is −8 m/s². Work out the total distance travelled between t = 0 and t = 9 seconds.

13.A packet contains s sweets. The sweets are shared equally between f friends. Write an expression for the number of sweets each friend receives.

14.Solve 4x − (2x − 6) = 18

15.Expand and simplify (x − 3)²