Algebra worksheet — GCSE Higher

1.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.

2.The expression 6n + 15 is written as 3(2n + 5). Which statement is correct?

3.Solve the inequality 2(3x − 1) ≥ 4x + 8.

4.A proof that (n + 3)² − (n − 3)² is always a multiple of a certain number begins: Line 1: (n + 3)² − (n − 3)² = (n² + 6n + 9) − (n² − 6n + 9). Which expression correctly completes Line 2?

5.Amelia's mother is three times as old as Amelia. Four years ago her mother was five times as old as Amelia was then. Work out Amelia's age now.

6.A student solves the simultaneous equations 2x + y = 11 and x − y = 1 by elimination, adding the two equations together. Which of these is the correct result of that step?

7.Solve x² − 5x + 6 = 0 by factorising.

8.A rectangular lawn is 4 m longer than it is wide. Its area is 96 m². Work out the length of the lawn.

9.Solve (3x + 2)/5 = (x + 4)/3

10.Factorise x² − 64.

11.Which of these statements is an equation with exactly one solution?

12.Which expression means 'triple c, then add double d'?

13.The equation x² = 5x − 3 is to be solved using iteration. Work out which of these iterative formulas comes from a correct rearrangement of the equation.

14.A car park charges by the hour. Parking for 1 hour costs £5, 2 hours costs £9, 3 hours costs £13 and 4 hours costs £17, with the cost increasing by the same amount for each extra hour. Work out an expression, in terms of n, for the cost, in pounds, of parking for n hours.

15.A delivery van's distance-time graph shows the following: it travels 9 km in the first 15 minutes at a steady speed, stops for 45 minutes to unload, then travels a further 21 km in the next 30 minutes, also at a steady speed. Work out the average speed, in km/h, for the whole journey.