Algebra worksheet — GCSE Higher

1.Solve 2(x + 3) = 10

2.Work out the equation of the straight line that passes through (−2, 3) and (4, −9).

3.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.

4.Simplify (2x² + 7x + 3) ÷ (x² − 9), giving your answer as a single fraction.

5.A sequence has the position-to-term rule n² + 1, where n is the position number. Work out how much bigger the 5th term is than the 4th term.

6.A rectangular garden has width w metres and length (w + 3) metres. A gardener writes its perimeter as 2w + 3. Which statement corrects the gardener's mistake?

7.A candle is 30 cm tall and burns down at a steady rate of 1 cm per hour. Write down the function for the height of the candle y, in centimetres, after x hours.

8.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.

9.p = 4. Work out the value of 2p³.

10.A curve has equation y = x³ − 4x. Work out the coordinates of the point where the curve crosses the y-axis.

11.Solve 3x + 14 = 8x − 6

12.A coach company charges a booking fee plus a price for each passenger. A booking for 1 passenger costs £9, for 2 passengers costs £15, for 3 passengers costs £21, and for 4 passengers costs £27. Work out an expression, in terms of n, for the cost in pounds of a booking for n passengers.

13.A sequence has the position-to-term rule n² + 2, where n is the position number. Work out the 6th term.

14.Make x the subject of the formula y = 4(x − 6).

15.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.