Algebra worksheet — GCSE Higher

1.Solve x² + 3x − 10 = 0.

2.A cafe sells coffees at £c each and pastries at £p each. Three coffees and two pastries cost £9.60. Two coffees and two pastries cost £7.60. Work out the price of one coffee.

3.A cinema sells adult tickets for £10 and child tickets for £6. A family group buys 9 tickets in total, spending £74. Work out how many adult tickets were bought.

4.A machine bought for £2,400 loses 12% of its value every year. After how many complete years does its value first fall below £1,500?

5.A park is drawn on a grid in which 1 unit represents 1 km. The car park is at the point (0, 0) and the lake is at the point (3, 5). Work out the direct distance, in km, from the car park to the lake, giving your answer to 1 decimal place.

6.Solve the inequality 4x + 1 > 2x + 9.

7.Which of these rules generates the sequence 6, 11, 16, 21, …?

8.A car passes the 15 km marker on a road and passes the 195 km marker 3 hours later. Work out the gradient of the distance-time graph, that is the rate of change of distance with time.

9.Solve x² − 100 = 0.

10.Solve 4x − (2x − 6) = 18

11.The tangent to a curve at the point (6, 1) has gradient −3. Work out the y-coordinate of the point where this tangent crosses the y-axis.

12.Solve 7x − 5 = 3x + 11

13.A geometric sequence has first term 3 and common ratio √2. Work out the 6th term of the sequence, giving your answer in the form a√2.

14.A point has coordinates (x, y). In which two quadrants is the product x × y positive?

15.The table shows the speed, in m/s, of a cyclist at times, in seconds, 1 second apart: 0 at t = 0, 7 at t = 1, 12 at t = 2, 15 at t = 3, 16 at t = 4, 14 at t = 5, 9 at t = 6. Using the trapezium rule with strip width 1 second, estimate the distance the cyclist travels between t = 2 and t = 5 only.