Algebra worksheet — GCSE Higher

1.A line has equation y = −4x + 1. Work out the equation of the line perpendicular to it that passes through the point (0, 3).

2.A geometric sequence has first term 3 and common ratio 2. Work out the 5th term of the sequence.

3.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?

4.Work out the value of m² + 3m when m = −2

5.A circle has centre (0, 0) and radius 9. Work out the equation of the circle.

6.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?

7.Solve the simultaneous equations x + y = 1 and 2x + y = 5.

8.A circular running track is modelled on a grid whose centre is the origin, where each unit represents 1 metre. A floodlight at the point (30, 40) stands on the edge of the track. A second floodlight stands on the edge of the track at the point (0, k), where k is positive. Work out the value of k.

9.Work out the gradient of the straight line with equation 2x + y = 8.

10.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.

11.Solve the inequality 5 − x ≤ 2.

12.Describe the single transformation that maps the graph of y = f(x) onto the graph of y = f(−x).

13.The first five terms of a quadratic sequence are 5, 8, 13, 20, 29. Work out the next term in the sequence.

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 straight line passes through the points (2, 7) and (5, 16). Work out the value of y when x = 0.