Algebra worksheet — GCSE Higher

1.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.

2.Solve 4x − (2x − 6) = 18

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

4.The first five terms of a quadratic sequence are 2, 5, 10, 17, 26. Work out the next term in the sequence.

5.Write down the first four terms of the sequence with nth term 6n − 5.

6.Write y = x² + 12x + 40 in the form (x + a)² + b, and hence write down the minimum value of y.

7.Six years ago Harry was three times as old as his brother Leo. Harry is now 24 years old. Work out Leo's age now.

8.A walker's distance-time graph is described as follows: she walks 3 km in the first 15 minutes at a steady speed, rests for 10 minutes, then walks a further 3 km in the next 20 minutes, also at a steady speed. Work out her speed, in km/h, during the first 15 minutes.

9.A circle has centre (0, 0) and passes through the point (7, 24). Work out the equation of the circle.

10.A number machine multiplies its input by 2 and then subtracts 5. Work out the output when the input is 6.

11.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.

12.The graph of y = f(x) has a minimum turning point at (2, −3). The graph of y = −f(x) + a has a maximum turning point at (2, 9). Work out the value of a.

13.Ben is asked to find the inverse of f(x) = 4 − 3x. He writes f⁻¹(x) = (4 − x)/3. Which statement about Ben's answer is correct?

14.A rule turns each input x into an output y. The inputs are x = −1, 0, 1, 2 and the matching outputs are y = 5, 3, 1, −1. Work out the rule.

15.A rectangular sheep pen has perimeter P, length l and width w, connected by the formula P = 2l + 2w. A farmer has 60 m of fencing for the perimeter and sets the width at 8 m. Work out the length of the pen.