Algebra worksheet — GCSE Higher

1.A car's speed-time graph shows the following: its speed increases steadily from 0 m/s to 20 m/s over the first 10 seconds, then stays constant at 20 m/s for the next 15 seconds. Work out the total distance travelled in the first 25 seconds.

2.The equation x² − x − 6 = 0 has roots x = 3 and x = −2. It can be rearranged as xₙ₊₁ = xₙ² − 6. This formula is used with starting value x₀ = 2.9, close to the root x = 3. Work out what happens to the sequence of values as n increases.

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

4.The iterative formula xₙ₊₁ = 12 ÷ (xₙ + 2) is used repeatedly, starting from x₀ = 1. Work out the value that xₙ approaches, correct to 2 decimal places.

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

6.A straight line has gradient 3 and passes through the point (1, 4). Work out the equation of the line.

7.Which expression is equivalent to 7x − 3(2x − 6)?

8.Which of these statements is an identity?

9.A straight line has equation 4y = 12x + 20. Work out the gradient of the line.

10.Meera writes the statement 3(x + 4) = 3x + 12. Which of these correctly describes what she has written, with a reason?

11.Solve 5(x + 3) = 40

12.Work out the gradient of the straight line with equation 3y = 12 − 6x.

13.A school trip costs a £15 deposit plus £9 per student for the coach. The total cost for a class is £186. Work out how many students went on the trip.

14.A cycle route is 84 km long. Freya sets off along it at a steady 14 km/h. Write down the function for the distance y, in kilometres, that is still to be cycled after x hours.

15.The trapezium rule is used to estimate the area under a curve between x = 2 and x = 6. The curve is concave up (it curves upwards, like the inside of a bowl) throughout this interval. Which statement about the estimate is correct?