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.A cyclist's velocity increases from 3 m/s to 11 m/s over 5 seconds, at a constant rate. Work out the cyclist's acceleration, in m/s².

3.Which of these is an identity?

4.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.

5.Work out the value of n² − n when n = −3

6.The point (5, −12) lies on the circle x² + y² = 169, which has centre (0, 0). Work out the equation of the tangent to the circle at (5, −12), giving your answer in the form y = mx + c.

7.Solve the inequality x² ≥ 16, giving your answer using set notation.

8.Write down the expression that means the same as m² × m × 3.

9.A taxi charges a £3 fixed fee plus £2 for each mile travelled. Write an expression, in pounds, for the total cost of a journey of n miles.

10.Solve x² − x − 12 = 0.

11.The point (18, 24) lies on the circle x² + y² = 900, which has centre (0, 0). The tangent to the circle at (18, 24) crosses the y-axis at the point Q. Work out the y-coordinate of Q.

12.Factorise 3x² + 10x − 8.

13.Work out the value of 5m² + 3m when m = −2.4

14.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.

15.The line y = 2x + 7 and the circle x² + y² = 4 are given. By finding the discriminant of the resulting quadratic, without solving it fully, work out how many points the line and the circle intersect at.