Algebra worksheet — GCSE Higher

1.On Monday, a runner covers 15 km in 2.5 hours. On Tuesday, she covers 12 km in 1.5 hours. Using the formula speed = distance ÷ time, work out on which day she ran faster, and by how much.

2.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?

3.For 0 ≤ x ≤ 360, the equation sin x = 0.5 has two solutions. What are they?

4.The first four terms of a sequence are 9, 14, 19, 24. Work out an expression, in terms of n, for the nth term.

5.A point has coordinates (x, y), where x + y = 0 and x is not 0. In which two quadrants could this point lie?

6.To solve 6x − 4 = 2x + 20, Yusuf's first step is to subtract 2x from both sides. Work out what equation this gives.

7.Expand and simplify 2(a + 6) − 2(a − 7)

8.The expression 6n + 15 is written as 3(2n + 5). Which statement is correct?

9.The diagram shows a distance–time graph for a cyclist travelling at a constant speed, for the first 6 minutes of a journey. Distance is in kilometres and time is in minutes. Work out how far the cyclist would travel in 20 minutes at the same speed.

10.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.

11.The cost, in pounds, of hiring a van for d days is given by the formula C = 25 + 18d. A customer's hire cost £133. Work out how many days, d, they hired the van for, by first rearranging the formula to make d the subject.

12.The discriminant of a quadratic equation is greater than zero. Which statement about the solutions of that equation is correct?

13.Which of these equations is equivalent to 5x − 2 = 3x + 8?

14.A sequence has the position-to-term rule n² + 1, where n is the position number. Work out how much bigger the 5th term is than the 4th term.

15.Solve 4x² − 9 = 0.