Algebra worksheet — GCSE Higher

1.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.

2.A student says 4(2x − 3) is equivalent to 8x − 3. Which statement gives the correct verdict and reason?

3.A plumber charges a call-out fee of £30 plus £25 per hour worked. Work out the total charge for a job that takes 3 hours.

4.The nth term of a sequence is 4n + 2. A term in the sequence has value 30. Work out its position, n, in the sequence.

5.Work out the values of x and y that satisfy both x + y = 10 and x − y = 4.

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

7.Write down the gradient of the line with equation y = −x + 3.

8.A rectangular field has length (3a + 2) metres and width (a − 1) metres. Write a simplified expression for the perimeter of the field.

9.Work out the coordinates of the point where the graph of y = 2x − 6 crosses the x-axis.

10.Solve 2x² − 32 = 0.

11.Ethan is 10 years old and his father is 40 years old. Work out how many years ago Ethan's father was seven times as old as Ethan.

12.The graph of y = x² − 5x + 6 crosses the x-axis at two points. By factorising, work out the x-coordinates of these two points.

13.A cyclist's speed rises from rest to a maximum — quickly at first, then more and more slowly — so her speed-time graph is a curve that is concave down (its gradient decreases as time goes on). A trapezium estimate is made for the distance travelled during this phase, using two points on the curve. Is the trapezium estimate an overestimate or an underestimate of the true distance, and why?

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.Work out the value of a² − 2b when a = −3 and b = 4.