Algebra worksheet — GCSE Higher

1.Solve the inequality x² − 5x + 6 < 0.

2.A car park charges by the hour. Parking for 1 hour costs £5, 2 hours costs £9, 3 hours costs £13 and 4 hours costs £17, with the cost increasing by the same amount for each extra hour. Work out an expression, in terms of n, for the cost, in pounds, of parking for n hours.

3.Isla says that the lines y = 2x + 1 and y = −2x + 3 are parallel. Write down the statement that gives the correct answer for the correct reason.

4.Work out the equation of the straight line that passes through (−2, 3) and (4, −9).

5.Simplify (5x² + 3x − 2) − (2x² − x + 5)

6.Solve the inequality 5 − x ≤ 2.

7.A circle has equation x² + y² = 25. Does the point (3, 4) lie on this circle?

8.The nth term of a sequence is n² + 2n − 4. Work out the 7th term.

9.The first four terms of a sequence are 2, 6, 10, 14. Priya says the nth term is 4n. Work out the correct expression for the nth term.

10.Point R has coordinates (3, −5). Point R is reflected in the line y = 2 to point S. Write down the coordinates of S.

11.A rule turns each input x into an output y. The inputs are x = 1, 2, 3, 4 and the matching outputs are y = −5, −3, −1 and one missing value. Work out the missing value of y.

12.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.

13.By completing the square, find the turning point of the curve y = 3x² + 12x + 7.

14.A square patio of side length n slabs is surrounded by a single border of square paving slabs of the same size. For a patio with side length n, the total number of slabs used for the patio and its border together is 9 when n = 1, 16 when n = 2, 25 when n = 3, and 36 when n = 4. Work out an expression, in terms of n, for the total number of slabs.

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