Algebra worksheet — GCSE Higher

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

2.Expand and simplify 4(2x − 1) − 3(x + 2) − 5x

3.f(x) = 2x − 1. Work out ff(x).

4.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.

5.Expand and simplify (x + 1)(x + 2)(x + 3).

6.Line C passes through (0, 0) and (4, 2). Line D passes through (0, 0) and (2, 2). Write down which of the two lines is the steeper.

7.Solve the inequality 2(x − 1) ≤ 8.

8.Factorise fully 56x − 24

9.A proof that (n + 3)² − (n − 3)² is always a multiple of a certain number begins: Line 1: (n + 3)² − (n − 3)² = (n² + 6n + 9) − (n² − 6n + 9). Which expression correctly completes Line 2?

10.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.

11.A rule multiplies the input by a fixed number and then adds a fixed number. An input of 1 gives an output of 5, and an input of 3 gives an output of 11. Work out the rule, writing the input as x and the output as y.

12.A rectangular lawn is 4 m longer than it is wide. Its area is 96 m². Work out the length of the lawn.

13.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.

14.To rearrange the formula y = 3x − 8 to make x the subject, Priya writes: 'Add 8 to both sides to get y + 8 = 3x, then divide both sides by 3 to get x = y + 8 ÷ 3.' Work out the correct expression for x.

15.The nth term of a sequence is 4n − 3. Work out the 7th term of the sequence.