Algebra worksheet — GCSE Foundation

1.Leo is three times as old as his brother. His brother is x years old. Write down an expression for Leo's age.

2.Simplify k + k + k + k + k.

3.A geometric sequence has first term 3 and common ratio 2. Work out the 5th term of the sequence.

4.Work out the equation of the straight line through the points (−3, 4) and (1, −8).

5.Solve the inequality 5 − x ≤ 2.

6.A square has sides of length y cm. Write down an expression for the perimeter of the square.

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

8.A phone plan costs a fixed £15 per month plus 8p per minute of calls. In one month, Jamal's bill was £23.80. Form an equation using m for the number of minutes, and solve it to find how many minutes Jamal used that month.

9.A straight line passes through the points (0, 4) and (1, 9). Write down the gradient of the line.

10.A market stall's cost of hiring n tables is modelled by two formulas: Formula A: C = 3(2n + 5); Formula B: C = 6n + 15, where C is in pounds. A stallholder says the two formulas always give the same cost. Work out the cost given by each formula when n = 4, and use your results to decide whether the stallholder is correct.

11.A rectangular garden has length (x + 7) m and width (x − 7) m. Work out an expression for the area of the garden, giving your answer in its simplest form.

12.Jack is x years old. His brother Kwame is 3 years older than Jack. Write down an expression for Kwame's age.

13.A pizza shop charges a fixed delivery fee of £3, plus £9 for each pizza ordered. Write down the function for the total cost y, in pounds, of ordering x pizzas.

14.The graph of W = 840 ÷ L shows how the width, W metres, of a rectangular field of area 840 m² depends on its length, L metres. Use the relationship to work out the width when the length is 35 m, and hence the perimeter of the field.

15.The graph of y = mx + 6 passes through the point (−2, 0). Work out the value of m.