Algebra worksheet — GCSE Foundation

1.Two numbers have a sum of 45. The larger number is 9 more than the smaller number. Form an equation using n for the smaller number, and solve it to find the larger number.

2.Expand and simplify (x − 3)²

3.y = x + 10. Work out the value of y when x = 0.

4.Mia buys 3 identical notebooks and a pen costing £1.50. She pays a total of £9.90. Form an equation using n for the cost of one notebook, and solve it to find n.

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

6.A theatre has rows of seats arranged so that row 1 has 12 seats, row 2 has 17 seats, row 3 has 22 seats and row 4 has 27 seats, with each row having 5 more seats than the row before. Work out an expression, in terms of n, for the number of seats in row n.

7.The first four terms of a sequence are 6, 13, 20, 27. Work out an expression, in terms of n, for the nth term.

8.Work out the y-intercept of the graph of y = x² + 3x − 10.

9.The simultaneous equations 2x + 3y = 12 and x − y = 1 are given. Work out the value of y.

10.A quadratic graph has roots at x = −3 and x = 5, and it crosses the y-axis at (0, −15). Work out the equation of the curve in the form y = (x − a)(x − b).

11.A plant is 4 cm tall in week 1. Each week after that, its height increases by 5 cm. Work out the first week in which the plant is taller than 30 cm.

12.The graph of P = 480 ÷ V shows how the pressure, P pascals, of a gas depends on its volume, V cm³, at constant temperature. Use the relationship to work out the volume when the pressure is 32 pascals, and then work out by how much the volume increases when the pressure drops to 24 pascals.

13.For the graph of y = 1/x, where x cannot be zero, which of these statements is correct?

14.A water tank empties according to y = −5x + 200, where y is the number of litres left after x minutes. Work out the coordinates of the point where this graph crosses the x-axis.

15.Write down the expression that means the same as p + p + p + q.