Algebra worksheet — GCSE Foundation

1.Here are the first five terms of an arithmetic sequence: 4, 7, 10, 13, 16. Work out the 9th term.

2.Which of these quadratic graphs does NOT cross the x-axis at all?

3.Work out the gradient of the straight line with equation 3y = 12 − 6x.

4.A sequence has the position-to-term rule n² + 2, where n is the position number. Work out the 6th term.

5.A car passes the 15 km marker on a road and passes the 195 km marker 3 hours later. Work out the gradient of the distance-time graph, that is the rate of change of distance with time.

6.A number, n, is doubled and then 7 is subtracted. The result is 15. Form an equation and solve it to find n.

7.A box contains 6 chocolates. Write down an expression for the total number of chocolates in c boxes.

8.The graph of y = x² − 7x + 2 crosses the x-axis at two points. One root, read from the graph, is approximately x = 0.30. Using the fact that the sum of the two roots of x² − 7x + 2 = 0 is 7, estimate the other root, correct to 2 decimal places.

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

10.The simultaneous equations x = 2 and x + y = 9 are given. Work out the value of y.

11.A plumber charges a £35 call-out fee plus £20 for each hour worked, h. On a certain job the total charge was £115. Work out how many hours the plumber worked.

12.Work out the value of (x − 4)/2 + 3 when x = 10

13.Solve 3x + 14 = 8x − 6

14.The point P has coordinates (0, 12). Write down the axis that P lies on and the y-coordinate of P.

15.The formula for the perimeter of a rectangle is P = 2(l + w). One rectangle has l = 9 cm and w = 4 cm. A second rectangle has l = 6 cm and w = 5 cm. Work out how many cm greater the perimeter of the first rectangle is than the perimeter of the second.