Algebra worksheet — GCSE Foundation

1.Which of these equations gives a straight-line graph when plotted?

2.x = 5. Work out the value of 3x² − 4.

3.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.

4.Work out the gradient of the straight line with equation 2x + y = 8.

5.Solve x² − 100 = 0.

6.A ball's height, h metres, t seconds after being thrown follows h = (t − 1)(9 − t). Given that the ball is at ground level at t = 1 and t = 9, work out at what time t the ball reaches its maximum height, using symmetry.

7.Work out the value of 3x² − 4x when x = −2.

8.The first five terms of a sequence are 6, 10, 14, 18, 22. Work out an expression, in terms of n, for the nth term.

9.Sophie's mother is 34 years old. In x years' time she will be 50 years old. Work out the value of x.

10.The point D has coordinates (3, −8). Write down the distance of D from the y-axis.

11.Which of these statements is an equation with exactly one solution?

12.A currency conversion graph shows that £4 is equivalent to 5 US dollars. Use this to work out how many US dollars are equivalent to £24.

13.A candle is 30 cm tall and burns down at a steady rate of 1 cm per hour. Write down the function for the height of the candle y, in centimetres, after x hours.

14.A ball is thrown in the air. Its height, h metres, above the ground after t seconds is given in this table: when t = 0, h = 0; when t = 1, h = 15; when t = 2, h = 20; when t = 3, h = 15; when t = 4, h = 0. Use the table to find the two times, in seconds, at which the ball is at ground level.

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