Algebra worksheet — GCSE Foundation

1.a = 2 and b = 5. Work out the value of ab².

2.A car park charges by the hour. Parking for 1 hour costs £5, 2 hours costs £9, 3 hours costs £13 and 4 hours costs £17, with the cost increasing by the same amount for each extra hour. Work out an expression, in terms of n, for the cost, in pounds, of parking for n hours.

3.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.

4.A ramp rises 3 m over a horizontal distance of 12 m. Work out the gradient of the ramp.

5.Point P has coordinates (2, −5). P is reflected in the x-axis to point Q. Write down the coordinates of Q.

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

7.y = 5x − 1. Work out the value of y when x = 3.

8.Tom buys 2 notebooks and 6 pencils on Monday, priced at p pence each for a notebook and q pence each for a pencil. On Tuesday he buys 3 more notebooks and 1 more pencil. Write a simplified expression, in pence, for the total amount Tom has spent on notebooks and pencils.

9.The first five terms of a quadratic sequence are 5, 8, 13, 20, 29. Work out the next term in the sequence.

10.Expand 2(x − 13)

11.The point C is 6 units to the right of the origin and 0 units up. Write down the coordinates of C.

12.Priya buys b balloons for a party. Each balloon costs 15p. Write down an expression for the total cost, in pence.

13.A box holds n pencils. A shop has 6 full boxes and 4 loose pencils. All of these pencils are shared equally between 2 classes. Write down the expression for the number of pencils each class receives.

14.The graph of y = (x − 2)(x + 5) crosses the x-axis at two points. Work out the x-coordinates of these two points.

15.A number machine multiplies its input by 3. The output is 15. Work out the input.