Algebra worksheet — GCSE Foundation

1.Grace says that 2(x + 1) and 2x + 2 always have the same value. Work out the value of both expressions when x = 3.

2.Which expression means 'add 3 to n, then multiply the result by 4'?

3.Harry will spend at most £150 on a party. The cake costs £60 and each helium balloon costs £3. Solve an inequality to find all the possible numbers of balloons, x, that he can buy.

4.Grace has t books. Noah has 1 book fewer than Grace. Write down an expression for the number of books Noah has.

5.Work out the coordinates of the point where the graph of y = 2x − 6 crosses the x-axis.

6.y = 3x − 2. Work out the value of y when x = 4.

7.A number machine multiplies its input by 3 and then adds 7. The output is 1. Work out the input.

8.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.

9.The formula for the volume of a cuboid is V = lwh, where l is the length, w is the width and h is the height. Make h the subject of the formula.

10.Write down the coefficient of xy in the expression 4x²y − 7xy + 2.

11.A charity's fundraising total, T pounds, over d days follows T = (d − 3)(30 − d) for 3 ≤ d ≤ 30, where T = 0 marks the start and end of the campaign. Work out how many days the campaign runs for, from start to end.

12.A model rocket's height is given by h = −5t² + 20t, where h is in metres and t is in seconds. A student says the graph of h against t is n-shaped. Which statement gives the correct verdict on the SHAPE and the reason that settles it from the equation?

13.Expand and simplify (x − 3)²

14.n = 3. Work out the value of (2n)².

15.Factorise x² − 64.