Algebra worksheet — GCSE Foundation

1.Which of these is an equation, rather than an expression, a formula or an identity?

2.The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. A rectangular garden has a perimeter of 46 m and a length of 14 m. Rearrange the formula to make w the subject, then work out the width of the garden.

3.The diagram shows the graph of a function. Which equation could it represent?

4.A straight line passes through the points (0, 4) and (1, 9). Write down the gradient of the line.

5.A cycle route is 84 km long. Freya sets off along it at a steady 14 km/h. Write down the function for the distance y, in kilometres, that is still to be cycled after x hours.

6.A sequence has the position-to-term rule 5n − 2, where n is the position number. Which of these is a term in the sequence?

7.The diagram shows the graph of the cost, in pounds, of a taxi journey plotted against the distance travelled, in miles, for journeys of up to 4 miles. The same fixed charge and the same cost per mile apply to longer journeys. Work out the cost of a 6-mile journey.

8.Simplify 2a + 3b − a + 2b − b

9.Solve the simultaneous equations x + y = 1 and 2x + y = 5.

10.Rosie is asked whether 4(x + 3) = 4x + 12 is an equation or an identity. Which statement is correct? Give a reason for your answer.

11.A stack of firewood has 3 logs in the top layer. Each layer below has 4 more logs than the layer above it. Work out the number of logs in the 6th layer from the top.

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

13.A quadratic curve has a root at x = −2 and its turning point has x-coordinate 3. Work out the curve's other root, using the symmetry of the graph.

14.Write down the gradient of the line with equation y = −x + 3.

15.A printer starts a job with 480 sheets of paper loaded and prints at a steady rate. The number of sheets left, S, after t minutes is given by S = 480 − 24t. Work out how many minutes it takes for the paper to run out completely.