Algebra worksheet — GCSE Foundation

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

2.A delivery van's distance-time graph shows the following: it travels 9 km in the first 15 minutes at a steady speed, stops for 45 minutes to unload, then travels a further 21 km in the next 30 minutes, also at a steady speed. Work out the average speed, in km/h, for the whole journey.

3.The triangular numbers begin 1, 3, 6, 10, 15, ... Work out the next term in the sequence.

4.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.

5.Which expression is equivalent to 5x − (x + 3)?

6.Harry is 14 years old and Mia is 8 years old. Will Harry ever be exactly twice as old as Mia? Give a reason for your answer.

7.A sequence begins at 60, and each term after that is found by subtracting 7 from the term before it. Work out the 5th term of the sequence.

8.The nth term of a sequence is 4n − 3. Work out the 7th term of the sequence.

9.Write down the expression that means the same as 3 × y × y.

10.The diagram shows the graph of a straight line, drawn on a grid numbered from −5 to 5 on both axes. Which equation could represent the line?

11.A straight line has equation y = 4x + 3. A second line is parallel to the first line and passes through the point (0, −5). Work out the equation of the second line.

12.A quadratic graph has roots at x = −3 and x = 5, and it crosses the y-axis at (0, −15). Work out the equation of the curve in the form y = (x − a)(x − b).

13.Make x the subject of the formula y = 4(x − 6).

14.The formula for the profit, £P, made on an item is P = S − C, where S is the selling price and C is the cost price. Make S the subject of the formula.

15.Work out the distance of the point (−6, 4) from the x-axis.