Algebra worksheet — GCSE Foundation

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

2.The diagram shows a straight line passing through the origin, drawn on a numbered grid. Which of these points lies on the line?

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.Solve 5(x + 3) = 40

5.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.

6.Work out the values of x and y that satisfy both x + y = 10 and x − y = 4.

7.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).

8.A sequence starts at 2. Each term after that is found using the rule "double the previous term, then add 1". Work out the 4th term of the sequence.

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

10.Solve x² − 2x − 24 = 0.

11.A point has coordinates (−6, 9). Work out the sum of the x-coordinate and the y-coordinate.

12.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?

13.The first four terms of a sequence are 4, 6, 8, 10. Work out an expression, in terms of n, for the nth term.

14.Simplify 5x + 3y − 2x + y.

15.The volume of a cuboid is given by the formula V = lwh. Work out V, in cm³, when l = 2, w = 3 and h = 6.