Algebra worksheet — GCSE Foundation

1.Work out the gradient of the straight line that passes through the points (−1, 5) and (3, −7).

2.Write down the expression that means the same as m² × m × 3.

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.The nth term of a sequence is 4n + 2. A term in the sequence has value 30. Work out its position, n, in the sequence.

5.Solve the inequality x + 5 < 12.

6.Aisha saves money each week. In week 1 she has saved £15 in total, in week 2 she has saved £23 in total, in week 3 she has saved £31 in total and in week 4 she has saved £39 in total, with the total increasing by the same amount each week. Work out an expression, in terms of n, for the total amount she has saved, in pounds, after week n.

7.Here are the first five terms of an arithmetic sequence: 4, 7, 10, 13, 16. Work out the 9th term.

8.Solve 3x − 1 = 8

9.A sequence begins at 50, and each term after that is found by subtracting 8 from the term before it. Priya says the 8th term of the sequence is negative. Is Priya correct?

10.A rope of length L metres is cut into 6 equal pieces, and 4 metres is then removed from one piece. Write an expression, in metres, for the length of that piece after the cut.

11.A straight line passes through the points (2, 5) and (4, 11). Work out the gradient of the line.

12.A table shows y = x² − 6x + 5 at these points (x, y): (0, 5), (1, 0), (2, −3), (3, −4), (4, −3), (5, 0), (6, 5). Using the symmetry shown, write down the x-coordinate of the turning point.

13.Solve the inequality 3x + 6 ≤ 0.

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

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