Algebra worksheet — GCSE Foundation

1.Work out the gradient of the straight line with equation 3y = 12 − 6x.

2.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.

3.A geometric sequence starts at 4, and each term after that is found by multiplying the term before it by 3. Write down the first four terms of the sequence.

4.A scout leader is 44 years old and one of the scouts is 16 years old. Work out how many years it will be until the leader is exactly twice as old as the scout.

5.Solve 2x² = 18.

6.A pattern is made from tiles. Pattern 1 has 7 tiles, pattern 2 has 11 tiles, pattern 3 has 15 tiles, and pattern 4 has 19 tiles, with each new pattern having 4 more tiles than the one before it. Work out an expression, in terms of n, for the number of tiles in pattern n.

7.A triangle has vertices at (1, 1), (1, 5) and (6, 1). Work out the area of the triangle.

8.Which of these is an identity?

9.A currency conversion graph shows that £4 is equivalent to 5 US dollars. Use this to work out how many US dollars are equivalent to £24.

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 = 2 and b = 5. Work out the value of a²b.

12.The first four terms of a sequence are 6, 13, 20, 27. Work out an expression, in terms of n, for the nth term.

13.A ramp rises 3 m over a horizontal distance of 12 m. Work out the gradient of the ramp.

14.Point R has coordinates (3, −5). Point R is reflected in the line y = 2 to point S. Write down the coordinates of S.

15.A table shows values of y = x² − x − 6 for x from −3 to 4: at x = −3, y = 6; x = −2, y = 0; x = −1, y = −4; x = 0, y = −6; x = 1, y = −6; x = 2, y = −4; x = 3, y = 0; x = 4, y = 6. Using the table, write down the two roots of x² − x − 6 = 0.