Algebra worksheet — GCSE Foundation

1.Expand 2(x − 13)

2.On Monday, a runner covers 15 km in 2.5 hours. On Tuesday, she covers 12 km in 1.5 hours. Using the formula speed = distance ÷ time, work out on which day she ran faster, and by how much.

3.The first four terms of a sequence are 4, 9, 14, 19. Work out an expression, in terms of n, for the nth term.

4.The graph of a straight line has equation y = 4x − 5. Beth says the y-intercept is 4. Work out the correct y-intercept.

5.A hall is set out in rows of chairs for an assembly. Row 1 has 50 chairs, row 2 has 45 chairs, row 3 has 40 chairs, and row 4 has 35 chairs, with each row after the first having 5 fewer chairs than the one before. Work out an expression, in terms of n, for the number of chairs in row n.

6.Two expressions are 6(x − 1) and 6x − 6. A student says these are equivalent for every value of x. Is the student correct?

7.Which of these statements is an equation with exactly one solution?

8.Solve 6x + 4 = 28

9.Write down the gradient of the line with equation y = 6 + 4x.

10.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.

11.The formula y = x² + 1 gives y in terms of x. Work out the value of y when x = −2.

12.A wall is tiled in rows, and every row uses the same number of tiles. One row uses 10 tiles, two rows use 20 tiles and three rows use 30 tiles. Work out how many tiles are needed for 7 rows.

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

14.A point has coordinates (x, y). In which two quadrants is the product x × y positive?

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