Algebra worksheet — GCSE Foundation

1.The point A is at (5, −3). In which quadrant does A lie?

2.The graph of y = x² − 7x + 2 crosses the x-axis at two points. One root, read from the graph, is approximately x = 0.30. Using the fact that the sum of the two roots of x² − 7x + 2 = 0 is 7, estimate the other root, correct to 2 decimal places.

3.A ball is dropped and bounces. The height of each bounce after the first is 8 cm less than the bounce before it. The first bounce reaches 60 cm. Work out the height of the 5th bounce.

4.A square tile has an area of 144 cm². Work out the side length of the tile.

5.Which expression is equivalent to 0.5(4x + 6) − x?

6.x = 5. Work out the value of 3x² − 4.

7.Which of these equations is equivalent to 5x − 2 = 3x + 8?

8.A geometric sequence begins 80, 40, 20, 10, ... Work out the next term in the sequence.

9.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.

10.A gym charges a joining fee plus a monthly fee. Anna paid £100 in total after 3 months of membership. Ben paid £160 in total after 6 months of membership (same joining fee and monthly fee as Anna). Work out the monthly fee.

11.Expand 7(a + 8)

12.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.

13.Noah says that y = 3 is the solution of the equation y + 10 = 12. Noah is wrong. Work out the correct value of y.

14.Which of these points lies in the first quadrant?

15.A taxi company charges a £2.50 booking fee plus £1.80 per mile. A journey costs £15.10 in total. Work out the number of miles travelled.