Algebra worksheet — GCSE Foundation

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

2.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.

3.Solve the inequality 2(x − 1) ≤ 8.

4.Write down the gradient of the line with equation y = −x + 3.

5.Solve (2x + 1)/3 = 5

6.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.

7.A straight line has equation y = 2x − 7. Write down the coordinates of the point where the line crosses the y-axis.

8.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.

9.The first five cube numbers are 1, 8, 27, 64, 125. Write down the next cube number in the sequence.

10.A car's fuel tank contains 50 litres when it starts a journey. After travelling for 2 hours, it contains 38 litres, and fuel is used at a constant rate. Work out the rate at which fuel is used, in litres per hour.

11.A box holds n pencils. A shop has 6 full boxes and 4 loose pencils. All of these pencils are shared equally between 2 classes. Write down the expression for the number of pencils each class receives.

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

13.y = 5x − 1. Work out the value of y when x = 3.

14.A gardener charges a fixed fee of £15 plus £8 for each hour worked. The total charge, £T, for a job lasting h hours is given by T = 15 + 8h. Work out the charge for a job lasting 4 hours, and identify what kind of statement T = 15 + 8h is.

15.The equation 3(2x − 1) = 4x + 9 is rearranged by expanding the brackets. Which of these is the correctly expanded equation?