Algebra worksheet — GCSE Foundation

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

2.The graph of y = x² − 5x + 6 crosses the x-axis at two points. By factorising, work out the x-coordinates of these two points.

3.The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. A rectangular garden has a perimeter of 46 m and a length of 14 m. Rearrange the formula to make w the subject, then work out the width of the garden.

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

5.A sequence has the position-to-term rule n² + 1, where n is the position number. Work out how much bigger the 5th term is than the 4th term.

6.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.

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

8.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.

9.A straight line passes through the points (−1, 2) and (3, 14). Work out the equation of the line.

10.A line segment has one endpoint at (−6, 2) and its midpoint at (−1, 5). Work out the coordinates of the other endpoint.

11.A printer starts a job with 480 sheets of paper loaded and prints at a steady rate. The number of sheets left, S, after t minutes is given by S = 480 − 24t. Work out how many minutes it takes for the paper to run out completely.

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

13.Solve 4x − (2x − 6) = 18

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

15.a = 3 and b = 5. Work out the value of a²b.