Algebra worksheet — GCSE Foundation

1.Which of these equations gives a straight-line graph when plotted?

2.Work out the y-intercept of the graph of y = x² + 3x − 10.

3.The first four terms of a sequence are 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.

4.A car's speed increases steadily while it accelerates. Its speed v m/s after t seconds is given by v = u + at, where u is the starting speed in m/s and a is the acceleration in m/s². A car starts at u = 4 m/s and accelerates at a = 2 m/s² until it reaches v = 20 m/s. Work out t, the time taken in seconds.

5.Solve x − 4 = −9

6.A fundraising chain letter starts with 3 people taking part in round 1. Each following round has 4 times as many people taking part as the round before. Work out the number of people taking part in round 4.

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

8.Solve x² − 2x − 24 = 0.

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

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

11.Solve the inequality 9 − 2x ≥ 1.

12.Expand and simplify 2(a + 6) − 2(a − 7)

13.A vertical line passes through the point (4, 7). Write down the equation of this line.

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

15.Simplify (5x² + 3x − 2) − (2x² − x + 5)