Algebra worksheet — GCSE Foundation

1.The first four terms of a sequence are 6, 13, 20, 27. Work out an expression, in terms of n, for the nth term.

2.Solve the inequality 4x + 1 > 2x + 9.

3.Which of these quadratic graphs does NOT cross the x-axis at all?

4.A school trip costs a £15 deposit plus £9 per student for the coach. The total cost for a class is £186. Work out how many students went on the trip.

5.Work out the value of 3a − 2b when a = 5 and b = 4

6.Work out the gradient of the straight line with equation 2x + y = 8.

7.A hiker's distance-time graph shows the following: he walks 5 km in the first 1 hour at a steady speed, rests for 1 hour, then walks a further 9 km in the next 2 hours, also at a steady speed. Work out his average speed for the whole journey, in km/h.

8.Three consecutive integers add up to 72. Using n for the smallest integer, form an equation and solve it to find the smallest of the three integers.

9.Solve x² − 100 = 0.

10.Solve the inequality 2(x − 1) ≤ 8.

11.Expand 2(x − 13)

12.The diagram shows the graph of a quadratic function. Write down the values of x where the graph crosses the x-axis.

13.A geometric sequence starts at 3, and each term after that is found by multiplying the term before it by 2. Write down the first four terms.

14.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.

15.A quadratic curve has a minimum turning point at (3, −4). Which of these statements about the curve must be true?