Algebra worksheet — GCSE Foundation

1.Solve 4x + 3 = 19

2.The solution set of an inequality is x ≥ 7. Write down the value that does NOT satisfy this inequality.

3.A straight line passes through the points (2, 7) and (5, 16). Work out the value of y when x = 0.

4.The formula for converting a distance in miles, m, to kilometres, k, is k = 8m ÷ 5. Work out k when m = 10.

5.The graph of y = x² − 2x − 8 takes these values: when x = −2, y = 0; when x = −1, y = −5; when x = 0, y = −8; when x = 3, y = −5; when x = 4, y = 0. Use these values to write down the two solutions of x² − 2x − 8 = 0.

6.The diagram shows a distance–time graph for a cyclist travelling at a constant speed, for the first 6 minutes of a journey. Distance is in kilometres and time is in minutes. Work out how far the cyclist would travel in 20 minutes at the same speed.

7.A distance-time graph shows a car travelling at a constant speed, covering 90 km in 2 hours. Work out the car's speed in km/h.

8.Factorise fully 5x + 5y − 5

9.Solve the simultaneous equations x + y = 15 and x − y = 3. Work out the value of x.

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

11.Which of these values of x is a solution of x² + 2x − 15 = 0?

12.Which of these is a formula?

13.A sequence begins at 50, and each term after that is found by subtracting 8 from the term before it. Priya says the 8th term of the sequence is negative. Is Priya correct?

14.A cyclist's journey is shown on a distance–time graph. The graph is a straight line from (0 minutes, 0 km) to (40 minutes, 12 km). Work out her speed in kilometres per hour.

15.The simple interest, £I, earned on a savings account is given by the formula I = PRT/100, where P is the amount invested in pounds, R is the interest rate per year and T is the time in years. Rearrange the formula to make P the subject.