Algebra worksheet — GCSE Foundation

1.A student solves the simultaneous equations 2x + y = 11 and x − y = 1 by elimination, adding the two equations together. Which of these is the correct result of that step?

2.A water butt holds 200 litres and is being drained at a steady 8 litres per minute. Write down the function for the amount of water y, in litres, left after x minutes.

3.Solve x² − 6x = 0.

4.A rule turns each input x into an output y. The inputs are x = 1, 2, 3, 4 and the matching outputs are y = −5, −3, −1 and one missing value. Work out the missing value of y.

5.Solve the inequality 6x ≥ 18.

6.A geometric sequence starts at 4, and each term after that is found by multiplying the term before it by 3. Write down the first four terms of the sequence.

7.A number, w, satisfies the statement "three times w, minus 5, is at least 16". Which of these is the correct inequality for w?

8.Solve the inequality 5x − 3 > 2x + 9.

9.A walker's distance-time graph is described as follows: she walks 3 km in the first 15 minutes at a steady speed, rests for 10 minutes, then walks a further 3 km in the next 20 minutes, also at a steady speed. Work out her speed, in km/h, during the first 15 minutes.

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

11.Solve the simultaneous equations 2x + y = 7 and x − y = 2.

12.Which of these is an inequality?

13.Which expression means 'triple c, then add double d'?

14.To solve 5x − 4 = 2x + 8, Chloe's working is shown. Line 1: 5x − 4 = 2x + 8. Line 2: 3x − 4 = 8. Line 3: 3x = 4. Line 4: x = 4/3. Chloe has made a mistake in her working. Which line contains the mistake?

15.Point P has coordinates (5, 2). Point P is rotated 180° about the origin to point Q. Write down the coordinates of Q.