Algebra worksheet — GCSE Foundation

1.A sequence has the position-to-term rule n² + 2, where n is the position number. Work out the 6th term.

2.Work out the equation of the straight line through the points (−3, 4) and (1, −8).

3.Solve the simultaneous equations 3x + 2y = 16 and x + y = 7. Work out the value of y.

4.Line C passes through (0, 0) and (4, 2). Line D passes through (0, 0) and (2, 2). Write down which of the two lines is the steeper.

5.Solve 5x² − 15x = 0.

6.Amelia is buying books. Each book costs £5 and she has at most £30 to spend. Write down an inequality for x, the number of books she can buy.

7.Factorise fully 56x − 24

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

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

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

11.Priya says that x = 6 is the solution of the equation 4x + 8 = 24. Priya is wrong. Work out the correct value of x.

12.A delivery van's distance-time graph shows the following: it travels 9 km in the first 15 minutes at a steady speed, stops for 45 minutes to unload, then travels a further 21 km in the next 30 minutes, also at a steady speed. Work out the average speed, in km/h, for the whole journey.

13.The formula for the perimeter of a square is P = 4s, where s is the side length. Make s the subject of the formula.

14.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.

15.The nth term of a sequence is 4n − 3. Work out the 7th term of the sequence.