Algebra worksheet — GCSE Foundation

1.Matchsticks are laid out as a row of squares, with each new square sharing a side with the square before it. The first square uses 4 matchsticks and every extra square uses 3 more. Work out how many matchsticks a row of 4 squares uses.

2.Simplify 5a/6 − a/3

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

4.The graph of y = 24/x is drawn for x > 0. Work out the value of y when x = 6.

5.Write down the coordinates of the point that is 4 units to the left of the origin and 7 units up.

6.A point has coordinates (x, y). In which two quadrants is the product x × y positive?

7.A sequence has the position-to-term rule: the term is the square of the position number. Its first four terms are 1, 4, 9, 16. Work out the 10th term.

8.Solve the simultaneous equations 5x − 2y = 16 and 3x + 2y = 16. Work out the value of x.

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

10.Oliver buys b pens. Each pen costs £2. Write down an expression for the total cost, in pounds.

11.A pattern is made from tiles. Pattern 1 uses 4 tiles, pattern 2 uses 7 tiles, pattern 3 uses 10 tiles and pattern 4 uses 13 tiles, with each pattern using 3 more tiles than the one before. Work out an expression, in terms of n, for the number of tiles used in pattern n.

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

13.A quadratic graph has roots at x = −3 and x = 5, and it crosses the y-axis at (0, −15). Work out the equation of the curve in the form y = (x − a)(x − b).

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.A sequence begins at 60, and each term after that is found by subtracting 7 from the term before it. Work out the 5th term of the sequence.