Algebra worksheet — GCSE Foundation

1.There are 50 adults on a coach to the Lake District. Every adult is either a man or a woman. There are 10 more men than women. Work out the number of men.

2.How many turning points does the graph of y = x² − 7x + 10 have?

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

4.The first four terms of a sequence are 18, 15, 12, 9. Work out an expression, in terms of n, for the nth term.

5.Expand 2(x − 13)

6.Which of these is a factor of 15x + 20?

7.Meera writes the statement 3(x + 4) = 3x + 12. Which of these correctly describes what she has written, with a reason?

8.Factorise fully 56x − 24

9.The nth term of a sequence is n² + 3. Work out the first term of the sequence that is greater than 50.

10.Harry is 14 years old and Mia is 8 years old. Will Harry ever be exactly twice as old as Mia? Give a reason for your answer.

11.The formula for the energy stored in a stretched spring is E = (1/2)kx², where E is in joules, k is the spring constant in N/m and x is the extension in m. A spring with a spring constant of 40 N/m is stretched so that its extension is 0.3 m. Work out the energy stored in the spring.

12.Which expression is equivalent to 4(x − 2) + 10?

13.A wall is tiled in rows, and every row uses the same number of tiles. One row uses 10 tiles, two rows use 20 tiles and three rows use 30 tiles. Work out how many tiles are needed for 7 rows.

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

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