Algebra worksheet — GCSE Foundation

1.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.

2.Here are the first four terms of an arithmetic sequence: 5, 9, 13, 17. Work out the 5th term.

3.Write down the expression that means 5 more than half of n.

4.A scout leader is 44 years old and one of the scouts is 16 years old. Work out how many years it will be until the leader is exactly twice as old as the scout.

5.The point F has x-coordinate −1 and lies 6 units above the x-axis. Write down the coordinates of F.

6.An equation has exactly one value of x that makes it true, but an identity is true for every value of x. Which of these best explains why 3x + 5 = 20 is an equation rather than an identity?

7.Make m the subject of the formula w = m − 8.

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

9.A point has coordinates (−6, 9). Work out the sum of the x-coordinate and the y-coordinate.

10.A box contains 6 chocolates. Write down an expression for the total number of chocolates in c boxes.

11.Factorise fully 12x² + 18x.

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

13.Solve the inequality x − 10 < −3.

14.The point (−4, 7) is moved 4 units to the right and 9 units down. Write down the coordinates of the point it reaches.

15.Work out the gradient of the straight line with equation y = (2x/5) − 3.