Algebra worksheet — GCSE Foundation

1.Expand and simplify 2(a + 6) − 2(a − 7)

2.The area of a circle is given by the formula A = πr², where r is the radius. Rearrange the formula to make r the subject.

3.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.

4.The first four terms of a sequence are 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.

5.Make b the subject of the formula a = 5b.

6.A student is asked whether 3(x − 4) = 3x − 4 is an identity. Which statement gives the correct verdict and reason?

7.Make p the subject of the formula n = p/3.

8.A number, n, is doubled and then 7 is subtracted. The result is 15. Form an equation and solve it to find n.

9.Write down the expression that means the same as m² × m × 3.

10.Explain why the equation 4x + 3 = 4x + 10 has no solution for x.

11.A theatre has rows of seats arranged so that row 1 has 12 seats, row 2 has 17 seats, row 3 has 22 seats and row 4 has 27 seats, with each row having 5 more seats than the row before. Work out an expression, in terms of n, for the number of seats in row n.

12.Which expression is equivalent to 7x − 3(2x − 6)?

13.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.

14.An arithmetic sequence has first term 40 and common difference −6. Work out the 9th term of the sequence.

15.A car's speed increases steadily while it accelerates. Its speed v m/s after t seconds is given by v = u + at, where u is the starting speed in m/s and a is the acceleration in m/s². A car starts at u = 4 m/s and accelerates at a = 2 m/s² until it reaches v = 20 m/s. Work out t, the time taken in seconds.