Algebra worksheet — GCSE Foundation

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

2.Work out the gradient of the straight line with equation 2x + y = 8.

3.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.

4.A recipe gives the cooking time, in minutes, for a chicken as T = 40m + 20, where m is the mass in kg. A chicken has a mass of 1.8 kg. Work out the cooking time in hours and minutes.

5.A ribbon of length L metres is cut into 5 equal pieces, and then 3 metres is removed from one piece. Write down an expression, in metres, for the length of that piece after 3 metres is removed.

6.y = 3x − 2. Work out the value of y when x = 4.

7.Given that (x + 2)(x − 7) = 0, write down the two solutions of x.

8.Work out the value of 3x² − 4x when x = −2.

9.Which expression is equivalent to 0.5(4x + 6) − x?

10.Make x the subject of the formula y = 3(x + 2).

11.A packet contains s sweets. The sweets are shared equally between f friends. Write an expression for the number of sweets each friend receives.

12.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.

13.Write down 0.2x with its coefficient written as a fraction in its simplest form.

14.Write down the expression that means the same as (x + 7) ÷ 4.

15.Grace says that 2(x + 1) and 2x + 2 always have the same value. Work out the value of both expressions when x = 3.