Algebra worksheet — GCSE Foundation

1.Make x the subject of the formula y = 4x − 3.

2.Which of these is an equation, rather than an expression, a formula or an identity?

3.Grace has t books. Noah has 1 book fewer than Grace. Write down an expression for the number of books Noah has.

4.A straight line has equation 4y = 12x + 20. Work out the gradient of the line.

5.A student solves the simultaneous equations 2x + y = 11 and x − y = 1 by elimination, adding the two equations together. Which of these is the correct result of that step?

6.Isla says that the lines y = 2x + 1 and y = −2x + 3 are parallel. Write down the statement that gives the correct answer for the correct reason.

7.Solve the inequality 4x + 1 > 2x + 9.

8.A pattern is made from tiles. Pattern 1 has 7 tiles, pattern 2 has 11 tiles, pattern 3 has 15 tiles, and pattern 4 has 19 tiles, with each new pattern having 4 more tiles than the one before it. Work out an expression, in terms of n, for the number of tiles in pattern n.

9.Two numbers have a sum of 24. Their difference is 6. Work out the two numbers.

10.A box holds n pencils. A shop has 6 full boxes and 4 loose pencils. All of these pencils are shared equally between 2 classes. Write down the expression for the number of pencils each class receives.

11.A currency conversion graph shows that £4 is equivalent to 5 US dollars. Use this to work out how many US dollars are equivalent to £24.

12.Factorise fully 12x² + 18x.

13.Which expression means the same as a × a × a?

14.Solve x² − 6x = 0.

15.A rectangle has length k cm and width 5 cm less than its length. Write down an expression for the width of the rectangle, in cm.