Algebra worksheet — GCSE Foundation

1.Write down the expression that means the same as 3 × y × y.

2.Point P has coordinates (5, 2). Point P is rotated 180° about the origin to point Q. Write down the coordinates of Q.

3.A stack of firewood has 3 logs in the top layer. Each layer below has 4 more logs than the layer above it. Work out the number of logs in the 6th layer from the top.

4.Solve 3x − 5 = 4.

5.A straight line passes through the points (0, 4) and (1, 9). Write down the gradient of the line.

6.A graph has equation y = 3x + 2. Which word or phrase best describes its shape?

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

8.A cafe sells coffees at £c each and pastries at £p each. Three coffees and two pastries cost £9.60. Two coffees and two pastries cost £7.60. Work out the price of one coffee.

9.Solve the simultaneous equations 2x + y = 7 and x − y = 2.

10.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.

11.A geometric sequence starts at 3, and each term after that is found by multiplying the term before it by 2. Write down the first four terms.

12.The first five terms of a sequence are 2, 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.

13.Which expression is equivalent to 2(x + 6)?

14.A geometric sequence begins 80, 40, 20, 10, ... Work out the next term in the sequence.

15.The first four terms of a sequence are 11, 18, 25, 32. Ravi thinks the nth term is 7n. Work out the correct expression for the nth term.