Algebra worksheet — GCSE Foundation

1.Point R has coordinates (3, −5). Point R is reflected in the line y = 2 to point S. Write down the coordinates of S.

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

3.A plant is 4 cm tall in week 1. Each week after that, its height increases by 5 cm. Work out the first week in which the plant is taller than 30 cm.

4.Work out the y-intercept of the graph of y = x² + 3x − 10.

5.The formula for the perimeter of a square is P = 4s, where s is the side length. Make s the subject of the formula.

6.A sequence starts at 2. Each term after that is found using the rule "double the previous term, then add 1". Work out the 4th term of the sequence.

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

8.A gas company charges a standing charge plus a rate per unit used. The total cost, y in pounds, for using x units is given by y = 0.15x + 20. Work out the cost of using 200 units.

9.The nth term of a sequence is 3n + 2. Work out the 4th term of the sequence.

10.Solve x − 4 = −9

11.Factorise fully 56x − 24

12.The formula for converting a temperature in Fahrenheit, F, to Celsius, C, is C = 5(F − 32) ÷ 9. Work out C, to 1 decimal place, when F = 98.6.

13.Ben writes n + 4 ≤ 9. Which statement describes what Ben has written? Give a reason for your answer.

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

15.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.