Algebra worksheet — GCSE Higher

1.A phone plan costs a fixed £15 per month plus 8p per minute of calls. In one month, Jamal's bill was £23.80. Form an equation using m for the number of minutes, and solve it to find how many minutes Jamal used that month.

2.Work out the equation of the straight line that passes through (−2, 3) and (4, −9).

3.Write down the expression that means 5 more than half of n.

4.The numbers x and y satisfy x + y = 10 and xy = 21. Work out the pair of values.

5.The point (5, −12) lies on the circle x² + y² = 169, which has centre (0, 0). Work out the equation of the tangent to the circle at (5, −12), giving your answer in the form y = mx + c.

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

7.A sequence has nth term 3n + 4. Two terms are missing from the list of its first five terms: 7, 10, _, 16, _. Work out the missing 3rd and 5th terms added together.

8.A car park charges by the hour. Parking for 1 hour costs £5, 2 hours costs £9, 3 hours costs £13 and 4 hours costs £17, with the cost increasing by the same amount for each extra hour. Work out an expression, in terms of n, for the cost, in pounds, of parking for n hours.

9.The nth term of a sequence is 3n² + 2n − 1. Work out the 10th term.

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

11.Which of these is an identity?

12.The cost, in pounds, of hiring a van for d days is given by the formula C = 25 + 18d. A customer's hire cost £133. Work out how many days, d, they hired the van for, by first rearranging the formula to make d the subject.

13.Simplify 2/(x + 1) + 3/(x − 2), giving your answer as a single fraction.

14.A sequence has the position-to-term rule n² + 2, where n is the position number. Work out the 6th term.

15.A rule turns each input x into an output y. The inputs are x = 0, 1, 2, 3 and the outputs are y = 4, 7, 10, 13. Work out the output when x = 5.