Algebra worksheet — GCSE Foundation

1.A taxi charges a £3 fixed fee plus £2 for each mile travelled. Write an expression, in pounds, for the total cost of a journey of n miles.

2.A park is drawn on a grid in which 1 unit represents 1 km. The car park is at the point (0, 0) and the lake is at the point (3, 5). Work out the direct distance, in km, from the car park to the lake, giving your answer to 1 decimal place.

3.Work out the value of m² + 3m when m = −2

4.The first four terms of a sequence are 6, 13, 20, 27. Work out an expression, in terms of n, for the nth term.

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

6.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.

7.The first term of an arithmetic sequence is 5, and each term after that increases by 6. Work out the 8th term of the sequence.

8.Work out the value of (x − 4)/2 + 3 when x = 10

9.Explain why the equation 4x + 3 = 4x + 10 has no solution for x.

10.A gym charges a joining fee plus a monthly fee. Anna paid £100 in total after 3 months of membership. Ben paid £160 in total after 6 months of membership (same joining fee and monthly fee as Anna). Work out the monthly fee.

11.A plumber charges a call-out fee of £30 plus £25 per hour worked. Work out the total charge for a job that takes 3 hours.

12.A geometric sequence has first term 3 and common ratio 2. Work out the 5th term of the sequence.

13.In the expression 5x² − 3x + 7, which of these is a single term of the expression?

14.A geometric sequence starts at 4, and each term after that is found by multiplying the term before it by 3. Write down the first four terms of the sequence.

15.The nth term of a sequence is 4n + 2. A term in the sequence has value 30. Work out its position, n, in the sequence.