Algebra worksheet — GCSE Foundation

1.A taxi charges a fixed fee of £3 plus £2 for every mile travelled. The journey is m miles. Write down an expression for the total cost, in pounds.

2.Write down the expression that means the same as (x + 7) ÷ 4.

3.Work out the value of 3n − 2 when n = 1

4.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.

5.Which of these is a term, rather than a whole expression, an equation, or a formula?

6.Write down the expression that means the same as m² × m × 3.

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

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

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

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

11.The nth term of a sequence is 2n² + 1. Work out the 4th term of the sequence.

12.To solve 5x − 4 = 2x + 8, Chloe's working is shown. Line 1: 5x − 4 = 2x + 8. Line 2: 3x − 4 = 8. Line 3: 3x = 4. Line 4: x = 4/3. Chloe has made a mistake in her working. Which line contains the mistake?

13.A parcel delivery company's cost graph shows the following: the cost is a flat £5 for parcels weighing up to 2 kg, and then rises by £2 for each additional kg above 2 kg. Use the graph to work out the weight of a parcel that costs £17.

14.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.

15.Amelia's mother is three times as old as Amelia. Four years ago her mother was five times as old as Amelia was then. Work out Amelia's age now.