Algebra worksheet — GCSE Foundation

1.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.

2.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.

3.A taxi firm charges a fixed fee of £3.50 plus £2.20 per mile. Work out the total cost of a journey of 6 miles.

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.In a shop a shirt costs £x and a pair of trousers costs £(2x + 30). Together the two items cost at least £150. Work out the lowest possible price of the shirt.

6.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.

7.A car's speed increases steadily while it accelerates. Its speed v m/s after t seconds is given by v = u + at, where u is the starting speed in m/s and a is the acceleration in m/s². A car starts at u = 4 m/s and accelerates at a = 2 m/s² until it reaches v = 20 m/s. Work out t, the time taken in seconds.

8.Work out the coordinates of the point halfway between (−9, −2) and (−1, −2).

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

10.The first five terms of a quadratic sequence are 5, 8, 13, 20, 29. Work out the next term in the sequence.

11.A square has sides of length y cm. Write down an expression for the perimeter of the square.

12.Make b the subject of the formula a = 5b.

13.Factorise fully 12x² + 18x.

14.Work out the gradient of the straight line with equation y = (2x/5) − 3.

15.A plumber charges a £40 call-out fee plus £25 for each hour worked. The total charge, £C, for a job lasting h hours is given by C = 40 + 25h. Work out the charge for a job lasting 3 hours, and name what kind of statement C = 40 + 25h is.