Algebra worksheet — GCSE Foundation

1.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.

2.The first four terms of a sequence are 9, 14, 19, 24. Work out an expression, in terms of n, for the nth term.

3.Simplify k + k + k + k + k.

4.Make x the subject of the formula y = 3(x + 2).

5.A printer starts a job with 480 sheets of paper loaded and prints at a steady rate. The number of sheets left, S, after t minutes is given by S = 480 − 24t. Work out how many minutes it takes for the paper to run out completely.

6.Point P has coordinates (2, −5). P is reflected in the x-axis to point Q. Write down the coordinates of Q.

7.A gardener charges a fixed fee of £15 plus £8 for each hour worked. The total charge, £T, for a job lasting h hours is given by T = 15 + 8h. Work out the charge for a job lasting 4 hours, and identify what kind of statement T = 15 + 8h is.

8.On a map, where each grid unit represents 1 km, Ravi's house is at (−3, 4) and the library is at (6, 4). Work out the distance between Ravi's house and the library.

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

10.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.

11.A straight line has gradient 3 and passes through the point (1, 4). Work out the equation of the line.

12.A straight line has equation 4y = 12x + 20. Work out the gradient of the line.

13.Sophie's mother is 34 years old. In x years' time she will be 50 years old. Work out the value of x.

14.Write down the gradient of the line with equation y = 7x − 2.

15.Simplify 2b − 1 + 2b − 4 + 2b