Algebra worksheet — GCSE Foundation

1.Which expression is equivalent to 4(x − 2) + 10?

2.A straight line has equation y = 4x + 3. A second line is parallel to the first line and passes through the point (0, −5). Work out the equation of the second line.

3.A sequence has the position-to-term rule: the nth term is 3n. Write down the first four terms of the sequence.

4.A straight line has equation y = 4 − 3x. Work out the gradient of the line.

5.The first four terms of a sequence are 4, 6, 8, 10. Work out an expression, in terms of n, for the nth term.

6.Given that (x − 4)(x + 9) = 0, write down the two solutions of x.

7.A mobile phone tariff charges a fixed £15 plus 20p for every minute of calls made, so the total monthly charge, £C, for m minutes of calls is given by C = 15 + 0.2m. In a month where Ali's charge was £46.60, work out how many minutes of calls he made.

8.Solve the simultaneous equations 4x + 3y = 25 and 4x − y = 1. Work out the value of y.

9.A rectangular photo has length (x + 3) cm and width x cm. Its area is 40 cm². Work out the value of x.

10.Grace has t books. Noah has 1 book fewer than Grace. Write down an expression for the number of books Noah has.

11.A sequence has the position-to-term rule: the term is the square of the position number. Its first four terms are 1, 4, 9, 16. Work out the 10th term.

12.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.

13.Write down the coefficient of xy in the expression 4x²y − 7xy + 2.

14.A quadratic graph has equation y = (x − 4)². A student says this graph crosses the x-axis at two different points. Explain why the student is wrong.

15.A scout leader is 44 years old and one of the scouts is 16 years old. Work out how many years it will be until the leader is exactly twice as old as the scout.