Algebra worksheet — GCSE Foundation

1.Solve 2x + 1 = 9

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.Four sequences are shown below. Sequence P: 4, 8, 16, 32, ... Sequence Q: 4, 8, 12, 16, ... Sequence R: 4, 7, 12, 19, ... Sequence S: 4, 9, 16, 25, ... Work out which of the sequences P, Q, R and S is geometric.

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

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.The volume of a cuboid is given by the formula V = lwh. Work out V, in cm³, when l = 2, w = 3 and h = 6.

7.Harry will spend at most £150 on a party. The cake costs £60 and each helium balloon costs £3. Solve an inequality to find all the possible numbers of balloons, x, that he can buy.

8.A quadratic graph y = ax² + bx + c has its turning point on the y-axis. Which statement about its roots must be true?

9.A mobile phone plan charges a fixed monthly fee plus an amount for each gigabyte of data used. The total cost £C for using g gigabytes in a month is given by C = 15 + 2g. What does the number 2 represent in this formula?

10.Simplify x + x + 4

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

12.A coach company charges a booking fee plus a price for each passenger. A booking for 1 passenger costs £9, for 2 passengers costs £15, for 3 passengers costs £21, and for 4 passengers costs £27. Work out an expression, in terms of n, for the cost in pounds of a booking for n passengers.

13.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.

14.Which expression means the same as 3 × a × b?

15.The triangular numbers begin 1, 3, 6, 10, 15, ... Work out the next term in the sequence.