Algebra worksheet — GCSE Foundation

1.Solve the simultaneous equations x + y = 1 and 2x + y = 5.

2.The first five cube numbers are 1, 8, 27, 64, 125. Write down the next cube number in the sequence.

3.A phone company works out a monthly bill, £B, using the formula B = 18 + 0.05t, where £18 is the fixed monthly charge and t is the number of extra text messages sent beyond the free allowance, each charged at 5p. Farida's bill for one month is £24.50. Work out the number of extra text messages, t, she sent.

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

5.Write down the expression that means the same as w ÷ 6.

6.The equation 3(2x − 1) = 4x + 9 is rearranged by expanding the brackets. Which of these is the correctly expanded equation?

7.A rectangle has length k cm and width 5 cm less than its length. Write down an expression for the width of the rectangle, in cm.

8.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.

9.A distance-time graph shows a car travelling at a constant speed, covering 90 km in 2 hours. Work out the car's speed in km/h.

10.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.

11.Oliver buys b pens. Each pen costs £2. Write down an expression for the total cost, in pounds.

12.Make x the subject of the formula y = 4x − 3.

13.a = 2 and b = 5. Work out the value of a²b.

14.A stack of firewood has 3 logs in the top layer. Each layer below has 4 more logs than the layer above it. Work out the number of logs in the 6th layer from the top.

15.Tom is asked to classify the statement 5(2x − 3) = 10x − 15. Which statement about it is correct?