Algebra worksheet — GCSE Foundation

1.A box holds n pencils. A shop has 6 full boxes and 4 loose pencils. All of these pencils are shared equally between 2 classes. Write down the expression for the number of pencils each class receives.

2.There are 30 students in a Year 10 maths class. There are 2 more boys than girls. Work out the number of boys and the number of girls.

3.A fundraising chain letter starts with 3 people taking part in round 1. Each following round has 4 times as many people taking part as the round before. Work out the number of people taking part in round 4.

4.Solve the inequality 5 − x ≤ 2.

5.Which of these values of x is a solution of x² + 2x − 15 = 0?

6.Which expression means 'add 3 to n, then multiply the result by 4'?

7.The graph of y = x² − 2x − 8 crosses the x-axis at x = −2 and x = 4. Work out the x-coordinate of the turning point of the curve, using the symmetry of the graph.

8.Simplify (5x² + 3x − 2) − (2x² − x + 5)

9.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.

10.a = 2 and b = 5. Work out the value of ab².

11.A graph has equation y = 3x + 2. Which word or phrase best describes its shape?

12.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.

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

14.The first five terms of a sequence are 6, 10, 14, 18, 22. Work out an expression, in terms of n, for the nth term.

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