Algebra worksheet — GCSE Foundation

1.Jack is x years old. His brother Kwame is 3 years older than Jack. Write down an expression for Kwame's age.

2.The first five square numbers are 1, 4, 9, 16, 25. Write down the next square number in the sequence.

3.A ball is thrown in the air. Its height, h metres, above the ground after t seconds is given in this table: when t = 0, h = 0; when t = 1, h = 15; when t = 2, h = 20; when t = 3, h = 15; when t = 4, h = 0. Use the table to find the two times, in seconds, at which the ball is at ground level.

4.A straight line has gradient −2 and passes through the point (3, 1). Work out the equation of the line.

5.In a sequence, each term is half the term before it. The sequence begins 100, 50, 25. Write down the next term.

6.The point F has x-coordinate −1 and lies 6 units above the x-axis. Write down the coordinates of F.

7.Solve the inequality x − 10 < −3.

8.The cost, in pounds, of hiring a van for d days is given by the formula C = 25 + 18d. A customer's hire cost £133. Work out how many days, d, they hired the van for, by first rearranging the formula to make d the subject.

9.A taxi firm charges a fixed fee of £3.50 plus £2.20 per mile. Work out the total cost of a journey of 6 miles.

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

11.Work out the y-intercept of the graph of y = x² + 3x − 10.

12.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.

13.A lift has a weight limit: it must carry no more than 630 kg. Let w be the total weight, in kg, carried by the lift. Which inequality describes this?

14.The nth term of a sequence is 2n − 1. Work out the 6th term of the sequence.

15.Solve 3(2x − 1) = 27