Algebra worksheet — GCSE Foundation

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

2.A sequence starts at 2. Each term after that is found using the rule "double the previous term, then add 1". Work out the 4th term of the sequence.

3.Write down the gradient of the line with equation y = 7x − 2.

4.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.

5.A ball's height, h metres, t seconds after being thrown follows h = (t − 1)(9 − t). Given that the ball is at ground level at t = 1 and t = 9, work out at what time t the ball reaches its maximum height, using symmetry.

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

7.A pizza shop charges a fixed delivery fee of £3, plus £9 for each pizza ordered. Write down the function for the total cost y, in pounds, of ordering x pizzas.

8.Work out the value of 5y + 9 when y = 0

9.Simplify 2a + 3b − a + 2b − b

10.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.

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

12.A number machine multiplies its input by 3. The output is 15. Work out the input.

13.Solve 6x − 5 = 3x + 13.

14.Leo is three times as old as his brother. His brother is x years old. Write down an expression for Leo's age.

15.The simultaneous equations x = 2 and x + y = 9 are given. Work out the value of y.