Algebra worksheet — GCSE Foundation

1.Here are the first five terms of an arithmetic sequence: 4, 7, 10, 13, 16. Work out the 9th term.

2.Solve 5x − 9 = 16

3.A printer starts a job with 480 sheets of paper loaded and prints at a steady rate. The number of sheets left, S, after t minutes is given by S = 480 − 24t. Work out how many minutes it takes for the paper to run out completely.

4.A vertical line passes through the point (4, 7). Write down the equation of this line.

5.The line y = 3x + 6 meets the x-axis at one point. Work out the coordinates of that point.

6.Two brothers have ages that add up to 30. The elder brother is 6 years older than the younger brother. Work out the age of the younger brother.

7.Work out the value of a² − 2b when a = −3 and b = 4.

8.A candle is 30 cm tall and burns down at a steady rate of 1 cm per hour. Write down the function for the height of the candle y, in centimetres, after x hours.

9.Which expression means the same as a × a × a?

10.A sequence has the position-to-term rule 5n − 2, where n is the position number. Which of these is a term in the sequence?

11.A plumber charges a £40 call-out fee plus £25 for each hour worked. The total charge, £C, for a job lasting h hours is given by C = 40 + 25h. Work out the charge for a job lasting 3 hours, and name what kind of statement C = 40 + 25h is.

12.Which of these is a formula, rather than an expression, an equation, or an identity?

13.A caterer uses the formula C = 6p + 20 to work out the total cost, £C, of a buffet for p people, where £20 covers fixed costs. A customer is charged £92. Work out how many people, p, the buffet was for.

14.The first five terms of a quadratic sequence are 5, 8, 13, 20, 29. Work out the next term in the sequence.

15.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.