Algebra worksheet — GCSE Foundation

1.The braking distance of a car, in metres, is estimated using the formula d = 0.4v² + 6, where v is the speed in mph. A car travelling at 35 mph brakes. Work out the estimated braking distance.

2.A tree is 2 metres tall. Each year its height increases by 10% of its height at the start of that year. Work out the height of the tree after 3 years, giving your answer to 1 decimal place.

3.Which expression means the same as 3 × a × b?

4.Harry is 14 years old and Mia is 8 years old. Will Harry ever be exactly twice as old as Mia? Give a reason for your answer.

5.A person's body mass index is given by the formula B = m ÷ h², where m is the mass in kg and h is the height in metres. Work out B, to 1 decimal place, when m = 68 and h = 1.6.

6.Solve the inequality 2(3x − 1) ≥ 4x + 8.

7.Look at the statement 2x + 5 = 17. Considering whether it is an expression, an equation, a formula, or an identity, which classification is correct?

8.A colony of bacteria doubles in number every hour. At 9am there are 5 bacteria in the colony. Work out how many bacteria there will be at 12 noon.

9.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.

10.A taxi company charges a £2.50 booking fee plus £1.80 per mile. A journey costs £15.10 in total. Work out the number of miles travelled.

11.Kai writes the expression 8 − 3x + 5x² and says it has three terms. Ryan says it only has two terms because a number on its own is not a term. Work out the correct number of terms in the expression.

12.A mobile phone tariff charges a fixed £15 plus 20p for every minute of calls made, so the total monthly charge, £C, for m minutes of calls is given by C = 15 + 0.2m. In a month where Ali's charge was £46.60, work out how many minutes of calls he made.

13.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.

14.A regular hexagon has sides of length (x + 2) cm. Write down an expression, in terms of x, for the perimeter of the hexagon.

15.The graph of y = x² − 2x − 8 takes these values: when x = −2, y = 0; when x = −1, y = −5; when x = 0, y = −8; when x = 3, y = −5; when x = 4, y = 0. Use these values to write down the two solutions of x² − 2x − 8 = 0.