Algebra worksheet — GCSE Higher

1.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.

2.Describe the single transformation that maps the graph of y = x² onto the graph of y = x² + 3.

3.Write down the expression that means 5 more than half of n.

4.A tap fills a tank at a varying rate. A graph shows the rate of flow, in litres per minute, against time, in minutes. What does the area under this graph represent?

5.Ethan is 10 years old and his father is 40 years old. Work out how many years ago Ethan's father was seven times as old as Ethan.

6.The first four terms of a sequence are 9, 14, 19, 24. Work out an expression, in terms of n, for the nth term.

7.Which expression is equivalent to 7x − 3(2x − 6)?

8.The nth term of a sequence is 4n − 3. Work out the 7th term of the sequence.

9.Solve x² − 5x + 6 = 0 by factorising.

10.A packet contains s sweets. The sweets are shared equally between f friends. Write an expression for the number of sweets each friend receives.

11.p = 4. Work out the value of 2p³.

12.Factorise fully 5x + 5y − 5

13.A rule turns each input into an output. An input of 0 gives an output of −1, an input of 1 gives an output of 1, and an input of 2 gives an output of 3. Work out the rule, writing the input as x and the output as y.

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

15.A phone company works out a monthly bill, £B, using the formula B = 18 + 0.05t, where £18 is the fixed monthly charge and t is the number of extra text messages sent beyond the free allowance, each charged at 5p. Farida's bill for one month is £24.50. Work out the number of extra text messages, t, she sent.