Algebra worksheet — GCSE Higher

1.The diagram shows the graph of the cost, in pounds, of a taxi journey plotted against the distance travelled, in miles, for journeys of up to 4 miles. The same fixed charge and the same cost per mile apply to longer journeys. Work out the cost of a 6-mile journey.

2.Which expression is equivalent to 3(2x − 5) + 4x?

3.A rope of length L metres is cut into 6 equal pieces, and 4 metres is then removed from one piece. Write an expression, in metres, for the length of that piece after the cut.

4.How many turning points does the graph of y = x² − 7x + 10 have?

5.A circle has centre (0, 0) and radius 9. Work out the equation of the circle.

6.A speed-time graph for a car shows the speed increasing steadily from 5 m/s to 17 m/s over 6 seconds. Work out the acceleration of the car, in m/s².

7.A coach company charges a booking fee plus a price for each passenger. A booking for 1 passenger costs £9, for 2 passengers costs £15, for 3 passengers costs £21, and for 4 passengers costs £27. Work out an expression, in terms of n, for the cost in pounds of a booking for n passengers.

8.A ribbon of length L metres is cut into 5 equal pieces, and then 3 metres is removed from one piece. Write down an expression, in metres, for the length of that piece after 3 metres is removed.

9.A number, n, is tripled and then 4.5 is added. The result is 22.5. Form an equation and solve it to find n.

10.Simplify (2x² + 7x + 3) ÷ (x² − 9), giving your answer as a single fraction.

11.Factorise 3x² + 10x − 8.

12.A circle has centre (0, 0) and equation x² + y² = 100. Work out which one of these points lies on the circle.

13.Six years ago Harry was three times as old as his brother Leo. Harry is now 24 years old. Work out Leo's age now.

14.Solve x² − 8x + 3 = 0 by completing the square. Give your answers in surd form.

15.The first four terms of a sequence are 11, 18, 25, 32. Ravi thinks the nth term is 7n. Work out the correct expression for the nth term.