Algebra worksheet — GCSE Higher

1.Expand and simplify 2(a + 6) − 2(a − 7)

2.By completing the square, find the turning point of the curve y = x² − 10x + 30.

3.A candidate solves the simultaneous equations y = x − 2 and y = x² − 4x + 2 by substitution. They write: "x − 2 = x² − 4x + 2, so x² − 3x + 4 = 0." Which of these is a correct comment on the candidate's working?

4.Write down the expression that means the same as m² × m × 3.

5.Which expression is equivalent to 3(x + 4) − 2(x − 1)?

6.A ramp rises 3 m over a horizontal distance of 12 m. Work out the gradient of the ramp.

7.A circle has centre (0, 0) and equation x² + y² = 50. Work out the radius of the circle, giving your answer as a surd in its simplest form.

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

9.Solve 4(x − 3) = 2x + 6.

10.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?

11.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.

12.Matchsticks are laid out as a row of squares, with each new square sharing a side with the square before it. The first square uses 4 matchsticks and every extra square uses 3 more. Work out how many matchsticks a row of 4 squares uses.

13.A walker's distance-time graph is described as follows: she walks 3 km in the first 15 minutes at a steady speed, rests for 10 minutes, then walks a further 3 km in the next 20 minutes, also at a steady speed. Work out her speed, in km/h, during the first 15 minutes.

14.A theatre has rows of seats arranged so that row 1 has 12 seats, row 2 has 17 seats, row 3 has 22 seats and row 4 has 27 seats, with each row having 5 more seats than the row before. Work out an expression, in terms of n, for the number of seats in row n.

15.Solve (2x + 1)/3 = 5