Algebra worksheet — GCSE Higher

1.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.

2.A company's weekly profit, P thousand pounds, when it makes x thousand items is modelled by P = x² − 8x + 12, for x ≥ 0. Work out the values of x for which the company makes a loss.

3.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.

4.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.

5.Work out the smallest positive value of x, in degrees, for which y = tan x is undefined.

6.Meera writes the statement 3(x + 4) = 3x + 12. Which of these correctly describes what she has written, with a reason?

7.The tangent to a curve at the point (6, 1) has gradient −3. Work out the y-coordinate of the point where this tangent crosses the y-axis.

8.Harry will spend at most £150 on a party. The cake costs £60 and each helium balloon costs £3. Solve an inequality to find all the possible numbers of balloons, x, that he can buy.

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

10.A line has equation y = −4x + 1. Work out the equation of the line perpendicular to it that passes through the point (0, 3).

11.Make x the subject of the formula y = x/2 − 5.

12.A car park charges a £4 fixed fee plus £3 for each hour. Kofi has exactly £25 to spend on parking. Using the inequality 4 + 3h ≤ 25, work out the greatest number of whole hours, h, he can park for.

13.Four sequences are shown below. Sequence P: 3, 6, 12, 24, … Sequence Q: 1, 4, 9, 16, … Sequence R: 2, 4, 8, 14, … Sequence S: 5, 10, 15, 20, … Work out which of the sequences P, Q, R and S is geometric.

14.A car's journey is represented by a velocity-time graph. The total distance travelled, found from the area under the graph, is 350 metres, and the total time for the journey is 25 seconds. Work out the car's average speed for the whole journey, in m/s.

15.a = 2 and b = 5. Work out the value of a²b.