Algebra worksheet — GCSE Higher

1.The table shows the height, in metres, of a firework rocket at various times, in seconds, during its flight: 40 at t = 2, 54 at t = 3, and 60 at t = 4. Use the chord between t = 2 and t = 4 to estimate the gradient of the height-time graph at t = 3, stating the correct units.

2.The iterative formula xₙ₊₁ = 12 ÷ (xₙ + 2) is used repeatedly, starting from x₀ = 1. Work out the value that xₙ approaches, correct to 2 decimal places.

3.Make x the subject of the formula y = 5x + 3.

4.Line L has equation y = 3x − 2. Work out the gradient of a line perpendicular to L.

5.A taxi charges a £3 fixed fee plus £2 for each mile travelled. Write an expression, in pounds, for the total cost of a journey of n miles.

6.A straight line has gradient −2 and passes through the point (3, 1). Work out the equation of the line.

7.Make x the subject of the formula y = 4x − 3.

8.Write down the first four terms of the sequence with nth term 6n − 5.

9.The table shows some values of f(x): when x = 0, f(x) = 5; when x = 1, f(x) = 8; when x = 2, f(x) = 4; when x = 3, f(x) = 1. Work out the value of f(x − 1) when x = 2.

10.Which of these equations represents the graph of y = 2ˣ translated by 3 units in the positive y-direction?

11.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.

12.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.

13.Line L has equation y = 3x + 1. Which of these lines is perpendicular to L?

14.The numbers x and y satisfy x + y = 10 and xy = 21. Work out the pair of values.

15.The graph of y = f(x) has x-intercepts at x = −2 and x = 6 and crosses the y-axis at (0, −12). Work out the x-intercepts and the y-intercept of y = −f(x).