Algebra worksheet — GCSE Higher

1.A ball is thrown in the air. Its height, h metres, above the ground after t seconds is given in this table: when t = 0, h = 0; when t = 1, h = 15; when t = 2, h = 20; when t = 3, h = 15; when t = 4, h = 0. Use the table to find the two times, in seconds, at which the ball is at ground level.

2.A tap's flow rate, in litres per minute, is plotted against time, in minutes, on a graph. What are the units of the area under this graph?

3.The first five terms of a quadratic sequence are 5, 8, 13, 20, 29. Work out the next term in the sequence.

4.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.

5.An exponential model has equation y = A × bˣ, where b > 1. Its graph passes through the points (1, 135) and (2, 405). Work out the value of A.

6.A square tile has an area of 144 cm². Work out the side length of the tile.

7.The graph of y = f(x) crosses the x-axis at x = −3 and x = 7, and crosses the y-axis at (0, 21). A second graph crosses the x-axis at x = −7 and x = 3, and crosses the y-axis at the same point, (0, 21). The second graph is y = g(x). Which of these could be the equation of g(x)?

8.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.

9.A point has coordinates (x, y). In which two quadrants is the product x × y positive?

10.The first five terms of a quadratic sequence are 2, 5, 10, 17, 26. Work out the next term in the sequence.

11.For 0 ≤ x ≤ 360, the equation sin x = 0.5 has two solutions. What are they?

12.The point (−4, 3) lies on the circle x² + y² = 25, which has centre (0, 0). Work out the equation of the tangent to the circle at (−4, 3), giving your answer in the form y = mx + c.

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

14.A straight line passes through the points (2, 7) and (5, 16). Work out the value of y when x = 0.

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