Algebra worksheet — GCSE Higher

1.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.

2.A geometric sequence has first term 3 and common ratio 2. Work out the 5th term of the sequence.

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

4.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.

5.Expand and simplify 4(2x − 1) − 3(x + 2) − 5x

6.The graph of y = f(x) has a minimum turning point at (3, −5), crosses the x-axis at x = 1, and crosses the y-axis at (0, −2). Exactly one of these statements about the graph of y = −f(x + 2) is true. Which statement is true?

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

8.A sequence has nth term 3n + 4. Two terms are missing from the list of its first five terms: 7, 10, _, 16, _. Work out the missing 3rd and 5th terms added together.

9.A cafe sells coffees at £c each and pastries at £p each. Three coffees and two pastries cost £9.60. Two coffees and two pastries cost £7.60. Work out the price of one coffee.

10.f(x) = 2x + 1. Work out the value of x for which f⁻¹(x) = 5.

11.Solve the simultaneous equations x + y = 1 and 2x + y = 5.

12.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.

13.A rectangular lawn is 4 m longer than it is wide. Its area is 96 m². Work out the length of the lawn.

14.Solve x² + 7x = 0.

15.A straight line has equation y = 4 − 3x. Work out the gradient of the line.