Algebra worksheet — GCSE Higher

1.Work out the equation of the straight line that passes through (−2, 3) and (4, −9).

2.Which of these pairs of lines are perpendicular to each other?

3.A geometric sequence begins 80, 40, 20, 10, ... Work out the next term in the sequence.

4.A car is decelerating. The tangent to its velocity-time graph at t = 12 seconds passes through the points (8, 22) and (16, 6), where velocity is in m/s and time is in seconds. Work out the gradient of this tangent, in m/s².

5.There are 50 adults on a coach to the Lake District. Every adult is either a man or a woman. There are 10 more men than women. Work out the number of men.

6.Work out the equation of the straight line through the points (−2, 1) and (0, 7).

7.Write y = x² + 12x + 40 in the form (x + a)² + b, and hence write down the minimum value of y.

8.A box holds n pencils. A shop has 6 full boxes and 4 loose pencils. All of these pencils are shared equally between 2 classes. Write down the expression for the number of pencils each class receives.

9.Solve the simultaneous equations 5x − 2y = 16 and 3x + 2y = 16. Work out the value of x.

10.A car park charges by the hour. Parking for 1 hour costs £5, 2 hours costs £9, 3 hours costs £13 and 4 hours costs £17, with the cost increasing by the same amount for each extra hour. Work out an expression, in terms of n, for the cost, in pounds, of parking for n hours.

11.A rectangle has length (2x + 5) cm and width (x − 2) cm. Work out an expression, in terms of x, for the perimeter of the rectangle. Give your answer in its simplest form.

12.Using the table of values of f(x) (x = 0, 1, 2, 3 gives f(x) = 5, 8, 4, 1), work out the value of −f(x) when x = 1.

13.The simultaneous equations 2x + 3y = 12 and x − y = 1 are given. Work out the value of y.

14.The equation x² − 6x + k = 0 has exactly one solution. Work out the value of k.

15.Expand and simplify (2x − 1)(x + 5)(x − 2). Write down the coefficient of x in your answer.