Algebra worksheet — GCSE Higher

1.Solve 5(x + 3) = 40

2.Solve the inequality 3x + 6 ≤ 0.

3.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.

4.Work out the coordinates of the reflection of (6, −3) in the y-axis.

5.Solve (2x + 1)/3 = 5

6.Which expression means 'y squared, multiplied by 3'?

7.A company's cost, in £, for producing x items is shown on a graph. The tangent to the curve at x = 50 passes through (30, 400) and (70, 800). Interpret the gradient of this tangent in the context of the company's costs.

8.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.

9.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.

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

11.Tom is asked to classify the statement 5(2x − 3) = 10x − 15. Which statement about it is correct?

12.The graph of y = f(x) has a minimum point at (4, −1). Write down the coordinates of the corresponding turning point on the graph of y = −f(x).

13.The discriminant of a quadratic equation is greater than zero. Which statement about the solutions of that equation is correct?

14.The first five terms of a quadratic sequence are 4, 7, 12, 19, 28. Work out an expression, in terms of n, for the nth term.

15.x = 5. Work out the value of 3x² − 4.