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

3.Expand and simplify 2(a + 6) − 2(a − 7)

4.Meera writes the statement 3(x + 4) = 3x + 12. Which of these correctly describes what she has written, with a reason?

5.A plumber charges a call-out fee of £30 plus £25 for each hour worked. The total bill for a job was £130. Work out how many hours the plumber worked.

6.Which of these statements is an equation with exactly one solution?

7.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).

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

9.A water butt holds 200 litres and is being drained at a steady 8 litres per minute. Write down the function for the amount of water y, in litres, left after x minutes.

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

11.Solve 3(2x − 1) = 27

12.A coastguard radar at the origin covers a circular region modelled by x² + y² = 400, where each unit represents 1 kilometre. A boat travels along the straight line that touches the boundary of the region at the point (12, 16). Work out the equation of the line the boat travels along.

13.A circle has centre (0, 0) and equation x² + y² = 100. Work out which one of these points lies on the circle.

14.The graph of y = f(x) has a maximum turning point at (−1, 6). Write down the coordinates of the maximum turning point of the graph of y = f(x − 3).

15.A circular pond has equation x² + y² = 20, with lengths in metres from the centre of the garden. A straight path runs along the line y = 2x, entering the pond and leaving it again. Work out the coordinates of the two points where the path meets the edge of the pond.