Algebra worksheet — GCSE Higher

1.To solve 5x − 4 = 2x + 8, Chloe's working is shown. Line 1: 5x − 4 = 2x + 8. Line 2: 3x − 4 = 8. Line 3: 3x = 4. Line 4: x = 4/3. Chloe has made a mistake in her working. Which line contains the mistake?

2.A colony of bacteria doubles in number every hour. At 9am there are 5 bacteria in the colony. Work out how many bacteria there will be at 12 noon.

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

4.By completing the square, find the turning point of the curve y = x² + 8x − 3.

5.A triangle has vertices at (1, 1), (1, 5) and (6, 1). Work out the area of the triangle.

6.Expand and simplify (x − 3)²

7.Write down the first four terms of the sequence with nth term 6n − 5.

8.A van's value depreciates by 18% each year. After 2 years it is worth £5,379.20. Work out its value when it was new, correct to the nearest pound.

9.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.

10.The height, h metres, of a ball t seconds after a stopwatch is started follows h = (t − 1)(5 − t) for 1 ≤ t ≤ 5, where h = 0 means the ball is at ground level. Work out the two times at which the ball is at ground level.

11.A number machine multiplies its input by 2 and then subtracts 5. Work out the output when the input is 6.

12.A cycle route is 84 km long. Freya sets off along it at a steady 14 km/h. Write down the function for the distance y, in kilometres, that is still to be cycled after x hours.

13.Work out the coordinates of the midpoint of the line segment joining (−3, 5) and (7, 9).

14.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.

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