Algebra worksheet — GCSE Higher

1.A rectangle has area 24x + 18. Ffion factorises the area as 6(4x + 3). Work out the value of the area when x = 2, and decide whether 6 and (4x + 3) are correctly identified as factors of 24x + 18.

2.The graph of y = x² + 2x − 15 crosses the x-axis at two points. By factorising, work out the x-coordinates of these two points.

3.Solve 4(x − 3) = 2x + 6.

4.The expression 6n + 15 is written as 3(2n + 5). Which statement is correct?

5.The table shows some values of f(x): when x = 0, f(x) = 5; when x = 1, f(x) = 8; when x = 2, f(x) = 4; when x = 3, f(x) = 1. Work out the value of f(x − 1) when x = 2.

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

7.Which expression means 'triple c, then add double d'?

8.Two numbers have a sum of 45. The larger number is 9 more than the smaller number. Form an equation using n for the smaller number, and solve it to find the larger number.

9.Solve the inequality 6.3x + 1.8 ≤ 40. Hence write down the greatest number with exactly one decimal place that satisfies the inequality.

10.The area of a circle is given by the formula A = πr², where r is the radius. Rearrange the formula to make r the subject.

11.Line L has equation y = 3x − 2. Work out the gradient of a line perpendicular to L.

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

13.Work out the value of 5m² + 3m when m = −2.4

14.The braking distance of a car, in metres, is estimated using the formula d = 0.4v² + 6, where v is the speed in mph. A car travelling at 35 mph brakes. Work out the estimated braking distance.

15.A bath is filled with water; the graph of volume (litres) against time (minutes) is a curve, since the flow rate changes. The tangent to the curve at t = 10 minutes passes through the points (8, 130) and (12, 190), and the volume in the bath at t = 10 minutes is 160 litres. Use the gradient of this tangent to estimate the volume in the bath 5 minutes after t = 10 minutes.