Algebra worksheet — GCSE Higher

1.Make x the subject of the formula y = (x − 4)/5.

2.A theatre's front row has 18 seats. Each row behind has 4 more seats than the row in front. Which row has exactly 62 seats?

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

4.Solve 3x + 14 = 8x − 6

5.The table shows the height, in metres, of a firework rocket at various times, in seconds, during its flight: 40 at t = 2, 54 at t = 3, and 60 at t = 4. Use the chord between t = 2 and t = 4 to estimate the gradient of the height-time graph at t = 3, stating the correct units.

6.A hiker's distance-time graph shows the following: he walks 5 km in the first 1 hour at a steady speed, rests for 1 hour, then walks a further 9 km in the next 2 hours, also at a steady speed. Work out his average speed for the whole journey, in km/h.

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

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

9.The point (4, 2) lies on the circle x² + y² = 20. Work out the equation of the tangent to the circle at (4, 2).

10.A quadratic graph has roots at x = −3 and x = 5, and it crosses the y-axis at (0, −15). Work out the equation of the curve in the form y = (x − a)(x − b).

11.For the graph of y = 1/x, where x cannot be zero, which of these statements is correct?

12.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.

13.(2x + 3)(x + a) ≡ 2x² + 11x + 12 is an identity. Work out the value of a.

14.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.

15.Simplify 5a/6 − a/3