Algebra worksheet — GCSE Higher

1.Solve the inequality 2(x − 1) ≤ 8.

2.A tap's flow rate, in litres per minute, is plotted against time, in minutes, on a graph. What are the units of the area under this graph?

3.y = 5 − 2x. Work out the value of x when y = 11.

4.Solve the inequality 9 − 2x ≥ 1.

5.Work out the value of 2x² when x = −3

6.A coach company charges a booking fee plus a price for each passenger. A booking for 1 passenger costs £9, for 2 passengers costs £15, for 3 passengers costs £21, and for 4 passengers costs £27. Work out an expression, in terms of n, for the cost in pounds of a booking for n passengers.

7.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.

8.The nth term of a geometric sequence is given by aₙ = 3 × 2ⁿ⁻¹. Work out the position of the first term that is greater than 1,000.

9.A plumber charges a call-out fee plus an hourly rate for a job. The total cost, £C, for a job lasting h hours is given by the formula C = 40 + 25h. What does the number 40 represent in this formula?

10.The equation 3(2x − 1) = 4x + 9 is rearranged by expanding the brackets. Which of these is the correctly expanded equation?

11.Show that the equation x³ − x − 3 = 0 has a solution between x = 1 and x = 2, by working out f(1) and f(2), where f(x) = x³ − x − 3.

12.To rearrange the formula y = 3x − 8 to make x the subject, Priya writes: 'Add 8 to both sides to get y + 8 = 3x, then divide both sides by 3 to get x = y + 8 ÷ 3.' Work out the correct expression for x.

13.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.

14.Make x the subject of the formula y = 2x − 9.

15.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.