Mathematical problem solvingAQA A-Level Maths: Mind map

Exam questions on Mathematical problem solving

1. A rectangular garden is fenced on three sides using 40 m of fencing, the fourth side being a wall. Each of the two sides perpendicular to the wall has length $x$ metres, and the area of the garden is $A\ \mathrm{m}^2$.
   State the values of $x$ for which the model is realistic, justifying your answer.2 marks
2. Firm A charges a fixed £3.50 plus £1.80 per mile for a taxi journey. Firm B charges a fixed £2.00 plus £2.20 per mile.
   A customer is making a 6-mile journey. Which firm should they choose, and by how much does it save them?2 marks
3. A cylindrical water tank has internal radius 1.5 m and internal height 2.0 m.
   Find the capacity of the tank in litres, to 3 significant figures. (1 m$^3$ = 1000 litres.)3 marks