What do you do if the interpreted result is unreasonable?

Repeat the cycle with a better specification, more information or corrected working.

What is a constraint?

A condition that limits the variables, such as a fixed length of fencing.

To extract and organise the information and form equations.

200 at x=10, from -2(x-10)^2+200.

Why check roots of a quadratic against the context?

A root may be negative or outside the realistic domain.

How do you check an answer is reasonable?

Estimate with numbers rounded to 1 significant figure.

Why quote answers to 3 s.f.?

Inputs are rarely exact, so extra digits would suggest false accuracy.

What is an unstructured problem?

One that gives no steps, so you plan the method yourself.

What should a final answer include?

A statement in the context of the problem, with units.

Mathematical problem solvingAQA A-Level Maths: Flashcards

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What are the four stages of the problem solving cycle?

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What are the four stages of the problem solving cycle?: Specify the problem, collect information, process and represent, interpret the results.
What do you do if the interpreted result is unreasonable?: Repeat the cycle with a better specification, more information or corrected working.
What is a constraint?: A condition that limits the variables, such as a fixed length of fencing.
Why draw a diagram?: To extract and organise the information and form equations.
Garden with 40 m fencing on three sides: area?: $A=x(40-2x)=40x-2x^2$
Maximum of $40x-2x^2$ ?: $200$ at $x=10$ , from $-2(x-10)^2+200$ .
Why check roots of a quadratic against the context?: A root may be negative or outside the realistic domain.
How do you check an answer is reasonable?: Estimate with numbers rounded to 1 significant figure.
Cylinder volume formula?: $\pi r^2h$
Why quote answers to 3 s.f.?: Inputs are rarely exact, so extra digits would suggest false accuracy.
What is an unstructured problem?: One that gives no steps, so you plan the method yourself.
What should a final answer include?: A statement in the context of the problem, with units.

Exam questions on Mathematical problem solving

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
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
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

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).