Forming equations from contextIB MYP Maths Standard: Revision notes

Section 1

From words to algebra

Start by choosing a letter for the unknown and writing down what it stands for, with units, such as $m$ = number of minutes. Then translate the words: 'more than' and 'plus' mean $+$ ; 'less than' and 'minus' mean $-$ ; 'twice' means $\times2$ ; 'per' means multiplied by the rate; 'total' usually means add. A fixed charge plus a charge per unit gives a formula such as $C=12+0.05m$ .

Key termsunknownfixed chargerate

Exam tip

Write 'Let $m$ = number of minutes' before you start. It stops you mixing up what the letters mean.

Section 2

Forming and solving an equation

Follow five steps: define the unknown, form an equation, solve it, check it in the original problem, and answer in a sentence with units. Example: a bill of SGD 30.50 on the plan $C=12+0.05m$ gives $12+0.05m=30.5$ , so $0.05m=18.5$ and $m=370$ minutes. Check: $12+0.05\times370=12+18.5=30.5$ .

Key termsform an equationcheck

Common mistake

Giving a bare number such as $370$ with no units or sentence. Say '370 minutes'.

Section 3

Geometric situations

For shapes, write each side as an expression and use a rule you know. A rectangle's perimeter is $2(\text{length}+\text{width})$ . For a rectangle with sides $(2x+3)$ and $(x-1)$ and perimeter 46: $2(3x+2)=46$ , so $6x+4=46$ , $x=7$ . The sides are 17 cm and 6 cm. Angles in a triangle add up to $180^\circ$ , and angles on a straight line add up to $180^\circ$ , so these give equations too.

Key termsperimeter

Common mistake

Using the area formula when the question gives the perimeter, or forgetting to double the sum of length and width.

Section 4

Inequalities from context

Some situations have a limit rather than an exact value. Translate the wording: 'at most' and 'no more than' mean $\le$ ; 'at least' means $\ge$ ; 'fewer than' means $<$ ; 'more than' means $>$ . Example: a bill of at most SGD 20 on $12+0.05m$ gives $12+0.05m\le20$ , so $m\le160$ . If the unknown must be a whole number, check which whole numbers fit. If you multiply or divide by a negative number, reverse the sign.

Key termsat mostat least

Exam tip

Test one value inside your solution set and one outside to check the direction of the sign.

Section 5

Interpreting the answer (criterion D)

Always say what your answer means in the real situation. Check that it is reasonable: a length cannot be negative, and a number of people must be a whole number. If the equation gives a value that cannot happen, reject it and say why. To compare two options, find where they are equal (the break-even point) and then test either side of it. For coach hire with $360+12s$ and $20s$ , the break-even is $s=45$ , so for 38 students the cheaper company is the one with no fixed charge. Models are simplifications, so mention what they ignore, such as extra fees.

Key termsinterpretreasonablebreak-even

Common mistake

Stopping at $x=45$ without stating which option is cheaper for the number of students in the question.

That's the notes covered.

Carry on to the next subtopic.

Exam questions on Forming equations from context

A mobile phone plan in Singapore costs a fixed charge of 12 Singapore dollars (SGD) per month plus SGD 0.05 for each minute of calls. The monthly bill is $C$ dollars when $m$ minutes of calls are made.
Maria wants her monthly bill to be at most SGD 20. Form and solve an inequality to find the greatest number of minutes of calls she can make.2 marks
A rectangle has length $(2x+3)$ cm and width $(x-1)$ cm. Its perimeter is 46 cm.
Hence find the area of the rectangle.2 marks
A school is hiring a coach for a trip. Company A charges AED 360 plus AED 12 for each student. Company B charges AED 20 for each student and has no fixed charge.
Form and solve an equation to find the number of students, $s$ , for which both companies charge the same amount.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).