Secondary 3 G2 Mathematics Tutor Bukit Timah | Quadratic Equations in Word-Problem Modelling. Did you know? The quadratic equation is often the easy part; translating the story correctly is harder.
This Secondary 3 G2 Mathematics tutor guide for Bukit Timah families explains quadratic equations in word-problem modelling with worked examples, checks and realistic limits. Read the quick answer first, then use the relevant section to repair a specific misunderstanding.
Quick answer
In a rectangle problem, let x cm be the width. If length is x+3 cm and area is 40 cm², write x(x+3)=40 before expanding. x²+3x−40=0 factors to (x+8)(x−5)=0. The candidates are x=5 and x=−8. Width must be positive, so the physical answer is 5 cm, with length 8 cm.
Find the exact question
Define the unknown first · Solve the rectangle model · Check the story · Two consecutive integers · The negative root may be meaningful in another story · A right-triangle problem · Solve the triangle · A cost model · Interpret two valid roots · Common modelling errors
Define the unknown first
In a rectangle problem, let x cm be the width. If length is x+3 cm and area is 40 cm², write x(x+3)=40 before expanding.
Try a new example with changed values and explain why the method applies. Check the original conditions and units rather than relying only on a calculator result.
Solve the rectangle model
x²+3x−40=0 factors to (x+8)(x−5)=0. The candidates are x=5 and x=−8. Width must be positive, so the physical answer is 5 cm, with length 8 cm.
Try a new example with changed values and explain why the method applies. Check the original conditions and units rather than relying only on a calculator result.
Check the story
A rectangle 5 cm by 8 cm has area 40 cm² and length exceeds width by 3 cm. Checking the original constraints matters more than merely checking the polynomial.
Try a new example with changed values and explain why the method applies. Check the original conditions and units rather than relying only on a calculator result.
Two consecutive integers
If consecutive positive integers have product 72, let the smaller be n. Then n(n+1)=72, so n²+n−72=0=(n+9)(n−8). The positive pair is 8 and 9.
Try a new example with changed values and explain why the method applies. Check the original conditions and units rather than relying only on a calculator result.
The negative root may be meaningful in another story
If the problem instead asks for any two consecutive integers with product 72, −9 and −8 are also consecutive and multiply to 72. Context determines which roots to keep.
Try a new example with changed values and explain why the method applies. Check the original conditions and units rather than relying only on a calculator result.
A right-triangle problem
Suppose perpendicular legs measure x and x+7 cm and hypotenuse is 13 cm. Pythagoras gives x²+(x+7)²=169, or 2x²+14x−120=0.
Try a new example with changed values and explain why the method applies. Check the original conditions and units rather than relying only on a calculator result.
Solve the triangle
Divide by two: x²+7x−60=0=(x+12)(x−5). The positive solution x=5 gives legs 5 and 12, with hypotenuse 13.
Try a new example with changed values and explain why the method applies. Check the original conditions and units rather than relying only on a calculator result.
A cost model
Suppose x identical tickets each cost (20−x) dollars under a hypothetical pricing rule, and revenue is $96. Then x(20−x)=96, giving x²−20x+96=0.
Try a new example with changed values and explain why the method applies. Check the original conditions and units rather than relying only on a calculator result.
Interpret two valid roots
Factor (x−8)(x−12)=0. Both x=8 and x=12 produce $96: eight tickets at $12 or twelve at $8. A model can have two contextually valid answers.
Try a new example with changed values and explain why the method applies. Check the original conditions and units rather than relying only on a calculator result.
Common modelling errors
Students may reverse a ‘three more than’ relationship, forget brackets in an area formula, or reject a root without explaining why. Write the variable meaning and conditions at the beginning.
Try a new example with changed values and explain why the method applies. Check the original conditions and units rather than relying only on a calculator result.
A seven-day revision routine
Day 1: identify the key definition and the given quantities. Day 2: reproduce a worked example with reasons. Day 3: change the numbers. Day 4: solve an unlabelled problem. Day 5: diagnose the first error. Day 6: combine the idea with another topic. Day 7: retest independently after a delay.
Frequently asked questions
How should I start? Name the unknown and what the question actually asks. How can I verify the answer? Substitute it into the original information and check that all restrictions are met. Why can a correct-looking number be wrong? The model may have used the wrong reference, denominator or condition.
Official syllabus and tutorial context
Consult the 2027 SEC G2 Mathematics K210 syllabus for the exact assessment scope. The unchanged eduKateSG three-pupil Mathematics reference describes tutorials near Sixth Avenue. Confirm the current tutor, class fit, fees, venue and timetable directly.
Further Mathematics revision
Related resources: Quadratic Graphs, Standard Form and Accuracy and Probability Rules.