DSE Maths: Quadratic Equations — Tutor Lesson Plan (factorising, formula, discriminant)

2026-10-27

Tutor lesson-prep guides · Secondary maths

Most students only memorise the formula. Build the zero-product idea first, then the formula covers the cases that do not factorise.

Objectives — the student can solve by factorising, use the quadratic formula for the general case, and use the discriminant to describe the roots.

01 Prerequisites (3-minute check)

If any of these fails, fix it before the lesson starts.

Skill	Quick check	Pass mark
Expanding	Expand (x−2)(x−3)	x² − 5x + 6
Linear equations	Solve 3x − 7 = 8	x = 5
Surds	Simplify √48	4√3

02 Lesson flow (60 minutes)

Time	Stage	Tutor does	Student does
0-8 min	Zero product	When is x²−5x+6 zero?	x = 2 or 3
8-22 min	Factorising	Cross-multiplication method	Three alone
22-38 min	Formula	2x²+3x−2 = 0	Two alone
38-50 min	Discriminant	Δ > 0, = 0, < 0	Classify five
50-56 min	Applications	Area and number problems	Set up and solve
56-60 min	Exit check	Three questions marked at once	Finish alone

03 Teaching script (read it out)

Scene 1: Roots make the product zero

x² − 5x + 6 = (x−2)(x−3). A product is zero when a factor is zero, so x = 2 or x = 3.
Everything in this unit rests on that sentence.

Student repeats: product zero, so each factor may be zero.

Scene 2: The formula handles what will not factorise

For ax² + bx + c = 0, x = (−b ± √(b²−4ac)) / 2a.
With 2x² + 3x − 2: a = 2, b = 3, c = −2, giving (−3 ± 5)/4, so x = 1/2 or −2.
Write a, b and c down before substituting.

Warn: when c is negative, take the sign with it.

Scene 3: The discriminant describes the roots

Δ = b² − 4ac. Positive: two distinct real roots. Zero: a repeated root. Negative: no real roots.
“Find k so that the equation has two distinct real roots” means solve Δ > 0.

Student classifies three equations.

04 Question types and worked steps

Type	Example	Steps	Answer
Factorising	x² − 5x + 6 = 0	(x−2)(x−3) = 0	x = 2 or 3
Formula	2x² + 3x − 2 = 0	(−3 ± 5)/4	x = 1/2 or −2
Discriminant	x² + 2x + 5 = 0	Δ = 4 − 20 = −16	No real roots
Unknown coefficient	x² + kx + 4 = 0 has a double root	k² − 16 = 0	k = ±4

Sanity check (teach this): Substitute the roots back: they must satisfy the equation. A wrong Δ is usually a sign error in b² or 4ac.

05 Independent practice (3 questions)

Question	Answer	What to watch
x² − 7x + 12 = 0	x = 3 or 4	Factorising first
x² + x − 1 = 0	x = (−1 ± √5)/2	Formula and surd form
Roots of x² + 4x + 9 = 0	None, since Δ < 0	Sign of Δ

06 Common mistakes and what to say

Mistake	Student writes	Say this
Only one root	x = 2	Quadratics usually have two roots; give both.
Sign of c lost	treating −2 as 2	Write a, b, c with signs first.
Discriminant reversed	Δ < 0 said to give two roots	Negative Δ means no real roots.
No check	stops at the answer	Substitute back.

07 Homework (paper, section and question numbers)

Secondary chapter index — Use the three questions on this page

08 Exit check (last 5 minutes)

Question	Answer	Decision
Roots of x²−5x+6 = 0	2 and 3	All right: move to functions
What does Δ < 0 mean?	No real roots	One wrong: re-teach the discriminant
Roots of 2x²+3x−2 = 0	1/2 and −2	Two wrong: repeat scene 2

09 Tutor FAQ

Teaching completing the square?

Recognise only; DSE solving relies on factorising and the formula.

Calculator allowed?

For checking yes, but write a, b, c by hand once.

What applications appear?

Area problems, consecutive integers, sum and product of two numbers.

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A TutorZone lesson-prep guide. Written by the TutorZone team; questions and lesson flow are original and are not taken from any school or publisher material.