Dennis's E-Math Paper 1: Ultimate Pre-Exam Strategy

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🗺️ BATTLEFIELD INTELLIGENCE: PAPER 1 TOPIC DISTRIBUTION

🔴 PRIMARY TARGETS (60-70% of marks)

1. Ratio & Percentage

in Context

2. Statistics & Probability

Data Analysis

3. Indices & Standard Form

Critical Weakness

4. Coordinate Geometry

Lines & Gradients

5. Mensuration

Volume & Area Ratios

6. Inequalities

Solving & Graphing

🔵 SECONDARY TARGETS (30-40% of marks)

7. Algebraic Manipulation

Foundational Skill

8. Quadratic Functions

Completing the Square

9. Geometric Proofs

Similarity & Congruence

⚠️ CRITICAL INJURIES IDENTIFIED: THE FATAL SEVEN

Topic	Hard Injury	Concrete Example	Type
Algebraic Manipulation Bedok View P2 Q1	Sign handling failure with negative brackets	−(3x + 5) = −3x + 5 ✓ −(3x + 5) = −3x − 5	P-Layer
Algebraic Manipulation Northbrooks P2 Q8	Cannot convert non-standard equations to quadratic form	Given: 2/x + 3/(x+1) = 5 Attempted to solve directly ✓ Multiply by LCD: x(x+1) first	C-Layer
Quadratic Functions Kranji P1 Q24	Sign errors when completing square with negative coefficient	Given: y = −x² + 6x − 5 −(x² + 6x) − 5 ✓ −(x² − 6x) − 5	P-Layer
Geometric Proofs Regent P1 Q3	Applying theorems without verifying conditions	Used Pythagoras without checking for right angle ✓ First verify: Is there a 90° angle?	C-Layer
Indices & Standard Form Northbrooks P2 Q4	Complete freeze with complex index expressions	Given: (p³q⁻²)² ÷ p⁻¹q³ Gave up immediately ✓ Apply 4-step SOP systematically	P/C-Layer
Coordinate Geometry Anglo-Chinese P2 Q3	Missing conceptual link: parallel → equal gradients	Line L₁: y = 3x + 2. Find L₂ parallel, through (1, 5) Didn't recognize m₁ = m₂ ✓ Immediately write m₂ = 3	C-Layer
Mensuration Northbrooks P1 Q21	Missing volume-length relationship	Similar cylinders, height ratio 2:3 Volume ratio = 2:3 ✓ Volume ratio = 2³:3³ = 8:27	C-Layer

🔥 EMERGENCY REPAIR #1: COMPLEX INDICES EXPRESSIONS

THE PROBLEM: Expressions like (p³q⁻²)² ÷ p⁻¹q³ cause instant cognitive overload → complete freeze

THE SOLUTION: MEMORIZE THIS 4-STEP SOP

THE INDICES SOP

STEP 1: Brackets First → (aᵐ)ⁿ = aᵐⁿ

STEP 2: Negatives to Positives → a⁻ⁿ = 1/aⁿ (move up/down)

STEP 3: Combine Same Bases → aᵐ × aⁿ = aᵐ⁺ⁿ; aᵐ ÷ aⁿ = aᵐ⁻ⁿ

STEP 4: Handle Coefficients Separately

🎯 GUIDED EXAMPLE: Simplify (p³q⁻²)² ÷ p⁻¹q³

Step 1 (Brackets): (p³q⁻²)² = p⁶q⁻⁴

Now we have: p⁶q⁻⁴ ÷ p⁻¹q³

Step 2 (Combine bases using aᵐ ÷ aⁿ = aᵐ⁻ⁿ):

For 'p': p⁶ ÷ p⁻¹ = p⁶⁻⁽⁻¹⁾ = p⁷
For 'q': q⁻⁴ ÷ q³ = q⁻⁴⁻³ = q⁻⁷

Result: p⁷q⁻⁷

Final Answer (Positive Index): p⁷/q⁷

📝 CLONE PRACTICE (Do These Now!)

(a⁴b⁻¹)³ ÷ (a⁻²b⁵)
√(9x⁶y⁻⁴) × (2x⁻¹y)²
(8m⁻⁶n³)^(1/3) ÷ (2m⁻³n)

Follow the SOP exactly. Get 3 consecutive successes!

🔥 EMERGENCY REPAIR #2: PARALLEL LINES = EQUAL GRADIENTS

THE PROBLEM: Dennis knows "parallel" and "equation of line" but cannot connect them

IF "Line A is PARALLEL to Line B"
THEN
Gradient of A = Gradient of B

THE 3-STEP PARALLEL LINE SOP

STEP 1: Find Gradient → Rearrange to y = mx + c, identify m

STEP 2: Copy Gradient → Because parallel, new line has same m

STEP 3: Find Intercept → Substitute point into y = mx + c, solve for c

🎯 GUIDED EXAMPLE

Given: Line L₁ has equation y = 3x + 2

Find: Line L₂ parallel to L₁, passing through (1, 5)

Step 1: Gradient of L₁ = 3

Step 2: Gradient of L₂ = 3 (parallel!)

Step 3: Substitute (1, 5): 5 = 3(1) + c → c = 2

Final Answer: y = 3x + 2

📝 REINFORCEMENT PRACTICE

Line L is parallel to y = 3x + 2 and passes through the points (1, 5) and (-1, k). Find k.
Are y = 2x + 1 and 4y = 8x + 10 parallel? Explain.

💊 THREE-THERAPY COMBAT PROTOCOL

🎯 THERAPY 1: MINIMIZE COGNITIVE LOAD

No deep thinking. Only memorized trigger-action pairs.

WHEN YOU SEE

IMMEDIATELY DO

−(A + B)

Write −A − B

Both x² and x

Move all to one side → = 0

y = −x² + ...

Factor negative first

"parallel"

Write m₁ = m₂

Similar shapes

Write V₁/V₂ = (L₁/L₂)³

Shaded segment

Area = Sector − Triangle

🔄 THERAPY 2: BEHAVIORIST CONDITIONING

Install correct behaviors through physical repetition.

DAY-BEFORE ACTIONS:

SOP Read-Aloud (30 min): Read each topic SOP aloud once
Error Re-runs: Redo every question from Fatal Seven table
Flashcard Drill: 10 random cards → 2-second recall each

🔗 THERAPY 3: STRENGTHEN CONNECTIONS

Build concept ↔ concept and concept ↔ procedure links.

Length (1-D) Power 1

Example: 2:4 = 1:2

Area (2-D) Power 2

Example: 2²:4² = 4:16

Volume (3-D) Power 3

Example: 2³:4³ = 8:64

✅ THE FATAL SEVEN: PRE-EXAM CHECKLIST

Before entering the exam hall, verify you can recall each of these instantly:

Algebra: −(A + B) = −A − B (change ALL signs)

Quadratic Standard Form: Move everything to one side → = 0

Completing Square (negative a): Factor out negative FIRST

Geometry: Verify right angle BEFORE using Pythagoras

Indices: 4-step SOP (Brackets → Negatives → Combine → Coefficients)

Parallel Lines: m₁ = m₂ instantly when you see "parallel"

Volume Ratio: V₁/V₂ = (L₁/L₂)³ and Segment = Sector − Triangle

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⚡ IF-THEN TRIGGER LIST: INSTANT RESPONSES

🔴 IF: Problem says "parallel"

THEN: Find corresponding/alternate angles AND set gradients equal (m₁ = m₂)

🟢 IF: Asked for "shortest distance"

THEN: Consider using Area = ½ × base × height to find perpendicular distance

The Logic: The "shortest distance" from a point to a line is always the perpendicular height (h). If you can see the problem as a triangle, you can use its area to find this height.

Example: In ΔABC, if you know the Area and the base AB, you can find the height from C to AB using:
h = (2 × Area) / base.

🟣 IF: Equation contains fractions

THEN: Multiply both sides by LCD (Lowest Common Denominator) immediately

🟠 IF: See both x² and x terms

THEN: Move everything to one side, set = 0, then solve quadratic

🔵 IF: Similar shapes/solids problem

THEN: Write ratios immediately: Length (k), Area (k²), Volume (k³)

Quantity	Formula	Rule	Example (2:4=1:2)
Length (1-D)	(L₁/L₂ = k)	Ratio in 1 power	1 : 2
Area (2-D)	(A₁/A₂ = k²)	Ratio in square	1²:2² = 1:4
Volume (3-D)	(V₁/V₂ = k³)	Ratio in cube	1³:2³ = 1:8

🟢 IF: Asked to "prove" or "show that"

THEN: Work backwards from the answer, but write forwards in your solution

Your Thought Process (Work Backwards)

Goal: Prove ΔABC ~ ΔADE.
Need: Two pairs of equal angles.
Given: DE || BC.
So: ∠ADE = ∠ABC (Found one!).
What else? Ah, ∠A is common. Done!

Your Written Solution (Write Forwards)

∠BAC = ∠DAE (Common Angle)
∠ABC = ∠ADE (Corr. Angles, DE || BC)
∴ ΔABC ~ ΔADE (AA Similarity)

🎖️ FINAL COMBAT BRIEFING

"DENNIS,"

Paper 1 is not about deep thinking.
It's about speed, accuracy, and following SOPs.

YOUR MISSION IS SIMPLE:

1. IDENTIFY the topic of each question

2. ACTIVATE the correct SOP from memory

3. EXECUTE flawlessly — extreme care on negative signs and brackets

You've trained for this.
Trust your preparation.
Execute with confidence.

⚔️ GOOD LUCK. YOU'VE GOT THIS. ⚔️

🎯 DENNIS'S E-MATH PAPER 1

ULTIMATE PRE-EXAM COMBAT STRATEGY