ECAT Prep Cheatsheet — BitWithBite

⚙ ECAT

ECAT Prep

Mathematics, Physics, Chemistry, and English for ECAT/NTS Engineering entry test — high-yield preparation guide.

📖 5 sections

⏰ 15 min read

✅ Quizzes included

01Mathematics High-Yield▼

ECATMath key topics

ALGEBRA:
Quadratic: x=(-b+-sqrt(b^2-4ac))/2a
Log laws: log(ab)=log a+log b, log(a/b)=log a-log b, log a^n=n log a
Sequences: arithmetic an=a1+(n-1)d, geometric an=a1*r^(n-1)

TRIGONOMETRY:
sin^2+cos^2=1, 1+tan^2=sec^2, 1+cot^2=csc^2
Double angle: sin2A=2sinAcosA, cos2A=cos^2A-sin^2A
Sine rule: a/sinA=b/sinB, Cosine rule: a^2=b^2+c^2-2bc*cosA

CALCULUS:
Derivatives: d/dx[x^n]=nx^(n-1), d/dx[sin x]=cos x, d/dx[e^x]=e^x
Integrals: integral[x^n dx]=x^(n+1)/(n+1)+C

COMBINATORICS:
Permutations: P(n,r)=n!/(n-r)!
Combinations: C(n,r)=n!/(r!(n-r)!)
Binomial: (a+b)^n=sum C(n,k)*a^(n-k)*b^k

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ECAT Math: Practice calculation speed. Many marks lost to arithmetic errors. Always double-check your substitution into formulas.

02Physics High-Yield▼

ECATPhysics formulas

MECHANICS:
SUVAT: v=u+at, s=ut+0.5at^2, v^2=u^2+2as
Projectile: Range=u^2*sin2theta/g, Max height=u^2*sin^2theta/2g
Circular: a=v^2/r=omega^2*r, F=mv^2/r
Gravitation: F=Gm1m2/r^2, g=GM/r^2

THERMODYNAMICS:
Ideal gas: PV=nRT
First law: delta U = Q - W
Carnot efficiency: eta = 1-T2/T1

WAVES & OPTICS:
v=f*lambda, Doppler: f_obs=f*(v+-v_obs)/(v-+v_src)
Snell: n1*sin(theta1)=n2*sin(theta2), n=c/v
Lens: 1/f=1/v-1/u, m=v/u

ELECTRICITY:
Coulomb: F=kq1q2/r^2, E=kq/r^2
Capacitor: C=Q/V, E=0.5CV^2, series/parallel rules
Magnetic: F=qvB*sin(theta), F=BIL*sin(theta)

03Chemistry High-Yield▼

Topic	Key points
Moles	n=m/Mr, n=cV, n=PV/RT
Titration	n(acid)Va = n(base)Vb at equivalence point
Electrochemistry	Cathode=reduction, Anode=oxidation (CORA: Cathode Oxidation Reduction Anode — WRONG: its reverse!)
Rates	rate=k[A]^m[B]^n. Arrhenius: k=Ae^(-Ea/RT)
Thermodynamics	delta G=delta H - T*delta S. Spontaneous if G<0
Organic	Alkyl halides: SN1 (tertiary), SN2 (primary). Elimination vs substitution.

ECATElectrochemistry

MNEMONIC: LEO the lion says GER
Loss of Electrons = Oxidation
Gain of Electrons = Reduction

Electrolytic cell vs Galvanic cell:
Galvanic (battery): spontaneous, produces electricity
Electrolytic: non-spontaneous, requires external electricity

Anode: OXIDATION (both cells)
Cathode: REDUCTION (both cells)

Nernst equation: E = E0 - (RT/nF)*ln(Q)
At 25C: E = E0 - (0.0592/n)*log(Q)

❓ Quiz

In an electrolytic cell, where does reduction occur?

Reduction (gain of electrons) always occurs at the cathode in both electrolytic and galvanic cells. CRED: Cathode Reduction, Electrolytic/galvanic Distinction doesn't matter for cathode=reduction.

04English (ECAT/NTS)▼

Section	Focus areas
Vocabulary	Synonyms, antonyms, contextual meaning, analogies
Grammar	Tenses, articles, prepositions, conjunctions, subject-verb agreement
Reading	Main idea, inference, tone, purpose, detail questions
Sentence completion	Choose word that fits grammar AND meaning
Error identification	Find the grammatically incorrect part of a sentence

ECATEnglish quick tricks

ANALOGIES (hot::cold = teacher::student):
Identify the relationship: opposite, part-whole, cause-effect,
function, degree, type-of

SYNONYMS quick list:
Ambiguous=unclear, Benevolent=kind, Candid=honest,
Daunt=intimidate, Ephemeral=short-lived, Fastidious=meticulous,
Garner=gather, Harbinger=sign, Impede=block, Judicious=wise

COMMON PREPOSITIONS:
account FOR, accuse OF, agree WITH/TO, apply FOR,
capable OF, consist OF, depend ON, differ FROM,
indulge IN, interfere WITH, object TO, result IN

05Past Paper MCQ Patterns▼

Maths frequency

Calculus 20%, Algebra 20%, Trigonometry 20%, Coordinate Geometry 15%, Statistics 10%, Others 15%

Physics frequency

Mechanics 30%, Electricity 25%, Waves 20%, Thermodynamics 15%, Modern 10%

Chemistry frequency

Organic 25%, Physical 30%, Inorganic 20%, Analytical 15%, Biochemistry 10%

English frequency

Vocabulary 40%, Grammar 30%, Comprehension 30%

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Download and solve 10 years of past papers. ECAT/NTS repeat question patterns. You will see the same question types repeatedly. Speed matters — 100 questions in 120 minutes.

ECAT10-day revision sprint

Days 1-2: Mathematics — formulas + 50 MCQs each day
Days 3-4: Physics — SUVAT + Electricity + 50 MCQs
Days 5-6: Chemistry — Organic + Electrochemistry + 50 MCQs
Day 7: English — vocabulary list + grammar rules
Days 8-9: Full past papers (timed)
Day 10: Light revision + rest + early sleep