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Junior College

 

PURE MATH

 

Functions

 

  Exam Questions

  Inverse Function and Composite Function

 

Graph Sketching

 

  Basic Questions

  Asymptotes

 

Conics, Circles, Ellipses, Hyperbola

 

  Basic Questions

  Circle. Standard Form. Midpoint. Y Coordinate of Center

 

Inequalities

  

  Practice Questions

  Graphical Solution to inequalities

  Modulus. Inequality. Algebraic Method

  Positive value of k that gives exactly 2 real roots  

  Exam Questions

  Inequalities with numerator always positive

  Replacing x

  Discriminant, no. of real roots

 

Sequences, Recurrence Relations

 

  Practice Questions

  Recurrence Relation and Inequality

  Recurrence Relation and inequality (2)

  Recurrence Relation, Uk in terms of Un, factorial

  Forward & Backward Substitution to find Un

 

  Exam Questions

  Recurrence. Savings. %Withdraw. GP. Inequality

 

Arithmetic and Geometric Series

 

  Exam Questions

  AP GP. Same a and r=d

  Geometric Progression. Compounding Interests

 

Summation Notation

 

  Practice Questions

  Lower Limit =3, Upper limit = 2n+2

 

  Exam Questions

  Partial Fraction. Method of difference

  Series. Proof Series smaller than 11/156. Using earlier part

  MOD. Summation. Geometric Progression. Hence. Deduce

  MOD. Summation. Hence. f(r)-f(r-1)

 

Mathematical Induction

 

  Exam Questions

  P(0) is true

  

Application of Differentiation

 

  Exam Questions

  Simple Parametric Equation (involving t)

  Gradient, Normal, Tangent, Cut twice.

  Cylinder within Sphere. Maximum Volume

  Application of Differentiation (a)

  Application of Differentiation(b)

  Implicit Differentiation. Simulatenous eqn 3 variables

  Chain Rule. Rate of Change. Volume. Surface Area. Sphere

  Rate of Change of Area of Trapezium 

 

 

Binomial Expansion and Maclaurin's Series

 

  Concepts

  Basic

  nCr = (n-1)C(r-1) +(n-1)Cr

  

  Exam Questions

  Multiplying 2 expansions. Validity range.

  

  Practice Questions

  Using standard series, e^x and sin(2x)

  Maclaurin expansion ln(1+cosx)

 

Limits

 

  Practice Questions

  2^(1/n). Maclaurin's expansion 

  substitution, factorisation, conjugate, infinity

 

Integration

  

  Integration by parts

    Practice Questions

    Integration by parts, inverse trigo

 

 

Application of Integration

  

  Lecture

  Volume of solid generated by Rotating Sin(x) graph about       the y-axis. Self overlap y axis.

  Bowl. Volume of solid. Depth. Rotate about y axis.

 

  Practice Question

  x=acost, y=bsint, area enclosed by ellipse

 

  Exam Questions

  Integration. Sum of Rectangles. Geometric Progression

  Volume. Parametric. Sin(x). Cos(x). w.r.t X-axis and Y-axis

  Volume. Self Overlap x axis, quadratic in y. 

  Rotate about Line y = 2. Translation before integration

 

Differential Equations

 

  TJC Application of Differential Eqn Tutorial Solutions

  Qn 1 

  Qn 2

  Qn 3

  Qn 4

  Qn 5

  Qn 6i

  Qn 6ii

  Qn 8

  POYO qn 1

  POYO qn 2

  POYO qn 3

  POYO qn 4

  POYO qn 5

  POYO qn 6 

  Exam Questions

  Differential Equation. Integrate twice.

 

Vectors I  

 

    Exam Questions

    Ratio Theorem

    Ratio Theorem. Find Ratios Simultaneously

    Vector Dot Product Properties Part (1 and 2)

    Vector Sphere Rectange |m| part 3

    3 pxq = px2r linear relationship?

Vectors 2 Planes

    Reflected lines in plane

Vectors 3  Planes

    Exam Questions  

    3 Planes no point in common, find condition for a and b

   

Complex number

    Loci find greatest value arg(...)

    Loci Circle Half Line Inequalities Shading

    Loci Range of values of arg(z-...) least values of |z-...|

    max min arg locus 

 

STATISTICS

 

Permutation and Combinations

  

  Solutions to Practice Questions from "Comprehensive Guide to Mathematics" (Questions not provided, Solution only)

   Seating 8 people on 10 seats, Round Table, 2 couples, identical seats

Probability

   Accidents and alcohol, conditional probablity Tree

   Chan and Lee Table

   Conditional Probability. P(Boy entered|Boy picked)

   Probability table, Conditional Probability, Sunny Day Party

   Probability no woman sit at table A

   Probability Table, Conditional Probability, Torpedo

 

Binomial Distribution

   Binomial Distribution. 1-p 4 Engine Plane 

 

Poisson Distribution

   Poisson Distribution. P(At least 1 typo)

 

Normal Distribution

  

  Practice Questions

  Mean Mass

 

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