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Junior College






  Exam Questions

  Inverse Function and Composite Function


Graph Sketching


  Basic Questions



Conics, Circles, Ellipses, Hyperbola


  Basic Questions

  Circle. Standard Form. Midpoint. Y Coordinate of Center




  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




  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)




  Practice Questions

  2^(1/n). Maclaurin's expansion 

  substitution, factorisation, conjugate, infinity




  Integration by parts

    Practice Questions

    Integration by parts, inverse trigo



Application of Integration



  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 




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


   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

Secondary School Math


  Solve Quadratic Equations

    Completing the square. Factorisation. [-b+-sqrt(bsquare-4ac)]/(2a)]


Math from University Courses


  Business Math

    Application of Integration in Business Problems (SMU)

    Basic Integration Techniques (SMU)

    Application of Differentiation (Assembly Line Example)


  Financial Math

    Black Schole's Option Pricing Formula

    Differentiating x^(x^x)

    Integration by parts, x(logx)^2, Max(x,x^2)

    Probability table, Conditional Probability, Sunny Day Party

    Probability no woman sit at table A

    Probability Table, Conditional Probability, Torpedo

    Binomial Distribution. 1-p 4 Engine Plane to 2 Engine Plane

    Poisson Distribution. P(At least 1 typo)

    Conditional Probability. P(Boy entered|Boy picked)


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