You can book a free math lesson with me by clicking on this link
Junior College
PURE MATH
Functions
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
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
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
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
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
Exam Questions
Differential Equation. Integrate twice.
Vectors I
Exam Questions
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
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-...|
STATISTICS
Permutation and Combinations
Seating 8 people on 10 seats, Round Table, 2 couples, identical seats
Probability
Accidents and alcohol, conditional probablity Tree
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
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
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