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If you’re looking for clear, personalized help in math or physics, this is a live 1-on-1 lesson with me, Tim Chen. I work with students from a wide range of programs. Whether you’re preparing for big exams, tackling tough topics, or aiming for top scores and universities.

  

Lessons are always tailored to your pace, your goals, and your learning style. I’ll help you build a solid understanding, improve problem-solving, and feel more confident step by step.

  

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Course Contents

Part I – Core Topics

Unit 1: Straight Lines

Explores linear equations and systems.

• Lines in the Cartesian plane

• Graphing a straight line

• Perpendicular bisectors

• Simultaneous equations

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Unit 2: Sets and Venn Diagrams

Introduces set theory and visual representations.

• Sets

• Intersection and union

• Complement of a set

• Special number sets

• Interval notation

• Venn diagrams

• Venn diagram regions

• Problem solving with Venn diagrams

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Unit 3: Surds and Exponents

Covers radicals and exponent rules.

• Surds and other radicals

• Division by surds

• Exponents

• Laws of exponents

• Scientific notation

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Unit 4: Equations

Focuses on polynomial and algebraic equations.

• Power equations

• Equations in factored form

• Quadratic equations

• Solving polynomial equations using technology

• Solving other equations using technology

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Unit 5: Sequences and Series

Studies arithmetic, geometric, and financial applications.

• Number sequences

• Arithmetic sequences

• Geometric sequences

• Growth and decay

• Financial mathematics

• Series

• Arithmetic series

• Finite geometric series

• Infinite geometric series

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Unit 6: Measurement

Covers geometry of 2D and 3D figures.

• Circles, arcs, and sectors

• Surface area

• Volume

• Capacity

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Unit 7: Right Angled Triangle Trigonometry

Applies trigonometry to right-angled contexts.

• Trigonometric ratios

• Inverse trigonometric ratios

• Right angles in geometric figures

• Problem solving with trigonometry

• True bearings

• Angle between line and plane

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Unit 8: The Unit Circle and Radian Measure

Introduces radians and unit circle geometry.

• Radian measure

• Arc length and sector area

• The unit circle

• Special multiples of π/6 and π/4

• Pythagorean identity

• Finding angles

• Equation of a straight line

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Unit 9: Non-Right Angled Triangle Trigonometry

Generalizes trigonometry beyond right triangles.

• Area of a triangle

• Cosine rule

• Sine rule

• Problem solving with trigonometry

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Unit 10: Points in Space

Works with 3D coordinates and geometry.

• Points in space

• Measurement in 3D

• Trigonometry in space

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Unit 11: Probability

Covers experimental and theoretical probability models.

• Experimental probability

• Two-way tables

• Sample space and events

• Theoretical probability

• Predictions with probability

• Addition law of probability

• Independent events

• Dependent events

• Conditional probability

• Formal definition of independence

• Bayes’ theorem

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Unit 12: Sampling and Data

Introduces statistical sampling and data types.

• Errors in sampling and data collection

• Sampling methods

• Writing surveys

• Types of data

• Simple discrete data

• Grouped discrete data

• Continuous data

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Unit 13: Statistics

Analyzes data using measures and graphs.

• Measures of central tendency

• Choosing appropriate measures

• Frequency tables

• Grouped data

• Spread of data

• Box and whisker diagrams

• Outliers

• Parallel boxplots

• Cumulative frequency graphs

• Variance and standard deviation

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Unit 14: Quadratic Functions

Focuses on properties and problem solving with quadratics.

• Quadratic functions

• Graphs of quadratics

• Using the discriminant

• Finding a quadratic from its graph

• Intersection of graphs

• Quadratic problem solving

• Optimisation with quadratics

• Quadratic inequalities

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Unit 15: Functions

Covers fundamental function properties and operations.

• Relations and functions

• Function notation

• Domain and range

• Rational functions

• Composite functions

• Inverse functions

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Unit 16: Transformations of Functions

Explores transformations of graphs.

• Translations

• Stretches

• Reflections

• Miscellaneous transformations

• Graph of \(y = 1/f(x)\)

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Unit 17: Trigonometric Functions

Examines periodic functions and modeling.

• Periodic behaviour

• Sine and cosine functions

• General sine and cosine forms

• Modeling periodic behaviour

• Fitting trig models to data

• Tangent function

• Trigonometric equations

• Using trig models

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Part II – Advanced Topics

Unit 1: Further Trigonometry

Expands trigonometric tools.

• Reciprocal trig functions

• Inverse trig functions

• Algebra with trig functions

• Double angle identities

• Compound angle identities

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Unit 2: Exponential Functions

Extends exponentials to algebraic contexts.

• Rational exponents

• Algebraic expansion & factorisation

• Exponential equations

• Exponential functions

• Growth and decay

• Natural exponential

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Unit 3: Logarithms

Explores logarithmic functions and laws.

• Logarithms (base 10)

• Logarithms (base \(a\))

• Laws of logarithms

• Natural logarithms

• Logarithmic equations

• Change of base rule

• Solving exponential equations with logs

• Logarithmic functions

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Unit 4: Introduction to Complex Numbers

Introduces basic complex number theory.

• Complex numbers

• Sum of two squares factorisation

• Operations with complex numbers

• Equality of complex numbers

• Properties of conjugates

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Unit 5: Real Polynomials

Studies polynomial theory and applications.

• Polynomials and operations

• Zeros, roots, and factors

• Polynomial equality

• Polynomial division

• Remainder theorem

• Factor theorem

• Fundamental Theorem of Algebra

• Sum and product of roots theorem

• Graphing cubic/quartic functions

• Polynomial equations

• Cubic inequalities

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Unit 6: Further Functions

Explores more advanced function types.

• Even and odd functions

• Graph of \(\left[f\left(x\right)\right]^2\)

• Absolute value functions

• Rational functions

• Partial fractions

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Unit 7: Counting

Introduces combinatorial principles.

• Product principle

• Sum principle

• Factorial notation

• Permutations

• Combinations

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Unit 8: The Binomial Theorem

Expands binomial expressions.

• Binomial expansions

• Binomial theorem for n ∈ ℤ⁺

• Binomial theorem for n ∈ ℚ

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Unit 9: Reasoning and Proof

Formalizes mathematical reasoning.

• Logical connectives

• Proof by deduction

• Proof by equivalence

• Definitions

• Proof by exhaustion

• Disproof by counterexample

• Proof by contrapositive

• Proof by contradiction

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Unit 10: Proof by Mathematical Induction

Develops induction as a proof tool.

• Process of induction

• Principle of induction

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Unit 11: Linear Algebra

Covers systems of equations and matrix methods.

• Systems of equations

• Row operations

• Solving 2×2 systems

• Solving 3×3 systems

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Unit 12: Vectors

Explores vector algebra in 2D and 3D.

• Vectors and scalars

• Geometric operations

• Vectors in the plane

• Magnitude of a vector

• Plane vector operations

• Vectors in space

• Operations in space

• Vector algebra

• Vector between points

• Parallelism

• Scalar product

• Angle between vectors

• Proof with vector geometry

• Vector product

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Unit 13: Vector Applications

Applies vectors to geometry and physics.

• Lines in 2D and 3D

• Angle between lines

• Constant velocity problems

• Shortest distance point-line

• Intersecting lines

• Line relationships

• Planes

• Angles in space

• Intersecting planes

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Unit 14: Complex Numbers

Extends complex analysis and geometry.

• Complex plane

• Modulus and argument

• Geometry in complex plane

• Polar form

• Euler’s form

• De Moivre’s theorem

• Roots of complex numbers

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Unit 15: Limits

Analyzes function behavior with limits.

• Limits

• Existence of limits

• Limits at infinity

• Trigonometric limits

• Continuity

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Unit 16: Introduction to Differential Calculus

Introduces derivatives formally.

• Rates of change

• Instantaneous rates

• Gradient of a tangent

• Derivative function

• Differentiation from first principles

• Differentiability and continuity

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Unit 17: Rules of Differentiation

Covers main differentiation techniques.

• Simple rules

• Chain rule

• Product rule

• Quotient rule

• Derivatives of exponential functions

• Derivatives of logarithmic functions

• Derivatives of trigonometric functions

• Derivatives of inverse trig functions

• Second and higher derivatives

• Implicit differentiation

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Unit 18: Properties of Curves

Analyzes curves with derivatives.

• Tangents and normals

• Increasing/decreasing functions

• Stationary points

• Curve shape

• Inflection points

• Understanding functions & derivatives

• L’Hôpital’s rule

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Unit 19: Applications of Differentiation

Applies derivatives in real problems.

• Rates of change

• Optimisation

• Related rates

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Unit 20: Introduction to Integration

Begins integral calculus.

• Approximating area under a curve

• Riemann integral

• Antidifferentiation

• Fundamental Theorem of Calculus

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Unit 21: Techniques for Integration

Explores integration strategies.

• Discovering integrals

• Rules for integration

• Particular values

• Integrating \(f\left(ax+b\right)\)

• Partial fractions

• Substitution

• Integration by parts

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Unit 22: Definite Integrals

Applies definite integrals in geometry.

• Definite integrals

• Substitution in definite integrals

• Area under a curve

• Area above a curve

• Area between functions

• Area between curve and y-axis

• Solids of revolution

• Problem solving by integration

• Improper integrals

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Unit 23: Kinematics

Applies calculus to motion.

• Displacement

• Velocity

• Acceleration

• Speed

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Unit 24: Maclaurin Series

Expands functions with power series.

• Maclaurin series

• Convergence

• Composite functions

• Addition and subtraction

• Differentiation and integration

• Multiplication

• Division

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Unit 25: Differential Equations

Solves differential equations with various methods.

• Differential equations

• Euler’s method

• \(dy/dx = f(x)\)

• Separable differential equations

• Logistic growth

• Homogeneous equations \(dy/dx = f(y/x)\)

• Integrating factor method

• Series solutions from DEs

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Unit 26: Bivariate Statistics

Analyzes data relationships.

• Association between variables

• Pearson’s correlation

• Line of best fit by eye

• Least squares regression

• Regression of x on y

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Unit 27: Discrete Random Variables

Explores probability distributions.

• Random variables

• Discrete distributions

• Expectation

• Variance and standard deviation

• Properties of \(aX+b\)

• Binomial distribution

• Binomial probabilities with technology

• Mean and SD of binomial

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Unit 28: Continuous Random Variables

Covers continuous probability and normal distribution.

• Probability density functions

• Measures of centre and spread

• Normal distribution

• Normal probabilities

• Standard normal distribution

• Normal quantiles

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Subjects I Teach

• Standardized Tests
  • SAT math
  • ACT math

• AP Courses
  • AP Calculus AB / BC
  • AP Physics 1 / 2 / CM / CEM
  • AP Statistics
  • AP Precalculus

•  IBDP
  • IB Mathematics AA / AI
  • IB Physics
  • IB Internal Assessment (IA) Guidance

•  A-Level Subjects
  • A-Level Mathematics
  • A-Level Physics

• Other Subjects
  • Algebra 1 / 2
  • Geometry
  • Precalculus
  • Physics
  • Functions / Advanced Functions
  • Integrated Math (IM1 – IM4)

 

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About Me

I’ve worked with students from all over the world, helping them get through challenging material, prepare for competitive exams, and feel more confident in math and physics. I focus on clear explanations, strong fundamentals, and real progress.

 

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Lesson Format

• Live 1-on-1 via Zoom
• Flexible scheduling
• Lessons in English or Mandarin
• Optional whiteboard, handouts, or recordings based on your preference

If you’re serious about improving or want to feel more in control of your learning, let’s work together. Book a trial or message me with any questions.