Objectives
We provide personalized assistance on school math subjects, ranging from pre-calculus to IB/AP Math, as well as the AMC series if requested. Course difficulty will be designed and adjusted based on the student's need. Practice problems will be chosen from the AMC series, AIME, AP tests, IB tests, HMMT, AoPS textbooks, and other sources. For students taking standardized exams (AP, IB, SAT Level 2), this program will cover a plethora of resources, including practice tests and tips, to ace the exam. Upon request, we also provide professional training of competition math, such as Math is Cool, Mu Alpha Theta, and the AMC series. Since classes will be delivered privately on Zoom, the student will receive individual attention from the instructor and speedy replies to their questions, even when class is not in session. Please contact the instructor for more details.
Course Outline (IB Mathematics HL)
#
Topic
Lesson Description
01
Polynomial 1
Definitions, Factor Theorem, Remainder Theorem, Division Algorithm, Rational Root Theorem, Descartes’ Rule of Signs.
02
Polynomial 2
Vieta’s Formulas, complex roots. Working on problems and proofs.
03
Induction, Intro to series and sequences
Principle of Mathematical Induction, strong inductions, working on induction proofs. Definitions, telescoping series, Maclaurin series, power series (assuming knowledge of calculus).
04
Geometry
Similar triangles, trigonometry, power of a point, Euclid’s Theorem, Ceva's Theorem, Menelaus Theorem.
05
Vectors
Definitions, dot product, cross product, planes, calculate distances from point to plane/line to plane. Parametric equations, vector equations, and Cartesian equations.
06
Complex Numbers
Modulus, argument, polar form. De Moivre’s Theorem, Roots of Unity, Euler’s Formula.
07
Combinatorics and Probability
Permutations, combinations, combinatorics identities, law of probability, independent events, case work, complementary counting, etc.
08
Calculus 1
Integration techniques, trig substitutions, circular functions, integration by parts, integrating factor method.
09
Calculus 2
Differential equations, Separable Differential Equations, Euler’s method, homogeneous differential equations.
10
Intro to Linear Algebra
Solving systems of equations using matrices, matrix identities, linear and geometric transformations, basis and spanning sets, eigenvectors and eigenvalues.
Course Outline (Pre-Calculus/IB Applications and Interpretation HL1)
#
Topic
Lesson Description
01
Sets and Venn Diagram
Definitions, Intersection and Union, Complement of a Set, Interval Notations, Venn Diagrams.
02
Probability
Experimental Probability, Theoretical Probability, The Addition Law of Probability, Independent Events, Dependent events, Conditional Probability.
03
Sampling and Data
Errors in sampling, Sampling Methods, Writing Surveys, Types of Data.
04
Statistics
Center of data, Frequency table, Measuring the Spread of Data, Box and Whisker Diagrams, Outliers, Cumulative Frequency Graphs, Variance and Standard Deviation.
05
Sequences
Number sequences, Arithmetic sequences, Geometric Sequences, Growth and Decay, Financial Mathematics.
06
Series
Definitions, Arithmetic Series, Finite Geometric Series, Infinite Geometric Series.
07
Right Triangles
Trigonometry, Right Angles, Problem Solving with Trig, True Bearings, Projection.
08
Unit Circle
Radian Measure, Arc Length and Sector Area, The Unit Circle, The Pythagorean Identity, Finding Angles, The Equation of a Straight Line.
09
Non-Right Triangles
Area of a triangle, the Cosine Rule, the Sine Rule, Problem Solving with trig.
10
Quadratic Functions
Definitions, Graph, Using the Discriminant, Intersection of Graphs, Problem Solving with Quadratic Functions, Optimization, Quadratic Inequalities.