IGCSE Mathematics Tutor , IB Mathematics Tutor, IB Physics Tutor , IB 數學補習,IB 物理補習。GCE AL Mathematics 補習,GCE AL Physics 補習,GCE AL Tutor,Statistics
Total Time: 3 hours 15 minutes
Total Score Weight: 50% Multiple Choice + 50% Free Response
Part A: No calculator allowed – 30 questions – 60 minutes
Part B: Graphing calculator allowed – 15 questions – 45 minutes
Part A: Graphing calculator allowed – 2 questions – 30 minutes
Part B: No calculator allowed – 4 questions – 60 minutes
Note: BC covers more advanced topics; the exam format is the same as AB.
Unit 1: Limits and Continuity
✅ Tested on AB
✅ Tested on BC
1.1 Introducing Limits
1.2 Defining Limits and Using Limit Notation
1.3 Estimating Limits from Graphs
1.4 Estimating Limits from Tables
1.5 Determining Limits Using Algebraic Properties
1.6 Limits Involving Trigonometric Functions
1.7 Selecting Procedures for Determining Limits
1.8 Squeeze Theorem
1.9 Connecting Multiple Representations of Limits
1.10 Defining Continuity at a Point
1.11 Removable Discontinuities
1.12 Intermediate Value Theorem
1.13 Asymptotes and Infinite Limits
1.14 Limits at Infinity and End Behavior
Unit 2: Differentiation – Definition and Basic Rules
✅ Tested on AB
✅ Tested on BC
2.1 Defining the Derivative and Derivative Notation
2.2 Average and Instantaneous Rate of Change
2.3 Estimating Derivatives from Graphs and Tables
2.4 Basic Differentiation Rules (Power, Constant, Sum, Difference)
2.5 Product Rule
2.6 Quotient Rule
2.7 Derivatives of Trigonometric Functions
2.8 The Chain Rule
2.9 Derivatives of Exponential Functions
2.10 Derivatives of Logarithmic Functions
2.11 Derivatives of Inverse Trigonometric Functions
2.12 Implicit Differentiation
2.13 Differentiating Inverse Functions
2.14 Related Rates
2.15 Local Linearity and Linear Approximation
✅ Tested on AB
✅ Tested on BC
3.1 The Chain Rule for Composite Functions
3.2 Implicit Differentiation
3.3 Differentiating Inverse Functions
3.4 Differentiating Inverse Trigonometric Functions
3.5 Higher‑Order Derivatives
3.6 Calculating Derivatives of Parametric Equations (BC Only)
3.7 Calculating Derivatives of Vector‑Valued Functions (BC Only)
3.8 Derivatives of Polar Functions (BC Only)
✅ Tested on AB
✅ Tested on BC
4.1 Interpreting the Meaning of the Derivative in Context
4.2 Straight‑Line Motion: Position, Velocity, Acceleration
4.3 Rates of Change in Applied Contexts
4.4 Introduction to Related Rates
4.5 Solving Related Rates Problems
4.6 Approximating Values Using Linearization
4.7 L’Hospital’s Rule (BC Only)
✅ Tested on AB
✅ Tested on BC
5.1 Mean Value Theorem
5.2 Extreme Value Theorem
5.3 Determining Intervals of Increase and Decrease
5.4 First Derivative Test for Local Extrema
5.5 Using the Candidates Test for Absolute Extrema
5.6 Determining Concavity
5.7 Second Derivative Test
5.8 Sketching Graphs of Functions from Derivatives
5.9 Connecting a Function, Its First Derivative and Second Derivative
5.10 Optimization Problems
5.11 Solving Motion Problems Involving Velocity and Acceleration
✅ Tested on AB
✅ Tested on BC
6.1 Exploring Accumulations of Change
6.2 Approximating Areas with Riemann Sums
6.3 Riemann Sums, Summation Notation and Definite Integrals
6.4 Fundamental Theorem of Calculus Part 1
6.5 Fundamental Theorem of Calculus Part 2
6.6 Properties of Definite Integrals
6.7 Integration by Substitution
6.8 Integrals of Exponential and Logarithmic Functions
6.9 Integrals of Trigonometric Functions
6.10 Integrating Inverse Trigonometric Functions
6.11 Integration by Parts (BC Only)
6.12 Partial Fraction Decomposition (BC Only)
6.13 Improper Integrals (BC Only)
✅ Tested on AB
✅ Tested on BC
7.1 Modeling Situations with Differential Equations
7.2 Verifying Solutions to Differential Equations
7.3 Sketching Slope Fields
7.4 Reasoning Using Slope Fields
7.5 Separation of Variables
7.6 General and Particular Solutions
7.7 Exponential Growth and Decay Models
7.8 Logistic Differential Equations (BC Only)
✅ Tested on AB
✅ Tested on BC
8.1 Finding the Average Value of a Function
8.2 Connecting Position, Velocity and Acceleration with Integrals
8.3 Using Accumulation Functions in Applied Contexts
8.4 Area Between Curves (Cartesian)
8.5 Volumes of Solids with Known Cross‑Sections
8.6 Volumes Using the Disk Method
8.7 Volumes Using the Washer Method
8.8 Arc Length of Cartesian Curves (BC Only)
8.9 Area of Polar Curves (BC Only)
8.10 Arc Length of Parametric and Polar Curves (BC Only)
❌ Not tested on AB
✅ Tested on BC
9.1 Defining and Differentiating Parametric Equations
9.2 Second Derivatives of Parametric Equations
9.3 Finding Arc Lengths of Parametric Curves
9.4 Vector‑Valued Functions: Motion
9.5 Derivatives of Vector‑Valued Functions
9.6 Speed, Velocity and Acceleration for Vectors
9.7 Polar Coordinates and Polar Curves
9.8 Area Enclosed by Polar Curves
9.9 Tangent Lines to Polar Curves
❌ Not tested on AB
✅ Tested on BC
10.1 Convergence of Infinite Sequences
10.2 Series and the nth‑Term Test for Divergence
10.3 Geometric Series
10.4 Telescoping Series
10.5 Integral Test for Convergence
10.6 Comparison Tests
10.7 Alternating Series Test and Absolute / Conditional Convergence
10.8 Ratio Test and Root Test
10.9 Determining Error Bounds for Alternating Series
10.10 Taylor Polynomials and Approximations
10.11 Lagrange Error Bound
10.12 Maclaurin Series for Common Functions
10.13 Radius and Interval of Convergence for Power Series
AB = Units 1‑8 only
BC = All 10 Units (AB content + Units 9 & 10)
All BC exam questions build on AB knowledge; BC students still need full mastery of AB topics.