ibtaskmaker.com - A Questionbank for IB DP Mathematics Analysis and Approaches

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► Number and Algebra

Number and Algebra

Core SL

Analysis & Approaches SL

Analysis & Approaches HL

▼

Sequences, Series and Patterns

Arithmetic Sequences and Series

Geometric Sequences and Series

Finance

Infinite Geometric Series	Binomial Theorem
Binomial Coefficients

Binomial Theorem (Rational Indices)

Counting Principles

Exponents and Logarithms

Scientific Notation

Laws of (Integer) Exponents

Logarithms in Bases 10 and e

Laws of (Rational) Exponents	Laws of Logarithms
Change of Base of Logarithms	Exponential Equations

Proof

Simple Deductive Proof

Proof by Induction	Proof by Contradiction
Disproof by Counterexample

Complex Numbers

Properties of Complex Numbers	The Complex Plane
The Polar and Euler Forms of Complex Numbers	Complex Roots of Real Polynomials
De Moivre's Theorem	Powers and Roots of Complex Numbers

Other Topics

Solutions of Systems of Linear Equations

Partial Fractions

► Functions

Functions

Core SL

Analysis & Approaches SL

Analysis & Approaches HL

▼

Polynomials

Linear Equations and Their Graphs

Quadratic Functions and Their Graphs	Solving Quadratic Equations and Inequalities
The Discriminant

Polynomial Functions, Their Equations and Graphs	The Factor and Remainder Theorems
The Sum and Product of the Roots of a Polynomial

Properties of Functions

Functions: Notation, Domain, and Range

Graphing and Sketching Functions

Key Features of Graphs

The Intersection of Graphs

Composite Functions	Rational Functions (Linear) and Their Graphs
Exponential and Logarithmic Functions and Their Graphs	Solving Equations Graphically and Analytically
Using Technology to Solve Equations

Rational Functions (Quadratic) and Their Graphs

Solving Inequalities Graphically and Analytically

Transformations

Graphing Inverse Functions

Determining Inverse Functions	Transformations of Graphs
Composite Transformations

Odd and Even Functions	Domain Restrictions of Inverse Functions
Self Inverse Functions	Transformations Involving the Modulus Function
Transformations Involving Squaring	Reciprocal Functions
Modulus Equations and Inequalities

► Geometry and Trigonometry

Geometry and Trigonometry

Core SL

Analysis & Approaches SL

Analysis & Approaches HL

▼

Lines and Planes

Distance and Midpoint Between Two Points (2D & 3D)

Angles Between Lines, and a Line and Plane

Construction of Diagrams From Given Information

Vectors: Adding, Subtracting, Scalar Multiplication	Magnitude of Vectors
The Scalar and Vector Products	The Angle Between Two Vectors
The Vector Equation of a Line	The Relationship Between Two Lines
Equations of Planes	The Intersection of Planes, and Planes and Lines
The Angle Between Planes, and Planes and Lines

Trigonometry

Right-Angled Triangle Trigonometry

The Sine and Cosine Rules

The Area of a Triangle

Circles: Radians, Arcs, Sectors	The Unit Circle
Exact Values of Trigonometric Ratios	The Ambiguous Case of the Sine Rule
Pythagorean and Double Angle Identities (sin and cos)	Circular Functions
Solving Trigonometric Equations	Quadratic Trigonometric Equations

Reciprocal Trigonometric Functions and Their Graphs	Inverse Trigonometric Functions and Their Graphs
Compound Angle Identities	Double Angle Identity for tan
Relationships Between Graphs of Trigonometric Functions

3-Dimensional Shapes

Volume and Surface Area of 3D Solids

► Statistics and Probability

Statistics and Probability

Core SL

Analysis & Approaches SL

Analysis & Approaches HL

▼

Analyzing Data

Reliability and Bias	Outliers
Sampling Techniques	Quartiles, Percentiles, Range and the IQR
Mean, Mode and Median	Standard Deviation and Variance
The Effect of Constant Change of Data	Linear Correlation
The Correlation Coefficient

Representing Data

Histograms	Cumulative Frequency Graphs
Box-and-Whisker Diagrams	Scatter Diagrams, Lines of Best Fit

Probability of Events

Simple Probability	Complementary Events
Venn, Tree, Sample Space Diagrams	Addition Rule
Mutual Exclusivity	Dependent and Independent Events
Conditional Probability

Bayes' Theorem (Up to Three Events)

Probability Distributions

Binomial Distribution	Mean and Variance of Binomial Distribution
The Normal Distribution	Inverse Normal Calculations
Discrete Probability Distributions	Expectation

Standardized Normal Distribution

Inverse Normal (Unknown Mean and Standard Deviation)

Variance of Discrete Probability Distributions	Continuous Random Variables
Mode and Median of Continuous Random Variables	Mean, Variance and Standard Deviation of Continuous Random Variables
Linear Transformations of Random Variables

► Calculus

Calculus

Core SL

Analysis & Approaches SL

Analysis & Approaches HL

▼

Differential Calculus

Limits

Increasing and Decreasing Functions

Derivatives With Integer Exponents

Tangents and Normals to Curves

Rates of Change

Derivatives With Rational Exponents	Derivatives of other functions
Chain Rule	Product Rule
Quotient Rule	The Second Derivative
The Graphs of a Function and its Derivatives	Maximum and Minimum Points
Optimization	Points of Inflection
Kinematics

Convergence and Divergence of Limits	Differentiation from First Principles
Higher Derivatives	l'Hôpital's Rule
Implicit Differentiation	Related Rates
Derivatives of Inverse and Reciprocal Functions

Integral Calculus

Integrals With Integer Exponents

Determining Constant Terms

Definite Integrals and Area Using Technology

Indefinite Integrals	Integration By Substitution
Definite Integrals	The Area Between Curves

Integration By a Given Substitution	Integrals of Inverse and Reciprocal Functions
Rewriting the Integrand Using Partial Fractions	Integration by Parts
Repeated Integration by Parts	Area Between Curve and the y-Axis
Volumes of Revolution

Series & Differential Equations

First Order Differential Equations	Euler's Method of Numerical Solutions
Separation of Variables	Homogeneous Differential Equations
The Integrating Factor	Maclaurin Series
Creating New Maclaurin Series from Others	Maclaurin Series From Differential Equations

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