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IB Mathematics HL Analysis & Approaches

Formula Booklet
Syllabus Year 1 & 2
Using the TI-84 (pdf Guide)
Background Knowledge 

Background Knowledge - Logarithms 
Significant figures

Percentage of Students awarded grades 1-7


IB Learner Profile
IB Grade Descriptors
Command Terms
200 Exploration Ideas
Examples of IAs
More Ideas for the IA
       *Exploration ppt
        Exploration Timeline
Exploration - Frequently Asked Q
       Exploration and ToK Math
Extended Essay Titles

General IB Related Documents
IB vs AP Comparison
IB Calculator Policy
Picture

Chapter 1 - From Patterns to Generalizations
Sequences Series & Induction
Sequences and Series(extra questions pdf)
Geometric Series on Excel
Summation Notation with Rules(pdf)
Sigma Notation pdf
Plotting a Series on the TI-84
​
Video on types of proof
Mathematical Induction Example
Probability and Combinatorics
Good Counting Principles Website
Binomial Theorem
Binomial Expansion Paper Questions
Chapter 2 - Introducing Functions
p73 Graphing Radical Functions
​
p73 Graphing Parabolas
​
p74 Points of Intersection

p75 Function of relation?
p 82 Three forms of quadratics
p86 Graphing Rational Functions w/Transformations 
p86 Graphing Rational Functions(w/slant asymptotes)
p86 Domain and Range (Rat F - 44:05)\

Chapter 3 - Complex Numbers

3.2
Complex numbers ................................... 161
Complex Numbers Basics

Systems of Equations
Completing the square
3.3
Polynomial equations and
Inequalities .............................................. 175
Polynomial Inequalities

3.4 The fundamental theorem of algebra ....184
Quadratic Formula

Quadratic Formula 2
Discriminant
Discriminant IB Problem
3.5
Solving equations and inequalities .........195

3.6 Solving systems of linear equations .... 200

Chapter 4 - Differentiation
Piecewise on TI-84
4.1 Limits, continuity and convergence .... 220
4.2 The derivative of a function ....................236
4.3 Differentiation rules ................................249
4.4 Graphical interpretation of the
derivatives ...............................................262
4.5 Applications of differential Calculus ......278
4.6 Implicit differentiation and related
rates ..........................................................288

Chapter 5 - Analysing data and quantifying
randomness: statistics and
probability
5.1 Sampling .. 308
5.2 Descriptive statistics .. 317
5.3 The justification of statistical
techniques .335
5.4 Correlation, causation and linear
regression .347

Chapter 6 - Relationships in space
6.1 The properties of three-dimensional
space ........................................................369
6.2 Angles of measure ...................................378
6.3 Ratios and identities ...............................384
v
6.4 Trigonometric functions ..........................410
6.5 Trigonometric equations ........................ 420
Chapter review ..................................................437
Modelling and investigation activity.............. 440


Extra Problems for Revision
IB Math Videos(worked Problems)
OSC Free Revision Videos
2003 Problems in all Areas (pdf - older)

Review Videos (worked questions)
Andrew Chambers Channel
Induction
Calculus & Induction

Excel Applications
Future Value (spreadsheet)
Future Value (vid)
Chapter 7 Generalizing relationships: exponents,
logarithms and integration  442
7.1 Integration as antidifferentiation and
definite integrals .................................... 444
7.2 Exponents and logarithms .................... 460
7.3 Derivatives of exponential and logarithmic
functions; tangents and normals ..........483
7.4 Integration techniques .......................... 488
Chapter review .................................................. 514
Modelling and investigation activity ..............516

Chapter 8 Modelling change: more calculus  518
8.1 Areas and volumes ..................................520
8.2 Kinematics ...............................................528
8.3 Ordinary differential equations
8.4
Limits revisited ........................................550
Chapter review ..................................................565
Modelling and investigation activity.............. 568

Chapter 9 Modelling 3D space: Vectors 570

9.1
Geometrical representation of
Vectors ......................................................573
9.2 Introduction to vector algebra .............. 586
9.3 Scalar product and its properties ..........597
9.4 Vector equation of a line ........................ 605
9.5 Vector product and properties ............... 614
9.6 Vector equation of a plane ...................... 621
9.7
Lines, planes and angles .......................628
9.8 Application of vectors ..............................633
Chapter review ..................................................643
Modelling and investigation activity ............. 646

Chapter 10 Equivalent systems of representation:

more complex numbers 648
10.1 Forms of a complex number ...................650
10.2 Operations with complex numbers in
polar form .................................................656
10.3 Powers and roots of complex numbers in
polar form .................................................664
Chapter review ..................................................676
Modelling and investigation activity ..............678

Chapter 11 Valid comparisons and informed

decisions: probability distributions 680
11.1 Axiomatic probability systems ...............683
11.2 Probability distributions......................... 696
11.3 Continuous random variables ............... 706
11.4 Binomial distribution ............................... 712
11.5 The normal distribution........................... 718