Analysis & Approaches

Algebra

Contents:

1.1: Scientific notation

pg1 A&A HL - Topic 1 - Algebra Notes.jpg
 
 
 

1.2: Arithmetic Sequences

pg2 A&A HL - Topic 1 - Algebra Notes.jpg

Video

Exercises

Screenshot 2020-03-31 at 22.01.26.png

Solutions

Screenshot 2020-03-31 at 22.01.47.png
 

1.3: Geometric Sequences

pg3 A&A HL - Topic 1 - Algebra Notes.jpg

Video

 

1.4: Compound Interest

pg4 A&A HL - Topic 1 - Algebra Notes.jpg
 

1.5: Exponents & Logs

pg5 A&A HL - Topic 1 - Algebra Notes.jpg

Video

Exercises

AASL - Exponent Posters G.jpg
AASL - Exponent Posters B.jpg

Solutions

AASL - Exponent Posters Answers.jpg
 

1.6: Simple proofs

pg6 A&A HL - Topic 1 - Algebra Notes.jpg
 

1.7: More logarithms

pg7 A&A HL - Topic 1 - Algebra Notes.jpg
pg8 A&A HL - Topic 1 - Algebra Notes.jpg

Videos

Exercises

AA - Logs GBB Posters G.jpg
AA - Logs GBB Posters Blue.jpg
AA - Logs GBB Posters Black.jpg

Solutions

AA - Logs GBB Posters Ans.jpg
 

1.8: Infinite Geometric Series

pg9 A&A HL - Topic 1 - Algebra Notes.jpg

Videos

 

1.9: Binomial Theorem

pg10 A&A HL - Topic 1 - Algebra Notes.jp
pg11 A&A HL - Topic 1 - Algebra Notes.jp

Exercises

AASL - Binomial Expansion G.jpg
AASL - Binomial Expansion Blue.jpg
AASL - Binomial Expansion Black.jpg

Solutions

AASL - Binomial Expansion Ans.jpg
 

Standard Level content

 
 

Additional Higher Level content

1.10: Combinations & Permutations [AHL]

 
pg12 A&A HL - Topic 1 - Algebra Notes.jp
pg13 A&A HL - Topic 1 - Algebra Notes.jp

1.11: Partial Fractions [AHL]

 
pg14 A&A HL - Topic 1 - Algebra Notes.jp

1.12: Complex Numbers Intro [AHL]

 
pg15 A&A HL - Topic 1 - Algebra Notes.jp

Videos

pg15 A&A HL - Topic 1 - Algebra Notes.jp

Videos

1.13: Polar form & Euler’s form [AHL]

 
pg17 A&A HL - Topic 1 - Algebra Notes.jp
pg18 A&A HL - Topic 1 - Algebra Notes.jp
 
 

1.14: Complex roots & de Moivre’s thm. [AHL]

 
pg19 A&A HL - Topic 1 - Algebra Notes.jp
pg20 A&A HL - Topic 1 - Algebra Notes.jp

1.15: Proof by Induction, Contradiction, etc [AHL]

 
pg21 A&A HL - Topic 1 - Algebra Notes.jp
pg22 A&A HL - Topic 1 - Algebra Notes.jp
 
 

1.16: Systems of 3 Equations [AHL]

 
pg23 A&A HL - Topic 1 - Algebra Notes.jp
pg24 A&A HL - Topic 1 - Algebra Notes.jp

Functions

2.1: Linear functions

pg1 A&A HL - Topic 2 - Functions Notes.j
 
 

Problems:

  1. Find the slope of a line passing through (-1,0) & (3,-8):

  2. Parallel, perpendicular, or neither: y=3x+4 & y=3x+7

  3. Parallel, perpendicular, or neither: y+x/3=2 & y=3x-5

  4. Find eq. of a line that’s parallel to y=0.5x+5 and passes (4,-5)

  5. Find eq. of a line that’s perpendicular to y=2x-3 and passes (-5,3)

 

2.2: Domain, range, inverses

pg2 A&A HL - Topic 2 - Functions Notes.j

Problems:

  1. Find the range of f(x)=2ˣ + 1:

  2. Find the domain of g(x)=2x² – 3x + 2:

  3. If f(x)=0.2x – 6, find f⁻¹(x):

  4. If g(x)=e²ˣ + 1, find g⁻¹(x):

 
 

2.3/2.4: Graphs

pg3 A&A HL - Topic 2 - Functions Notes.j
pg4 A&A HL - Topic 2 - Functions Notes.j
 

2.5: Composite functions

pg5 A&A HL - Topic 2 - Functions Notes.j

Video

Problems:

  1. If f(x)=2x & g(x)=3x+5, find (f º g)(x):

  2. If f(x)=2x & g(x)=3x+5, find (g º f)(x):

  3. If f(x)=x²+1 & g(x)=2x-7, find (f º g)(x):

  4. If f(x)=4/x, find (f º f)(x):

  5. If f(x)=4x²+x & g(x)=2x, find (f º g⁻¹)(x):

 

2.6: Forms of quadratics

pg6 A&A HL - Topic 2 - Functions Notes.j
 

2.7: Solving quadratics

pg7 A&A HL - Topic 2 - Functions Notes.j

Videos

pg8 A&A HL - Topic 2 - Functions Notes.j

Video

 

Problems:

  1. Factor x² – 2x – 35:

  2. Factor 2x² + 5x – 3:

  3. Hence, find the roots of y = 2x² + 5x – 3:

  4. Solve 5x² – 27x + 10 = 0:

  5. How many real roots does y = 3x² + 5x + 7 have?

 

2.8: Reciprocal & rational functions 

pg9 A&A HL - Topic 2 - Functions Notes.j

Video

 

2.9: Exponential & logarithmic functions 

pg10 A&A HL - Topic 2 - Functions Notes.
 

2.10: Solving equations

pg11 A&A HL - Topic 2 - Functions Notes.

Video

 

2.11: Transformations

pg12 A&A HL - Topic 2 - Functions Notes.

Standard Level content

 
 

Additional Higher Level content

2.12: Polynomials [AHL]

pg13 A&A HL - Topic 2 - Functions Notes.
pg14 A&A HL - Topic 2 - Functions Notes.
pg15 A&A HL - Topic 2 - Functions Notes.
 

2.13: More rational functions [AHL]

pg16 A&A HL - Topic 2 - Functions Notes.
 

2.14: Odd & even functions, self-inverse [AHL]

pg17 A&A HL - Topic 2 - Functions Notes.
 

2.15: Solving inequalities [AHL]

pg18 A&A HL - Topic 2 - Functions Notes.
 

2.16: Absolute value graphs, and more [AHL]

pg19 A&A HL - Topic 2 - Functions Notes.
 
 
 

3.1: 3D Geometry

pg1 A&A HL - Topic 3 - Trig Notes.jpg
 

3.2: SOHCAHTOA & triangle rules

pg2 A&A HL - Topic 3 - Trig Notes.jpg
 

3.3: Trigonometric applications

pg3 A&A HL - Topic 3 - Trig Notes.jpg
 

3.4: Arcs & sectors + radians

pg4 A&A HL - Topic 3 - Trig Notes.jpg
 

3.5: Unit circle and exact values

pg5 A&A HL - Topic 3 - Trig Notes.jpg

Problems:

  1. Find sin(150°):

  2. Find cos(3π/4):

  3. Find sin(-60°):

  4. Solve x=cos⁻¹(-0.5), for 0<x<360°:

  5. Solve x=sin⁻¹(√3/2), for –π<x<π:

 

3.6: Trigonometric identities

pg6 A&A HL - Topic 3 - Trig Notes.jpg
 

3.7: Trigonometric graphs

pg7 A&A HL - Topic 3 - Trig Notes.jpg

Video

 

3.8: Solving trigonometric equations

pg8 A&A HL - Topic 3 - Trig Notes.jpg

Video

Exercises

Solving Trig Eqs Worksheet - OWN.jpg

Solutions

Solving Trig Eqs Worksheet - Solutions.j
 
 

Standard Level content

 

3.9: Reciprocal trigonometric ratios [AHL]

 

Additional Higher Level content

pg9 A&A HL - Topic 3 - Trig Notes.jpg
 

3.10: Compound angle formula [AHL]

pg10 A&A HL - Topic 3 - Trig Notes.jpg
 

3.11: Other trig properties [AHL]

pg11 A&A HL - Topic 3 - Trig Notes.jpg
 

3.12: Vector basics [AHL]

pg12 A&A HL - Topic 3 - Trig Notes.jpg
pg13 A&A HL - Topic 3 - Trig Notes.jpg

Problems:

  1. Calculate (2i + 5j) + (4i – 7j):

  2. Calculate (i + 8j) – 2(3i – j):

  3. If v = (12i + 5j), calculate |v|:

  4. If w = (-i + 2j – 2k), calculate |w|:

 

3.13: Scalar (dot) product & angles [AHL]

pg14 A&A HL - Topic 3 - Trig Notes.jpg

Problems:

  1. Calculate (2i + 5j)⋅(4i – 7j):

  2. Calculate (i – 3j – 2k)⋅(5i + 11j – 9k):

  3. Find the angle between (i – 3j – 2k) & (5i + 11j – 9k):

  4. Are (2i + 5j) & (-10i + 4j) parallel, perpendicular or neither?:

 
 

3.14: Vector equations of lines [AHL]

pg15 A&A HL - Topic 3 - Trig Notes.jpg
pg16 A&A HL - Topic 3 - Trig Notes.jpg
 

3.15: Intersections of lines [AHL]

pg17 A&A HL - Topic 3 - Trig Notes.jpg
 
 
 
 
 

3.16: Vector product [AHL]

pg18 A&A HL - Topic 3 - Trig Notes.jpg
 
 
 

3.17: Planes [AHL]

pg19 A&A HL - Topic 3 - Trig Notes.jpg
pg20 A&A HL - Topic 3 - Trig Notes.jpg
 

3.18: Intersections of planes [AHL]

pg21 A&A HL - Topic 3 - Trig Notes.jpg
pg22 A&A HL - Topic 3 - Trig Notes.jpg

4.1: Basics & concepts

 
A&A SL - Topic 4 - Stats Notes.jpg
 
 

4.2: Presentation of data

 
A&A SL - Topic 4 - Stats Notes pg2.jpg

Videos

A&A SL - Topic 4 - Stats Notes pg3.jpg

4.3: Averages & dispersion 

 
A&A SL - Topic 4 - Stats Notes pg4.jpg

Videos

Exercise Links: IXL Averages 1, IXL Averages 2,

IXL Standard Deviation, Khan Academy Averages 1

A&A SL - Topic 4 - Stats Notes pg5.jpg

4.4: Regression & correlation

 
A&A SL - Topic 4 - Stats Notes pg6.jpg

Videos

4.5: Probability basics

 
A&A SL - Topic 4 - Stats Notes pg7.jpg

4.6: Venn diagrams, probability trees, conditional prob.

 
A&A SL - Topic 4 - Stats Notes pg8.jpg
A&A SL - Topic 4 - Stats Notes pg9.jpg

Videos

 

4.7: Discrete random variables

A&A SL - Topic 4 - Stats Notes pg10.jpg

4.8: Binomial distribution

 
A&A SL - Topic 4 - Stats Notes pg11.jpg

Videos

 
 

4.9/4.12: Normal distribution

A&A SL - Topic 4 - Stats Notes pg12.jpg
A&A SL - Topic 4 - Stats Notes pg13.jpg
 
 

4.10: x-on-y regression & 4.11: Conditional independence

A&A SL - Topic 4 - Stats Notes pg14.jpg
 

Standard Level content

 
 

Additional Higher Level content

4.13: Bayes’ Theorem [AHL] 

 
A&A HL - Topic 4 - Stats Notes pg15.jpg

Video

4.14: Continuous Random Variables [AHL] 

 
A&A HL - Topic 4 - Stats Notes pg16.jpg

5.1: Limits, slopes of curves

pg1 A&A HL - Topic 5 - Calculus Notes.jp
 
 
 

5.2: Increasing & decreasing regions

pg2 A&A HL - Topic 5 - Calculus Notes.jp
 

5.3: Derivatives of polynomials

pg3 A&A HL - Topic 5 - Calculus Notes.jp

Problems:

  1. If f(x) = 4x², find f'(x):

  2. If g(x) = 5x³ – 2x, find g'(x):

  3. If f(x) = x⁻ ² + 7, find f’(x):

  4. If y = x + 12 – 2x, find dy/dx:

 
 

Exercise Links: 

IXL Differentiation

Khan Academy Diff. 1

Khan Academy Diff. 2

 

5.4: Equations of tangents and normals

pg4 A&A HL - Topic 5 - Calculus Notes.jp
 
 
 
 

Exercises

2 - Tangent:Normal Revision Sheet.jpg

Solutions

Revision Sheet Answers 2.jpg
 

5.5: Introduction to integration

pg5 A&A HL - Topic 5 - Calculus Notes.jp

Problems:

  1. Find ∫2xdx:

  2. Find ∫(4t³-2)dt:

  3. Find ∫9x²dx:

 
 
pg6 A&A HL - Topic 5 - Calculus Notes.jp
 

5.6: Given derivatives

pg7 A&A HL - Topic 5 - Calculus Notes.jp
pg8 A&A HL - Topic 5 - Calculus Notes.jp

Videos

Exercises

1 - Derivatives Revision Sheet.jpg

Solutions

Revision Sheet Answers 1.jpg
 

5.7: Second derivatives and derivative graphs

pg9 A&A HL - Topic 5 - Calculus Notes.jp
 

5.8: Stationary points & inflection points 

pg10 A&A HL - Topic 5 - Calculus Notes.j
pg11 A&A HL - Topic 5 - Calculus Notes.j

Exercises

3 - Stationary:Inflexion Revision Sheet.

Solutions

Revision Sheet Answers 3.jpg
 

5.9: Kinematics

pg12 A&A HL - Topic 5 - Calculus Notes.j
 

5.10: Integral rules

pg13 A&A HL - Topic 5 - Calculus Notes.j
 
 
 

5.11: Definite integrals & area

pg14 A&A HL - Topic 5 - Calculus Notes.j
 

Standard Level content

 
 

Additional Higher Level content

 

5.12: Limits & first principles [AHL]

pg15 A&A HL - Topic 5 - Calculus Notes.j
 

5.13: L’Hôpitals’s rule [AHL]

pg16 A&A HL - Topic 5 - Calculus Notes.j
 

5.14: Implicit diff. & related rates [AHL]

pg17 A&A HL - Topic 5 - Calculus Notes.j
 
 
pg18 A&A HL - Topic 5 - Calculus Notes.j
 
 
 

5.15: More given derivatives [AHL]

pg19 A&A HL - Topic 5 - Calculus Notes.j
 
 
 

5.16: Int by substitution & parts [AHL]

pg20 A&A HL - Topic 5 - Calculus Notes.j
pg21 A&A HL - Topic 5 - Calculus Notes.j
 
 
 
 
 

5.17: Volume of revolution [AHL]

pg22 A&A HL - Topic 5 - Calculus Notes.j
 

5.18: Differential equations [AHL]

pg23 A&A HL - Topic 5 - Calculus Notes.j
pg24 A&A HL - Topic 5 - Calculus Notes.j
pg25 A&A HL - Topic 5 - Calculus Notes.j
pg26 A&A HL - Topic 5 - Calculus Notes.j
pg27 A&A HL - Topic 5 - Calculus Notes.j
 

5.19: Maclaurin series [AHL]

pg28 A&A HL - Topic 5 - Calculus Notes.j
pg29 A&A HL - Topic 5 - Calculus Notes.j
pg30 A&A HL - Topic 5 - Calculus Notes.j

Other Notes

Math AA
Lecture Notes (Math AA):-
 
Formula Booklets (Math AA):-

 

Exercise:-

Topic 1. Number and algebra

complex numbers

Topic 2. Functions

Topic 3. Geometry and trigonometry

trigonometry

vectors

Topic 4. Statistics and probability

statistics

probability

Topic 5. Calculus

 

Math AA HL P3 questions:-

involves: Trigonometry, Limits, Maclaurin series, Recursion

(from specimen 2019)

[Question]

[Solution]

involves: Functions, Trigonometry, Differentiation

(from specimen 2019)

[Question]

[Solution]

involves: Trigonometry, Differentiation, Limits

(from specimen no. 2)

[Question]

[Solution]

involves: Complex numbers

(from specimen no. 2)

[Question]

[Solution]

 

Math AA HL tests:-
Sequences – Binomial theorem – Mathematical induction

OLD TESTS  (from Math HL – before 2019)

NEW TESTS  (for Math AA HL – since 2019)

 
Functions – Polynomials :-

OLD TESTS (from Math HL – before 2019)

NEW TESTS (for Math AA HL – since 2019) 

 
Exponents – Logarithms:-

OLD TESTS (from Math HL – before 2019) 

NEW TESTS (for Math AA HL – since 2019)  

 

Trigonometry:-

OLD TESTS (from Math HL – before 2019)

NEW TESTS (for Math AA HL – since 2019)

 

Vectors:-

OLD TESTS (from Math HL – before 2019)

NEW TESTS (for Math AA HL – since 2019)

 

Statistics – Probability:-

OLD TESTS (from Math HL – before 2019)

NEW TESTS (for Math AA HL – since 2019)

 

Derivatives:-

OLD TESTS (from Math HL – before 2019)

NEW TESTS (for Math AA HL – since 2019)

 

Integrals:-

OLD TESTS (from Math HL – before 2019)

NEW TESTS (for Math AA HL – since 2019)

 

Complex numbers:-

OLD TESTS (from Math HL – before 2019)

NEW TESTS (for MAA HL – since 2019)

 

REVISION TESTS :-

OLD TESTS (from Math HL – before 2019)

 

 

Math AA SL Tests:-
Sequences – Binomial theorem:-
OLD TESTS (from Math SL – before 2019)
NEW TESTS (for MAA SL – since 2019)

 

Lines – Quadratics – Functions:-
OLD TESTS (from Math SL – before 2019)
NEW TESTS (for MAA SL – since 2019)

 

Exponents – Logarithms:-

OLD TESTS (from Math SL – before 2019)

NEW TESTS (for MAA SL – since 2019)

 

Trigonometry:-

OLD TESTS (from Math SL – before 2019)

NEW TESTS (for MAA SL – since 2019)

 

Derivatives:-

OLD TESTS (from Math SL – before 2019)

NEW TESTS (for MAA SL – since 2019)

 

Integrals:-

OLD TESTS (from Math SL – before 2019)

NEW TESTS (for MAA SL – since 2019)

 

Statistics and Probability:-

OLD TESTS (from Math SL – before 2019)

NEW TESTS (for MAA SL – since 2019)

 

 
 
 

Math AI

Lecture Notes (Math AI):-

Topic 1. Number and algebra

Topic 2. Functions

Topic 3. Geometry and trigonometry

Topic 4. Statistics and probability

Topic 5. Calculus

 

Formula Booklets (Math AI):-

 

Math AI Exercise:-

Topic 1. Number and algebra

1A. Basic algebra

  • ——————————————————
  • [MAI 1.7] Infinite series                                             [S] 

1B. Complex numbers – Matrices

Topic 2. Functions 

 

2A. Theory of functions

    • ——————————————————

2B. Modelling with functions

  • ——————————————————
  • [MAI 2.20-2.24] Other Models – Linearization        [S]

Topic 3. Geometry and trigonometry

 

3A. Trigonometry

    • —————————————————-

3B. Vectors – Graph theory

  • ——————————————————-
  •  

Topic 4. Statistics and probability

 

Topic 4A. Descriptive Statistics – Probability

    • ——————————————————-
  • [MAI 4.15] Markov chains                                          [S]

Topic 4B. Further Statistics


Topic 5. Calculus

 

Topic 5A. Differentiation

    • —————————————————–

Topic 5B. Integration

 

Math AI P3 – Questions:-

involves: Statistics – Hypothesis Testing

(from specimen 2019)

[Question]

[Solution]

involves: Modelling functions, Diff. equations, Euler’s method

(from specimen 2019)

[Question]

[Solution]

involves: Modelling functions, Distributions

(from specimen no. 2)

[Question]

[Solution]

involves: Sequences, Matrices – Transformations

(from specimen no. 2)

[Question]

[Solution]

 

 

Math AI HL Tests:-

CUMULATIVE TESTS – MOCK EXAMS

  • [Exam 1]   [solutions]    [word]          Sequences, Exponents and Logarithms, Functions, Modelling
  • [Exam 2]  [solutions]    [word]          Trigonometry, Descriptive Statistics, Probability distributions

IB Past Papers 1995 to 2023

IB Past Papers 2023
IB Past Papers 2022
IB Past Papers 2021
IB Past Papers 2020
IB Past Papers 2019
IB Past Papers 2018
IB Past Papers 2017
IB Past Papers 2016
IB Past Papers 2015
IB Past Papers 2014
IB Past Papers 2013
IB Past Papers 2012
IB Past Papers 2011
IB Past Papers 2010
IB Past Papers 2009
IB Past Papers 2008
IB Past Papers 2007
IB Past Papers 2006
IB Past Papers 2005
IB Past Papers 2004
IB Past Papers 2003
IB Past Papers 2002
IB Past Papers 2001
IB Past Papers 2000
IB Past Papers 1999
IB Past Papers 1998
IB Past Papers 1997
IB Past Papers 1996
IB Past Papers 1995
IB Past Papers 1991

 

International Baccalaureate (IB) Mathematics curriculum can be challenging, but with the right resources, students can excel. This comprehensive guide highlights top free IB Math resources, covering both Analysis & Approaches (AA) and Applications & Interpretation (AI) courses, to help you master the syllabus and achieve your academic goals.

1. IB Maths Resources from Intermathematics

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IB Maths Resources

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Christos Nikolaidis

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Save My Exams

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This platform provides notes on various IB subjects, including Mathematics. The resources cover topics from the standard level section, offering content, formulas, and real-world examples required for the IB exam.

IB Free Resources

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For students working on their Internal Assessment (IA), TutorChase offers guidance and examples to help you excel. Their resources provide insights into the assessment criteria and offer tips for success.

TutorChase

8. GeoGebra

GeoGebra is an interactive mathematics software suite for learning and teaching science, technology, engineering, and mathematics. It offers tools for geometry, algebra, statistics, and calculus, making it a versatile resource for IB Math students.

Wikipedia

9. PrepScholar’s IB Math Study Guide

PrepScholar provides a comprehensive study guide and notes for both SL and HL levels of IB Math: Analysis & Approaches. Their resources include topic overviews and specific subject summaries to aid in your revision.

PrepScholar Blog

10. Clastify’s Math IA Format and Structure Guide

Clastify offers a detailed guide on the format and structure of the Math IA, providing insights into what examiners look for and how to structure your investigation effectively.

Clastify

11. Quizlet’s IB Math SL Key Words Flashcards

Quizlet provides flashcards covering key terms and definitions essential for the IB Math SL course. These flashcards are a great tool for reinforcing your understanding of important concepts.

Quizlet

12. The Math Examiner’s AA SL Resources

The Math Examiner offers resources specifically tailored for the Math AA SL course, including practice questions and tests to help you prepare effectively.

The Math Examiner

13. IB Maths’ Revision Slides and Practice Exercises

IB Maths provides revision slides and practice exercises covering topics such as Algebra, Functions, Trigonometry, Statistics, Probability, and Calculus, catering to both SL and HL courses.

IB Math Resources

14. IB Mathematics Key Concepts by Revision Village

Revision Village offers concise videos summarizing key concepts tested in IB Mathematics exams, serving as helpful refreshers during your revision process.

Revision Village

15. IB Math Past Papers by PrepScholar

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PrepScholar Blog

Utilizing these free resources can significantly enhance your understanding and performance in IB Mathematics. Remember to practice consistently, seek help when needed, and make the most of the materials available to you.