Mr Flynn IB: IB Mathematics video lessons, IA guidance and past paper solutions
AA HL

Analysis & Approaches · HL

Build the depth, fluency and exam judgement AA HL demands.

A structured video course for students who want difficult ideas explained clearly, then practised in the way IB questions actually test them.

What you’ll learn

Understand the method and know when to use it.

The goal is not simply to watch more videos. It is to make unfamiliar IB questions feel more manageable because the underlying mathematics is clear.

  • 01Understand the reasoning behind core AA HL methods
  • 02Recognise common IB question structures
  • 03Move from worked examples to independent exam questions
  • 04Use the calculator strategically rather than mechanically

Full curriculum

See exactly what is covered.

The curriculum is structured directly from the complete course syllabus. Open any topic to see its lesson sequence.

01Number and algebra47 lessons
  1. 1.1Scientific notation
  2. 1.2.1Arithmetic sequences and series
  3. 1.2.2Sigma notation
  4. 1.3Geometric sequences and series
  5. 1.4.1Compound interest
  6. 1.4.2Depreciation
  7. 1.4.3Inflation
  8. 1.5.1Laws of exponents
  9. 1.5.2Introduction to logs
  10. 1.5.3The number e
  11. 1.6Simple deductive proofs
  12. 1.7.1More exponents
  13. 1.7.2Laws of logarithms
  14. 1.7.3Change of base law
  15. 1.8.1Sum of an infinite geometric series
  16. 1.8.2System of linear equations
  17. 1.8.3Roots of a polynomial
  18. 1.9.1Binomial expansion
  19. 1.9.2Binomial Expansion (finding a term)
  20. 1.10.1Counting principles Introduction (product and addition principles)
  21. 1.10.2Factorials and arrangements
  22. 1.10.3Algebra of factorials
  23. 1.10.4Combinations and permutations
  24. 1.10.5Keeping objects together or separated
  25. 1.10.6Binomial theorem extension
  26. 1.11Partial fractions
  27. 1.12.1Complex numbers introduction
  28. 1.12.2Operations with complex numbers
  29. 1.13.1Modulus-argument form
  30. 1.13.2Euler form
  31. 1.13.3Complex operations and geometric interpretation
  32. 1.13.4Properties of complex conjugates
  33. 1.14.1Complex solutions to polynomial equations
  34. 1.14.2De Moivre's theorem
  35. 1.14.3Roots of complex numbers
  36. 1.14.4Roots of unity
  37. 1.15.1Proof by induction (intro and series)
  38. 1.15.2Proof by induction (differentiation)
  39. 1.15.3Proof by induction (divisibility)
  40. 1.15.4Proof by induction (inequalities)
  41. 1.15.5Proof by induction (De Moivre)
  42. 1.15.6Proof by contradiction (intro)
  43. 1.15.7Proof by contradiction (√2)
  44. 1.15.8Proof by contradiction (infinite primes)
  45. 1.15.9Proof by counter example
  46. 1.16.1System of linear equations (HL only)
  47. 1.16.2System of linear equations part 2
02Functions36 lessons
  1. 2.1.1Gradient of a line
  2. 2.1.2Equation of a straight line
  3. 2.1.3Parallel and perpendicular lines
  4. 2.2.1Functions introduction
  5. 2.2.2Evaluating functions
  6. 2.2.3Inverse functions
  7. 2.3Sketching functions
  8. 2.4.1Features of graphs
  9. 2.4.2Asymptotes
  10. 2.5.1Composite functions
  11. 2.5.2Finding inverse functions
  12. 2.6.1Quadratics 3 forms
  13. 2.6.2Factorising quadratics
  14. 2.6.3Vertex form
  15. 2.7.1Solving quadratic equations
  16. 2.7.2Quadratic inequalities
  17. 2.7.3The discriminant
  18. 2.8Rational functions
  19. 2.9.1Exponential modelling
  20. 2.9.2Logarithmic functions
  21. 2.10.1Solving equations using substitution
  22. 2.10.2Solving equations using gdc
  23. 2.11.1Transformations
  24. 2.11.2Composite transformations
  25. 2.12.1Dividing polynomials
  26. 2.12.2Factor and remainder theorems
  27. 2.12.3Graphs of polynomials
  28. 2.12.4Sum and product of roots
  29. 2.13.1Rational functions with quadratics (in denominator)
  30. 2.13.2Rational functions with quadratics (in numerator)
  31. 2.14Even and odd functions
  32. 2.15Solving inequalities
  33. 2.16.1Graphs of modulus functions
  34. 2.16.2Modulus equations and inequalities
  35. 2.16.3Reciprocal transformations
  36. 2.16.4Graphs of
03Geometry and trigonometry48 lessons
  1. 3.1.1Midpoint of a line segment
  2. 3.1.2Distance between 2 points
  3. 3.1.3Volume and surface area
  4. 3.1.4Trigonometry in 3d
  5. 3.2.1Pythagoras’ theorem
  6. 3.2.2Soh cah toa
  7. 3.2.3Sine rule
  8. 3.2.4Cosine rule
  9. 3.2.5Area of a triangle
  10. 3.3.1Bearings
  11. 3.3.2Angles of elevation and depression
  12. 3.4.1Radians
  13. 3.4.2Arcs and sectors
  14. 3.5.1Mr. Flynn’s exact triangles
  15. 3.5.2Unit circle
  16. 3.5.3The CAST diagram
  17. 3.5.4Graphs of sin cos and tan
  18. 3.5.5Sine rule ambiguous case
  19. 3.6Trig identities
  20. 3.7.1Sinusoidal graphs
  21. 3.7.2Sinusoidal modelling
  22. 3.8.1Solving trig equations
  23. 3.8.2Solving trig equations with identities
  24. 3.9.1Reciprocal trig identities
  25. 3.9.2Inverse trigonometric functions
  26. 3.10Compound angle identities
  27. 3.11Symmetry in trig functions
  28. 3.12.1Vectors introduction
  29. 3.12.2Operations with vectors
  30. 3.12.3Magnitude and unit vectors
  31. 3.13.1Scalar product and angle between vectors
  32. 3.13.2Properties of the scalar product
  33. 3.14.1Vector equation of a line
  34. 3.14.2Parametric form and cartesian equations of a line
  35. 3.14.3Angle between two lines
  36. 3.14.4Vectors and kinematics
  37. 3.15.1Intersecting lines
  38. 3.15.2Distance between a point and a line
  39. 3.16.1Vector product
  40. 3.16.2Properties of the vector product
  41. 3.16.3Areas using the vector product
  42. 3.17.1Vector equation of a plane
  43. 3.17.2Cartesian equation of a plane
  44. 3.18.1Intersection between a line and a plane
  45. 3.18.2Intersection between two planes
  46. 3.18.3Intersection of 3 planes
  47. 3.18.4Angle between a line and a plane
  48. 3.18.5Angle between two planes
04Statistics and probability29 lessons
  1. 4.1.1. Discrete v continuous data
  2. 4.1.2Sampling techniques
  3. 4.2.1. Histograms and cumulative frequency curves
  4. 4.2.2box and whisker diagrams
  5. 4.2.3interpreting box plots
  6. 4.2.4Outliers
  7. 4.3.1Averages and spread
  8. 4.3.2Frequency tables
  9. 4.3.3Constant changes in data
  10. 4.3.4Variance and standard deviation by hand
  11. 4.4Linear regression and correlation
  12. 4.5Probability formulae
  13. 4.6.1Venn diagrams
  14. 4.6.2Tree diagrams
  15. 4.7Discrete random variables
  16. 4.8Binomial distribution
  17. 4.9Normal distribution
  18. 4.10Regression line of x on y
  19. 4.11Testing for independence
  20. 4.12Normal distribution (finding mean and standard deviation)
  21. 4.13Bayes theorem
  22. 4.14.1Variance and standard deviation
  23. 4.14.2Variance and standard deviation of a discrete random variable
  24. 4.14.3Continuous random variables intro
  25. 4.14.4Mean of a continuous random variable
  26. 4.14.5Median and mode of a discrete random variable
  27. 4.14.6Median and mode of a continuous random variable
  28. 4.14.7Variance of a continuous random variable
  29. 4.14.8Linear transformations of X
05Calculus58 lessons
  1. 5.1.1Introduction to differentiation
  2. 5.1.2Introduction to limits
  3. 5.2Increasing and decreasing functions
  4. 5.3.1Differentiation power rule
  5. 5.3.2Derivative at a point
  6. 5.4Tangents and normals
  7. 5.5.1Integration (power rule)
  8. 5.5.2Finding
  9. 5.5.3Definite integration
  10. 5.5.4Area under the curve
  11. 5.5.5Finding a limit
  12. 5.6.1Differentiating trig, ex and lnx
  13. 5.6.2Chain rule
  14. 5.6.3Product rule
  15. 5.6.4Quotient rule
  16. 5.7.1Relationship between graph and derivatives
  17. 5.7.2Sketching derivatives
  18. 5.7.3Sketching derivatives with gdc
  19. 5.8.1Classifying stationary points
  20. 5.8.2Finding points of inflexion
  21. 5.8.3Optimization
  22. 5.9Kinematics
  23. 5.10.1Integrating
  24. 5.10.2Integrating sin and cos
  25. 5.10.3Inverse chain rule
  26. 5.10.4Integration by substitution
  27. 5.11Area between 2 curves
  28. 5.12.1Continuous functions
  29. 5.12.2Differentiable functions
  30. 5.12.3Differentation from first principles
  31. 5.12.4Higher derivatives
  32. 5.13L'Hopital's rule
  33. 5.14.1Implicit differentiation
  34. 5.14.2Related rates of change
  35. 5.15.1More derivative rules
  36. 5.15.2More integration rules
  37. 5.15.3Integration using partial fractions
  38. 5.16.1Integration by substitution (HL only)
  39. 5.16.2Integration by parts
  40. 5.16.3Repeated integration by parts
  41. 5.17.1Area between curve and y-axis
  42. 5.17.2Volume of revolution (intro and x-axis)
  43. 5.17.3Volume of revolution (y axis)
  44. 5.17.4Volume of revolution between 2 curves
  45. 5.18.1Differential equations introduction
  46. 5.18.2Separation of variables
  47. 5.18.3Euler's method introduction
  48. 5.18.4Euler's method example
  49. 5.18.5Homogenous differential equations
  50. 5.18.6Integrating factor
  51. 5.19.1Maclaurin series introduction
  52. 5.19.2Maclaurin series
  53. 5.19.3Maclaurin series (substitutions and products)
  54. 5.19.4Maclaurin (binomial series)
  55. 5.19.5Maclaurin series (differentiation and integration)
  56. 5.19.6Maclaurin series (sigma notation)
  57. 5.19.7Maclaurin series (differential equations)
  58. 5.19.8Euler's identity

Also included

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IA

Internal Assessment guidance

Clear guidance for understanding the IA process, developing an idea and improving the finished exploration.

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Past-paper solutions

Worked solutions that show how to approach IB Mathematics questions and communicate the method clearly.