Subjects 05 MathematicsIB diploma course · Higher level
Mathematics: Analysis and Approaches HL. The whole course, unit by unit. Open each lesson for explanations, practice, review and exam-ready resources.
Next lesson
1.1 Operations with numbers in standard form
1.1 Operations with numbers in standard form 0 %
0 of 83 lessons complete
1. Number and Algebra
2. Functions
3. Geometry and Trigonometry
4. Statistics and Probability
5. Calculus
All 01 1. Number and Algebra02 2. Functions03 3. Geometry and Trigonometry04 4. Statistics and Probability05 5. Calculus
01 1. Number and Algebra 16 lessons · 16 units
Unit 01
1.1 Operations with numbers in standard form 0 /1
Unit 02
1.2 Arithmetic sequences and series 0 /1
Unit 03
1.3 Geometric sequences and series 0 /1
Unit 04
1.4 Financial applications of geometric sequences and series 0 /1
Unit 05
1.5 Introduction to logarithms 0 /1
Unit 06
1.6 Simple deductive proof 0 /1
Unit 07
1.7 Laws of exponents and logarithms 0 /1
Unit 08
1.8 Sum of an infinite convergent geometric sequence 0 /1
Unit 09
1.9 The binomial theorem for positive integer exponents 0 /1
Unit 10
1.10 Permutations, combinations and the extended binomial theorem 0 /1
Unit 11
1.11 Partial fractions 0 /1
Unit 12
1.12 Complex numbers in Cartesian form and the Argand diagram 0 /1
Unit 13
1.13 Modulus–argument (polar) and Euler form 0 /1
Unit 14
1.14 De Moivre's theorem, powers and roots of complex numbers 0 /1
Unit 15
1.15 Proof by induction, contradiction and counterexample 0 /1
Unit 16
1.16 Systems of linear equations 0 /1
02 2. Functions 16 lessons · 16 units
Unit 01
2.1 Equations of straight lines: parallel and perpendicular gradients 0 /1
Unit 02
2.2 Functions: notation, domain, range and inverse as a reflection 0 /1
Unit 03
2.3 Graphs of functions and sketching 0 /1
Unit 04
2.4 Key features of graphs and intersections using technology 0 /1
Unit 05
2.5 Composite functions, the identity function and finding an inverse 0 /1
Unit 06
2.6 The quadratic function and its graph 0 /1
Unit 07
2.7 Solving quadratic equations and inequalities; the discriminant 0 /1
Unit 08
2.8 Reciprocal and rational functions; equations of asymptotes 0 /1
Unit 09
2.9 Exponential and logarithmic functions 0 /1
Unit 10
2.10 Solving equations graphically and analytically 0 /1
Unit 11
2.11 Transformations of graphs 0 /1
Unit 12
2.12 Polynomial functions: factor and remainder theorems, sum and product of roots 0 /1
Unit 13
2.13 Rational functions and their graphs 0 /1
Unit 14
2.14 Odd and even functions, self-inverse functions and domain restriction 0 /1
Unit 15
2.15 Solving inequalities graphically and analytically 0 /1
Unit 16
2.16 Graphs of modulus, reciprocal and related transformations 0 /1
03 3. Geometry and Trigonometry 18 lessons · 18 units
Unit 01
3.1 Three-dimensional geometry: distance, midpoint, volume and angles 0 /1
Unit 02
3.2 Trigonometric ratios, the sine and cosine rules, and area of a triangle 0 /1
Unit 03
3.3 Applications of trigonometry: elevation, depression and bearings 0 /1
Unit 04
3.4 Radian measure, arc length and sector area 0 /1
Unit 05
3.5 The unit circle, exact trigonometric ratios and the ambiguous case 0 /1
Unit 06
3.6 The Pythagorean identity and double angle formulae 0 /1
Unit 07
3.7 Circular functions: graphs, amplitude, period and transformations 0 /1
Unit 08
3.8 Solving trigonometric equations 0 /1
Unit 09
3.9 Reciprocal trigonometric ratios and inverse circular functions 0 /1
Unit 10
3.10 Compound angle identities 0 /1
Unit 11
3.11 Relationships and symmetry between trigonometric functions 0 /1
Unit 12
3.12 Vectors: notation, components and algebra 0 /1
Unit 13
3.13 The scalar (dot) product and the angle between vectors 0 /1
Unit 14
3.14 Vector equation of a line 0 /1
Unit 15
3.15 Coincident, parallel, intersecting and skew lines 0 /1
Unit 16
3.16 The vector (cross) product 0 /1
Unit 17
3.17 Vector and Cartesian equations of a plane 0 /1
Unit 18
3.18 Intersections and angles between lines and planes 0 /1
04 4. Statistics and Probability 14 lessons · 14 units
Unit 01
4.1 Populations, samples, sampling techniques and reliability of data 0 /1
Unit 02
4.2 Presenting data: histograms, cumulative frequency and box plots 0 /1
Unit 03
4.3 Measures of central tendency and dispersion 0 /1
Unit 04
4.4 Linear correlation and the regression line of y on x 0 /1
Unit 05
4.5 Probability: sample space, events and expected occurrences 0 /1
Unit 06
4.6 Combined, mutually exclusive, conditional and independent events 0 /1
Unit 07
4.7 Discrete random variables and expected value 0 /1
Unit 08
4.8 The binomial distribution 0 /1
Unit 09
4.9 The normal distribution and normal probability calculations 0 /1
Unit 10
4.10 The regression line of x on y 0 /1
Unit 11
4.11 Conditional probability and testing for independence 0 /1
Unit 12
4.12 Standardization of normal variables and inverse normal calculations 0 /1
Unit 13
4.13 Bayes' theorem 0 /1
Unit 14
4.14 Properties of discrete and continuous random variables 0 /1
05 5. Calculus 19 lessons · 19 units
Unit 01
5.1 Introduction to limits and the derivative 0 /1
Unit 02
5.2 Increasing and decreasing functions 0 /1
Unit 03
5.3 Differentiating polynomials with integer exponents 0 /1
Unit 04
5.4 Tangents and normals 0 /1
Unit 05
5.5 Introduction to integration and area under a curve 0 /1
Unit 06
5.6 Further differentiation: chain, product and quotient rules 0 /1
Unit 07
5.7 The second derivative 0 /1
Unit 08
5.8 Maxima, minima, optimisation and points of inflexion 0 /1
Unit 09
5.9 Kinematics: displacement, velocity and acceleration 0 /1
Unit 10
5.10 Indefinite integration, reverse chain rule and substitution 0 /1
Unit 11
5.11 Definite integrals and areas between curves 0 /1
Unit 12
5.12 Limits, continuity, first principles and higher derivatives 0 /1
Unit 13
5.13 Evaluating limits with l'Hôpital's rule 0 /1
Unit 14
5.14 Implicit differentiation, related rates and optimisation 0 /1
Unit 15
5.15 Further derivatives and their indefinite integrals 0 /1
Unit 16
5.16 Integration by substitution and by parts 0 /1
Unit 17
5.17 Areas about the y-axis and volumes of revolution 0 /1
Unit 18
5.18 First order differential equations 0 /1
Unit 19
5.19 Maclaurin series 0 /1
NEXT Turn the syllabus into a daily plan
83 lessons.one. Every lesson opens with a teaching video and an audio episode, both free and public, and the notes, flashcards and exam-style questions sit underneath them. Nothing to set up first.