Subjects 05 MathematicsIB diploma course · Higher level
Mathematics: Applications and Interpretation HL. The whole course, unit by unit. Open each lesson for explanations, practice, review and exam-ready resources.
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1.1 Using standard form
1.1 Using standard form 0 %
0 of 78 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 15 lessons · 15 units
Unit 01
1.1 Using standard form 0 /1
Unit 02
1.2 Sequences and Sigma Notation 0 /1
Unit 03
1.3 Geometric Sequences 0 /1
Unit 04
1.4 Financial applications: compound interest and annual depreciation 0 /1
Unit 05
1.5 Exponents and Logarithms 0 /1
Unit 06
1.6 Approximating and estimating 0 /1
Unit 07
1.7 Loan repayments and amortization 0 /1
Unit 08
1.8 Use of technology to solve systems of linear equations and polynomial equations 0 /1
Unit 10
1.10 Expressions with non-integer exponents 0 /1
Unit 11
1.11 Sum of infinite geometric sequences 0 /1
Unit 12
1.12 Complex numbers introduction 0 /1
Unit 13
1.13 Complex numbers continued 0 /1
Unit 14
1.14 Introduction to matrices 0 /1
Unit 15
1.15 Eigenvalues and eigenvectors 0 /1
02 2. Functions 10 lessons · 10 units
Unit 01
2.1 Equations of a line 0 /1
Unit 02
2.2 Functions, domains, range, graphs 0 /1
Unit 03
2.3 Graph of a function 0 /1
Unit 04
2.4 Features of a graph 0 /1
Unit 05
2.5 Modelling functions 0 /1
Unit 06
2.6 Modelling skills 0 /1
Unit 07
2.7 Composite functions, finding inverse function incl domain restriction 0 /1
Unit 08
2.8 Transformations of graphs, composite transformations 0 /1
Unit 09
2.9 HL modelling functions 0 /1
Unit 10
2.10 Scaling large numbers, log-log graphs 0 /1
03 3. Geometry and Trigonometry 16 lessons · 16 units
Unit 01
3.1 3D space, volume, angles and midpoints 0 /1
Unit 02
3.2 2D and 3D trigonometry 0 /1
Unit 03
3.3 Angles of elevation and depression 0 /1
Unit 04
3.4 The circle, arc and area of sector, degrees only 0 /1
Unit 05
3.5 Intersection of lines, equations of perpendicular bisectors 0 /1
Unit 06
3.6 Voronoi diagrams 0 /1
Unit 08
3.8 Unit circle, Pythag identity, solving trig equations graphically 0 /1
Unit 09
3.9 Matrix transformations 0 /1
Unit 10
3.10 Vector definitions 0 /1
Unit 11
3.11 Vector equation of a line in 2d and 3d 0 /1
Unit 12
3.12 Vector applications to kinematics 0 /1
Unit 13
3.13 Scalar and vector products 0 /1
Unit 15
3.15 Adjacency matrices and tables 0 /1
Unit 16
3.16 Tree and cycle algorithms, Chinese postman, travelling salesman 0 /1
04 4. Statistics and Probability 19 lessons · 19 units
Unit 01
4.1 Introduction to Statistics 0 /1
Unit 02
4.2 Presentation of data 0 /1
Unit 03
4.3 Mean, median, and mode 0 /1
Unit 04
4.4 Correlation of Data 0 /1
Unit 05
4.5 Trial and outcome 0 /1
Unit 07
4.7 Discrete random variables 0 /1
Unit 08
4.8 Binomial distribution 0 /1
Unit 09
4.9 Normal distribution 0 /1
Unit 10
4.10 Spearman’s rank correlation coefficient 0 /1
Unit 11
4.11 Expected and observed frequencies, hypotheses, chi-squared, goodness of fit, t-test 0 /1
Unit 12
4.12 Data collection, reliability and validity tests 0 /1
Unit 13
4.13 Non-linear regression 0 /1
Unit 14
4.14 Linear transformation of a single RV, E(X) and VAR(X), unbiased estimators 0 /1
Unit 15
4.15 Central limit theorem 0 /1
Unit 16
4.16 Confidence intervals 0 /1
Unit 17
4.17 Poisson distribution 0 /1
Unit 18
4.18 T and Z test, type I and II errors 0 /1
Unit 19
4.19 Transition matrices – Markov chains 0 /1
05 5. Calculus 18 lessons · 18 units
Unit 01
5.1 Introduction to Limits 0 /1
Unit 02
5.2 Increasing and decreasing functions 0 /1
Unit 03
5.3 Introduction to derivatives 0 /1
Unit 04
5.4 Tangents and normals 0 /1
Unit 05
5.5 Introduction to integration 0 /1
Unit 06
5.6 Stationary points, local max and min 0 /1
Unit 08
5.8 Trapezoid rule 0 /1
Unit 09
5.9 Differentiating standard functions and derivative rules 0 /1
Unit 10
5.10 Second derivatives, testing for max and min 0 /1
Unit 11
5.11 Indefinite integration, reverse chain, by substitution 0 /1
Unit 12
5.12 Areas under a curve onto x or y axis. Volumes of revolution about x and y 0 /1
Unit 13
5.13 Kinematic problems 0 /1
Unit 14
5.14 Setting up a DE, solve by separating variables 0 /1
Unit 16
5.16 Eulers method for 1st order DEs 0 /1
Unit 17
5.17 Phase portrait 0 /1
Unit 18
5.18 Eulers method for 2nd order DEs 0 /1
NEXT Turn the syllabus into a daily plan
78 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.