Subjects 05 MathematicsIB diploma course · Standard level
Mathematics: Analysis and Approaches SL. The whole course, unit by unit. Open each lesson for explanations, practice, review and exam-ready resources.
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1.1 Operations with numbers in standard form
1.1 Operations with numbers in standard form 0 %
0 of 51 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 9 lessons · 9 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
02 2. Functions 11 lessons · 11 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
03 3. Geometry and Trigonometry 8 lessons · 8 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
04 4. Statistics and Probability 12 lessons · 12 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
05 5. Calculus 11 lessons · 11 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
NEXT Turn the syllabus into a daily plan
51 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.