IB Mathematics: Applications and Interpretation SL

The Applications and Interpretation Standard Level course, in teaching order: a prerequisites unit, then ten units in Year 12 and five in Year 13.

These units are ready here. Prerequisites & Foundations is still in the lessons. More units will appear here as they are finished.

1. 12.1
   12.1 · 2 weeks Sequences & Series Arithmetic and geometric sequences, sigma notation, financial applications and time value of money. 12.1.1 Arithmetic Sequences12.1.2 Arithmetic Series12.1.3 Geometric Sequences12.1.4 Series & Sigma Notation12.1.5 Geometric Series12.1.6 Mixed Practice & Exam Prep 0 0 of 94 skills done
2. 12.2
   12.2 · 3 weeks Finance The Finance Solver for compound interest, depreciation, loans and annuities, then rounding, bounds and percentage error. 12.2.1 Finance Solver: compound interest and depreciation12.2.2 Amortisation and annuities12.2.3 When PpY ≠ CpY12.2.4 Rounding and percentage error 0 0 of 58 skills done
3. 12.3
   12.3 · 1 week Coordinate Geometry Straight lines in two dimensions and three-dimensional coordinate geometry. 12.3.1 3D coordinates: distance and midpoint12.3.2 Straight lines: gradient, parallel and perpendicular 0 0 of 20 skills done
4. 12.4
   12.4 · 2 weeks Solving Equations with Technology Systems of linear equations and polynomial equations, solved on the GDC. 12.4.1 Solving systems of equations12.4.2 Modelling with systems of equations12.4.3 Polynomial equations with the solver12.4.4 Solving and forming polynomial equations12.4.5 Graphs of polynomial equations12.4.6 Where two graphs meet12.4.7 Mixed practice: equations and systems12.4.8 Unit review 0 0 of 45 skills done
5. 12.5
   12.5 · 1 week Functions Introduction to functions, domain and range, inverses, graphing and systems of equations. 12.5.1 Function notation, domain and range12.5.2 Key features and models of graphs12.5.3 Inverse functions12.5.4 Closest point on a graph12.5.5 Review: the approach model and graph transformations12.5.6 Unit review 0 0 of 16 skills done
6. 12.6
   12.6 · 2 weeks Exponents & Logarithms Exponential expressions, logarithms, log laws and logarithmic scales. 12.6.1 Laws of exponents: negative and fractional indices12.6.2 Logarithms and solving exponential and log equations12.6.3 Mixed exponent and logarithm practice12.6.4 Unit review 0 0 of 9 skills done
7. 12.7
   12.7 · 8 weeks Mathematical Models Linear, quadratic, exponential, cubic and sinusoidal models with GDC applications. 12.7.1 Linear, quadratic, cubic, variation and exponential models12.7.2 Sinusoidal models: Ferris wheels, tides and daylight12.7.3 Mixed modelling practice12.7.4 Unit review 0 0 of 15 skills done
8. 12.8
   12.8 · 2 weeks Voronoi Diagrams Voronoi diagrams, perpendicular bisectors, nearest neighbour interpolation. 12.8.1 Voronoi diagrams in the real world12.8.2 Equation of a perpendicular bisector12.8.3 Sites, cells, edges and vertices12.8.4 Adding a site: the incremental algorithm12.8.5 Nearest neighbour interpolation12.8.6 The toxic waste dump problem12.8.7 Unit review 0 0 of 19 skills done
9. 12.9
   12.9 · 2 weeks Differentiation Introduction to differentiation, power rule, tangents, normals and optimisation. 12.9.1 Gradient, increasing and decreasing12.9.2 From the graph of f to the graph of f′12.9.3 From the graph of f′ back to f12.9.4 Sketching f and f' from graphs12.9.5 Differentiating powers of x12.9.6 Expanding, splitting fractions and increasing or decreasing12.9.7 Gradient at a point and where the gradient equals a value12.9.8 Equation of a tangent and of a normal12.9.9 Tangents, normals and gradient with technology12.9.10 Harder tangent and normal problems12.9.11 Stationary points: where the gradient is zero12.9.12 Maximum and minimum points on a domain12.9.13 Optimisation in context12.9.14 Unit review 0 0 of 48 skills done
10. 12.10
    12.10 · 2 weeks Geometry & Trigonometry 3D trigonometry, sine and cosine rules, bearings, arcs and sectors. 12.10.1 Right-angled trigonometry and angles between lines12.10.2 Sine rule and cosine rule12.10.3 Area of a triangle12.10.4 Mixed practice: rules of trigonometry12.10.5 Angles in 3D shapes12.10.6 Bearings12.10.7 Angles of elevation and depression12.10.8 Applications of trigonometry: 3D, bearings, elevation12.10.9 Volumes and surface areas of solids12.10.10 Arc length and sector area12.10.11 Grazing goat problems: sectors round a shed12.10.12 Grazing goat problems: sector and triangle area12.10.13 Unit review 0 0 of 60 skills done
11. 13.1
    13.1 · 2 weeks Probability Tree diagrams, Venn diagrams, two-way tables and conditional probability. 13.1.1 Theoretical and experimental probability13.1.2 Venn diagrams for probability13.1.3 Tree diagrams and sample spaces13.1.4 Probability from two-way tables13.1.5 Combined events and mutually exclusive events13.1.6 Conditional probability13.1.7 Independent events13.1.8 Mixed practice: choosing the right tool13.1.9 Probability review: the boy or girl problem13.1.10 Unit review 0 0 of 48 skills done
12. 13.2
    13.2 · 2 weeks Probability Distributions Discrete random variables, binomial and normal distributions. 13.2.1 Discrete random variables and distribution tables13.2.2 Expected value of a discrete random variable13.2.3 Fair games and further distributions13.2.4 The binomial distribution13.2.5 Binomial probabilities with the calculator13.2.6 Mean, variance and binomial practice13.2.7 The normal distribution: properties and when it is a good model13.2.8 Normal probability calculations with the GDC13.2.9 Inverse normal calculations and normal practice13.2.10 Distributions review: chapter 8 checklist and short quiz13.2.11 Unit review 0 0 of 45 skills done
13. 13.3
    13.3 · 3 weeks Statistics Data types, central tendency, dispersion, histograms and regression. 13.3.1 Data, sampling and averages13.3.2 Spread and standard deviation13.3.3 Changing every value13.3.4 Quartiles, box plots and outliers13.3.5 Histograms and cumulative frequency graphs13.3.6 Scatter diagrams and correlation13.3.7 Linear regression and prediction13.3.8 Spearman's rank correlation and comparison with Pearson's r13.3.9 Statistics review: exam questions13.3.10 Unit review 0 0 of 44 skills done
14. 13.4
    13.4 · 3 weeks Hypothesis Testing Chi-squared tests, t-tests and Spearman's rank correlation. 13.4.1 What a hypothesis test is13.4.2 Chi-squared goodness of fit13.4.3 Testing the fit of a model13.4.4 Chi-squared test for independence13.4.5 One-sample t-test for a mean13.4.6 Two-sample pooled t-test13.4.7 Spearman's rank correlation13.4.8 Unit review 0 0 of 31 skills done
15. 13.5
    13.5 · 2 weeks Integration Anti-derivatives, trapezium rule and integrals as accumulation. 13.5.1 Distance as area under a speed-time graph13.5.2 Anti-differentiation: reversing the power rule13.5.3 Expanding, splitting fractions and boundary conditions13.5.4 Definite integrals and area under a curve13.5.5 Accumulation: rate in, amount out13.5.6 Unit mixed practice: areas, rates and accumulation13.5.7 The trapezium rule13.5.8 The trapezium rule with data, and its error13.5.9 Unit review 0 0 of 41 skills done