Advanced Function Analysis
Domain, range, intercepts and asymptotes, function composition and decomposition, piecewise models, sketching from features, and mixed equations and.
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📚 Scholi · Grade 12
Mathematics
Units follow the order of the Scholi programme. Pick a topic and start.
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- Units
- 12
- Topics
- 12
- Ready
- 12
Course plan
Units and topics
Go in order, or start from any topic.
ReadyIn the labPlanned
Unit 1Ready
Advanced Function Analysis
1 topic · 1 topic open
Unit 2Ready
Polar & Parametric Equations
1 topic · 1 topic open
Polar & Parametric Equations
Convert points and equations between rectangular and polar form, graph polar curves, and write and graph parametric curves with orientation.
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Unit 3Ready
Vectors
1 topic · 1 topic open
Unit 4Ready
Matrices
1 topic · 1 topic open
Unit 5Ready
Limits & Continuity
1 topic · 1 topic open
Limits & Continuity
Estimate limits from tables and graphs, evaluate limits analytically and at infinity, classify discontinuities, and apply the intermediate-value theorem.
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Unit 6Ready
The Derivative — Tangent Lines
1 topic · 1 topic open
The Derivative — Tangent Lines
Watch secant lines become tangent lines, build the limit definition of the derivative, and write the equation of a tangent line.
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Unit 7Ready
The Derivative — Rules
1 topic · 1 topic open
The Derivative — Rules
Master the power, product, quotient, and chain rules and differentiate polynomial, rational, radical, exponential, logarithmic, and trig functions.
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Unit 8Ready
Applications of the Derivative
1 topic · 1 topic open
Applications of the Derivative
Find increasing/decreasing intervals, extrema, concavity, and inflection points, solve optimization and related-rates problems, and apply the mean-value.
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Unit 9Ready
The Integral
1 topic · 1 topic open
The Integral
Estimate definite integrals with Riemann sums, apply the fundamental theorem of calculus, and evaluate integrals by antidifferentiation and u-substitution.
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Unit 10Ready
Applications of Integration
1 topic · 1 topic open
Applications of Integration
Find area between curves, volumes of solids of revolution and known cross-sections, the average value of a function, and total displacement and distance.
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Unit 11Ready
Differential Equations
1 topic · 1 topic open
Differential Equations
Explore slope fields, sketch solution curves, and solve separable differential equations. Interactive Grade 12 lesson with practice.
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Unit 12Ready
Distributions & Inference
1 topic · 1 topic open
Distributions & Inference
Expected value and variance, binomial and normal distributions, confidence intervals for a proportion, and one-sample hypothesis tests.
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New units appear here as they are added. The order follows the Scholi programme.
In every topic
How a topic works
Four parts. You see it with a tool, then try it, then practise.
Learn
Starts with a scene. You move in short steps.
Explore
You use the tool yourself. Break it, fix it.
Practice
Easy, medium, hard. Questions with the same tool.
Summary
Rules, words and formulas on one page.