Int 3 for Programmers
The whole Integrated Math 3 syllabus with the code first and the rule second. Polynomials, radicals, logarithms, series, trigonometry, statistics and conics, drilled by hand because the exam is sat on paper.
Contents
The whole Integrated Math 3 syllabus, taught to somebody who can already program: the code comes first and the rule arrives afterwards to explain what you watched happen. Functions and inverses, equations and systems, polynomials, radicals, rational functions, exponentials and logarithms, sequences and series, triangle trigonometry, the unit circle, identities, statistics and inference, geometric modelling, conics, and an honours unit. Drilled by hand throughout, because the exam is sat on paper.
Functions, transformations, composition and inverses
A function is a rule that turns each input into exactly one output, which is a promise you have already relied on every time you called a function you wrote. This section turns that familiar object into the one an exam asks about: its domain and range written in proper notation, its graph and the features you read off it, what happens to that graph when you change the formula, how functions are added and composed, and how a function is run backwards.
- 10 min
What a function promises
Notation, domain and range, read from an equation, a table and a graph.
- 8 min
Writing down a set of numbers
Inequalities, interval notation and set-builder notation, and how to move between them.
- 9 min
The families of shapes
The parent functions you are expected to recognise on sight, and what tells them apart.
- 9 min
Reading a graph properly: intercepts, rising and falling
Where a curve meets the axes, and the stretches of input on which it climbs or drops.
- 10 min
High points, low points and the far ends
Relative and absolute extrema, end behaviour, and one graph described feature by feature.
- 9 min
How fast it changed, on average
The slope between two points on a curve, what it measures, and what its units are.
- 10 min
Rules that change partway through
Piecewise definitions, absolute value as a piecewise rule, and step functions.
- 11 min
Drawing a piecewise rule, and reading one back
Sketching each piece over its own stretch, the hollow and filled circles, and writing the rule from a picture.
- 11 min
Moving and stretching a graph
The four changes you can make to a formula, and what each does to the picture.
- 10 min
Two changes at once, and why the order matters
Combining transformations, reading them off a formula, and the factoring trap.
- 10 min
Comparing two functions given in different ways
One function as a table, one as an equation, one as a graph, and how to line them up fairly.
- 8 min
Symmetry, and how to test for it
Even and odd functions, seen on the graph and proved from the equation.
- 8 min
Adding, multiplying and dividing functions
New functions built from old ones, and what happens to the domain when you do.
- 10 min
Feeding one function into another
Composition, the notation for it, why the order matters, and its domain.
- 10 min
Running a function backwards
Inverses from a table, from a graph, and by swapping x and y in the equation.
- 9 min
When a function cannot be reversed
One-to-one functions, the horizontal line test, and restricting a domain to fix the problem.
- 8 min
Proving that two functions undo each other
The composition test, done both ways, and why one way is not enough.
- 10 min
Where two functions meet
Solving f(x) = g(x) by graph, by table and by algebra, and checking the answer.
- 9 min
Using a function to describe something real
The modelling cycle, and how to judge where a model stops telling the truth.
- Easy
The car park meter
Coding problem · Piecewise functions, Step functions
- Easy
Which readings are in range
Coding problem · Interval notation, Domain
- Medium
The fastest stretch of growth
Coding problem · Average rate of change
- Medium
When the other plan wins
Coding problem · Solving f(x) = g(x), Linear models
- Hard
What to charge before fees
Coding problem · Inverse functions, Modelling
- Easy
Evaluating, domains, ranges and rates
Coding problem · Function notation, Domain and range, Average rate of change
- Medium
Transformations by hand
Coding problem · Transformations, Even and odd, Parent functions
- Medium
Composition and inverses by hand
Coding problem · Composition, Inverse functions
- Medium
Domains, intervals and piecewise values by hand
Coding problem · Interval notation, Domain, Piecewise functions, Step functions
- Medium
Symmetry and verification by hand
Coding problem · Even and odd, Composition, Verifying inverses
Section quiz
Equations, inequalities, systems and constraints
Opens once you finish Functions, transformations, composition and inverses, including its quiz.
Polynomial expressions, equations and functions
Opens once you finish Equations, inequalities, systems and constraints, including its quiz.
Rational exponents and radical functions
Opens once you finish Polynomial expressions, equations and functions, including its quiz.
Rational expressions, equations and functions
Opens once you finish Rational exponents and radical functions, including its quiz.
Exponential and logarithmic functions
Opens once you finish Rational expressions, equations and functions, including its quiz.
Sequences, series, the Binomial Theorem and counting
Opens once you finish Exponential and logarithmic functions, including its quiz.
Trigonometry of general triangles
Opens once you finish Sequences, series, the Binomial Theorem and counting, including its quiz.
The unit circle and the trigonometric functions
Opens once you finish Trigonometry of general triangles, including its quiz.
Trigonometric identities and equations
Opens once you finish The unit circle and the trigonometric functions, including its quiz.
Statistics: distributions, study design, inference and decisions
Opens once you finish Trigonometric identities and equations, including its quiz.
Geometric modelling, solids and density
Opens once you finish Statistics: distributions, study design, inference and decisions, including its quiz.
Circles, conics and coordinate geometry
Opens once you finish Geometric modelling, solids and density, including its quiz.
Honours extensions
Opens once you finish Circles, conics and coordinate geometry, including its quiz.
Integrated Math 3
Opens once every section is finished and every quiz is passed.