YOUR SUBJECT LESSONS
Mathematics
Explore functions, equations and data.
- 01Name the unknown and its domain.
- 02Write the relation before inserting numbers.
- 03Substitute your answer to check it.
FROM PRINCIPLE TO PRACTICE
Lessons in a useful order
From foundations to high school: a mental model, worked example and four exercises with solutions per chapter.
Mathematics
Fractions: share the same whole
A fraction compares a quantity with a whole divided into equal parts.
Lesson and 4 exercisesMathematics
Powers and roots: count the factors
A positive integer power counts equal factors.
Lesson and 4 exercisesMathematics
Equations: keep the balance level
An equation states that two expressions have the same value.
Lesson and 4 exercisesMathematics
Statistics: centre and spread
The mean balances the sum of values; the median divides an ordered series in half.
Lesson and 4 exercisesMathematics
Right triangles: choose the ratio
The hypotenuse is opposite the right angle.
Lesson and 4 exercisesMathematics
Proportionality and percentages
Quantities are proportional when one constant factor maps every value of the first to the second.
Lesson and 4 exercisesMathematics
Expand, factor and recognise identities
Expansion turns products into sums by distribution.
Lesson and 4 exercisesMathematics
Pythagoras: lengths and right-angle checks
In a right triangle, the hypotenuse squared equals the sum of squares of the perpendicular sides.
Lesson and 4 exercisesMathematics
Similar triangles and parallel-line ratios
Similar triangles share angles and have proportional corresponding sides.
Lesson and 4 exercisesMathematics
Functions: an input and its image
A function gives each input in its domain one output.
Lesson and 4 exercisesMathematics
Vectors: displacement, not location
A point locates a position; a vector describes direction, orientation and length of a displacement.
Lesson and 4 exercisesMathematics
Inequalities: a region of solutions
An inequality compares expressions.
Lesson and 4 exercisesMathematics
Coordinate geometry: midpoint, distance and line
In an orthonormal frame, distance is the norm of coordinate differences, by Pythagoras.
Lesson and 4 exercisesMathematics
Quadratics: discriminant and roots
A polynomial ax² + bx + c with nonzero a draws a parabola.
Lesson and 4 exercisesMathematics
Derivatives: local slope
A rate of change compares two points.
Lesson and 4 exercisesMathematics
Sequences: add or multiply each step
A sequence gives values indexed by integers.
Lesson and 4 exercisesMathematics
Probability: read a tree
A probability lies between zero and one.
Lesson and 4 exercisesMathematics
Unit circle and radians
On the unit circle, angle θ gives coordinates (cos θ, sin θ).
Lesson and 4 exercisesMathematics
Exponential and logarithm: inverse operations
The exponential is positive and changes sums into products.
Lesson and 4 exercisesMathematics
Antiderivatives and integrals: accumulate change
An antiderivative F of f satisfies F′ = f.
Lesson and 4 exercisesMathematics
Binomial model: count successes
A binomial model requires a fixed number of independent trials, two outcomes and constant success probability p.
Lesson and 4 exercisesMathematics
Limits: describe behaviour near a point
A limit describes behaviour as x approaches a value or infinity, even if the function is undefined at that point.
Lesson and 4 exercisesMathematics
Conditional probability: change the reference group
P(B given A) measures B within A when P(A)>0, using P(A∩B)/P(A).
Lesson and 4 exercisesFurther reading
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