Notes
Reading material from teachers and learners: theory, worked examples and questions that make you think. Some notes are made with AI, and they always say so.
Choose a topic to see its subtopics.20 notes
Sequences and SeriesHigh School (9–10)
The Sum of an Arithmetic Progression: Quick Revision
A brief note on The Sum of an Arithmetic Progression: the two forms of the sum formula, the sum of the first n natural numbers, working back from a sum, and the nth term from the sum. With a worked example, practice, a program and questions to check yourself.
Sequences and SeriesHigh School (9–10)
Patterns and the nth Term: Quick Revision
A brief note on Patterns and the nth Term: what makes an AP, the common difference, the nth term, the nth term from the end, and problems with two given terms, three numbers in an AP and counting. With a worked example, practice, a program and questions to check yourself.
Quadratic EquationsHigh School (9–10)
The Quadratic Formula and the Nature of Roots: Quick Revision
A brief note on The Quadratic Formula and the Nature of Roots: completing the square, the quadratic formula and how to use it, and the discriminant that tells the kind of roots. With a worked example, practice, a program and questions to check yourself.
Quadratic EquationsHigh School (9–10)
Solving Quadratic Equations by Factorising: Quick Revision
A brief note on Solving Quadratic Equations by Factorising: the standard form, testing a root, splitting the middle term, special cases, and word problems with the roots that make sense. With a worked example, practice, a program and questions to check yourself.
Compound and Multiple AnglesHigh School (11–12)
Sum and Difference Formulae: Quick Revision
A brief note on Sum and Difference Formulae: the formulae for , and of a sum and a difference, allied angles, double, half and triple angles, and sums into products. With a worked example, practice, a program and questions to check yourself.
Trigonometric Functions and GraphsHigh School (11–12)
Trigonometric Functions and Their Graphs: Quick Revision
A brief note on Trigonometric Functions and Their Graphs: the unit circle and the identities, signs in the four quadrants, the values to know, periods, domains and ranges, and the graphs of . With a worked example, practice, a program and questions to check yourself.
Angles and Radian MeasureHigh School (11–12)
Angles and Radian Measure: Quick Revision
A brief note on Angles and Radian Measure: angles as turns of any size, coterminal angles and quadrants, degrees, minutes and seconds, the radian, arcs, sectors and angular speed. With a worked example, practice, a program and questions to check yourself.
Rational and Irrational NumbersHigh School (9–10)
Irrational Numbers and Proofs: Quick Revision
A brief note on Irrational Numbers and Proofs: proof by contradiction, the prime fact behind it, why the square root of a prime is irrational, and sums and products with irrational numbers. With a worked example, practice, a program and questions to check yourself.
Divisibility, HCF and LCMHigh School (9–10)
Primes, HCF and LCM: Quick Revision
A brief note on Primes, HCF and LCM: prime factorisation and the Fundamental Theorem, the HCF and the LCM from the primes, the product rule for two numbers, word problems and Euclid's division method. With a worked example, practice, a program and questions to check yourself.
Composite and Inverse FunctionsHigh School (11–12)
Combining and Reversing Functions: Quick Revision
The algebra of functions, composition and its domain, one-one and onto functions, inverses and their graphs, and functions as models of data. With a worked example, practice, a program and questions.
Graphs of FunctionsHigh School (11–12)
Graphs and Special Functions: Quick Revision
Reading graphs, parabolas, the modulus, signum, greatest-integer and fractional-part functions, moving and stretching graphs, and even, odd and monotone functions. With a worked example, practice, a program and questions.
Relations and FunctionsHigh School (11–12)
Sets, Relations and Functions: Quick Revision
Sets and their operations, Venn counting, ordered pairs and products, relations, and functions with their domain and range. With a worked example, practice, a program and questions.
Distance, Midpoint and Section FormulaeHigh School (9–10)
Distance and Section Formulas: Quick Revision
The distance formula, the midpoint and section formulas, points of trisection, the centroid, the area of a triangle and collinear points. With a worked example, practice, a program and questions.
The Cartesian PlaneHigh School (9–10)
The Cartesian Plane: Quick Revision
Coordinates, the four quadrants, points on the axes, reflections, lengths along grid lines and shapes from their corners. With a worked example, practice, a program and questions.
Algebraic Identities and FactorisationHigh School (9–10)
Factorising and Identities: Quick Revision
The factor theorem, factorising quadratics by splitting the middle term, factorising cubics by testing, and the algebraic identities. With a worked example, practice, a program and questions.
PolynomialsHigh School (9–10)
Polynomials and Their Zeroes: Quick Revision
Polynomials, their degree and value, zeroes and graphs, and the remainder and factor theorems. With a worked example, practice, a program and questions.
Exponents and RadicalsHigh School (9–10)
Roots and Powers: Quick Revision
Operations with real numbers, the rules for square roots, rationalising the denominator, and the laws of exponents with fractional and negative powers. With a worked example, practice, a program and questions.
Pairs of Linear EquationsHigh School (9–10)
Pairs of Linear Equations: Quick Revision
The three cases of a pair, the ratio test, and solving by graph, by substitution and by elimination, with problems in words. With a worked example, practice, a program and questions.
Rational and Irrational NumbersHigh School (9–10)
Rational or Irrational? Deciding Quickly
Rational and irrational numbers, decimals that end or repeat, the 2-and-5 rule, square roots and the real number line. With a worked example, practice, a program and questions.
Linear Equations in Two VariablesHigh School (9–10)
What the Graph of a Linear Equation Tells You
Linear equations in two variables, their solutions, the straight-line graph, intercepts, special lines and the slope. With a worked example, practice, a program and questions.