maddyhelps

Math 30-1

Toolkits

Deep dives on the ideas that show up everywhere. A unit page teaches you a topic once; a toolkit is the page you come back to — the full explanation, the table you actually need, worked examples, and the mistakes that cost marks.

Trigonometry

The unit circle

Build it from two triangles, read any angle with reference angles and CAST, and use it to solve equations. Includes the full table of exact values and the interactive circle.

Open the toolkit

Relations and functions

Exponents and logarithms

A logarithm is an exponent. The translation between forms, the five laws with the reason each works, a decision tree for solving equations, and the growth and decay setup.

Open the toolkit

Relations and functions

Transformations and mapping rules

Decode y = af[b(x − h)] + k, map any point to its image, get the order right, and describe each transformation the way markers want to read it.

Open the toolkit

Trigonometry

Trig identities

The identities sorted by what they are for, a strategy for proving, four worked proofs covering the shapes that recur, and how identities unlock equations.

Open the toolkit

Permutations and combinations

Counting: which tool?

Three questions that choose between the counting principle, permutations and combinations — plus restrictions, cases, complements, repeated letters and the binomial theorem.

Open the toolkit

Every unit

Word problem toolkit

A five-step method for turning a paragraph into mathematics, the words that signal each tool, strategies by unit, and worked examples.

Open the toolkit

How to use these

  • Stuck on a question type? Open the toolkit for that idea and find the worked example closest to it.
  • Revising? Read the tables and try the checks, then go to practice questions to see whether it stuck.
  • Writing the diploma? The toolkits cover what the formula sheet and data pages do not give you — see diploma prep.