Math 30-1 study guide
Math 30-1 · Work through your exam, one topic at a time.
Mathematics 30-1 is the pre-calculus stream course in Alberta's high school mathematics sequence, and the diploma examination is the provincial assessment attached to it. Students usually take it in Grade 12 as the route toward calculus and post-secondary programs in science, engineering, business, and health fields, though some write it while upgrading or returning to school as an adult. The course builds on Mathematics 20-1 and develops algebraic, graphical, and trigonometric reasoning: transformations of functions, polynomial, radical, rational, exponential, and logarithmic functions, the unit circle along with trigonometric identities and equations, and counting methods including permutations, combinations, and the binomial theorem. The exam samples those outcomes through multiple-choice and written-response items, with an emphasis on multi-step reasoning and justification rather than recall. Topics on this exam: Relations and Functions, Trigonometry, Exponents and Logarithms, and Permutations, Combinations, and the Binomial Theorem. The Math 30-1 study guide has 4 sections and about 1,348 words.
01Relations and Functions: Notation, Transformations, and Inverses
A function pairs each element of its domain with exactly one element of its range. Before graphing or computing, extract domain restrictions from the structure: denominators cannot be zero, even-indexed radicals need non-negative radicands, and logarithms need positive arguments.
357 words, about 2 min02Trigonometry: Unit Circle, Identities, and Sinusoidal Models
Convert with π radians = 180°. Arc length is s = rθ with θ in radians.
340 words, about 2 min03Exponents and Logarithms: Laws, Equations, and Models
An exponential function y = a·bˣ has a constant ratio; b 1 gives growth, 0 < b < 1 gives decay, and the multiplier is 1 + r for a growth rate r. The base e appears in continuous growth models.
335 words, about 2 min04Counting and the Binomial Theorem
Begin every counting problem by deciding whether order matters. If it does, use permutations: nPr = n!/(n − r)!.
316 words, about 2 min