HKDSE Maths M1 study guide
HKDSE Maths M1 · Work through your exam, one topic at a time.
This independent study page provides practice for HKDSE Maths M1. Its editorial learning areas include Calculus; Probability Statistics; Algebra Functions; Sequences Series. The questions develop subject knowledge and application through worked reasoning, distinctions between competing answers, and practical scenarios. Study the relevant guide before attempting a mixed set, then explain the evidence or calculation that supports each answer. Topics on this exam: Calculus, Probability Statistics, Algebra Functions, and Sequences Series. The HKDSE Maths M1 study guide has 4 sections and about 1,597 words.
01Calculus
Calculus practice develops the ability to move fluently between a function, its rate of change, and its accumulated total. Expect differentiation of composite, implicit and parametric forms, evaluation of definite and improper integrals, and questions that require you to justify a limit before differentiating. Chain rule: d/dx f(g(x)) = f'(g(x))·g'(x). The inner derivative is the most commonly dropped factor.
348 words, about 2 min02Statistics and Probability
This statistics and probability chapter explores how data are collected, summarized, and interpreted, and how probability models uncertainty. Expect measures of centre and spread, graphical displays, normal distributions and z-scores, counting-based probability, conditional probability, and critical evaluation of study design and correlation versus causation. Centre and spread: mean is sensitive to outliers, median is resistant; standard deviation measures typical distance from the mean. Range ignores the middle of the data.
397 words, about 2 min03Algebra and Functions
Algebra and function practice asks you to move fluently between symbolic, graphical, and verbal representations of relationships. Expect manipulation of polynomial, rational, radical, exponential, and logarithmic expressions; solving equations and inequalities; and reasoning about domain, range, inverse functions, and transformations. Questions often present a function in one form and require an answer in another, so translation skill matters as much as raw computation. Domain restrictions come first.
462 words, about 2 min04Sequences and series
Sequences and series examines arithmetic and geometric progressions, sigma notation, sums to infinity and the binomial expansion. You should be able to derive and apply the standard formulae, decide when an infinite sum converges, and extract a specified coefficient from a binomial expansion without expanding everything. For an arithmetic progression with first term a and common difference d: the nth term is a + (n − 1)d and the sum of n terms is (n/2)(2a + (n − 1)d). For a geometric progression with common ratio r: the nth term is ar^(n−1), the sum of n terms is a(1 − rⁿ)/(1 − r), and the sum to infinity is a/(1 − r), valid only when r < 1.
390 words, about 2 min