HSC Maths Ext 1 study guide
HSC Maths Ext 1 · Work through your exam, one topic at a time.
Mathematics Extension 1 is a one-unit Board Developed Stage 6 course in New South Wales, offered as course 11250 in Year 11 and 15250 in Year 12. It is designed for students who want a deeper, more rigorous treatment of mathematics than the Advanced course alone: the syllabus emphasises constructing mathematical arguments and proofs, using mathematical models extensively, and appreciating the interconnected nature of mathematics and its applications in science, engineering, finance and economics. The HSC Maths Ext 1 study guide has 7 sections and about 1,720 words.
01Functions: Graphs, Transformations and Inverse Relations
A function is a rule assigning each input in its domain exactly one output. For Ext 1 you must move fluently between algebraic, graphical and inequality descriptions.
287 words, about 1 min02Trigonometric Functions: Identities, Equations and Graphs
You need exact values, the ASTC sign pattern, radian measure, arc length l=r and sector area A= 12 r^2 . Know the Pythagorean identities, the reciprocal and quotient identities, and the compound-angle and double-angle formulas.
238 words, about 1 min03Calculus: Differentiation, Integration and Applications
Ext 1 calculus extends the standard course with the product, quotient and chain rules, derivatives of , , , e^x and x , and integration by substitution and by parts. You must differentiate implicitly, find equations of tangents and normals, locate stationary points and classify them, and evaluate definite integrals including areas between curves.
244 words, about 1 min04Combinatorics: Permutations, Combinations and the Binomial Theorem
Know the multiplication and addition principles, factorials, ^nP r=n!/(n-r)! for ordered arrangements and n{r}=n!/r!(n-r)!
232 words, about 1 min05Proof: Induction, Contradiction and Inequality Arguments
Ext 1 proof questions ask you to construct a logical argument, not just compute. Master mathematical induction (base case, inductive hypothesis, inductive step, conclusion), proof by contradiction (classic irrationality of 2 , infinitude of primes), direct proof, and inequality arguments using squares ( x^2 0 ), the AM–GM inequality, or analysing a difference.
261 words, about 1 min06Vectors: Components, Dot Product and Geometry
Work with vectors in component form and as directed segments. Know addition, scalar multiplication, magnitude a =a 1^2+a 2^2+a 3^2 , unit vectors, and the dot product a = a b =a 1b 1+a 2b 2+a 3b 3 .
213 words, about 1 min07Statistical Analysis: Probability, Distributions and Data
Ext 1 statistics blends probability with data analysis. Know discrete random variables, probability distributions summing to 1, expected value E(X)= xP(X=x) and variance Var(X)=E(X^2)-[E(X)]^2 .
245 words, about 1 min