UniGeniusHSC Maths Extension 1

Course map

Functions

  • Further work with functionsYear 11: Further work with functions
    • Sketch reciprocals, squares, absolute values and sums of functions from a given graph
    • Find and graph inverse functions and restrict domains so that an inverse exists
    • Convert between parametric and Cartesian forms
    • Solve rational, absolute value and quadratic inequalities
    LessonPractice
  • PolynomialsYear 11: Polynomials
    • Use the language of polynomials and sketch their graphs from their factors
    • Apply the remainder and factor theorems
    • Use sums and products of zeroes to solve problems
    LessonPractice

Trigonometric functions

  • Further trigonometryYear 11: Further trigonometry
    • Solve problems in three dimensions with trigonometry
    • Prove identities with compound angles and double angles
    • Solve trigonometric equations, including with the auxiliary angle form
    LessonPractice
  • Inverse trigonometric functionsYear 12: Inverse trigonometric functions
    • Use the definitions, domains and ranges of the inverse trigonometric functions
    • Sketch and transform their graphs and evaluate them exactly
    LessonPractice

Combinatorics

  • Permutations, combinations and the binomial theoremYear 11: Permutations and combinations; The binomial theorem
    • Count arrangements and selections, with and without restrictions, and use the pigeonhole principle
    • Expand binomials, find a given term and prove binomial identities
    LessonPractice

Proof

  • Proof by mathematical inductionYear 12: Proof by mathematical induction
    • Prove results for sums and for divisibility by induction
    • Find the error in a false proof by induction
    LessonPractice

Vectors

  • Introduction to vectorsYear 12: Introduction to vectors
    • Represent vectors in two and three dimensions and operate with them
    • Use the scalar product for angles, perpendicularity and projections, and prove geometric results
    • Model motion in two dimensions, including projectiles, with vectors
    LessonPractice

Calculus

  • Further calculus skillsYear 12: Further calculus skills
    • Differentiate inverse functions and inverse trigonometric functions
    • Integrate by substitution and with inverse trigonometric and trigonometric results
    LessonPractice
  • Further applications of calculusYear 12: Further applications of calculus
    • Use multiplicity of zeroes and related rates of change
    • Find areas between curves and volumes of solids of revolution
    • Solve differential equations and read slope fields
    LessonPractice

Statistical analysis

  • The binomial distribution and sampling distribution of the meanYear 12: The binomial distribution and sampling distribution of the mean
    • Use Bernoulli and binomial distributions, their means and variances
    • Describe the sampling distribution of the mean and use the central limit theorem
    LessonPractice

The HSC examination

  • The HSC examinationYear 11 and Year 12
    • Know the paper: sections, marks, time, reading time, calculators and the reference sheet
    • Write Section II answers, including proofs, that show the reasoning the marking rewards
    • Know that school-based assessment is set by your school
    LessonPractice

NSW HSC Mathematics Extension 1, Year 11 and Year 12. The HSC examines Year 11 and Year 12 content. School-based assessment is set by your school, so it is described in a lesson rather than practised here.

Independent preparation for NSW HSC Mathematics Extension 1. Not affiliated with or endorsed by the NSW Education Standards Authority (NESA).

Questions? support@unigenius.co.uk

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