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NSW HSC Mathematics Extension 1

HSC · NESAMathematics Extension 1508 cards

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Flashcards for the NSW HSC Mathematics Extension 1 course, following the Mathematics Extension 1 11-12 Syllabus (2024), examined from the 2027 HSC. Split into the syllabus's seven areas of study and then by focus area in its order. Extension 1 builds on Mathematics Advanced, so this deck covers only what Extension 1 adds. Where it matters, a card's extra notes whether a result is on the HSC reference sheet or must be recalled.

Adding it gives you your own copy, with every subdeck below. Each card then comes back just before you would forget it, and every one you get right or wrong counts towards your mastery of its topic. You can delete or suspend the parts you are not studying once it is yours.

What is inside (43 subdecks)

  • Calculus83 cards
    • 1 Further calculus skills34 cards
      • Further derivatives of functions18 cards
      • Techniques of integration16 cards
    • 2 Further applications of calculus49 cards
      • Areas between curves and volumes of solids of revolution9 cards
      • Differential equations20 cards
      • Further rates of change11 cards
      • Multiplicity of zeroes of polynomial functions9 cards
  • Combinatorics65 cards
    • 1 Permutations and combinations39 cards
    • 2 The binomial theorem26 cards
  • Functions111 cards
    • 1 Further work with functions57 cards
      • Graphical relationships20 cards
      • Inequalities10 cards
      • Inverse functions18 cards
      • Parametric form of a function or relation9 cards
    • 2 Polynomials54 cards
      • Language and graphs of polynomials22 cards
      • Remainder and factor theorems16 cards
      • Sums and products of zeroes of polynomials16 cards
  • Proof21 cards
    • 1 Proof by mathematical induction21 cards
  • Statistical analysis45 cards
    • 1 The binomial distribution and sampling distribution of the mean45 cards
      • Bernoulli distributions10 cards
      • Binomial distributions17 cards
      • Sampling distribution of the mean and the central limit theorem18 cards
  • Trigonometric functions86 cards
    • 1 Further trigonometry50 cards
      • Further trigonometric equations14 cards
      • Further trigonometric identities28 cards
      • Trigonometry in three dimensions8 cards
    • 2 Inverse trigonometric functions36 cards
      • Definitions of inverse trigonometric functions16 cards
      • Graphs of inverse trigonometric functions20 cards
  • Vectors97 cards
    • 1 Introduction to vectors97 cards
      • Motion in vector form14 cards
      • Operating with vectors35 cards
      • Projectile motion24 cards
      • Vector representation and notation24 cards

Some of its cards

  • How can the position of a moving object in 2D be described using a vector?
    As a position vector r=xi+yjr=xi+yj, whose components are functions of time
  • ∫dxa2−x2=[...]+c\displaystyle\int\dfrac{dx}{\sqrt{a^2-x^2}}=[...]+c
    ∫dxa2−x2=sin⁡−1xa+c\displaystyle\int\dfrac{dx}{\sqrt{a^2-x^2}}=\sin^{-1}\dfrac{x}{a} +c
  • What is a binomial?
    An expression with two terms
  • How is the graph of y=sin⁡−1xy=\sin^{-1}x obtained from the graph of y=sin⁡xy=\sin x restricted to −π2≤x≤π2-\frac{\pi}{2}\leq x\leq\frac{\pi}{2}?
    Reflect it in the line y=xy=x
  • What is a statistical population?
    The entire group of people or objects about which information is sought
  • Under what assumption can the gravitational force on a projectile be treated as constant and downward?
    When the object's motion stays close to the Earth's surface, over a small region
  • A vertical flagpole ABAB stands on level ground. From a point CC on the ground, 40 m from the base BB, the angle of elevation to the top AA is 28°. Find the height of the flagpole, to 1 decimal place.
    21.3 m
  • What is a parametric representation of a curve?
    A pair of equations giving xx and yy each as functions of a third variable, the parameter
  • Why do y=sin⁡xy=\sin x, y=cos⁡xy=\cos x and y=tan⁡xy=\tan x not have inverse functions over their full domains?
    They fail the horizontal line test: they are not one-to-one
  • What is a differential equation?
    An equation involving an unknown function and one or more of its derivatives

And 498 more once you add the deck.