VCE Methods Unit 1 Skills () « back to units

The skills below are aligned with the VCE Mathematical Methods Study Design 2023-2027. Skills are organised into key areas: Functions & Relations, Algebra, Circular Functions, Introduction to Calculus, and Probability Foundations. To master a skill, you will have to gain 10 stars.

There are 3 levels to each skill,

  1. Easy: A star will be taken away if you get 3 consecutive wrong answers.
  2. Medium: A star will be taken away if you get 2 consecutive wrong answers.
  3. Hard: A star will be taken away on each wrong answer.

Most skills have multiple types of questions with varying difficulties. If you keep getting wrong answers, the system may give you the simplest question to answer. The idea is to have you master these skills with a ground up approach. If you get an answer wrong, you can read the solution and helpful tips that briefly explain the skill/topic you are practising.

All the best with your VCE Methods Unit 1. If you see any issue, please do report it by clicking the red button at bottom left of this page.

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  1. Functions & Relations

    1. Identify domain and range from a graph FREE
    2. Express domain and range using interval notation
    3. Determine if a relation is a function (vertical line test)
    4. Evaluate functions using function notation f(a)
    5. Identify key features of graphs (intercepts, turning points, asymptotes)
    6. Sketch linear functions and identify gradient/intercept

  2. Polynomial Sketching

    1. Sketch quadratic functions (turning point form)
    2. Sketch quadratic functions (factored form)
    3. Sketch quadratic functions (general form — complete the square)
    4. Sketch cubic functions (factorisable)
    5. Sketch quartic functions (factorisable)
    6. Sketch power functions (x^n, x^(-n), x^(1/n))

  3. Inverse & Power Functions

    1. Identify graphs of power functions (hyperbola, truncus, square root, cube root)
    2. Find the inverse of a function algebraically
    3. Sketch inverse functions by reflecting in y = x

  4. Graph Transformations

    1. Apply translations to graphs (horizontal and vertical shifts)
    2. Apply dilations to graphs (stretches and compressions)
    3. Apply reflections to graphs (x-axis and y-axis)
    4. Determine the equation from a transformed graph
    5. Combine transformations in correct order

  5. Functions & Graphs (Advanced)

    1. Match equation to graph (polynomial family)
    2. Identify odd and even functions
    3. Determine axis intercepts of polynomial functions
    4. Sketch piecewise-defined functions

  6. Algebra

    1. Expand and simplify algebraic expressions
    2. Factorise quadratic expressions (monic and non-monic)
    3. Factorise by grouping
    4. Factorise sum and difference of cubes
    5. Simplify algebraic fractions
    6. Simplify expressions involving surds
    7. Rationalise denominators
    8. Apply index laws
    9. Convert between index and surd form
    10. Solve quadratic equations by factorising
    11. Solve quadratic equations using the quadratic formula
    12. Solve equations with surds or indices
    13. Solve simultaneous equations (linear-linear)
    14. Solve simultaneous equations (linear-quadratic)
    15. Solve polynomial equations using factor theorem
    16. Apply remainder theorem
    17. Long division of polynomials
    18. Solve literal equations
    19. Simplify rational expressions with polynomials
    20. Apply the discriminant
    21. Solve inequalities involving quadratics

  7. Circular Functions Intro

    1. Convert between degrees and radians
    2. Identify exact values of sin, cos, tan for standard angles
    3. Use the unit circle to find values in all four quadrants (ASTC)
    4. Use symmetry properties of circular functions
    5. Sketch y = sin(x) and y = cos(x) identifying key features
    6. Sketch y = tan(x) identifying asymptotes and key features
    7. Apply transformations to circular functions: y = A sin(n(x - b)) + c
    8. Determine amplitude, period, and phase shift from equation
    9. Determine amplitude, period, and phase shift from graph
    10. Solve trigonometric equations (basic: sin x = k)

  8. Introduction to Calculus

    1. Calculate average rate of change over an interval
    2. Estimate instantaneous rate of change from a graph
    3. Interpret rate of change in context (distance-time, volume-time)
    4. Identify intervals where a function is increasing or decreasing
    5. Sketch the gradient function from a given graph
    6. Trace a pseudocode algorithm (bisection method)

  9. Counting & Probability Intro

    1. Identify sample spaces for experiments
    2. Calculate probabilities using counting techniques
    3. Apply the addition rule for probability
    4. Apply the multiplication rule for independent events
    5. Calculate conditional probability P(A|B)
    6. Determine if events are independent
    7. Use tree diagrams to solve probability problems
    8. Apply the product rule for counting
    9. Calculate permutations and combinations
    10. Use combinations in probability calculations
    11. Simulation and estimation of probabilities

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