Unit 1
Mathematical Methods (Queensland)
Topic 0: Surds
Note: This topic is NOT part of the current Mathematical Methods syllabus. However, the manipulation of surds is widely considered a useful skill (both in methods and specialist). For this reason, I include a short course on surds here.
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Surds: What they are and why we need them
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Proof that the square root is equal to the power of 1/2
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Simplifying surds
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Adding and Subtracting surds by grouping like terms
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Multiplying surds
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Surds and the distributive law
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Dividing Surds
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Surds Rationalising denominators
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Rationalising denominators using conjugates
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Infinite nested radicals
Topic 1: Arithmetic Sequences and Series
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Sequence Notation
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Recurrence Relations
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Using a recurrence relation
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Defining a sequence in terms of n
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Applications of recurrence relations
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Applications of recurrence relations non arithmetic
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Using a calculator with recurrence relations
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Arithmetic sequence formula
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Rearranging the arithmetic sequence formula
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Arithmetic sequences using simultaneous equations
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Arithmetic sequences and series
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Simultaneous equations using arithmetic series and sequences
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Application of the arithmetic sequence
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Simple Interest using arithmetic sequences
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The Middle Term as the arithmetic mean in an arithmetic sequence
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Introduction to the Sum of an arithmetic series
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Arithmetic Series Formula Where it comes from and how to use it
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Arithmetic Series resulting in a quadratic
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Arithmetic Series and Simultaneous equations
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Finding the number of terms in an arithmetic sequence
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Arithmetic series Finding the number of terms that sum to a given number
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Application of arithmetic series
Topic 2: Functions and Graphs
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Set Notation: Introduction
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Interval Notation and Number Lines
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Relations Domain and Range
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Relations, Functions and the vertical line test
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domain and range notation
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Domain and Range of functions and relations
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Graphing on calculator using restricted domains
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What’s a function
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Function notation
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Function Notation: Better ways of representing functions
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Piecewise Functions
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Function Transformations intro
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Functions Transformation fx+a
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Function transformation f(x+a)
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Function transformation afx
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Functions transformations f(ax)
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Anatomy of a quadratic graph
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Solving Quadratics 3 ways
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3 forms of the quadratic equation
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Review of sketching quadratics two ways
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The quadratic formula and the discriminant
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Modelling and problem solving with quadratics
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solving simultaneous equations using quadratic and linear graphs
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Direct vs inverse proportion
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Equations of hyperbola and sketching
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Finding equation of reciprocal function from sketch
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Sketching Hyperbolas and why there’s an asymptote
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Sketching circles and finding equations of circles
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The square root function
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Intersecting Functions
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Direct and Indirect Proportion
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Factor Theorem Examples
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Long Division: Learn this before polynomial division
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Polynomial division
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Finding a linear factor of a polynomial
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Factorise solve and sketch a cubic
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Cubics in “Turning Point” Form: (But it’s not a turning point)
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Full quadratic review video
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Fitting Indirect Proportion function to data using TI Nspire
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Graphing and finding key points on the TI Nspire
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Determining intersections of functions graphically on the TI Nspire
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Sketching a graph on the TI Nspire
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Solving simultaneous equations using LinSolve TI Nspire
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Solving polynomials on the TI Nspire
Topic 3: Counting and Probability
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The Language of Sets
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Theoretical Probability with sets
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All Probabilities sum to 1
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Venn Diagrams the complement
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Experimental probability
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simplified tree diagram
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The Addition rule of probability
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Probability Tables intro
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Conditional Probability formula
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Conditional Probability Do you watch the bachelorette
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Conditional probability rearranging the formula
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Conditional Probability and Tree Diagrams
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Independent events intro and tests
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Independent events 2
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Pascal’s Triangle and Selections
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Binomial expansion using pascal’s triangle
Topic 4: Exponential Functions
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Index Law 1 – multiplication of indices
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Index Law 2 – dividing indices
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Index Law 3 – raising to the power of zero
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Index Law 4 – Raising a power to another power
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Index Law 5 – worked examples using the fifth index law
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Index Law 6 – expanding brackets around a fraction raised to a power
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Index law 7 Negative Indices – converting Negative indices into positive indices using fractions
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Index Laws Fractional indices
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Index Laws Negative bases
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Index Laws simplifying by decomposing
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Scientific notation Converting to scientific notation
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Scientific Notation Convert scientific notation to decimal
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Scientific notation Multiplying and dividing
Topic 5: Geometric Sequences and Series
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Geometric sequences and the recursive definition
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Geometric Sequence formula
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Geometric sequences finding the common ratio
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Geometric Sequences finding the value of n
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Geometric Sequences and simultaneous equations
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Geometric Sequences Geometric mean
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Compound interest as a geometric sequence
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Geometric series formula proof and example
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Geometric series find the value of n
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Regular deposits as a geometric series
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Geometric Series Sum to Infinity and Zeno’s Paradox
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Geometric series sum to infinity application
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Geometric Series Sum to infinity writing recurring decimals as fractions