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Fifth Year Maths Topics

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video
Number System and Radicals
Understanding the number systems
Prime factorisation
Greatest Common Factors (GCF)
Least Common Multiple (LCM)
Rational vs. Irrational numbers
Converting repeating decimals to fractions
video
Exponents
Product rule of exponents
Quotient rule of exponents
Power of a product rule
Power of a quotient rule
Power of a power rule
Negative exponent rule
Combining the exponent rules
Scientific notation
Convert between radicals and rational exponents
Solving for exponents
video
Linear Inequalities
Express linear inequalities graphically and algebraically
Solving one-step linear inequalities
Solving multi-step linear inequalities
Compound inequalities
video
Quadratic Equations and Inequalities
Solving quadratic equations by factorising
Solving quadratic equations by completing the square
Using quadratic formula to solve quadratic equations
Nature of roots of quadratic equations: The discriminant
Applications of quadratic equations
Solving quadratic inequalities
video
Introduction to Relations and Functions
Relationship between two variables
Understand relations between x- and y-intercepts
Domain and range of a function
Identifying functions
Function notation
video
Solving Simultaneous Equations
Determining number of solutions to linear equations
Solving simultaneous equations by graphing
Solving simultaneous equations by elimination
Solving simultaneous equations by substitution
Money related questions in linear equations
Unknown number related questions in linear equations
Distance and time related questions in linear equations
Rectangular shape related questions in linear equations
video
Inequalities in two variables
Graphing linear inequalities in two variables
Graphing simultaneous linear inequalities
Graphing quadratic inequalities in two variables
Graphing simultaneous quadratic inequalities
Applications of inequalities
What is linear programming?
Linear programming word problems
video
Imaginary and Complex Numbers
Introduction to imaginary numbers
Complex numbers and complex planes
Adding and subtracting complex numbers
Complex conjugates
Multiplying and dividing complex numbers
Distance and midpoint of complex numbers
Angle and absolute value of complex numbers
Polar form of complex numbers
Operations on complex numbers in polar form
video
Factorising Quadratic Functions
Factorise by taking out the greatest common factor
Factorise by grouping
Factorising difference of squares: x^2 - y^2
Factorising trinomials
Factoring difference of cubes
Factoring sum of cubes
video
Quadratic Functions
Characteristics of quadratic functions
Transformations of quadratic functions
Quadratic function in general form: y = ax^2 + bx + c
Quadratic function in vertex form: y = a(x-p)^2 + q
Completing the square
Converting from general to vertex form by completing the square
Shortcut: Vertex formula
Graphing parabolas for given quadratic functions
Finding the quadratic functions for given parabolas
Applications of quadratic functions
video
Operations of Polynomials
What is a polynomial?
Using algebra tiles to factorise polynomials
video
Polynomial Functions
What is a polynomial function?
Polynomial long division
Polynomial synthetic division
Remainder theorem
Factor theorem
Rational zero theorem
Characteristics of polynomial graphs
Multiplicities of polynomials
Imaginary zeros of polynomials
Determining the equation of a polynomial function
Applications of polynomial functions
Solving polynomial inequalities
Fundamental theorem of algebra
Descartes' rule of signs
video
Radicals
Operations with radicals
Conversion between entire radicals and mixed radicals
Adding and subtracting radicals
Multiplying radicals
Solving radical equations
video
Radical Functions
Basic radical functions
Transformations of radical functions
Square root of a function
video
Exponential Functions
Exponents: Product rule (a^x)(a^y) = a^(x+y)
Exponents: Division rule (a^x / a^y) = a^(x-y)
Exponents: Power rule (a^x)^y = a^(x * y)
Exponents: Negative exponents
Exponents: Zero exponent: a^0 = 1
Exponents: Rational exponents
Graphing exponential functions
Graphing transformations of exponential functions
Finding an exponential function given its graph
video
Rational Expressions
Simplifying rational expressions and restrictions
Adding and subtracting rational expressions
Multiplying rational expressions
Dividing rational expressions
Solving rational equations
Applications of rational equations
Simplifying complex fractions
Partial fraction decomposition
video
Reciprocal Functions
Graphing reciprocals of linear functions
Graphing reciprocals of quadratic functions
video
Function Operations
Function notation
Operations with functions
Adding functions
Subtracting functions
Multiplying functions
Dividing functions
Composite functions
Inequalities of combined functions
Inverse functions
One to one functions
Difference quotient: applications of functions
video
Logarithmic Functions
What is a logarithm?
Converting from logarithmic form to exponential form
Evaluating logarithms without a calculator
Common logarithms
Natural log: ln
Evaluating logarithms using change-of-base formula
Converting from exponential form to logarithmic form
Solving exponential equations with logarithms
Product rule of logarithms
Quotient rule of logarithms
Combining product rule and quotient rule in logarithms
Evaluating logarithms using logarithm rules
Solving logarithmic equations
Graphing logarithmic functions
Finding a logarithmic function given its graph
video
Exponential Growth and Decay
Exponential growth and decay by a factor
Exponential decay: Half-life
Exponential growth and decay by percentage
Continuous growth and decay
video
Trigonometry
Angle in standard position
Coterminal angles
Reference angle
Find the exact value of trigonometric ratios
ASTC rule in trigonometry (All Students Take Calculus)
Unit circle
Converting between degrees and radians
Trigonometric ratios of angles in radians
Radian measure and arc length
Law of sines
Law of cosines
Applications of the sine law and cosine law
video
Bearings
Introduction to bearings
Bearings and direction word problems
Angle of elevation and depression
video
Graphing Trigonometric Functions
Sine graph: y = sin x
Cosine graph: y = cos x
Tangent graph: y = tan x
Cotangent graph: y = cot x
Secant graph: y = sec x
Cosecant graph: y = csc x
Graphing transformations of trigonometric functions
Determining trigonometric functions given their graphs
video
Applications of Trigonometric Functions
Ferris wheel trig problems
Tides and water depth trig problems
Spring (simple harmonic motion) trig problems
video
Trigonometric Identities
Quotient identities and reciprocal identities
Pythagorean identities
Sum and difference identities
Cofunction identities
Double-angle identities
video
Scale Factors and Similarity
Enlargements and reductions with scale factors
Scale diagrams
Similar triangles
Similar polygons
video
Circle Geometry
Angles in a circle
Chord properties
Tangent properties
Circles and circumference
Arcs of a circle
Areas and sectors of circles
Inscribed Angles and Proofs
Central and inscribed angles in circles
video
Conics
Conics - Parabola
Conics - Ellipse
Conics - Circle
Conics - Hyperbola
video
Surface Area and Volume
Surface area and volume of prisms
Surface area and volume of pyramids
Surface area and volume of cylinders
Surface area and volume of cones
Surface area and volume of spheres
video
Sequences and series
Arithmetic sequences
Arithmetic series
Geometric sequences
Geometric series
Infinite geometric series
Sigma notation
Arithmetic mean vs. Geometric mean
video
Probability
Determining probabilities using tree diagrams and tables
Probability of independent events
Probability with Venn diagrams
video
Permutations and Combinations
Fundamental counting principle
Factorial notation
Path counting problems
Permutation vs. Combination
Permutations
Combinations
Problems involving both permutations and combinations
Pascal's triangle
Binomial theorem
video
Statistics
Median and mode
Mean
Range and outliers
Application of averages
video
Data and Graphs
Reading and drawing bar graphs
Reading and drawing histograms
Reading and drawing line graphs
Box-and-whisker plots and scatter plots
Stem-and-leaf plots
Pie charts
Reading and drawing Venn diagrams
Frequency tables and dot plots

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