Year 12

BSM offers hundreds of year 12 maths skills to explore and learn.

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    Primitive function 12
  • Understanding primitive function
  • Primitive function of a given function
  • The notation for primitive functions
  • "Antiderivative" and "Indefinite integral" as synonyms for primitive function
  • Properties of primitive function
  • Primitive function and continuity
  • Primitive functions of elementary functions
  • Methods for computing primitive functions
  • Calculate a primitive function using the table of usual antiderivatives
  • Calculate antiderivatives of the usual functions
  • Antiderivatives rules (sum, difference and constan rule)
  • Antiderivative power rule
  • Calculate antiderivatives of a sum
  • Calculate antiderivatives of a subtraction
  • Calculate antiderivatives of a rational fraction
  • Calculate the antiderivatives of composed functions
  • Calculate the antiderivative using integration by parts
  • Calculate the primitive using the table of usual antiderivatives
  • Antiderivative of trig functions
  • Antiderivative of exponential function
  • Calculate primitive function of function that takes the value y0 at x0
  • Interpretation geometries of primitive function
  • Graphing the primitive function
  • Calculate the antiderivatives of the addition
    Integration Calculus 12
  • Understanding integration
  • Fundamental theorems of integral calculus
  • Types of integrals (definite integral and indefinite integral)
  • Properties of integral calculus
  • Integral calculus formulas
  • Methods to find integrals
  • Finding integrals by integration by parts
  • Finding integrals by substitution method
  • Finding integrals by integration by partial fractions
  • Interpretation geometries of integration
  • Application of integral calculus
  • Find accumulation of changes in the function
  • Find average change
  • Calculate the area
  • Calculate the distance
  • Calculate the volumes
  • Calculate the surface area of revolution
  • Calculate the volume of revolution
  • Differentiation of Logarithmic Functions
    Differentiation 12
  • Understanding differential
  • Derivative of function as limits
  • Differentiation formulas
  • Interpretation geometries of differentiation
  • Understanding Differentiation Rules
  • Product Rule
  • Quotient Rule
  • Chain Rule
  • Differentiation of Elementary Functions
  • Differentiation of Trigonometric Functions
  • Differentiation of Inverse Trigonometric Functions
  • Differentiation of Special Functions
  • Higher-Order Differentiation
  • The second derivative
  • Real-Life Applications of Differentiation
  • Understand the relationship between differentiability and continuity
  • Distinguish between functions written in implicit form and explicit form
  • Use implicit differentiation to find the derivative of a function
    Differential Equations 12
  • Understanding Differential Equations
  • Order Of Differential Equations
  • Degree Of Differential Equations
  • Types Of Differential Equations
  • Ordinary Differential Equations
  • Linear Differential Equations
  • Methods For Solving Differential Equations
  • Solve Differential Equations
  • Applications Of Differential Equations
  • Differential Equations: Word Problems
    Complex Numbers 12
  • Complex Numbers: Mixed Review
  • The Real Part And The Imaginary Part Of A Complex Numbers
  • Pure Imaginary Numbers Or Real Numbers
  • Simplifying Pure Imaginary Numbers
  • Properties Of Complex Numbers
  • Complex Conjugates: Mixed Review
  • Properties Of Complex Conjugates
  • The Reciprocal Of A Complex Number
  • Modulus Of A Complex Number
  • Properties Of The Modulus Of A Complex Number
  • Relationship Between The Complex Conjugate And The Modulus
  • Relationship Between Addition And The Modulus Of A Complex Number
  • Modulus Of Products And Quotients
  • Solving Equations Involving The Modulus
  • Powers Of Complex Numbers And The Modulus
  • Argument Of Complex Numbers
  • Finding The Argument Of A Complex Number In Radians
  • Properties Of Argument Of Complex Numbers
  • Finding The Principal Argument Of A Complex Number
  • Finding The Argument Of A Complex Number Using The Inverse Tangent Function
  • Finding The Argument Of A Complex Number Using Positive Acute Angles
  • The Relationship Between The Complex Conjugate And The Argument
  • Finding Argument Of The Conjugate Of A Complex Number
  • Finding Arguments Of Products And Quotients
  • Finding The Argument Of Powers Of Complex Numbers (In Algebraic Form)
  • Finding The Modulus And The Argument Of A Complex Number
  • Polar Form Of A Complex Number
  • Writing A Complex Number In Polar Form Given Its Modulus And Principal Argument
  • Finding The Polar Form Of Complex Numbers Represented On The Argand Diagram
  • Finding The Modulus And Principal Argument Of Complex Numbers In Polar Form
  • Converting A Complex Number From The Cartesian To The Polar Form
  • Converting Complex Numbers From The Polar To The Cartesian Form
  • Polar Form Of The Conjugate Of A Complex Number
  • Multiplication Of Complex Numbers In Polar Form
  • The Quotient Of Complex Numbers In Polar Form
  • The Reciprocal Of A Complex Number In Polar Form 108) Euler’s Formula
  • Relationship Between Sine, Cosine, And The Exponential Function
  • Exponential Form Of A Complex Number
  • Converting Complex Numbers From Polar To Exponential Form
  • Converting Complex Numbers From Cartesian To Exponential Form
  • Converting Complex Numbers From Exponential To Cartesian Form
  • Converting Complex Numbers Between Exponential And Polar And Cartesian Form
  • Multiplication Of Complex Numbers In Exponential Form
  • Euler’s Formula
  • Division Of Complex Numbers In Exponential Form
  • Conjugate Of Complex Numbers In Exponential Form
  • Adding Complex Numbers In Exponential Form
  • Properties Of Complex Numbers In Exponential Form
  • De Moivre’s Theorem Formula
  • Using De Moivre’s Theorem To Find The Product Of Complex Powers
  • Using De Moivre’s Theorem To Find The Difference Of Complex Powers
  • Using De Moivre’s Theorem To Raise To A Power
  • Solving Problems With Powers Of Complex Numbers
  • Using De Moivre’s Theorem To Find The Roots Of A Complex Number
    Law of Sines and Cosines 12
  • Use Law Of Sines To Solve Oblique Triangles (AAS)
  • Use Law Of Sines To Solve Oblique Triangles (ASA)
  • Use Law Of Sines To Solve Oblique Triangle (The Ambiguous Case SSA - Single Solution)
  • Use Law Of Sines To Solve Oblique Triangle (The Ambiguous Case SSA - Two Solution)
  • Use Law Of Sines To Solve Oblique Triangle (The Ambiguous Case SSA - No Solution)
  • Find The Areas Of Oblique Triangles
  • Use Law Of Sines To Solve Real Life Problems
  • Use The Law Of Cosines To Solve Oblique Triangles (SSS)
  • Use The Law Of Cosines To Solve Oblique Triangles (SAS)
  • Use Law Of Cosines To Solve Real Life Problems
  • Use Heron’s Area Formula To Find Areas Of Triangles
    Vectors 12
  • Initial point of a vector
  • Terminal point of a vector
  • Direction of a vector
  • Magnitude of vector
  • Represent vectors graphically
  • Scalar multiplication of a vector
  • Represent Vector Operations Algebraically
  • Represent Vector Operations Graphically
  • Properties Of Vector Addition
  • Properties Of Vector Scalar Multiplication
  • Unit Vectors
  • Write A Linear Combination Of Unit Vectors
  • Find Direction Angles Of Vectors
  • Component Form Of A Vector
  • Transform A Vector Using Matrix Multiplication
  • Find The Area Of A Parallelogram Defined By Vectors
  • Find The Area Of A Triangle Defined By Vectors
  • Use Vectors To Determine Weight
  • Use Vectors To Find Speed And Direction
  • Finding Dot Products Of Two Vectors
  • Properties Of The Dot Product
  • Find The Angle Between Two Vectors
  • Orthogonal Vectors
  • Vector Components
  • Determine Work Using Vectors
  • Sum Of A Finite Arithmetic Sequence
    Sequences and Series 12
  • Determine whether a sequence is finite or infinite
  • Use Sequence Notation To Write The Terms Of A Sequence
  • Recursive Sequences
  • Factorial Notation
  • Simplify Factorial Notation Rational Expressions
  • Write The Terms Of A Sequence Involving Factorials
  • Evaluate A Sequence With Summation Notation
  • Properties Of Sums
  • Defining Series
  • Finding The Sum Of A Series
  • Using A Recursion Formula
  • Partial Sum Of An Arithmetic Sequence
  • Sum Of A Finite Geometric Sequence
  • Sum Of An Infinite Geometric Series
  • Use Sequences And Series To Solve Real World Problems
  • Find A Formula For A Finite Sum
  • Sums Of Powers Of Integers
  • Finite Differences
    Conics 12
  • Use the center, the radius, and the Pythagorean theorem to derive the equation of a circle.
  • Foci Of An Ellipse
  • Major And Minor Axis Of An Ellipse
  • Co-Vertices Of An Ellipse
  • Derive The Equation Of An Ellipse
  • Graph Ellipses
  • Graph Ellipses Using Translations
  • Eccentricity Of An Ellipse
  • Foci Of A Hyperbola
  • Axes Of A Hyperbola
  • Vertices Of A Hyperbola
  • Asymptotes Of A Hyperbola
  • Use The Distance Formula And Foci To Derive The Equation Of A Hyperbola
  • Graph Hyperbolas
  • Classify A Second Degree Equation As Either A Parabola, Circle, Ellipse, Or Hyperbola From General Equations.
  • Classify A Second Degree Equation As Either A Parabola, Circle, Ellipse, Or Hyperbola Using The Discriminant
  • Rotation Of Axes For An Ellipse
  • Rotation Of Axes For A Hyperbola
  • Rotation Of Axes For A Parabola
    Polar Form 12
  • Find The Modulus Of A Complex Number
  • Represent A Complex Number In Polar Form
  • Use Polar Form To Multiply Complex Numbers
  • Use Polar Form To Raise A Number To A Power
  • Plot Points In The Polar Coordinate System
  • Convert Points From Polar To Rectangular From
  • Convert Points From Rectangular To Polar Form
  • Convert Polar Equations To Rectangular Form
  • Graph Polar Equations By Plotting Points
  • Test For Symmetry In Polar Coordinates
  • Use Symmetry To Graph A Polar Equation
  • Special Polar Graphs: Limacons
  • Identify Special Polar Graphs: Rose Curves
  • Identify Special Polar Graphs: Lemniscates
  • Identify Special Polar Graphs: Circles
  • Graph A Rose Curve
  • Graph A Lemniscate
  • Identify The Type Of Conic From A Polar Equation
  • Graph A Conic From Its Polar Equation
  • Find The Polar Equation Of A Conic
    Trigonometry And The Unit Circle 12
  • Measure Angles Using Degree Measure
  • Measure Angles Using Radian Measure
  • Find Coterminal Angles In Degree Measure
  • Find Coterminal Angles In Radian Measure
  • Complementary Angles In Radian Measure
  • Supplementary Angles In Radian Measure
  • Convert An Angle Measure From Degrees To Radians
  • Convert An Angle Measure From Radians To Degrees
  • Find Arc Length
  • Find Linear Speed
  • Find Angular And Linear Speed
  • Find Area Of A Sector Of A Circle
  • Graph The Unit Circle
  • Use The Properties Of 30-60-90 Triangles To Find The Coordinate Points At The 〖30〗^° (π/6 radian) Angle Measure On The Unit Circle
  • Use The Properties Of 45-45-90 Triangles To Find The Coordinate Points At The 〖45〗^° (π/4 radian) Angle Measure On The Unit Circle
  • Use The Properties Of 30-60-90 Triangles To Find The Coordinate Points At The 〖60〗^° (π/3 radian) Angle Measure On The Unit Circle
  • Extend Your Knowledge Of The Coordinates At 〖30〗^°,〖45〗^° ,〖60〗^° Angles To Find Coordinates In The Other Three Quadrants Of The Unit Circle
  • Understand That For Any Angle θ On The Unit Circle With Points (x,y), □sin sin θ =y
  • Understand That For Any Angle θ On The Unit Circle With Points (x,y), □cos cos θ =x
  • Understand That For Any Angle θ On The Unit Circle With Points (x,y), □tan tan θ =y/x
  • Understand That For Any Angle θ On The Unit Circle With Points (x,y), □csc csc θ =1/y
  • Understand That For Any Angle θ On The Unit Circle With Points (x,y), □sec sec θ =1/x
  • Understand That For Any Angle θ On The Unit Circle With Points (x,y), □cot cot θ =x/y
  • Evaluate Trig Functions From Angle Measures On The Unit Circle
  • Evaluate Trigonometric Functions Of Acute Angles
    Tangent Functions 12
  • Identify Tangent Functions From The Equation
  • Identify Tangent Functions From The Graph
  • Identify Tangent Functions From The Table
  • Identify Tangent Functions From A Set Of Ordered Pairs
  • Domain Of Tangent Functions
  • Range Of Tangent Functions
  • Complete A Function Table From The Graph Of A Tangent Function
  • Write Tangent Functions To Solve Word Problems
  • Solve Problems Involving Tangent Functions
  • Evaluate Tangent Functions
  • Identify Increasing, Decreasing And Constant Intervals Of Tangent Functions
    Graphing Trig Functions 12
  • Determine the period from a sine or cosine function in equation form
  • Determine The Amplitude From A Sine Or Cosine Function In Equation Form
  • Determine The Period From A Sine Or Cosine Function In Graph Form
  • Determine The Amplitude From A Sine Or Cosine Function In Graph Form
  • Identify Minimum And Maximum Points Of Sine And Cosine Equations
  • Identify Symmetry In The Graphs Of Sine And Cosine
  • Graph Sine And Cosine Functions Using Transformations
  • Determine The Asymptotes From A Tangent Function In Equation Form
  • Determine The Asymptotes From A Tangent Function In Graph Form
  • Graph A Tangent Function
  • Identify Symmetry In Tangent Graphs
  • Graph A Tangent Function Using Transformations
  • Determine If Trig Functions Are Odd, Even, Or Neither
    Cosecant Functions 12
  • Identify Cosecant Functions From The Equation
  • Identify Cosecant Functions From The Graph
  • Identify Cosecant Functions From The Table
  • Identify Cosecant Functions From A Set Of Ordered Pairs
  • Domain Of Cosecant Functions
  • Range Of Cosecant Functions
    Secant Functions 12
  • Identify Secant Functions From The Equation
  • Identify Secant Functions From The Graph
  • Identify Secant Functions From The Table
  • Identify Secant Functions From A Set Of Ordered Pairs
  • Domain Of Secant Functions
  • Range Of Secant Functions
    Cotangent Functions 12
  • Identify Cotangent Functions From The Equation
  • Identify Cotangent Functions From The Graph
  • Identify Cotangent Functions From The Table
  • Identify Cotangent Functions From A Set Of Ordered Pairs
  • Domain Of Cotangent Functions
  • Range Of Cotangent Functions
    Graphing Reciprocal Trig Functions 12
  • Graph A Cosecant Function
  • Graph A Secant Function
  • Determine The Period From A Cosecant Or Secant Function In Equation Form
  • Determine The Period From A Cosecant Or Secant Function In Graph Form
  • Determine The Asymptotes For A Cosecant Function In Equation Form
  • Determine The Asymptotes For Secant Function In Equation Form
  • Determine The Asymptotes For A Cosecant Function In Graph Form
  • Determine The Asymptotes For Secant Function In Graph Form
  • Identify Symmetry In Cosecant Graphs
  • Identify Symmetry In Secant Graphs
  • Graph A Cotangent Function
  • Determine The Period From A Cotangent Function In Equation Form
  • Determine The Period From A Cotangent Function In Graph Form
  • Determine The Asymptotes From A Cotangent Function In Equation Form
  • Determine The Asymptotes From A Cotangent Function In Graph Form
  • Identify Symmetry Of Cotangent Graphs
  • Determine If Reciprocal Trig Functions Are Odd, Even, Or Neither
    Inverse Trig Functions 12
  • Understand That Arcsine, Arccosine, And Arctangent Represent The Inverse Of A Sine, Cosine, And Tangent Function Respectively
  • Evaluate Arcsine Functions Using Unit Circle Knowledge
  • Evaluate Arcsine Functions Using A Calculator
  • Graph The Arcsine Functions
  • Evaluate Arccosine Functions Using Unit Circle Knowledge
  • Evaluate Arccosine Functions Using A Calculator
  • Graph Arccosine Functions
  • Domain Of Arcsine And Arccosine Functions
  • Range Of Arcsine Functions
  • Range Of Arccosine Functions
  • Evaluate Arctangent Functions Using Unit Circle Knowledge
  • Evaluate Arctangent Functions Using A Calculator
  • Graph Arctangent Functions
  • Domain Of Arctangent Functions
  • Range Of Arctangent Functions
  • Properties Of Inverse Trig Functions
  • Rewrite A Trigonometric Expression Using Trig Identities
    Trig Identities 12
  • Use Reciprocal Identities To Evaluate Trig Functions
  • Use Quotient Identities To Evaluate Trig Functions
  • Use Pythagorean Identities To Evaluate Trig Functions
  • Use Cofunction Identities To Evaluate Trig Functions
  • Use Even/Odd Identities To Evaluate Trig Functions
  • Simplify A Trigonometric Expression Using Trig Identities
  • Factor A Trigonometric Expression Using Trig Identities
  • Add And Subtract Trigonometric Expressions Using Trig Identities
  • Trigonometric Substitution
  • Rewrite A Logarithmic Expression Using Trig Identities
  • Verify Trigonometric Identities
    Trig Formulas 12
  • Use The Sum And Difference Formulas For Sine To Evaluate A Trigonometric Function
  • Use The Sum And Difference Formulas For Cosine To Evaluate A Trigonometric Function
  • Use The Sum And Difference Formulas For Tangent To Evaluate A Trigonometric Function
  • Use Sum And Difference Formulas To Verify Identities
  • Use Sum And Difference Formulas To Solve A Trigonometric Equation
  • Use Multiple-Angle Formulas To Rewrite Trigonometric Functions
  • Use Multiple-Angle Formulas To Evaluate Trigonometric Functions
  • Use Double-Angle Formulas To Rewrite Trigonometric Functions
  • Use Double-Angle Formulas To Evaluate Trigonometric Functions
  • Use Power-Reducing Formulas To Rewrite Trigonometric Functions
  • Use Half-Angle Formulas To Rewrite Trigonometric Functions
  • Use Half-Angle Formulas To Evaluate Trigonometric Functions
  • Use Product-To-Sum Formulas To Rewrite Trigonometric Functions
  • Use Product-To-Sum Formulas To Evaluate Trigonometric Functions
  • Use Sum-To-Product Formulas To Rewrite Trigonometric Functions
  • Use Sum-To-Product Formulas To Evaluate Trigonometric Functions
  • Use Trigonometric Formulas To Rewrite Real Life Models
    Trigonometric Applications 12
  • Solve A Right Triangle For Any Missing Angles Using Trigonometry
  • Simple Harmonic Motion
  • Combining Like Terms Using Trigonometric Functions
  • Extract Square Roots From Trigonometric Equation
  • Solve A Right Triangle For Any Missing Sides Using Trigonometry
  • Find An Angle Of Depression
  • Find Directions In Terms Of Bearings
  • Solve Trigonometric Equations Of Quadratic Type
  • Rewrite Trigonometric Equations Of Quadratic Type To Get A Single Trig Function
  • Squaring And Converting To Quadratic Types
  • Use The Quadratic Formula To Solve Trigonometric Equations Of Quadratic Type
  • Use Inverse Functions To Solve Trigonometric Equations Of Quadratic Type
  • Solving A Multiple-Angle Equation
    Probability And Statistics 12
  • Identify Whether A Question Is A Statistical Question Or Not
  • Identify The Statistical Variable
  • Determine Whether A Statistical Variable Is Qualitative Or Quantitative
  • Identify The Difference Between A Sample And A Population
  • Identify Whether A Quantity Is A Statistic Or A Parameter
  • Identify A Statistical Study As A Sample Survey
  • Identify A Statistical Study As An Experiment
  • Know The Difference Between The Experimental Group And The Control Group
  • Identify A Statistical Study As An Observational Study
  • Determine If A Sampling Method Represents A Simple Random Sample
  • Identify A Sampling Method As Systematic Sampling
  • Identify A Sampling Method As Self-Selected Sampling
  • Identify A Sampling Method As Convenience Sampling
  • Determine If A Study Has Bias
  • Create Box And Whisker Plots From Sets Of Data
  • Create Data Distributions From Sets Of Data
  • Identify Skewed Distributions
  • Graph A Normal Distribution Given The Mean And Standard Deviation
  • Use Z-Scores To Compare Data Points From Different Scales
  • Evaluate Reports By Estimating Population Parameters
  • Use Multiple Samples To Make An Inference About A Population
  • Use Margin Of Error Formula For Quantitative Data
  • Use Margin Of Error Formula For Qualitative Data
  • Determine Whether A Statistical Variable Is Qualitative Or Quantitative
    Limits And Their Properties 12
  • Estimate A Limit Using A Numerical Approach
  • Estimate A Limit Using A Graphical Approach
  • Estimate A Limit Using An Analytic Approach
  • Learn That A Limit Can Fail To Exist When Behavior Differs From The Right And From The Left
  • Learn That A Limit Can Fail To Exist Because Of Unbounded Behavior
  • Limits And Oscillating Behavior
  • Use A Formal Definition Of Limit
  • Evaluate Basic Limits
  • Limit Of A Polynomial
  • Limit Of A Rational Function
  • Limit Of A Composite Function
  • Limits Of Trigonometric Functions
  • Evaluate A Limit Using The Dividing Out Technique
  • Evaluate A Limit Using The Rationalizing Technique
  • Evaluate A Limit Using The Squeeze Theorem
  • Determine Continuity At A Point And On An Open Interval
  • One-Sided Limits
  • Greatest Integer Function
  • Continuity On A Closed Interval
  • Charles’s Law And Absolute Zero
  • The Intermediate Value Theorem
  • Determine Infinite Limits From The Left
  • Determine Infinite Limits From The Right
  • Use Vertical Asymptotes To Help In Determining Limits
  • Properties Of Continuity
    Differentiation 12
  • Find The Slope Of The Tangent Line To A Curve At A Point
  • Use The Limit Definition To Find The Derivative Of A Function
  • Understand The Relationship Between Differentiability And Continuity
  • Find The Derivative Of A Function Using The Constant Rule
  • Find The Derivative Of A Function Using The Power Rule
  • Find The Derivative Of A Function Using The Constant Multiple Rule
  • Find The Derivative Of A Function Using The Sum Rule
  • Find The Derivative Of A Function Using The Difference Rule
  • Find The Derivative Of The Sine Function
  • Find The Derivative Of The Cosine Function
  • Use Derivatives To Find Rates Of Change
  • Find The Derivative Of A Function Using The Product Rule
  • Find The Derivative Of A Function Using The Quotient Rule
  • Find The Derivative Of A Trigonometric Function
  • Find A Higher-Order Derivative Of A Function
  • Find The Derivative Of A Composite Function Using The Chain Rule
  • Find The Derivative Of A Function Using The General Power Rule
  • Simplify Derivatives By Factoring Out The Least Powers
  • Simplify Derivatives Of A Quotient
  • Simplify Derivatives Of A Power
  • Find The Derivative Of A Trigonometric Function Using The Chain Rule
  • Distinguish Between Functions Written In Implicit Form And Explicit Form
  • Use Implicit Differentiation To Find The Derivative Of A Function
    Complex Numbers And Complex Plane 12
  • Write Trigonometric Forms Of Complex Numbers
  • Multiply Complex Numbers Written In Trigonometric Form
  • Divide Complex Numbers Written In Trigonometric Form
  • Use Demoivre’s Theorem To Find Powers Of Complex Numbers
  • Find Nth Roots Of Complex Numbers
  • Multiplying In The Complex Plane
  • Dividing In The Complex Plane