Alberta Grade 12 Math Curriculum

Functions

  • Domain and range
  • Identify functions
  • Linear functions
  • Linear functions over unit intervals
  • Evaluate functions
  • Add, subtract, multiply, and divide functions
  • Composition of functions
  • Identify inverse functions
  • Find values of inverse functions from tables
  • Find values of inverse functions from graphs
  • Find inverse functions and relations

Families of functions

  • Translations of functions
  • Reflections of functions
  • Dilations of functions
  • Transformations of functions
  • Function transformation rules
  • Describe function transformations

Quadratic relations

  • Characteristics of quadratic functions
  • Find the maximum or minimum value of a quadratic function
  • Graph a quadratic function
  • Match quadratic functions and graphs
  • Solve a quadratic equation using square roots
  • Solve a quadratic equation by factoring
  • Solve a quadratic equation by completing the square
  • Solve a quadratic equation using the quadratic formula
  • Using the discriminant

Polynomials

  • Divide polynomials using long division
  • Write a polynomial from its roots
  • Find the roots of factored polynomials
  • Rational root theorem
  • Complex conjugate theorem
  • Conjugate root theorems
  • Descartes’ Rule of Signs
  • Fundamental Theorem of Algebra
  • Match polynomials and graphs
  • Factor sums and differences of cubes
  • Solve equations with sums and differences of cubes
  • Factor using a quadratic pattern
  • Solve equations using a quadratic pattern
  • Pascal’s triangle
  • Pascal’s triangle and the Binomial Theorem
  • Binomial Theorem I
  • Binomial Theorem II

Rational functions

  • Rational functions: asymptotes and excluded values
  • Solve rational equations
  • Check whether two rational functions are inverses

Logarithms

  • Convert between exponential and logarithmic form: rational bases
  • Evaluate logarithms
  • Change of base formula
  • Identify properties of logarithms
  • Product property of logarithms
  • Quotient property of logarithms
  • Power property of logarithms
  • Properties of logarithms: mixed review
  • Evaluate logarithms: mixed review

Exponential and logarithmic functions

  • Domain and range of exponential and logarithmic functions
  • Evaluate exponential functions
  • Match exponential functions and graphs
  • Solve exponential equations by factoring
  • Solve exponential equations using common logarithms
  • Solve logarithmic equations I
  • Solve logarithmic equations II
  • Identify linear and exponential functions
  • Exponential functions over unit intervals
  • Describe linear and exponential growth and decay
  • Exponential growth and decay: word problems
  • Compound interest: word problems
  • Continuously compounded interest: word problems

Radical functions

  • Domain and range of radical functions
  • Solve radical equations

Roots and rational exponents

  • Roots of integers
  • Roots of rational numbers
  • Find roots using a calculator
  • Evaluate rational exponents
  • Operations with rational exponents
  • Nth roots
  • Simplify radical expressions with variables
  • Simplify expressions involving rational exponents

Systems of equations

  • Solve a system of equations by graphing
  • Solve a system of equations by graphing: word problems
  • Classify a system of equations
  • Solve a system of equations using substitution
  • Solve a system of equations using substitution: word problems
  • Solve a system of equations using elimination
  • Solve a system of equations using elimination: word problems
  • Solve a system of equations in three variables using substitution
  • Solve a system of equations in three variables using elimination
  • Determine the number of solutions to a system of equations in three variables

Systems of inequalities

  • Solve systems of inequalities by graphing
  • Find the vertices of a solution set
  • Linear programming
  • Graph solutions to quadratic inequalities
  • Solve quadratic inequalities

Matrices

  • Matrix vocabulary
  • Matrix operation rules
  • Add and subtract matrices
  • Multiply a matrix by a scalar
  • Linear combinations of matrices
  • Multiply two matrices
  • Simplify matrix expressions
  • Solve matrix equations
  • Determinant of a matrix
  • Is a matrix invertible?
  • Inverse of a 2 x 2 matrix
  • Inverse of a 3 x 3 matrix
  • Identify inverse matrices
  • Solve matrix equations using inverses

Trigonometry

  • Convert between radians and degrees
  • Radians and arc length
  • Quadrants
  • Coterminal and reference angles
  • Find trigonometric ratios using right triangles
  • Find trigonometric ratios using the unit circle
  • Find trigonometric ratios using reference angles
  • Inverses of trigonometric functions
  • Solve trigonometric equations
  • Trigonometric ratios: find a side length
  • Trigonometric ratios: find an angle measure
  • Solve a right triangle
  • Law of Sines
  • Law of Cosines
  • Solve a triangle
  • Area of a triangle: sine formula
  • Area of a triangle: Heron’s formula

Trigonometric functions

  • Find properties of sine functions
  • Write equations of sine functions from graphs
  • Write equations of sine functions using properties
  • Graph sine functions
  • Find properties of cosine functions
  • Write equations of cosine functions from graphs
  • Write equations of cosine functions using properties
  • Graph cosine functions
  • Graph sine and cosine functions

Trigonometric identities

  • Complementary angles
  • Symmetry and periodicity of trigonometric functions
  • Trigonometric identities I
  • Trigonometric identities II

Conic sections

  • Find properties of parabolas
  • Write equations of parabolas in vertex form
  • Graph parabolas
  • Find properties of circles
  • Write equations of circles in standard form
  • Graph circles
  • Find properties of ellipses
  • Find the eccentricity of an ellipse
  • Write equations of ellipses in standard form
  • Find properties of hyperbolas
  • Find the eccentricity of a hyperbola
  • Write equations of hyperbolas in standard form
  • Convert equations of conic sections from general to standard form

Complex numbers

  • Add and subtract complex numbers
  • Complex conjugates
  • Multiply and divide complex numbers
  • Add, subtract, multiply, and divide complex numbers
  • Absolute values of complex numbers
  • Powers of i

Complex plane

  • Introduction to the complex plane
  • Graph complex numbers
  • Addition in the complex plane
  • Subtraction in the complex plane
  • Graph complex conjugates
  • Absolute value in the complex plane
  • Midpoints in the complex plane
  • Distance in the complex plane

Polar form

  • Find the modulus and argument of a complex number
  • Convert complex numbers from rectangular to polar form
  • Convert complex numbers from polar to rectangular form
  • Convert complex numbers between rectangular and polar form
  • Match polar equations and graphs

Two-dimensional vectors

  • Find the magnitude of a vector
  • Find the direction angle of a vector
  • Find the component form of a vector
  • Find the component form of a vector from its magnitude and direction angle
  • Find a unit vector
  • Add and subtract vectors
  • Multiply a vector by a scalar
  • Find the magnitude or direction of a vector scalar multiple
  • Find the magnitude and direction of a vector sum
  • Linear combinations of vectors
  • Graph a resultant vector using the triangle method
  • Graph a resultant vector using the parallelogram method

Three-dimensional vectors

  • Find the magnitude of a three-dimensional vector
  • Find the component form of a three-dimensional vector
  • Find a three-dimensional unit vector
  • Add and subtract three-dimensional vectors
  • Scalar multiples of three-dimensional vectors
  • Linear combinations of three-dimensional vectors

Sequences and series

  • Find terms of a sequence
  • Find terms of a recursive sequence
  • Identify a sequence as explicit or recursive
  • Find a recursive formula
  • Find recursive and explicit formulas
  • Convert a recursive formula to an explicit formula
  • Convert an explicit formula to a recursive formula
  • Convert between explicit and recursive formulas
  • Introduction to sigma notation
  • Identify arithmetic and geometric series
  • Find the sum of a finite arithmetic or geometric series
  • Introduction to partial sums
  • Partial sums of arithmetic series
  • Partial sums of geometric series
  • Partial sums: mixed review
  • Convergent and divergent geometric series
  • Find the value of an infinite geometric series
  • Write a repeating decimal as a fraction

Logic

  • Identify hypotheses and conclusions
  • Counterexamples
  • Conditionals
  • Negations
  • Converses, inverses, and contrapositives
  • Biconditionals

Probability

  • Introduction to probability
  • Calculate probabilities of events
  • Combinations and permutations
  • Find probabilities using combinations and permutations
  • Find probabilities using two-way frequency tables
  • Identify independent events
  • Find conditional probabilities
  • Independence and conditional probability
  • Find conditional probabilities using two-way frequency tables
  • Find probabilities using the addition rule

Probability distributions

  • Identify discrete and continuous random variables
  • Write a discrete probability distribution
  • Graph a discrete probability distribution
  • Expected values of random variables
  • Variance and standard deviation of random variables
  • Write the probability distribution for a game of chance
  • Expected values for a game of chance
  • Choose the better bet
  • Find probabilities using the binomial distribution
  • Mean, variance, and standard deviation of binomial distributions
  • Find probabilities using the normal distribution
  • Use normal distributions to approximate binomial distributions

Statistics

  • Identify biased samples
  • Variance and standard deviation
  • Linear regression

Inquiry