Blog entry by Admin User
Anyone in the world
Canada Grade 12 math
266 skills
A. Functions
1 Domain and range
2 Identify functions
3 Find the slope of a linear function
4 Graph a linear function
5 Write the equation of a linear function
6 Linear functions over unit intervals
7 Evaluate functions
8 Find values using function graphs
9 Complete a table for a function graph
10 Add, subtract, multiply and divide functions
11 Composition of functions
12 Identify inverse functions
13 Find values of inverse functions from tables
14 Find values of inverse functions from graphs
15 Find inverse functions and relations
16 Identify graphs of continuous functions
B. Families of functions
1 Translations of functions
2 Reflections of functions
3 Dilations of functions
4 Transformations of functions
5 Function transformation rules
6 Describe function transformations
C. Quadratic relations
1 Characteristics of quadratic functions
2 Find the maximum or minimum value of a quadratic function
3 Graph a quadratic function
4 Match quadratic functions and graphs
5 Solve a quadratic equation using square roots
6 Solve a quadratic equation by factoring
7 Solve a quadratic equation by completing the square
8 Solve a quadratic equation using the quadratic formula
9 Using the discriminant
D. Polynomials
1 Divide polynomials using long division
2 Write a polynomial from its roots
3 Find the roots of factored polynomials
4 Rational root theorem
5 Complex conjugate theorem
6 Conjugate root theorems
7 Descartes' Rule of Signs
8 Fundamental Theorem of Algebra
9 Match polynomials and graphs
10 Even and odd functions
11 Factor sums and differences of cubes
12 Solve equations with sums and differences of cubes
13 Factor using a quadratic pattern
14 Solve equations using a quadratic pattern
15 Pascal's triangle
16 Pascal's triangle and the Binomial Theorem
17 Binomial Theorem I
18 Binomial Theorem II
E. Rational functions
1 Rational functions: asymptotes and excluded values
2 Solve rational equations
3 Check whether two rational functions are inverses
F. Logarithms
1 Convert between exponential and logarithmic form: rational bases
2 Evaluate logarithms
3 Change of base formula
4 Identify properties of logarithms
5 Product property of logarithms
6 Quotient property of logarithms
7 Power property of logarithms
8 Properties of logarithms: mixed review
9 Evaluate logarithms: mixed review
G. Exponential and logarithmic functions
1 Domain and range of exponential and logarithmic functions
2 Evaluate exponential functions
3 Match exponential functions and graphs
4 Solve exponential equations by rewriting the base
5 Solve exponential equations using common logarithms
6 Solve logarithmic equations I
7 Solve logarithmic equations II
8 Identify linear and exponential functions
9 Exponential functions over unit intervals
10 Describe linear and exponential growth and decay
11 Exponential growth and decay: word problems
12 Compound interest: word problems
13 Continuously compounded interest: word problems
H. Radical functions
1 Domain and range of radical functions
2 Solve radical equations
I. Roots and rational exponents
1 Roots of integers
2 Roots of rational numbers
3 Find roots using a calculator
4 Evaluate rational exponents
5 Operations with rational exponents
6 Nth roots
7 Simplify radical expressions with variables
8 Simplify expressions involving rational exponents
J. Systems of equations
1 Solve a system of equations by graphing
2 Solve a system of equations by graphing: word problems
3 Classify a system of equations
4 Solve a system of equations using substitution
5 Solve a system of equations using substitution: word problems
6 Solve a system of equations using elimination
7 Solve a system of equations using elimination: word problems
8 Solve a system of equations in three variables using substitution
9 Solve a system of equations in three variables using elimination
10 Determine the number of solutions to a system of equations in three variables
K. Systems of inequalities
1 Solve systems of inequalities by graphing
2 Find the vertices of a solution set
3 Linear programming
L. Nonlinear inequalities
1 Graph solutions to quadratic inequalities
2 Solve quadratic inequalities
3 Graph solutions to higher-degree inequalities
4 Solve higher-degree inequalities
M. Matrices
1 Matrix vocabulary
2 Matrix operation rules
3 Add and subtract matrices
4 Multiply a matrix by a scalar
5 Linear combinations of matrices
6 Multiply two matrices
7 Simplify matrix expressions
8 Solve matrix equations
9 Determinant of a matrix
10 Is a matrix invertible?
11 Inverse of a 2 x 2 matrix
12 Inverse of a 3 x 3 matrix
13 Identify inverse matrices
14 Solve matrix equations using inverses
N. Trigonometry
1 Convert between radians and degrees
2 Radians and arc length
3 Quadrants
4 Coterminal and reference angles
5 Find trigonometric ratios using right triangles
6 Find trigonometric ratios using the unit circle
7 Find trigonometric ratios using reference angles
8 Inverses of trigonometric functions
9 Solve trigonometric equations
10 Trigonometric ratios: find a side length
11 Trigonometric ratios: find an angle measure
12 Solve a right triangle
13 Law of Sines
14 Law of Cosines
15 Solve a triangle
16 Area of a triangle: sine formula
17 Area of a triangle: Heron's formula
O. Trigonometric functions
1 Find properties of sine functions
2 Write equations of sine functions from graphs
3 Write equations of sine functions using properties
4 Graph sine functions
5 Find properties of cosine functions
6 Write equations of cosine functions from graphs
7 Write equations of cosine functions using properties
8 Graph cosine functions
9 Graph sine and cosine functions
P. Trigonometric identities
1 Complementary angle identities
2 Symmetry and periodicity of trigonometric functions
3 Find trigonometric ratios using a Pythagorean or reciprocal identity
4 Find trigonometric ratios using multiple identities
5 Trigonometric sum and difference identities
Q. Conic sections
1 Find properties of parabolas
2 Write equations of parabolas in vertex form
3 Graph parabolas
4 Find properties of circles
5 Write equations of circles in standard form
6 Graph circles
7 Find properties of ellipses
8 Find the eccentricity of an ellipse
9 Write equations of ellipses in standard form
10 Find properties of hyperbolas
11 Find the eccentricity of a hyperbola
12 Write equations of hyperbolas in standard form
13 Convert equations of conic sections from general to standard form
R. Complex numbers
1 Introduction to complex numbers
2 Add and subtract complex numbers
3 Complex conjugates
4 Multiply and divide complex numbers
5 Add, subtract, multiply and divide complex numbers
6 Absolute values of complex numbers
7 Powers of i
S. Complex plane
1 Introduction to the complex plane
2 Graph complex numbers
3 Addition in the complex plane
4 Subtraction in the complex plane
5 Graph complex conjugates
6 Absolute value in the complex plane
7 Midpoints in the complex plane
8 Distance in the complex plane
T. Polar form
1 Find the modulus and argument of a complex number
2 Convert complex numbers from rectangular to polar form
3 Convert complex numbers from polar to rectangular form
4 Convert complex numbers between rectangular and polar form
5 Match polar equations and graphs
U. Two-dimensional vectors
1 Find the magnitude of a vector
2 Find the direction angle of a vector
3 Find the component form of a vector
4 Find the component form of a vector from its magnitude and direction angle
5 Find a unit vector
6 Add and subtract vectors
7 Multiply a vector by a scalar
8 Find the magnitude or direction of a vector scalar multiple
9 Find the magnitude and direction of a vector sum
10 Linear combinations of vectors
11 Graph a resultant vector using the triangle method
12 Graph a resultant vector using the parallelogram method
V. Three-dimensional vectors
1 Find the magnitude of a three-dimensional vector
2 Find the component form of a three-dimensional vector
3 Find a three-dimensional unit vector
4 Add and subtract three-dimensional vectors
5 Scalar multiples of three-dimensional vectors
6 Linear combinations of three-dimensional vectors
W. Sequences and series
1 Find terms of a sequence
2 Find terms of a recursive sequence
3 Identify a sequence as explicit or recursive
4 Find a recursive formula
5 Find recursive and explicit formulas
6 Convert a recursive formula to an explicit formula
7 Convert an explicit formula to a recursive formula
8 Convert between explicit and recursive formulas
9 Introduction to sigma notation
10 Identify arithmetic and geometric series
11 Find the sum of a finite arithmetic or geometric series
12 Introduction to partial sums
13 Partial sums of arithmetic series
14 Partial sums of geometric series
15 Partial sums: mixed review
16 Convergent and divergent geometric series
17 Find the value of an infinite geometric series
18 Write a repeating decimal as a fraction
X. Logic
1 Identify hypotheses and conclusions
2 Counterexamples
3 Conditionals
4 Negations
5 Converses, inverses and contrapositives
6 Biconditionals
Y. Probability
1 Introduction to probability
2 Calculate probabilities of events
3 Combinations and permutations
4 Find probabilities using combinations and permutations
5 Find probabilities using two-way frequency tables
6 Identify independent events
7 Find conditional probabilities
8 Independence and conditional probability
9 Find conditional probabilities using two-way frequency tables
10 Find probabilities using the addition rule
Z. Probability distributions
1 Identify discrete and continuous random variables
2 Write a discrete probability distribution
3 Graph a discrete probability distribution
4 Expected values of random variables
5 Variance of random variables
6 Standard deviation of random variables
7 Write the probability distribution for a game of chance
8 Expected values for a game of chance
9 Choose the better bet
10 Find probabilities using the binomial distribution
11 Mean, variance and standard deviation of binomial distributions
12 Find probabilities using the normal distribution I
13 Find probabilities using the normal distribution II
14 Find z-values
15 Find values of normal variables
16 Distributions of sample means
17 The Central Limit Theorem
18 Use normal distributions to approximate binomial distributions
AA. Statistics
1 Identify biased samples
2 Variance and standard deviation
3 Identify an outlier
4 Identify an outlier and describe the effect of removing it
5 Outliers in scatter plots
6 Match correlation coefficients to scatter plots
7 Calculate correlation coefficients
8 Find the equation of a regression line
9 Interpret regression lines
10 Analyze a regression line of a data set
11 Analyze a regression line using statistics of a data set
12 Find confidence intervals for population means
13 Find confidence intervals for population proportions
14 Interpret confidence intervals for population means
BB. Sets
1 Sets, subsets and complements
2 Set-builder notation
3 Unions and intersections of sets
266 skills
A. Functions
1 Domain and range
2 Identify functions
3 Find the slope of a linear function
4 Graph a linear function
5 Write the equation of a linear function
6 Linear functions over unit intervals
7 Evaluate functions
8 Find values using function graphs
9 Complete a table for a function graph
10 Add, subtract, multiply and divide functions
11 Composition of functions
12 Identify inverse functions
13 Find values of inverse functions from tables
14 Find values of inverse functions from graphs
15 Find inverse functions and relations
16 Identify graphs of continuous functions
B. Families of functions
1 Translations of functions
2 Reflections of functions
3 Dilations of functions
4 Transformations of functions
5 Function transformation rules
6 Describe function transformations
C. Quadratic relations
1 Characteristics of quadratic functions
2 Find the maximum or minimum value of a quadratic function
3 Graph a quadratic function
4 Match quadratic functions and graphs
5 Solve a quadratic equation using square roots
6 Solve a quadratic equation by factoring
7 Solve a quadratic equation by completing the square
8 Solve a quadratic equation using the quadratic formula
9 Using the discriminant
D. Polynomials
1 Divide polynomials using long division
2 Write a polynomial from its roots
3 Find the roots of factored polynomials
4 Rational root theorem
5 Complex conjugate theorem
6 Conjugate root theorems
7 Descartes' Rule of Signs
8 Fundamental Theorem of Algebra
9 Match polynomials and graphs
10 Even and odd functions
11 Factor sums and differences of cubes
12 Solve equations with sums and differences of cubes
13 Factor using a quadratic pattern
14 Solve equations using a quadratic pattern
15 Pascal's triangle
16 Pascal's triangle and the Binomial Theorem
17 Binomial Theorem I
18 Binomial Theorem II
E. Rational functions
1 Rational functions: asymptotes and excluded values
2 Solve rational equations
3 Check whether two rational functions are inverses
F. Logarithms
1 Convert between exponential and logarithmic form: rational bases
2 Evaluate logarithms
3 Change of base formula
4 Identify properties of logarithms
5 Product property of logarithms
6 Quotient property of logarithms
7 Power property of logarithms
8 Properties of logarithms: mixed review
9 Evaluate logarithms: mixed review
G. Exponential and logarithmic functions
1 Domain and range of exponential and logarithmic functions
2 Evaluate exponential functions
3 Match exponential functions and graphs
4 Solve exponential equations by rewriting the base
5 Solve exponential equations using common logarithms
6 Solve logarithmic equations I
7 Solve logarithmic equations II
8 Identify linear and exponential functions
9 Exponential functions over unit intervals
10 Describe linear and exponential growth and decay
11 Exponential growth and decay: word problems
12 Compound interest: word problems
13 Continuously compounded interest: word problems
H. Radical functions
1 Domain and range of radical functions
2 Solve radical equations
I. Roots and rational exponents
1 Roots of integers
2 Roots of rational numbers
3 Find roots using a calculator
4 Evaluate rational exponents
5 Operations with rational exponents
6 Nth roots
7 Simplify radical expressions with variables
8 Simplify expressions involving rational exponents
J. Systems of equations
1 Solve a system of equations by graphing
2 Solve a system of equations by graphing: word problems
3 Classify a system of equations
4 Solve a system of equations using substitution
5 Solve a system of equations using substitution: word problems
6 Solve a system of equations using elimination
7 Solve a system of equations using elimination: word problems
8 Solve a system of equations in three variables using substitution
9 Solve a system of equations in three variables using elimination
10 Determine the number of solutions to a system of equations in three variables
K. Systems of inequalities
1 Solve systems of inequalities by graphing
2 Find the vertices of a solution set
3 Linear programming
L. Nonlinear inequalities
1 Graph solutions to quadratic inequalities
2 Solve quadratic inequalities
3 Graph solutions to higher-degree inequalities
4 Solve higher-degree inequalities
M. Matrices
1 Matrix vocabulary
2 Matrix operation rules
3 Add and subtract matrices
4 Multiply a matrix by a scalar
5 Linear combinations of matrices
6 Multiply two matrices
7 Simplify matrix expressions
8 Solve matrix equations
9 Determinant of a matrix
10 Is a matrix invertible?
11 Inverse of a 2 x 2 matrix
12 Inverse of a 3 x 3 matrix
13 Identify inverse matrices
14 Solve matrix equations using inverses
N. Trigonometry
1 Convert between radians and degrees
2 Radians and arc length
3 Quadrants
4 Coterminal and reference angles
5 Find trigonometric ratios using right triangles
6 Find trigonometric ratios using the unit circle
7 Find trigonometric ratios using reference angles
8 Inverses of trigonometric functions
9 Solve trigonometric equations
10 Trigonometric ratios: find a side length
11 Trigonometric ratios: find an angle measure
12 Solve a right triangle
13 Law of Sines
14 Law of Cosines
15 Solve a triangle
16 Area of a triangle: sine formula
17 Area of a triangle: Heron's formula
O. Trigonometric functions
1 Find properties of sine functions
2 Write equations of sine functions from graphs
3 Write equations of sine functions using properties
4 Graph sine functions
5 Find properties of cosine functions
6 Write equations of cosine functions from graphs
7 Write equations of cosine functions using properties
8 Graph cosine functions
9 Graph sine and cosine functions
P. Trigonometric identities
1 Complementary angle identities
2 Symmetry and periodicity of trigonometric functions
3 Find trigonometric ratios using a Pythagorean or reciprocal identity
4 Find trigonometric ratios using multiple identities
5 Trigonometric sum and difference identities
Q. Conic sections
1 Find properties of parabolas
2 Write equations of parabolas in vertex form
3 Graph parabolas
4 Find properties of circles
5 Write equations of circles in standard form
6 Graph circles
7 Find properties of ellipses
8 Find the eccentricity of an ellipse
9 Write equations of ellipses in standard form
10 Find properties of hyperbolas
11 Find the eccentricity of a hyperbola
12 Write equations of hyperbolas in standard form
13 Convert equations of conic sections from general to standard form
R. Complex numbers
1 Introduction to complex numbers
2 Add and subtract complex numbers
3 Complex conjugates
4 Multiply and divide complex numbers
5 Add, subtract, multiply and divide complex numbers
6 Absolute values of complex numbers
7 Powers of i
S. Complex plane
1 Introduction to the complex plane
2 Graph complex numbers
3 Addition in the complex plane
4 Subtraction in the complex plane
5 Graph complex conjugates
6 Absolute value in the complex plane
7 Midpoints in the complex plane
8 Distance in the complex plane
T. Polar form
1 Find the modulus and argument of a complex number
2 Convert complex numbers from rectangular to polar form
3 Convert complex numbers from polar to rectangular form
4 Convert complex numbers between rectangular and polar form
5 Match polar equations and graphs
U. Two-dimensional vectors
1 Find the magnitude of a vector
2 Find the direction angle of a vector
3 Find the component form of a vector
4 Find the component form of a vector from its magnitude and direction angle
5 Find a unit vector
6 Add and subtract vectors
7 Multiply a vector by a scalar
8 Find the magnitude or direction of a vector scalar multiple
9 Find the magnitude and direction of a vector sum
10 Linear combinations of vectors
11 Graph a resultant vector using the triangle method
12 Graph a resultant vector using the parallelogram method
V. Three-dimensional vectors
1 Find the magnitude of a three-dimensional vector
2 Find the component form of a three-dimensional vector
3 Find a three-dimensional unit vector
4 Add and subtract three-dimensional vectors
5 Scalar multiples of three-dimensional vectors
6 Linear combinations of three-dimensional vectors
W. Sequences and series
1 Find terms of a sequence
2 Find terms of a recursive sequence
3 Identify a sequence as explicit or recursive
4 Find a recursive formula
5 Find recursive and explicit formulas
6 Convert a recursive formula to an explicit formula
7 Convert an explicit formula to a recursive formula
8 Convert between explicit and recursive formulas
9 Introduction to sigma notation
10 Identify arithmetic and geometric series
11 Find the sum of a finite arithmetic or geometric series
12 Introduction to partial sums
13 Partial sums of arithmetic series
14 Partial sums of geometric series
15 Partial sums: mixed review
16 Convergent and divergent geometric series
17 Find the value of an infinite geometric series
18 Write a repeating decimal as a fraction
X. Logic
1 Identify hypotheses and conclusions
2 Counterexamples
3 Conditionals
4 Negations
5 Converses, inverses and contrapositives
6 Biconditionals
Y. Probability
1 Introduction to probability
2 Calculate probabilities of events
3 Combinations and permutations
4 Find probabilities using combinations and permutations
5 Find probabilities using two-way frequency tables
6 Identify independent events
7 Find conditional probabilities
8 Independence and conditional probability
9 Find conditional probabilities using two-way frequency tables
10 Find probabilities using the addition rule
Z. Probability distributions
1 Identify discrete and continuous random variables
2 Write a discrete probability distribution
3 Graph a discrete probability distribution
4 Expected values of random variables
5 Variance of random variables
6 Standard deviation of random variables
7 Write the probability distribution for a game of chance
8 Expected values for a game of chance
9 Choose the better bet
10 Find probabilities using the binomial distribution
11 Mean, variance and standard deviation of binomial distributions
12 Find probabilities using the normal distribution I
13 Find probabilities using the normal distribution II
14 Find z-values
15 Find values of normal variables
16 Distributions of sample means
17 The Central Limit Theorem
18 Use normal distributions to approximate binomial distributions
AA. Statistics
1 Identify biased samples
2 Variance and standard deviation
3 Identify an outlier
4 Identify an outlier and describe the effect of removing it
5 Outliers in scatter plots
6 Match correlation coefficients to scatter plots
7 Calculate correlation coefficients
8 Find the equation of a regression line
9 Interpret regression lines
10 Analyze a regression line of a data set
11 Analyze a regression line using statistics of a data set
12 Find confidence intervals for population means
13 Find confidence intervals for population proportions
14 Interpret confidence intervals for population means
BB. Sets
1 Sets, subsets and complements
2 Set-builder notation
3 Unions and intersections of sets