Algebra 2 Curriculum

Below are skills needed, with links to resources to help with that skill. We also encourage plenty of exercises and book work. Curriculum Home

Important: this is a guide only.
Check with your local education authority to find out their requirements.

Algebra 2 | Numbers
☐ Perform arithmetic operations (addition, subtraction, multiplication, division) with expressions containing irrational numbers in radical form
Irrational Numbers
Surds
Squares and Square Roots
Irrational Number Definition
nth Roots
Is It Irrational?
Squares and Square Roots in Algebra
☐ Perform arithmetic operations on irrational expressions
Squares and Square Roots
nth Roots
Surds
Irrational Numbers
Squares and Square Roots in Algebra
Is It Irrational?
☐ Rationalize a denominator containing a radical expression
Rationalize the Denominator
Squares and Square Roots in Algebra
Conjugate
☐ Understand the meaning of algebraic numbers and transcendental numbers.
e - Euler's number
Pi
Transcendental Numbers
Algebraic Number
Irrational Numbers
☐ Investigate advanced concepts of prime numbers and factors, including: Coprimes, Mersenne primes, Perfect numbers, Abundant numbers, Deficient numbers, Amicable numbers, Euclid's proof that the set of prime numbers is endless, and Goldbach's conjecture.
Prime and Composite Numbers
Prime Numbers - Advanced
☐ Investigate numbers that are Pythagorean triples.
Pythagoras Theorem
Pythagorean Triples - Advanced
Pythagorean Triples
☐ Be familiar with well-known trancendental numbers, such as e, pi and the Liouville Constant.
Transcendental Numbers
Algebraic Number
e - Euler's number
Pi
Algebra 2 | Complex Numbers
☐ Write square roots of negative numbers in terms of i, and solve simple equations whose solutions are powers of i
Exponents of Negative Numbers
Real Numbers
Imaginary Numbers
Definition of Imaginary Numbers
i
Common Number Sets
The Evolution of Numbers
☐ Simplify powers of i
Imaginary Numbers
☐ Determine the conjugate of a complex number
Conjugate
Imaginary Numbers
Complex Numbers
Definition of Complex Number
☐ Perform arithmetic operations on complex numbers and write the answer in the form "a+bi" Note: This includes simplifying expressions with complex denominators.
Imaginary Numbers
Complex Number Calculator
Complex Numbers
☐ Represent a complex number on the Argand diagram
Complex Numbers
Vectors
Polar and Cartesian Coordinates
Complex Plane
☐ Know how to calculate the modulus and argument of a complex number, and express a complex number in polar form
Complex Numbers
Complex Number Multiplication
Complex Plane
Algebra 2 | Measurement
☐ Be familiar with the metric (SI) units used in Mathematics and Physics.
Measuring Metrically with Maggie
Common Metric Units
Metric System of Measurement
Unit Converter
Metric Numbers
Algebra 2 | Algebra
☐ Solve absolute value equations and inequalities involving linear expressions in one variable
Absolute Value Definition
Absolute Value
Absolute Value in Algebra
Intervals
☐ Simplify radical expressions
Radical Definition
Squares and Square Roots in Algebra
nth Roots
☐ Perform addition, subtraction, multiplication, and division of radical expressions
Fractional Exponents
Squares and Square Roots in Algebra
☐ Rationalize denominators involving algebraic radical expressions
Rationalize the Denominator
Squares and Square Roots in Algebra
Conjugate
☐ Perform arithmetic operations on rational expressions and rename to lowest terms
Rational Expressions
Rationalize the Denominator
Using Rational Expressions
Fractions in Algebra
☐ Simplify complex fractional expressions
Using Rational Expressions
Rational Expressions
Fractions in Algebra
☐ Solve radical equations
Solving Radical Equations
☐ Solve rational equations and inequalities
Rational Expressions
Using Rational Expressions
Solving Equations
Solving Rational Inequalities
☐ Use direct and inverse variation to solve for unknown values
Proportions
Directly Proportional and Inversely Proportional
☐ Understand what is meant by the terms and the degree of a polynomial and the degree of a rational expression.
Degree
General Form of a Polynomial
Polynomials
☐ Understand how mathematical modelling can be used to "model", or represent, how the real world works.
Mathematical Models
Activity: Soup Can
Mathematical Models 2
☐ Know how to decompose a rational expression into partial fractions.
Partial Fractions
☐ Determine whether a given value is a solution to a given radical equation in one variable.
Solving Radical Equations
Algebra 2 | Exponents
☐ Analyze and solve verbal problems that involve exponential growth and decay
Exponential Growth and Decay
☐ Rewrite algebraic expressions with fractional exponents as radical expressions
Fractional Exponents
Laws of Exponents
nth Roots
Squares and Square Roots in Algebra
☐ Rewrite algebraic expressions in radical form as expressions with fractional exponents
Fractional Exponents
Laws of Exponents
Squares and Square Roots in Algebra
nth Roots
☐ Evaluate exponential expressions, including those with base e
Exponents of Negative Numbers
Fractional Exponents
e - Euler's number
Laws of Exponents
☐ Solve exponential equations with or without common bases
Exponential Function Reference
Working with Exponents and Logarithms
☐ Graph exponential functions of the form y = bx for positive values of b, including b = e
Function Grapher and Calculator
Exponential Function Reference
e - Euler's number
☐ Solve an application which results in an exponential function
Exponential Growth and Decay
Compound Interest
☐ Apply the rules of exponents to simplify expressions involving negative and/or fractional exponents
Fractional Exponents
Laws of Exponents
Negative Exponents
Variables with Exponents - How to Multiply and Divide them
Exponents
nth Roots
Using Exponents in Algebra
☐ Rewrite algebraic expressions that contain negative exponents using only positive exponents
Negative Exponents
Exponents
Laws of Exponents
Reciprocal In Algebra
Using Exponents in Algebra
☐ Evaluate numerical expressions with negative and/or fractional exponents, without the aid of a calculator (when the answers are rational numbers)
Fractional Exponents
Laws of Exponents
Negative Exponents
Exponents
nth Roots
Using Exponents in Algebra
Algebra 2 | Inequalities
☐ Solve quadratic inequalities in one and two variables, algebraically and graphically (includes higher degree - graphically only).
Solving Inequalities
Intervals
Solving Quadratic Inequalities
Inequality Grapher
Graphing Linear Inequalities
☐ Know open and closed interval notation and how they relate to points on the number line and the solution of inequalities.
Solving Quadratic Inequalities
Intervals
Absolute Value in Algebra
Solving Rational Inequalities
☐ Know the properties of inequalities, including the Transitive Property, the Reversal Property, and the Law of Trichotomy.
Properties of Inequalities
Algebra 2 | Linear Equations
☐ Solve systems of three linear equations in three variables algebraically, using the substitution method or the elimination method.
Systems of Linear Equations
Algebra 2 | Quadratic Equations
☐ Use the discriminant to determine the nature of the roots of a quadratic equation
Quadratic Equations
Fundamental Theorem of Algebra
Quadratic Equation Solver
☐ Determine the sum and product of the roots of a quadratic equation by examining its coefficients.
Polynomials: Sums and Products of Roots
☐ Determine the quadratic equation, given the sum and product of its roots
Polynomials: Sums and Products of Roots
☐ Know and apply the technique of completing the square
Completing the Square
Derivation of Quadratic Formula
☐ Solve quadratic equations, using the quadratic formula
Derivation of Quadratic Formula
Quadratic Equations
Quadratic Equation Solver
Explore the Quadratic Equation
☐ Solve systems of equations involving one linear equation and one quadratic equation algebraically Note: This includes rational equations that result in linear equations with extraneous roots.
Systems of Linear and Quadratic Equations
☐ Solve systems of equations involving one linear equation and one quadratic equation graphically
Function Grapher and Calculator
Equation Grapher
Systems of Linear and Quadratic Equations
Systems of Linear and Quadratic Equations
☐ Solve quadratic equations by factoring
Quadratic Equation Solver
Quadratic Equations
Factoring Quadratics
☐ Apply quadratic equations to examples from the real world
Real World Examples of Quadratic Equations
Quadratic Equation Solver
Factoring Quadratics
Quadratic Equations
Algebra 2 | Logarithms
☐ Evaluate logarithmic expressions in any base
Introduction to Logarithms
Working with Exponents and Logarithms
Logarithms Can Have Decimals
☐ Apply the properties of logarithms to rewrite logarithmic expressions in equivalent forms
Introduction to Logarithms
Working with Exponents and Logarithms
☐ Solve a logarithmic equation by rewriting as an exponential equation
Introduction to Logarithms
Working with Exponents and Logarithms
☐ Graph logarithmic functions, using the inverse of the related exponential function
Inverse Functions
Logarithmic Function Reference
Working with Exponents and Logarithms
☐ Understand that Euler's number, e, is the base of the Natural Logarithms and the Natural Exponential Function.
Irrational Numbers
e - Euler's number
Exponential Function Reference
Exponential Growth and Decay
Introduction to Logarithms
Logarithmic Function Reference
Working with Exponents and Logarithms
☐ Write a logarithmic expression in exponential form and vice versa
Working with Exponents and Logarithms
Introduction to Logarithms
Algebra 2 | Polynomials
☐ Find the solutions to polynomial equations of higher degree that can be solved using factoring and/or the quadratic formula
Factoring in Algebra
Factoring Quadratics
Quadratic Equation Solver
Linear Equations
Quadratic Equations
Polynomial Definition
Solving Polynomials
☐ Approximate the solutions to polynomial equations of higher degree by inspecting the graph
How Polynomials Behave
Solving Polynomials
Approximate Solutions
Function Grapher and Calculator
☐ Factor polynomial expressions completely, using any combination of the following techniques: common factor extraction, difference of two perfect squares, quadratic trinomials
Factoring in Algebra
Factoring Quadratics
Special Binomial Products
Solving Polynomials
☐ Perform arithmetic operations with polynomial expressions containing rational coefficients
Polynomials
Adding and Subtracting Polynomials
Multiplying Polynomials
Polynomials - Long Multiplication
Dividing Polynomials
Polynomials - Long Division
☐ Identify and factor the difference of two cubes or the sum of two cubes.
Difference of Two Cubes
Factoring in Algebra
☐ Know and understand the Fundamental Theorem of Algebra.
Fundamental Theorem of Algebra
Solving Polynomials
☐ Divide a polynomial by a monomial or binomial, where the quotient has a remainder. Use Polynomial long division.
Polynomials - Long Division
Dividing Polynomials
☐ Investigate ways to search for all real roots (zeros) of a polynomial expression.
Polynomials: Bounds on Zeros
Solving Polynomials
Polynomials: The Rule of Signs
Fundamental Theorem of Algebra
☐ Know the rule of signs for polynomials.
Polynomials: The Rule of Signs
☐ Understand and apply The Remainder Theorem and The Factor Theorem.
Remainder Theorem and Factor Theorem
☐ Determine the sum and product of the roots of a cubic and higher poynomials by examining its coefficients.
Polynomials: Sums and Products of Roots
Algebra 2 | Sets
☐ Introduction to groups.
Introduction to Groups
☐ Understand what is meant by a Power Set of a given set, and that the power set for a set with n members has 2n members.
Power Set
Power Set Maker
Activity: Subsets
Algebra 2 | Logic
☐ Determine the negation of a statement and establish its truth value
Definition of Open Sentence
Open Sentences
Knights and Knaves Puzzle
Knights and Knaves 2 Puzzle
Lying about their age Puzzle
Triplets Puzzle
☐ Write a proof arguing from a given hypothesis to a given conclusion
Theorems Corollaries Lemmas
☐ Understand the principle of Mathematical Induction as a method of proof.
Mathematical Induction
☐ Understand what is meant by each of the terms: Theorems, Corollaries and Lemmas.
Theorems Corollaries Lemmas
Algebra 2 | Functions
☐ Determine the domain and range of a function from its equation
Domain Range and Codomain
What is a Function
Definition of Function
Definition of Domain of a Function
Range of a Function Definition
Set-Builder Notation
☐ Write functions in functional notation
What is a Function
☐ Use functional notation to evaluate functions for given values of the domain
Domain Range and Codomain
What is a Function
Evaluating Functions
☐ Find the composition of functions
Composition of Functions
Domain Range and Codomain
☐ Define the inverse of a function
Inverse Functions
Working with Exponents and Logarithms
☐ Determine the inverse of a function and use composition to justify the result
Composition of Functions
Inverse Functions
Domain Range and Codomain
☐ Perform transformations with functions and relations: f(x+a), f(x)+a, f(-x), -f(x), af(x)
Function Transformations
Even and Odd Functions
Function Grapher and Calculator
☐ Determine the domain and range of a function from its graph
Domain Range and Codomain
What is a Function
Common Functions Reference
Set-Builder Notation
☐ Identify relations and functions, using graphs
Function Grapher and Calculator
Common Functions Reference
What is a Function
☐ Introduction to functions
Definition of Function
What is a Function
Evaluating Functions
☐ Types of function
What is a Function
Graphs of Sine Cosine and Tangent
Common Functions Reference
☐ Understand the meaning of an asymptote and distinguish between the three types - horizontal asymptote, vertical asymptote and oblique asymptote.
Asymptote
Rational Expressions
☐ Find the equations of the horizontal, vertical and oblique asymptotes for a rational expression.
Rational Expressions
Asymptote
☐ Give the correct domain for the composition of two functions.
Composition of Functions
Domain Range and Codomain
☐ Recognize the properties, shape and symmetry of the graph of a cubic function.
Symmetry in Equations
Cube Function
☐ Understand the difference between Range and Codomain.
Domain Range and Codomain
☐ Understand that a function can be even, odd or neither even nor odd, and know how to determine whether a given function is even, odd or neither even nor odd.
Symmetry in Equations
Even and Odd Functions
☐ Define and understand the 'floor', 'ceiling', 'integer' and 'fractional part' functions, and investigate their graphs.
Floor and Ceiling Functions
Rounding Methods
☐ Add, subtract, multiply and divide functions; and find the Domain of the sum, difference, product or quotient respectively.
Operations with Functions
Domain Range and Codomain
☐ Understand what is meant by a 'Piecewise' function, how to define the various pieces, and how to determine the domain for such a function.
Piecewise Functions
Absolute Value Function
Floor and Ceiling Functions
☐ Write a domain or range of a function using Set Builder notation.
Set-Builder Notation
Algebra 2 | Sequences and Sums
☐ Identify an arithmetic or geometric sequence and find the formula for its nth term
Sequences
Definition of Arithmetic Sequence
Definition of Geometric Sequence
Arithmetic Sequences and Sums
Geometric Sequences and Sums
☐ Determine the common difference in an arithmetic sequence
Arithmetic Sequences and Sums
☐ Determine the common ratio in a geometric sequence
Geometric Sequences and Sums
☐ Determine a specified term of an arithmetic or geometric sequence
Arithmetic Sequences and Sums
Geometric Sequences and Sums
☐ Specify terms of a sequence, given its recursive definition
Number Sequences - Square Cube and Fibonacci
Fibonacci Sequence
Arithmetic Sequences and Sums
Geometric Sequences and Sums
Sequences
☐ Represent the sum of a series, using sigma notation
Sigma Notation
Partial Sums
Arithmetic Sequences and Sums
Geometric Sequences and Sums
☐ Determine the sum of the first n terms of an arithmetic or geometric series
Partial Sums
Arithmetic Sequences and Sums
Geometric Sequences and Sums
Sigma Notation
☐ Apply the binomial theorem to expand a binomial and determine a specific term of a binomial expansion
Factorial Function !
Combinations and Permutations
Combinations and Permutations Calculator
Pascal's Triangle
Binomial Theorem
☐ Know and apply sigma notation
Sigma Notation
Partial Sums
☐ Define the Fibonacci sequence and the Golden ratio and investigate the relationship between them.
The Pentagram
Fibonacci Sequence
Golden Ratio
Nature The Golden Ratio and Fibonacci Numbers
☐ Know the names of special sequences such as Triangular Numbers, Square Numbers, Cube Numbers, Tetrahedral Numbers and Fibonacci numbers; and how they are generated.
Number Sequences - Square Cube and Fibonacci
Fibonacci Sequence
Pascal's Triangle
Sequences
Tetrahedral Number Sequence
Triangular Number Sequence
Activity: A Walk in the Desert
Activity: Drawing Squares
☐ Know the formulae for: 1. The sum of the first n natural numbers. 2. The sum of the squares of the first n natural numbers. 3. The sum of the cubes of the first n natural numbers.
Partial Sums
Activity: A Walk in the Desert
☐ Investigate Pascal's Triangle and its properties; including its relationship to sets of numbers (such as triangular numbers and Fibonacci numbers), and the Binomial coefficients.
Tetrahedral Number Sequence
Fibonacci Sequence
Pascal's Triangle
Activity: Subsets
Triangular Number Sequence
☐ Use differences to find the rule for a sequence
Sequences
Sequences - Finding A Rule
Algebra 2 | Vectors
☐ Understand what is meant by a vector
Vectors
Vector Definition
☐ Know how to add and subtract vectors, and how to break a vector into two pieces
Vectors
Vector Definition
☐ Understand what is meant by the magnitude of a vector and how to multiply a vector by a scalar
Vectors
☐ Calculate the magnitude and direction of a vector from its x and y lengths, or vice versa
Vectors
Vector Calculator
☐ Understand unit vectors
Unit Vector
Vectors
☐ Know the two ways to find the dot product of two vectors (in 2 or 3 dimensions)
Dot Product
Vectors
Vector Calculator
☐ Know the two ways to find the cross product of two vectors (in 2 or 3 dimensions)
Cross Product
Vectors
Algebra 2 | Matrices
☐ Know how to add and subtract matrices, how to find the negative of a matrix, how to multiply a matrix by a constant, and how to find the transpose of a matrix.
Matrices
☐ Know the conditions under which two matrices can be multiplied, and how to perform the multiplication.
How to Multiply Matrices
Matrix Calculator
☐ Understand that multiplication of matrices is not commutative.
Commutative Associative and Distributive Laws
Definition of Commutative Law
How to Multiply Matrices
☐ Know what is meant by an identity matrix.
How to Multiply Matrices
Types of Matrix
☐ Evaluate the determinant of a 2 by 2 matrix or a 3 by 3 matrix.
Matrix Calculator
Determinant of a Matrix
☐ Know the conditions under which a matrix has a multiplicative inverse and what is meant by a singular matrix.
Determinant of a Matrix
Inverse of a Matrix
Matrix Calculator
☐ Find the inverse of a matrix (if it exists) by swapping around the elements and multiplying by the reciprocal of the determinant.
Inverse of a Matrix
Determinant of a Matrix
Matrix Calculator
☐ Find the inverse of a matrix (if it exists) using elementary row operations.
Inverse of a Matrix using Elementary Row Operations
Inverse of a Matrix
Matrix Calculator
☐ Find the inverse of a matrix (if it exists) using Minors, Cofactors and Adjugate.
Inverse of a Matrix using Minors Cofactors and Adjugate
Inverse of a Matrix
Determinant of a Matrix
Matrix Calculator
☐ Solve a system of linear equations using matrices.
Systems of Linear Equations
Matrices
Solving Systems of Linear Equations Using Matrices
Inverse of a Matrix
Matrix Calculator
Algebra 2 | Graphs
☐ Determine the center-radius form for the equation of a circle in standard form
Circle Equations
☐ Write the equation of a circle, given its center and a point on the circle
Circle Equations
Distance Between 2 Points
☐ Write the equation of a circle from its graph
Distance Between 2 Points
Circle Equations
☐ Graph and solve compound loci in the coordinate plane
Definition of Locus
Set of All Points
Ellipse
Hyperbola
☐ Write the equation of a circle, given its center and radius or given the endpoints of a diameter
Circle Equations
☐ Write the equation of a circle, given its graph. Note: The center is an ordered pair of integers and the radius is an integer.
Circle Equations
Completing the Square
☐ Find the center and radius of a circle, given the equation of the circle in center-radius form
Circle Equations
Completing the Square
☐ Graph circles of the form (x - h)2 + (y - k)2 = r2
Circle Equations
Equation Grapher
☐ Understand Conic Sections (circle, ellipse, parabola, hyperbola)
Set of All Points
Conic Sections
Ellipse
Parabola
Circle
Hyperbola
Eccentricity
☐ Find the x and y intercepts for a graph given its equation.
Y Intercept of a Straight Line
Linear Equations
Finding Intercepts From an Equation
☐ Investigate various approximate formulae for finding the perimeter of an ellipse, and compare them.
Perimeter of Ellipse
Ellipse
☐ Determine the equation of a curve given some points on the curve.
Graph of an Equation