Algebra 2 Curriculum

Below are skills needed, with links to resources to help with that skill. We also enourage 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
Definition of Irrational Number
nth Roots
Is It Irrational?
Squares and Square Roots
☐ Perform arithmetic operations on irrational expressions
Squares and Square Roots
nth Roots
☐ Rationalize a denominator containing a radical expression
Rationalize the Denominator
☐ Understand the meaning of algebraic numbers and transcendental numbers.
e - Euler's number
Transcendental Numbers
Algebraic Number
☐ 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 Numbers - Advanced
☐ Investigate numbers that are Pythagorean triples.
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
Imaginary Numbers
Definition of Imaginary Numbers
Definition of i (Unit Imaginary Number)
Common Number Sets
The Evolution of Numbers
Exponents of Negative Numbers
Real Numbers
☐ Simplify powers of i
Imaginary Numbers
☐ Determine the conjugate of a complex number
Conjugate
Imaginary Numbers
Complex Numbers
Definition of Complex Number
Fundamental Theorem of Algebra
☐ 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
☐ Know how to calculate the modulus and argument of a complex number, and express a complex number in polar form
Complex Numbers
Algebra 2 | Measurement
☐ Be familiar with the metric (SI) units used in Mathematics and Physics.
Common Metric Units
Metric System of Measurement
Unit Converter
Metric Numbers
Measuring Metrically with Maggie
Algebra 2 | Algebra
☐ Solve absolute value equations and inequalities involving linear expressions in one variable
Absolute Value
Absolute Value Function
Absolute Value in Algebra
Definition of Absolute Value
Intervals
☐ Simplify radical expressions
Definition of Radical
Squares and Square Roots in Algebra
nth Roots
☐ Perform addition, subtraction, multiplication, and division of radical expressions
Fractional Exponents
☐ Rationalize denominators involving algebraic radical expressions
Rationalize the Denominator
Conjugate
☐ Perform arithmetic operations on rational expressions and rename to lowest terms
Rational Expressions
Rationalize the Denominator
Using Rational Expressions
Solving Rational Inequalities
☐ Simplify complex fractional expressions
Using Rational Expressions
☐ Solve radical equations
Solving Radical Equations
☐ Solve rational equations and inequalities
Using Rational Expressions
Rational Expressions
Solving Equations
Solving Rational Inequalities
☐ Understand what is meant by the terms and the degree of a polynomial and the degree of a rational expression.
Degree (of an Expression)
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
☐ 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
Square Root Function
☐ Rewrite algebraic expressions in radical form as expressions with fractional exponents
Fractional Exponents
Laws of Exponents
Squares and Square Roots in Algebra
nth Roots
Square Root Function
☐ Evaluate exponential expressions, including those with base e
Exponents of Negative Numbers
Fractional Exponents
Working with Exponents and Logarithms
e - Euler's number
☐ 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
Exponential Growth and Decay
Working with Exponents and Logarithms
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
Working with Exponents and Logarithms
Using Exponents in Algebra
☐ Rewrite algebraic expressions that contain negative exponents using only positive exponents
Negative Exponents
Variables with Exponents - How to Multiply and Divide them
Exponents
Laws of Exponents
Reciprocal
Reciprocal Function
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
Solving Quadratic Inequalities
☐ Know open and closed interval notation and how they relate to points on the number line and the solution of 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
☐ 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
Factoring Quadratics
☐ 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
e - Euler's number
Introduction to Logarithms
Working with Exponents and Logarithms
Logarithmic Function Reference
☐ 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
Degree (of an Expression)
Factoring in Algebra
Definition of Polynomial
Solving Polynomials
Factoring Quadratics
Quadratic Equation Solver
☐ Approximate the solutions to polynomial equations of higher degree by inspecting the graph
Degree (of an Expression)
How Polynomials Behave
Solving Polynomials
Polynomials: Bounds on Zeros
Polynomials: The Rule of Signs
Approximate Solutions
☐ 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
Polynomials - Long Division
Simplify in Algebra
☐ Perform arithmetic operations with polynomial expressions containing rational coefficients
Polynomials
Definition of Polynomial
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
Solving Polynomials
☐ 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
Remainder Theorem and Factor Theorem
Simplify in Algebra
Dividing Polynomials
☐ Investigate ways to search for all real roots (zeros) of a polynomial expression.
Polynomials: Bounds on Zeros
Solving Polynomials
Solving Rational Inequalities
Polynomials: The Rule of Signs
☐ 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
Solving Polynomials
☐ 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
Knights and Knaves 2
Lying about their age
Triplets
☐ 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
Definition of Range of a function
Set-Builder Notation
☐ Write functions in functional notation
Linear Equations
What is a Function
Evaluating Functions
☐ 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
☐ 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
Working with Exponents and Logarithms
☐ Perform transformations with functions and relations: f(x+a), f(x)+a, f(-x), -f(x), af(x)
Function Transformations
Even and Odd Functions
☐ Determine the domain and range of a function from its graph
Domain, Range and Codomain
What is a Function
Square Function
Square Root Function
☐ Identify relations and functions, using graphs
Function Grapher and Calculator
☐ Introduction to functions
Definition of Function
What is a Function
Evaluating Functions
☐ Types of function
What is a Function
Absolute Value Function
Square Function
Cube Function
Exponential Function Reference
Logarithmic Function Reference
Floor and Ceiling Functions
Reciprocal Function
Sine Function - Graph Exercise
Square Root Function
☐ 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
Graph of an Equation
Solving Rational Inequalities
☐ Give the correct domain for the composition of two functions.
Composition of Functions
☐ 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
Reciprocal Function
Square Function
☐ Define and understand the 'floor', 'ceiling', 'integer' and 'fractional part' functions, and investigate their graphs.
Floor and Ceiling Functions
Piecewise Functions
Rounding Methods
☐ Add, subtract, multiply and divide functions; and find the Domain of the sum, difference, product or quotient respectively.
Operations with Functions
☐ 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
☐ 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 - Finding A Rule
Sequences
Definition of Arithmetic Sequence
Definition of Geometric Sequence
Arithmetic Sequences and Sums
Geometric Sequences and Sums
Activity: A Walk in the Desert
☐ Determine the common difference in an arithmetic sequence
Sequences - Finding A Rule
Sequences
Arithmetic Sequences and Sums
☐ Determine the common ratio in a geometric sequence
Sequences - Finding A Rule
Sequences
Geometric Sequences and Sums
☐ Determine a specified term of an arithmetic or geometric sequence
Sequences - Finding A Rule
Sequences
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
Sequences - Finding A Rule
☐ 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
Algebra - Expanding
Factorial Function !
Combinations and Permutations
Combinations and Permutations Calculator
Pascal's Triangle
Binomial Theorem
Quincunx Explained
☐ Know and apply sigma notation
Sigma Notation
Partial Sums
☐ Define the Fibonacci sequence and the Golden ratio and investigate the relationship between them.
Irrational Numbers
Number Sequences - Square, Cube and Fibonacci
The Pentagram
Fibonacci Sequence
Golden Ratio
Nature, The Golden Ratio and Fibonacci Numbers
Pascal's Triangle
Sequences
Sequences - Finding A Rule
☐ 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
Nature, The Golden Ratio and Fibonacci Numbers
Fibonacci Sequence
Pascal's Triangle
Sequences
Sequences - Finding A Rule
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.
Fibonacci Sequence
Pascal's Triangle
Quincunx Explained
Activity: Subsets
☐ Use differences to find the rule for a sequence
Sequences - Finding A Rule
Algebra 2 | Vectors
☐ Understand what is meant by a vector
Vectors
Definition of Vector
☐ Know how to add and subtract vectors, and how to break a vector into two pieces
Vectors
Definition of Vector
☐ Understand what is meant by the magnitude of a vector and how to multiply a vector by a scalar
Vectors
Definition of Vector
☐ Calculate the magnitude and direction of a vector from its x and y lengths, or vice versa
Vectors
Definition of Vector
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
☐ 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
☐ Evaluate the determinant of a 2 by 2 matrix or a 3 by 3 matrix.
Determinant of a Matrix
☐ Know the conditions under which a matrix has a multiplicative inverse and what is meant by a singular matrix.
Matrices
How to Multiply Matrices
Determinant of a Matrix
Inverse of a Matrix
☐ Find the inverse of a matrix (if it exists) by swapping around the elements and multiplying by the reciprocal of the determinant.
Matrices
Inverse of a Matrix
How to Multiply Matrices
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 (Gauss-Jordan)
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
Unit Circle
Circle Equations
☐ Write the equation of a circle, given its center and a point on the circle
Circle Equations
Unit Circle
☐ 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
Midpoint of a Line Segment
Distance Between 2 Points
☐ Write the equation of a circle, given its graph. Note: The center is an ordered pair of integers and the radius is an integer.
Midpoint of a Line Segment
Circle Equations
☐ Find the center and radius of a circle, given the equation of the circle in center-radius form
Circle Equations
☐ Graph circles of the form (x - h)2 + (y - k)2 = r2
Circle Equations
Equation Grapher
☐ Understand Conic Sections (circle, ellipse, parabola, hyperbola)
Graphing Quadratic Equations
Conic Sections
Ellipse
Parabola
Circle
Hyperbola
Eccentricity
Set of All Points
Reciprocal Function
☐ Find the x and y intercepts for a graph given its equation.
Y Intercept of a Straight Line
Finding Intercepts From an Equation
Linear Equations
☐ 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