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
☐ Speed and Velocity
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