Algebra 1

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

  1. Algebra 1 Topics
  2. Algebra 1 Calculator
  3. Slader Algebra 1
  4. Algebra 1 Book
  5. Emathinstruction Algebra 1
  6. Algebra 1 Regents

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

☐ Simplify radical terms (no variable in the radicand)
☐ Surds
☐ Perform the four arithmetic operations using like and unlike radical terms and express the result in simplest form

MathHelp’s Algebra 1 program is different because it’s an entire curriculum with a teacher inside. Developed at one of the top private schools in the country, the course is designed to simulate a $30,000-a-year private school education for a tiny fraction of the cost. Found a problem? Credits: 1 Prerequisite: Pre-algebra Recommended: 8th, 9th Test Prep: PSAT, SAT Course Description: Students will engage in real world and hands-on problem solving while using their developing skills in algebra.

☐ Simplifying Square Roots
☐ Understand and use scientific notation to compute products and quotients of large or small numbers.
☐ Scientific Notation
☐ Scientific Notation Definition
☐ Solve algebraic problems arising from situations that involve fractions, decimals, percents (decrease/increase and discount), and proportionality/direct variation
☐ Real World Examples of Quadratic Equations
☐ Evaluate expressions involving factorial(s), absolute value(s), and exponential expression(s)
☐ Laws of Exponents
☐ Absolute Value in Algebra
☐ Definition of Factorial
☐ Reciprocal
☐ Reciprocal In Algebra
☐ Zero Product Property
☐ Understand what is meant by a recurring decimal and how it is written.
☐ Converting Fractions to Decimals
☐ Know how to calculate n! for whole numbers n, and the relationship between n! and (n - 1)!
☐ Factorial Function !
☐ Understand what is meant by an imaginary number and a complex number.
☐ The Evolution of Numbers
☐ Imaginary Numbers
☐ Definition of Complex Number
☐ Understand what is meant by infinity and that infinity is not a Real number.
☐ Real Numbers
☐ Calculate rates using appropriate units (e.g., rate of a space ship versus the rate of a snail)

Algebra 1 Topics

☐ US Standard Speed
☐ Girl Boy and Dog Puzzle
☐ The Fly and The Trains Puzzle
☐ Solve problems involving conversions within the metric measurement system, given the relationship between the units
☐ Conversion of Length
☐ Metric Numbers
☐ Conversion of Volume
☐ Conversion of Temperature - Celsius to Fahrenheit
☐ Calculate the relative error in measuring square and cubic units, when there is an error in the linear measure (metric measurements)
☐ Errors in Measurement
☐ Unit of Measurement
☐ Solve problems involving conversions within the US standard measurement system, given the relationship between the units
☐ Conversion of Length
☐ Unit Converter
☐ Conversion of Temperature - Celsius to Fahrenheit
☐ Calculate the relative error in measuring square and cubic units, when there is an error in the linear measure (US standard measurements)
☐ Errors in Measurement
Algebra 1
☐ Unit of Measurement
☐ Translate a quantitative verbal phrase into an algebraic expression
☐ Introduction to Algebra
☐ Solving Word Questions
☐ Find values of a variable for which an algebraic fraction is undefined.
☐ Algebra Mistakes
☐ Using Rational Expressions
☐ Add or subtract fractional expressions with monomial or like binomial denominators
☐ Using Rational Expressions
☐ Multiply and divide algebraic fractions, and express the product or quotient in its simplest form
☐ Using Rational Expressions
☐ Recognize and factor the difference of two perfect squares
☐ Special Binomial Products
☐ Write verbal expressions that match given mathematical expressions
☐ Order of Operations - BODMAS
☐ Factor algebraic expressions completely, including trinomials with a lead coefficient of one (after factoring a GCF)
☐ Definition of Trinomial
☐ Solve literal equations for a given variable
☐ Solve equations involving fractional expressions.Note: Expressions which result in linear equations in one variable.
☐ Solving Equations
☐ Using Rational Expressions
☐ Solve algebraic proportions in one variable which result in linear or quadratic equations
☐ Distinguish the difference between an algebraic expression and an algebraic equation
☐ Translate verbal sentences into mathematical equations or inequalities
☐ Solving Inequality Word Questions
☐ Write algebraic equations or inequalities that represent a situation
☐ Solve complex equations of degree greater than two by making an appropriate change of variable.
☐ Degree
☐ Understand the difference between an equation and a formula.
☐ Know how to change the subject of a formula.
☐ Activity: Buffon's Needle
☐ Know the various meanings of the words 'Standard Form', including Scientific Notation.
☐ Standard Form
☐ Zero Product Property
Algebra 1 | Exponents
☐ Multiply and divide monomial expressions with a common base using the properties of exponents.Note: Use integral exponents only.
☐ Multiplying Polynomials
☐ Variables with Exponents - How to Multiply and Divide them
☐ Using Exponents in Algebra
☐ Determine whether a given value is a solution to a given linear equation in one variable or linear inequality in one variable
☐ Solving Inequalities
☐ Solve linear inequalities in one variable
☐ Determine whether a given point is in the solution set of a system of linear inequalities
☐ Graphing Linear Inequalities
☐ Graph linear inequalities
☐ Intervals
☐ Graphing Linear Inequalities
☐ Plot points using coordinates in three dimensions.
Algebra 1 | Linear Equations
☐ Solve systems of two linear equations in two variables algebraically
☐ Puzzle - Pencils and Jars
☐ Solve all types of linear equations in one variable
☐ Solving Equations
☐ Analyze and solve verbal problems whose solution requires solving a linear equation in one variable or linear inequality in one variable

Algebra 1 Calculator

☐ Balance when Adding and Subtracting
☐ Analyze and solve verbal problems whose solution requires solving systems of linear equations in two variables
☐ Solving Word Questions
☐ Solve a system of one linear and one quadratic equation in two variables, where only factoring is required.Note: The quadratic equation should represent a parabola and the solution(s) should be integers.
☐ Quadratic Equations
☐ Understand and apply the multiplication property of zero to solve quadratic equations with integral coefficients and integral roots
☐ Factoring Quadratics
☐ Solving Equations

Slader Algebra 1

☐ Understand the difference and connection between roots of a quadratic equation and factors of a quadratic expression
☐ Quadratic Equations
☐ Analyze and solve verbal problems that involve quadratic equations
☐ Solving Word Questions
☐ Add, subtract, and multiply monomials and polynomials
☐ Polynomials - Long Multiplication
☐ Definition of Monomial
☐ Like Terms
☐ Divide a polynomial by a monomial or binomial, where the quotient has no remainder. Use factoring with canceling, or Polynomial long division.
☐ Polynomials - Long Division
☐ Definition of Binomial
☐ Simplify fractions with polynomials in the numerator and denominator by factoring both and renaming them to lowest terms
☐ Polynomials - Long Division
☐ Understand Special Binomial Products
☐ Factoring in Algebra
☐ Use set-builder notation and/or interval notation to illustrate the elements of a set, given the elements in roster form

Algebra 1 Book

☐ Intervals
☐ Find the complement of a subset of a given set, within a given universe
☐ Sets and Venn Diagrams
☐ Understand the following terms: Member (or element) of a set, subset, Universal set, Null (or empty) set, intersection of sets (no more than three sets), union of sets (no more than three sets), the difference between two sets, the complement of a set

Emathinstruction Algebra 1

☐ Introduction to Sets
☐ Intervals
☐ Identify and apply the properties of real numbers (closure, commutative, associative, distributive, identity, inverse)Note: Students do not need to identify groups and fields, but students should be engaged in the ideas.
☐ Commutative Associative and Distributive Laws
☐ Definition of Real Numbers
☐ Definition of Associative Law
☐ Definition of Identity
☐ Definition of Multiplicative Identity
☐ Definition of Additive Inverse
☐ Closure
☐ Express the union or intersection of sets of numbers in interval notation.
☐ Intervals
☐ Sets and Venn Diagrams
☐ Sets and Venn Diagrams
☐ Determine when a relation is a function, by examining ordered pairs and inspecting graphs of relations
☐ What is a Function
☐ Definition of Domain of a Function
☐ Identify and graph linear, quadratic (parabolic), absolute value, and exponential functions
☐ Function Grapher and Calculator
☐ Linear Equations
☐ Graphing Quadratic Equations
☐ Absolute Value Function
☐ Investigate and generalize how changing the coefficients of a function affects its graph
☐ Graphing Quadratic Equations
☐ Parabola
☐ Find the roots of a parabolic function graphically.Note: Only quadratic equations with integral solutions.
☐ Function Grapher and Calculator
☐ Explore the Quadratic Equation
☐ Graph of an Equation
☐ What is a Function
☐ Definition of Domain of a Function
☐ Injective Surjective and Bijective
☐ Domain Range and Codomain
☐ Range of a Function Definition
☐ Definition of Function
☐ Determine if a function is one-to-one, onto, or both
☐ Increasing and Decreasing Functions
☐ Determine whether a function is injective, surjective or bijective.
☐ Increasing and Decreasing Functions
☐ Graph the slope as a rate of change between dependent and independent variables
☐ Slope Definition
☐ Slope of a Straight Line
☐ Calculate the Straight Line Graph
☐ Determine the slope of a line, given the coordinates of two points on the line
Algebra 1
☐ Gradient of a Straight Line
☐ Calculate the Straight Line Graph
☐ Linear Equations
☐ Write the equation of a line, given its slope and the coordinates of a point on the line
Slader
☐ Gradient of a Straight Line
☐ Point-Slope Equation of a Line
☐ Linear Equations
☐ Write the equation of a line, given the coordinates of two points on the line
☐ Equation of a Line from 2 Points
Algebra 1
☐ Linear Equations
☐ Write the equation of a line parallel to the x-axis or the y-axis
☐ Linear Equations
☐ Equation of a Straight Line
☐ Determine the slope of a line, given its equation in any form
☐ Gradient of a Straight Line
☐ General Form of Equation of a Line
☐ Determine if two lines are parallel, given their equations in any form
☐ Slope of a Straight Line
☐ Definition of Parallel Lines
☐ Determine whether a given point is on a line, given the equation of the line
☐ Determine the vertex, axis of symmetry, focus and directrix of a parabola, given its equation.
☐ Parabola
☐ Graphing Quadratic Equations
☐ Determine the vertex and axis of symmetry of a parabola, given its graph. Note: The vertex will have an ordered pair of integers and the axis of symmetry will have an integral value.
☐ Parabola
☐ Definition of Parabola
☐ Graph and solve systems of linear equations and inequalities with rational coefficients in two variables.
☐ Graphing Linear Inequalities
☐ Inequality Grapher
☐ Solve systems of linear and quadratic equations graphically. Note: Only use systems of linear and quadratic equations that lead to solutions whose coordinates are integers.
☐ Systems of Linear and Quadratic Equations
☐ Quadratic Equations
☐ Find the slope of a perpendicular line, given the equation of a line
☐ Gradient of a Straight Line
☐ Finding Parallel and Perpendicular Lines
☐ Determine whether two lines are parallel, perpendicular, or neither, given their equations
☐ Gradient of a Straight Line
☐ Perpendicular and Parallel
☐ Find the equation of a line, given a point on the line and the equation of a line perpendicular to the given line
☐ Point-Slope Equation of a Line
☐ Gradient of a Straight Line
☐ Find the equation of a line, given a point on the line and the equation of a line parallel to the desired line
☐ Gradient of a Straight Line
☐ Perpendicular and Parallel
☐ Find the midpoint of a line segment, given its endpoints
☐ Midpoint of a Line Segment
☐ Find the length of a line segment, given its endpoints
☐ Activity: A Walk in the Desert
☐ Find the equation of a line that is the perpendicular bisector of a line segment, given the endpoints of the line segment
☐ Midpoint of a Line Segment
☐ Bisect Definition
☐ Point-Slope Equation of a Line
☐ Investigate, justify, and apply the properties of triangles and quadrilaterals in the coordinate plane, using the distance, midpoint, and slope formulas
☐ Quadrilaterals - Square Rectangle Rhombus Trapezoid Parallelogram
☐ Distance Between 2 Points

Algebra 1 Regents

☐ Finding Parallel and Perpendicular Lines
☐ Find a set of ordered pairs to satisfy a given polynomial equation or other simple function; then plot the ordered pairs and draw the curve.
☐ Activity: Soup Can
☐ Recognize the symmetry in equations and their graphs.
☐ Function Grapher and Calculator
☐ Determine the area of an ellipse from its Cartesian formula
☐ Area Calculator
☐ Know how to convert the equation of a straight line between these types: Slope-intercept form, General form and point-slope form.
☐ General Form of Equation of a Line