Algebra 1 Workbook: The Self-Teaching Guide and Practice Workbook with Exercises and Related Explained Solution. You Will Get and Improve Your Algebra 1 Skills and Knowledge from A to Z. Algebra Calculator - get free step-by-step solutions for your algebra math problems This website uses cookies to ensure you get the best experience. By using this website, you agree to our Cookie Policy.
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.
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- Algebra 1 Quadratic Equations ☐ 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.
- The Algebra 1 course, often taught in the 9th grade, covers Linear equations, inequalities, functions, and graphs; Systems of equations and inequalities; Extension of the concept of a function; Exponential models; and Quadratic equations, functions, and graphs. Khan Academy's Algebra 1 course is built to deliver a comprehensive, illuminating, engaging, and Common Core aligned experience!
☐ 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
☐ 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)
☐ 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
☐ 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
☐ 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
☐ 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
☐ 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
☐ 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
Algebra 1 Worksheets
☐ 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
☐ 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
☐ 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
☐ 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
☐ 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
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Algebra 1 Series Andrew luck.
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Spacewalking
Algebra 1
One of the key components of a spacesuit is breathable air. Students will use previous oxygen usage data from two astronauts to predict if the astronauts can complete an upcoming spacewalk.
Suit Yourself
Algebra 1
Students will perform a brainstorming activity to create critical components of a spacesuit. Students will also evaluate the oxygen usage of two astronauts performing a spacewalk using linear equation concepts.
Weightless Wonder
Algebra 1, Algebra 2
Students will investigate the characteristics of quadratic functions to solve real-world problems involving the parabolic flights of NASA's Weightless Wonder jet.
Space Shuttle Ascent: Mass vs. Time
Algebra 1
Students will be asked to create scatter plots and find linear regression equations using mission data on the mass of the space shuttle during the first two minutes of the ascent phase.
Space Shuttle Ascent: Altitude vs. Time
Algebra 1
Students will be asked to create scatter plots and find quadratic regression equations using mission data on the altitude of the space shuttle during the first two minutes of the ascent phase.
Ascent: 50 Seconds to MECO
Algebra 1
Students will interpret velocity and acceleration graphs from the ascent phase of a space shuttle flight (8.5 minutes), and focus on the last 50 seconds before Main Engine Cut-Off, or MECO, to identify a linear function.
Lost in Space: Bone Density
Algebra 1
Students will explore slope and y-intercept and solve linear equations while investigating the risks of increased loss of Bone Mineral Density when the human body is in the reduced gravity of space compared to Earth's 1 g environment.
Exercising in Space
Algebra 1
Students will identify a direct variation, solve linear equations, and create tables based on the exercise equipment provided for astronauts on long duration missions on the ISS.
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