# Algebra 1 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 1 | Numbers
☐ Perform the four arithmetic operations using like and unlike radical terms and express the result in simplest form
☐ Understand and use scientific notation to compute products and quotients of large or small numbers.
☐ Solve algebraic problems arising from situations that involve fractions, decimals, percents (decrease/increase and discount), and proportionality/direct variation
☐ Evaluate expressions involving factorial(s), absolute value(s), and exponential expression(s)
☐ Understand that dividing by zero is undefined.
☐ Know how to calculate n! for whole numbers n, and the relationship between n! and (n - 1)!
☐ Understand what is meant by an imaginary number and a complex number.
☐ Understand what is meant by infinity and that infinity is not a Real number.
☐ Represent a repeating decimal as a fraction.
☐ Understand the geometric mean, how to calculate it, and its relationship to mean proportionals.
☐ Understand the harmonic mean, and how to calculate it.
Algebra 1 | Measurement
☐ Calculate rates using appropriate units (e.g., rate of a space ship versus the rate of a snail)
☐ Solve problems involving conversions within the metric measurement system, given the relationship between the units
☐ Calculate the relative error in measuring square and cubic units, when there is an error in the linear measure (metric measurements)
☐ Solve problems involving conversions within the US standard measurement system, given the relationship between the units
☐ Calculate the relative error in measuring square and cubic units, when there is an error in the linear measure (US standard measurements)
Algebra 1 | Algebra
☐ Translate a quantitative verbal phrase into an algebraic expression
☐ Find values of a variable for which an algebraic fraction is undefined.
☐ Add or subtract fractional expressions with monomial or like binomial denominators
☐ Multiply and divide algebraic fractions, and express the product or quotient in its simplest form
☐ Recognize and factor the difference of two perfect squares
☐ Write verbal expressions that match given mathematical expressions
☐ Factor algebraic expressions completely, including trinomials with a lead coefficient of one (after factoring a GCF)
☐ Solve literal equations for a given variable
☐ Solve equations involving fractional expressions. Note: Expressions which result in linear equations in one variable.
☐ 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, and simplify them.
☐ Write algebraic equations or inequalities that represent a situation
☐ Solve complex equations of degree greater than two by making an appropriate change of variable.
☐ Understand the difference between an equation and a formula.
☐ Know how to change the subject of a formula.
☐ Know the various meanings of the words 'Standard Form', including Scientific Notation.
Algebra 1 | Exponents
☐ Multiply and divide monomial expressions with a common base using the properties of exponents. Note: Use integral exponents only.
Algebra 1 | Inequalities
☐ Determine whether a given value is a solution to a given linear equation in one variable or linear inequality in one variable
☐ Solve linear inequalities in one variable
☐ Determine whether a given point is in the solution set of a system of linear inequalities
☐ Graph linear inequalities
Algebra 1 | Coordinates
☐ Plot points using coordinates in three dimensions.
Algebra 1 | Linear Equations
☐ Solve systems of two linear equations in two variables algebraically
☐ Solve all types of linear equations in one variable
☐ Analyze and solve verbal problems whose solution requires solving a linear equation in one variable or linear inequality in one variable
☐ Analyze and solve verbal problems whose solution requires solving systems of linear equations in two variables
☐ Show that, given a system of two equations in two variables, the two equations can be combined in various ways to give other equations with the same solutions; thus justifying the elimination method.
☐ 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.
☐ Understand and apply the multiplication property of zero to solve quadratic equations with integral coefficients and integral roots
☐ Understand the difference and connection between roots of a quadratic equation and factors of a quadratic expression
☐ Analyze and solve verbal problems that involve quadratic equations
Algebra 1 | Polynomials
☐ Add, subtract, and multiply monomials and polynomials
☐ Divide a polynomial by a monomial or binomial, where the quotient has no remainder. Use factoring with canceling, or Polynomial long division.
☐ Simplify fractions with polynomials in the numerator and denominator by factoring both and renaming them to lowest terms
☐ Understand Special Binomial Products
Algebra 1 | Sets
☐ Use set-builder notation and/or interval notation to illustrate the elements of a set, given the elements in roster form
☐ Find the complement of a subset of a given set, within a given universe
☐ 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
☐ 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.
☐ Express the union or intersection of sets of numbers in interval notation.
☐ Draw and interpret sets in Venn diagrams
Algebra 1 | Functions
☐ Determine when a relation is a function, by examining ordered pairs and inspecting graphs of relations
☐ Identify and graph linear, quadratic (parabolic), absolute value, and exponential functions
☐ Investigate and generalize how changing the coefficients of a function affects its graph
☐ Find the roots of a parabolic function graphically. Note: Only quadratic equations with integral solutions.
☐ Define a relation and function
☐ Determine when a relation is a function
☐ Determine if a function is one-to-one, onto, or both
☐ Determine whether a function is injective, surjective or bijective.
Algebra 1 | Graphs
☐ Graph the slope (gradient) as a rate of change between dependent and independent variables
☐ Determine the slope (gradient) of a line, given the coordinates of two points on the line
☐ Write the equation of a line, given its slope (gradient) and the coordinates of a point on the line
☐ Write the equation of a line, given the coordinates of two points on the line
☐ Write the equation of a line parallel to the x-axis or the y-axis
☐ Determine the slope (gradient) of a straight line, given its equation in any form
☐ Determine if two lines are parallel, given their equations in any form
☐ 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.
☐ 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.
☐ Graph and solve systems of linear equations and inequalities with rational coefficients in two variables.
☐ 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.
☐ Find the slope of a perpendicular line, given the equation of a line
☐ Determine whether two lines are parallel, perpendicular, or neither, given their equations
☐ Find the equation of a line, given a point on the line and the equation of a line perpendicular to the given line
☐ Find the equation of a line, given a point on the line and the equation of a line parallel to the desired line
☐ Find the midpoint of a line segment, given its endpoints
☐ Find the length of a line segment, given its endpoints
☐ Find the equation of a line that is the perpendicular bisector of a line segment, given the endpoints of the line segment
☐ Investigate, justify, and apply the properties of triangles and quadrilaterals in the coordinate plane, using the distance, midpoint, and slope (gradient) formulas
☐ 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.
☐ Recognize the symmetry in equations and their graphs.
☐ Determine the area of an ellipse from its Cartesian formula
☐ Know how to convert the equation of a straight line between these types: Slope-intercept form, General form and point-slope form.
☐ Find the coordinates of the point that divides a line segment in a given ratio.