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
Simplify radical terms (no variable in the radicand)
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.
Understand what is meant by The Modulo Operator and Congruence (e.g. 14 = 2 mod 12).
Understand how to use The Euclidean Algorithm to find the Greatest Common Factor of two integers.
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.
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.
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.