# 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)

☐ Surds

☐ 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.

☐ Degree

☐ 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.

☐ Inverse

☐ Closure

☐ 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

☐ Parabola

☐ Investigate and generalize how changing the coefficients of a function affects its graph

☐ Parabola

☐ Find the roots of a parabolic function graphically.
Note: Only quadratic equations with integral solutions.

☐ Parabola

☐ 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.

☐ Parabola

☐ 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

☐ 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

☐ Bisect

☐ 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

☐ Ellipse

☐ 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.