Algebra 1 Common Core worksheets

Use units to guide the solution of multi-step problems.

• Working with units

Define appropriate quantities for a descriptive model.

• Choosing the right quantity

Choose a level of accuracy suited to the measurement.

• How accurately to report

Use the structure of an expression to rewrite it.

• Difference of two squares
• Laws of logarithms
• Rational expressions
• Distributing
• Exponent laws
• Squaring a binomial
• Negative powers
• Simplifying roots
• Multiplying two brackets
• Algebraic fractions
• Logarithm laws
• Factor a difference of squares
• Difference of squares with coefficients
• Multiply a sum by a difference

Rewrite an expression to reveal properties: factor, complete the square, use exponent rules.

• Factoring x² + bx + c
• Difference of two squares
• Taking out a common factor
• Completing the square
• Common factor of two terms
• Common factor of three terms
• Factoring x² − bx + c
• Factoring x² + bx − c

Add, subtract and multiply polynomials; know they are closed under these.

• Adding and subtracting polynomials

Create equations and inequalities in one variable and solve them.

• Quadratic equation word problems
• Absolute value equations

Create equations in two variables and graph them.

• Writing linear equations
• Line equation from two points
• Point-slope equation of a line

Rearrange a formula to highlight a chosen quantity.

• Rearranging formulas

Explain each step in solving an equation.

• Dividing and signs

Solve linear equations and inequalities in one variable.

• Absolute value equations
• Solving absolute value equations
• Absolute value equations with coefficients

Solve quadratic equations by factoring, completing the square and the formula.

• Solving x² + bx + c = 0
• How many real solutions?
• Solving quadratics by square roots
• The discriminant
• Discriminant with a leading coefficient
• Solving x² = p by square roots
• Solving (x − h)² = k by square roots

Understand that a graph is the set of solutions of its equation.

• x- and y-intercepts of a line
• Finding the x-intercept
• Finding the y-intercept

Use function notation and evaluate functions.

• Function notation
• Exponential functions
• Evaluating functions
• Composing functions
• Evaluating exponential functions
• Solving exponential equations

Recognize that sequences are functions on the integers.

• Arithmetic and geometric sequences

Write a function in an equivalent form to reveal its properties.

• Completing the square

Write a function that describes a relationship between quantities.

• Write the rule from a situation

Write arithmetic and geometric sequences recursively and explicitly.

• Arithmetic and geometric sequences
• Arithmetic sequence nth term
• Common difference of a sequence
• Geometric sequence nth term
• Common ratio of a sequence

Identify the effect of replacing f(x) with f(x)+k, kf(x), f(kx) and f(x+k).

• Transformations of a function

Construct linear and exponential functions from a description or table.

• Writing linear equations
• Exponential functions

Interpret the parameters of a linear or exponential model.

• What the numbers in a rule mean

Compare the center and spread of two data sets.

• Comparing two data sets

Summarize categorical data in a two-way frequency table.

• Relative frequency

Distinguish between correlation and causation.

• Correlation and causation