# Materials

Chapter 1   Order Of Operations

1.1.1 Addition and Multiplication Which is correct?

1.1.2 Addition and Exponents Which is correct?

1.1.3 Multiply and Divide from left to right Which is correct?

1.1.4 Multiplication and Exponents Which is correct?

Chapter 2   Number Properties

~Multiplication

2.1.1 Multiplying fractions Which is better?

~Division

2.2.1 Division vs. multiplication by the reciprocal How do they differ?

2.2.2 Multiplication vs. division by the reciprocal (with integers) How do they differ?

2.2.3 Multiplication vs. division by the reciprocal (with fractions) How do they differ?

2.2.4 Simplifying fractional expressions Which is correct?

~Associative Property

2.3.1 Addition – Add 3 numbers in any order Why does it work?

2.3.3 Subtraction – Subtraction is not associative Which is correct?

2.3.4 Multiplication – Multiply 3 numbers in any order Why does it work?

2.3.5 Division – Division is not associative Which is correct?

~Commutative Property

2.4.1 Addition of Negatives – If rewrite subtraction as addition, can use commutative property Which is correct?

2.4.2 Subtraction – Subtraction is not commutative How do they differ?

~Distributive Property

2.5.1 Distributive Property and Order of Operations – Distribute vs. simplify in parentheses first Why does it work?

2.5.2 Common error: Fail to distribute over both terms Which is correct?

2.5.3 Common error: Incorrectly using the distributive property with multiplication Which is correct?

~Absolute Value

2.6.1 Simplifying expressions with absolute value Which is correct?

~Operations with Negative Numbers

2.7.1 Subtracting a negative vs. rewriting subtraction as addition of the opposite Which is correct?

Chapter 3   Linear Equations

~Solving Multi-Step Equations

3.1.1 Subtraction – Subtract first vs. distribute first Which is better?

3.1.2 Fractions – Eliminate fractions first vs. find common denominator first Which is better?

~Solving Multi-Step Equations

3.1.3 Incorrectly performing an operation on both sides of an equation Which is correct?

3.1.4 Fractions – Subtract first vs. find a common denominator first Which is better?

3.1.5 Division – Cross-multiply vs. multiply both sides of the equation by the same value Why does it work?

3.1.6 Subtract first vs. divide first (for equations of the form a(x + b) = c, where a is divisible by c) Which is better?

3.1.7 Distribute first vs. multiply first (for equations of the form a(x + b) = c, where a is a fraction) Which is better?

~Solving Equations with Variables on Both Sides

3.2.1 Subtract first vs. distribute first Which is better?

3.2.2 Combining like terms Which is correct?

3.2.3 Performing same operation twice on one side Which is correct?

3.2.4 Combining terms with common factors Which is better?

~Solving Literal Equations

3.3.1 Divide first vs. distribute first Which is better?

3.3.2 Move variables one at a time vs. all at once Which is better?

3.3.3 Subtract first vs. divide first Why does it work?

~Solving Proportions

3.4.1 Multiply first vs. cross-multiply Why does it work?

3.4.2 Equivalent fractions Which is better?

3.4.3 Unit rate Which is better?

3.4.4 Multiplying fractions vs. solving a proportion Which is correct?

Chapter 4    Graphing Linear Equations And Introduction To Functions And Relations

~Using a Table of Values

4.1.1 Table of values vs. slope-intercept form Which is better?

4.1.2 Choosing x-values for the table Which is better?

~Finding a Slope

4.2.1 Find a slope by graphing vs. by using the slope formula Why does it work?

~Graphing Lines using Intercepts

4.3.1 Shortcut to finding the intercepts Why does it work?

~Point-Slope Form

4.4.1 Choose either point Why does it work?

4.4.2 Graph an equation given in point-slope form using the point-slope or the slope-intercept method Which is better?

~Using Slope-Intercept Form

4.5.1 Given 2 points, find the y-intercept Which is better?

4.5.2 Forget which term represents the y-intercept Which is correct?

4.5.3 Confuse rise and run Which is correct?

4.5.4 Comparing the equations of lines with different slope values How do they differ?

4.5.5 Comparing the equations of lines with positive and negative slopes How do they differ?

4.5.6 Comparing the equations of lines with different y-intercepts How do they differ?

4.5.7 Comparing x-intercepts and y-intercepts How do they differ?

~Using Standard Form

4.6.1 Given an equation in standard form, graph using slope-intercept vs. intercepts Which is better?

~Slope of a Horizontal Line

4.7.1 Find slope by formula vs. t-table Why does it work?

~Slope of a Vertical Line

4.8.1 Find slope by formula vs. t-table Why does it work?

~Definition of a Function

4.9.1 Determine whether a relation is a function How do they differ?

4.9.2 Domain vs. range How do they differ?

Chapter 5    Inequalities

~Solving Inequalities using Multiplication and Division

5.1.1 Division by a positive vs. a negative number Which is correct?

5.1.2 Why we can ‘flip’ the inequality sign in division Why does it work?

5.1.3 ‘Flipping’ the inequality sign when dividing by a positive value Which is correct?

~Absolute Value Inequalities

5.2.1 Definition Why does it work?

5.2.2 Greater than Why does it work?

5.2.3 Addition Why does it work?

~Graphing Inequalities

5.3.1 Error shading by sign Which is correct?

5.3.2 Graphing an equation vs. graphing an inequality How do they differ?

5.3.3 Graphing inequalities with “and” vs. “or” How do they differ?

Chapter 6   Systems Of Equations

~Substitution

6.1.1 Substitute the first value you get into either equation to get the second value Why does it work?

6.1.2 Solve for x vs. solve for y Why does it work?

6.1.3 Substitute for a more or less efficient variable Which is better?

~Elimination

6.2.1 Substitute the first value you get into either equation to get the second value Why does it work?

6.2.2 Eliminate x vs. eliminate y How do they differ?

6.2.3 Common error Which is correct?

6.2.4 Why elimination works Why does it work?

~Substitution vs. Elimination

6.3.1 Both methods work Which is better?

6.3.2 Identifying when substitution is preferable Which is better?

6.3.3 Identifying when elimination is preferable Which is better?

Chapter 7   Polynomials

7.1.1 Addition – Missing terms Which is better?

7.1.2 Subtraction – Missing terms Which is better?

~Multiplying and Dividing Polynomials

7.2.1 Multiplying Polynomials – Area model vs. distributive property Why does it work?

7.2.2 Multiplying Polynomials – Distributive property vs. FOIL Why does it work?

7.2.3 Multiplying Polynomials – Forgetting to distribute to each term Which is correct?

7.3.1 Dividing Polynomials – Common error (no placeholders) Which is correct?

~Factoring – GCF

7.4.1 Finding GCF by factor tree vs. product pairs Which is better?

7.4.2 GCF of terms with variables by factor tree vs. product pairs Which is better?

7.4.3 Adding terms with common factors Which is better?

7.4.4 Adding terms with common factors Why does it work?

~Factoring Trinomials

7.5.1 Factor a trinomial in two variables How do they differ?

7.5.2 Factor a trinomial with lead coefficient not 1: Factor by trial and error vs. factor first Which is better?

7.5.3 Factor a trinomial with lead coefficient not 1: Factor by trial and error vs. splitting the middle term Which is better?

7.5.4 Solve a quadratic equation with lead coefficient not 1: Factor out a common factor first vs. don’t Which is better?

7.5.5 Factor a trinomial with lead coefficient not 1:Factor by splitting the middle term first vs. by factoring out a common factor first Which is better?

~Completing the Square

8.1.1 Derivation of the quadratic formula by completing the square Why does it work?

~Factoring

8.2.1 Factoring vs. quadratic formula Which is better?

~Division by a Variable

8.3.1 Why not to divide by a variable Which is correct?

8.4.1 Confuse sign of a Which is correct?

8.4.2 Confuse sign of b Which is correct?

8.4.3 Confuse sign of c Which is correct?

8.5.1 Graphing quadratic equations with positive vs. negative coefficients for xHow do they differ?

8.5.2 Graphing quadratic equations with fractional vs. whole-number coefficients for xHow do they differ?

8.5.3 How changing the coefficient of x2 affects the graph of a quadratic equation How do they differ?

8.5.4 How adding a constant to the quadratic equation affects the graph How do they differ?

8.5.5 How adding vs. subtracting a constant to the quadratic equation affects the graph How do they differ?

8.5.6 How adding a constant to x affects the graph How do they differ?

8.5.7 How adding vs. subtracting a constant to x affects the graph How do they differ?

Chapter 9   Exponents

~Operations with Terms with Exponents

9.1.1 Adding like terms with exponents Which is correct?

~Multiplication Properties: Product of Powers Property

9.2.1 Multiplication with exponents Which is correct?

~Multiplication Properties: Power of a Power Property

9.3.1 Rewriting terms with the same base Which is better?

9.3.2 Rewriting terms using perfect squares Which is better?

~Multiplication Properties: Power of a Product Property

9.4.1 Power of a product Why does it work?

9.4.2 Apply the exponent to each number being multiplied Which is correct?

9.4.3 Order of operations vs. power of a product property Why does it work?

9.4.4 Simplifying expressions with variables Which is correct?

9.4.5 Simplifying expressions with addition of integers Which is correct?

9.4.6 Simplifying expressions involving products and   exponents according to the order of operations Which is correct?

~Division Properties: Quotient of Powers Property

9.5.1 Division with exponents Why does it work?

9.5.2 Division with exponents Which is correct?

~Graphing Exponential Equations

9.6.1 Graphing linear vs. exponential functions How do they differ?

9.6.2 Graphing quadratic vs. exponential functions How do they differ?

Chapter 10   Radical Expressions and Equations

10.1.1 Prime factor vs. perfect square Which is better?

10.1.2 Confusing the square root with division by 2 Which is correct?

10.1.3 Forgetting to simplify the square root of a*a as a Which is correct?

10.1.4 Estimating the value of a square root Why does it work?

10.1.5 Values for which the square root of a number   is greater and less than the number How do they differ?

10.1.6 Square roots with numbers and variables Why does it work?

10.2.1 Multiplication of radicals Which is better?

10.2.2 Square root of a product vs. product of the square roots Why does it work?

10.3.1 Square root of a quotient vs. quotient of the square roots Why does it work?

10.3.2 Square root in the denominator of a fraction Which is better?

10.4.1 Square root of a sum vs. sum of square roots Which is correct?

10.4.2 Combining two unlike radical terms Which is correct?

10.4.3 Combining three like radical terms Which is correct?

10.4.4 Factoring the radicand to combine like radical terms Which is correct?

10.4.5 Square root of a difference vs. difference of square roots Which is correct?

10.5.1 Simplifying expressions with sums vs. products in the radicand How do they differ?

10.6.1 Factoring out radical terms as common factors Which is better?

10.6.2 Advantages of breaking terms into perfect squares first Which is better?

~Distance Formula

10.7.1 Distance formula and Pythagorean theorem Why does it work?

Chapter 11   Rational Expressions and Equations

11.1.1 Incorrect common denominator Which is correct?

11.1.2 Simplifying the fraction first vs. finding a common denominator first Which is better?

~Multiplication and Division

11.2.1 Error simplifying the numerator and denominator Which is correct?

11.2.2 Divide vs. multiply by the reciprocal Why does it work?

# Chapter 1 Order Of Operations

 chapter_1.pdf 1.1 MB

# Chapter 10 Radical Expressions and Equations

 chapter_10.pdf 5.63 MB

# Chapter 11 Rational Expressions and Equations

 chapter_11.pdf 1.33 MB

# Chapter 2 Number Properties

 chapter_2.pdf 3.69 MB

# Chapter 3 Linear Equations

 chapter_3.pdf 5.41 MB

# Chapter 4 Graphing Linear Equations And Introduction To Functions And Relations

 chapter_4.pdf 7.1 MB

# Chapter 5 Inequalities

 chapter_5.pdf 3.02 MB

# Chapter 6 Systems Of Equations

 chapter_6.pdf 3.79 MB

# Chapter 7 Polynomials

 chapter_7.pdf 4.97 MB