**Table of Contents**

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?*

2.3.2 Addition – Addition of negative numbers *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

~Adding and Subtracting 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?*

Chapter 8 Quadratics

~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?*

~Quadratic Formula

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?*

~Graphing Quadratic Equations

8.5.1 Graphing quadratic equations with positive vs. negative coefficients for *x*^{2 }*How do they differ?*

8.5.2 Graphing quadratic equations with fractional vs. whole-number coefficients for *x*^{2 }*How do they differ?*

~Graphing Quadratic Equations

8.5.3 How changing the coefficient of *x*^{2} 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

~Properties of Radicals: Square Roots

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?*

~Product Property of Radicals

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?*

~Quotient Property of Radicals

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?*

~Addition and Subtraction of Radicals

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?*

~Multiplication and Division of Radicals

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

~Simplifying Radical Expressions

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

~Addition and Subtraction

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?*

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blank_worked_example_page_b.pdf | 114 KB |

blank_worked_example_page_c.pdf | 112 KB |

chapter_1.pdf | 1.1 MB |

chapter_10.pdf | 5.63 MB |

chapter_11.pdf | 1.33 MB |

chapter_2.pdf | 3.69 MB |

chapter_3.pdf | 5.41 MB |

chapter_4.pdf | 7.1 MB |

chapter_5.pdf | 3.02 MB |

chapter_6.pdf | 3.79 MB |

chapter_7.pdf | 4.97 MB |

chapter_8.pdf | 4.7 MB |

chapter_9.pdf | 4.21 MB |