Gordon > Essential Questions

After studying each Chapter, you should be able to answer the following questions:

Chapter 10 Essential Questions           
1.  How are the GCF and the Distributive Property used to factor polynomials?

2.  How are monomials factored?

3.  If you know the product and one of its factors, how can you find the other factor of a polynomial? 

4.  How are Punnett Squares used in factoring trinomials?  

Chapter 9 Essential Questions           
1.  How are adding and multiplying polynomials different?      

2.  What do you do differently when finding the degree of a monomial versus finding the degree of a bi- or trinomial?

3.  What does FOIL stand for?

4. If the base & height of a rectangular prism are binomials, how is the volume computed?



Chapter 8 Essential Questions        

        1.  How are powers multiplied?  Divided?


        2.  How is a problem simplified with a negative exponent?


        3.  How is a number written in scientific notation?


        4.  The first part of a number written in scientific notation must be between what two numbers?                         How is the power portion determined?      

        5.  What is the square root of a number?       

        6.  What is the relationship between the square root of a number and the square of a number?
    7.  The Pythagorean Theorem involves what type of a triangle?

        8.  What is meant by the "legs and hypothenuse" of a triangle and what is their relation to  the  Pythagorean Theorem?

Chapter 7 Essential Questions      
1.  Given the coordinates of two points on a line, how do you find the slope?

2.  What is the slope-intercept form and how can it be used to draw the line it represents?

3.  Does the graph of y = -3x 8 pass through (-5, 23)?  How do you know?

4.  How do you determine the y-intercept of the graph of an equation?

5.  Given the equation y = 3x 6, can you write the equation of a line that is parallel to this line?  That is perpendicular?

Chapter 6 Essential Questions      
1.  What is the relationship between the domain and range of a relation?

2.   What are three ways of representing a relation?

3.  What is a linear equation?

4.  What are three examples of non-linear equations?

5.  What is the vertical line test for a function?

6.  Given a set of ordered pairs, a graph or a table, how would you determine if these relations are a function?

7.  Why is the distance formula a direct variation?

8.  In the equation y = 4x, what is the constant of variation?

Chapter 5 Essential Questions  
1.  How are probability and odds computed?  How are they different?  How are they similar?   

2.  What is a ratio?  How can two ratios be compared?

3.  What is the difference between a ratio and a proportion?

4.  How can proportions be used to compute distance on a map? To compare similar shapes?

5.  What does is mean when two objects are similar?

6.  What does "IS over OF = % over 100"  mean?  

7.  Percent is a ratio that compares a number to what?

8.  3 out of 5 means what?

9.  What is the formula for percent change?

10.  Is sales tax added or subtracted?  What about a discount?  How would you compute the cost of an item that is 30% off  with a  7% sales tax?

11.  How are compound events computed?

Chapter 4 Essential Questions      
1.  How do you multiply fractions?  How does it differ from dividing fractions?   

2.  How would you teach the Fundamental Counting Principal to someone using a sandwich as an example?   

3.  What is the multiplicative inverse or reciprocal of 1/2?

4.  What is the product of a number and its multiplicative inverse?   

5.  What happens if you multiply each side of an equation by the same number?

6. What strategy should you use when solving a multi-step equation (hint: think about the order of operations) 

7.  When solving an equation with variables on both sides, what should you do first?

Chapter 3 Essential Questions  
    1.  What are two examples of fractions whose cross products are equal? 

    2.  What is the importance of the denominator when adding and subtracting fractions?

    3.  What is a rational numbers?  

    4.  How can a rational number be represented as a fraction, a percent, a decimal and as a pie diagram?

    5.  How do you solve a one step addition or subtraction problem?

    6.  If you add or subtract something from one side of an equation, why must you do the same thing to the other side of the equation?  What happens if you don't do the same thing?

Chapter 2 Essential Questions   
    1.  How is a thermometer like a number line?  
    2.  Explain the difference between adding & multiplying negative & positive integers.
    3.  Why is it a good idea to change subtraction to addition?  What do you need to remember if you do  this?  Hint:  Keep/Change/Flip   
    4.  Why do opposites have the same Absolute Value?

     5.  How can you easily remember the quadrants of a coordinate plane?

     6.  What quadrant are x & y BOTH negative?

Chapter 1 Essential Questions

    1.   Why should we study Algebra?  When is it used in everyday life?

    2.   How do we translate verbal ideas to the language of Algebra?

    3.   How will the global economy affect you in the future?

    4.   Why is the Order of Operations an important part of Algebra?

    5.   What are common mistakes that you can make while doing the Order of Operations?

    6.   How are the Commutative & Associative properties similar?  Different?

    7.   When would you use the Simple Interest Formula?  What are the parts of the Simple Interest Formula and what do they mean?

    8.   When is the Distributive Property used?  Why is it a good idea to use arrows when performing this property?


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