1 Chapter Test

Do you know HOW?

1. Write an algebraic expression for the phrase the quotient of n and 6.
2. Write a word phrase for − 12 t + 2 . negative 12 t plus 2 .
3. Evaluate the expression − ( p q ) 2 ÷ ( − 8 ) negative . open p q close squared . divides open negative 8 close  for p = 2 and q = 4.
4. Dance The table shows how the total cost of dance classes at a studio depends on the number of classes you take. Write a rule in words and as an algebraic expression to model the relationship.

   Dance Classes

   Number of Classes	Total Cost
   1	( 1 × 15 ) + 20 open 1 times 15 close plus 20
   2	( 2 × 15 ) + 20 open 2 times 15 close plus 20
   3	( 3 × 15 ) + 20 open 3 times 15 close plus 20

Simplify each expression.

5. − 20 − ( − 5 ) · ( − 2 2 ) negative 20 minus open negative 5 close middle dot open negative , 2 squared , close
6. ( − 1 4 ) 3 open , negative , 1 fourth , close cubed
7. − 7 a b a , a ± 0 negative . fraction 7 eh b , over eh end fraction . comma . eh plus minus 0
8. − | − 25 | negative vertical line negative 25 vertical line
9. 16 25 square root of 16 over 25 end root
10. Is each statement true or false? If false, give a counterexample.
    1. For all real numbers a and b, a · b eh middle dot b  is equivalent to b · a . b middle dot eh .
    2. For all real numbers a and b, a ( b · c ) = a b · a c eh open b middle dot c close equals eh b middle dot eh c
11. Is the ordered pair (2, − 5 negative 5 ) a solution to the equation 4 + 3 x = − 2 y ? 4 plus 3 x equals negative 2 y question mark  Show your work.
12. Order the numbers − 7 8 , 7 4 , − 1 4 5 ,  and  − 13 16 negative , 7 eighths , comma , 7 fourths , comma negative 1 , and 4 fifths , comma , and , minus , 13 over 16  from least to greatest.
13. Soccer There are t teams in a soccer league. Each team has 11 players. Make a table, write an equation, and draw a graph to describe the total number of players p in the league. How many players are on 17 teams?

Simplify each expression.

14. 5 x 2 − x 2 5 , x squared , minus , x squared
15. 12 ÷ ( − 3 4 ) 12 divides open , negative , 3 fourths , close
16. − ( − 2 + 6 t ) negative open negative 2 plus 6 t close
17. − 3 [ b − ( − 7 ) ] negative 3 left bracket b minus open negative 7 close right bracket
18. Name the subset(s) of the real numbers to which each number belongs.
    1. − 2.324 negative , 2.324
    2. 46 square root of 46
19. Identify each property.
    1. a(b + c) = ab + ac
    2. (a + b) + c = a + (b + c)

Do you UNDERSTAND?

20. Is the set of positive integers the same as the set of nonnegative integers? Explain.
21. Error Analysis Find and correct the error in the work shown below.

    

22. Is the following statement true or false? If the product of three numbers is negative, then all the numbers are negative. If false, give a counterexample.
23. Reasoning You notice that 10°C = 50°F, 20°C = 68°F, and 30°C = 86°F. Use inductive reasoning to predict the value in degrees Fahrenheit of 40°C.
24. Reasoning When is the absolute value of a difference equal to the difference of the absolute values? Explain.

Table of Contents