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Math 9R Classwork/Homework: Chapter 2 Review

1) An addition table for a subset of real numbers is shown below. Which number is the identity element? Explain your answer.

[pic]

2) The operation * for the set {p,r,s,v} is defined in the accompanying table. What is the inverse element of r under the operation *?

[pic]

3) Use the binary operation table below to answer the questions.

[pic]

a. Is this set closed? _________

b. Is this set commutative? _____________

c. Find (1 ( 2) ( (4 ( 3)

d. True or false: (4 ( 3) ( 1 = 4 ( (3 ( 1)

4) The expression [pic] is equivalent to

(1) 1 (3) 7

(2) 0 (4) –7

5) If r = 2 and s = -7, what is the value of [pic]

(1) 5 (3) 9

(2) -5 (4) -9

6) Which equation illustrates the multiplicative inverse property?

(1) [pic] (3) [pic]

(2) [pic] (4) [pic]

**7) If a + b is less than c + d, and d + e is less than a + b, then e is

(1) less than c (3) less than d

(2) equal to c (4) greater than d

8) The sum of two negative numbers always has to be

(1) negative (3) zero

(2) positive (4) an integer

9) Which statement is true for all real number values of x?

(1) |x – 1| > 0 (3) [pic]

(2) |x – 1| > (x – 1) (4) [pic]

10) The additive inverse of [pic] is

(1)[pic] (3) 0

(2) [pic] (4) [pic]

11) Which equation illustrates the associative property?

(1)[pic] (3) [pic]

(2)[pic] (4) [pic]

12) Which interval notation represents the set of all numbers from 2 through 7, exclusive?

(1) (2,7] (3) [2,7)

(2) (2,7) (4) [2,7]

13) Twelve players make up a high school basketball team. The team jerseys are numbered 1 through 12. The players wearing the jerseys numbered 3, 6, 7, 8, and 11 are the only players who start a game. Using set notation, list the complement of this subset.

14) Consider the set of integers greater than -2 and less than 6. A subset of this set is the positive factors of 5. What is the complement of this subset?

(1) {0, 2, 3, 4}

(2) {-1, 0, 2, 3, 4}

(3) {-2, -1, 0, 2, 3, 4, 6}

(4) {-2, -1, 0, 1, 2, 3, 4, 5, 6}

15) Given:

[pic]

What is the intersection of sets A and B?

(1) {(1,8)}

(2) {(–2,–1)}

(3) {(–2,–1), (1,8)}

(4) {(–3,–4), (–2,–1), (–1,2), (–1,0), (1,8)}

16) Maureen tracks the range of outdoor temperatures over three days. She records the following information.

[pic]

Express the intersection of the three sets as an inequality in terms of temperature, t.

17) Write the set of integers greater than or equal to 14 and the positive factors of 28.

18) Given the set of rational numbers between 3 and 12 inclusive, write this set in set builder notation.

19) Use the graph below to answer the questions

a) Write this set in set builder notation.

b) Write this set in interval notation.

20) Write the set (-2, 4] in set builder notation.

21) Write the set [pic] as an inequality.

22) Graph the inequality on the number line below: [pic]

23) If a and b are integers, which equation is always true?

(1) [pic] (3) a – b = b – a

(2) a + 2b = b + 2a (4) a + b = b + a

24) Under which operation is the set {-1, 0, 1} closed?

(1) multiplication (3) addition

(2) division (4) subtraction

25) Which set is closed under division?

(1) {1} (3) integers

(2) counting numbers (4) whole numbers

|26) If the expression [pic] is evaluated, what would be done last? |

|(1) subtracting (3) adding |

|(2) squaring (4) dividing |

| |

|27) The expression 15 – 3[2 + 6(–3)] simplifies to |

|(1) –45 (3) 63 |

|(2) –33 (4) 192 |

| |

| |

|28) If [pic], then [pic] equals |

|(1) -36 (3) 6 |

|(2) -6 (4) 18 |

| |

|29) If a = 3 and b = -1, what is the value of [pic] |

|(1) -2 (3) -4 |

|(2) 2 (4) 4 |

| |

|30) What is the value of the expression [pic] when [pic] and [pic] |

|(1) -192 (3) -48 |

|(2) -108 (4) 48 |

| |

|31) What is the value of [pic], if x = 4 and y = –3? |

|(1) –2 (3) 10 |

|(2) 2 (4) 14 |

|32) If x = 4 and y = -2, the value of [pic] is |

|(1) 32 (3) -4 |

|(2) 8 (4) -8 |

| |

33) Which list shows the numbers [pic] in order from smallest to largest?

(1) [pic] (2) [pic]

(3) [pic] (4) [pic]

34) Which is an irrational number?

(1) [pic] (3)[pic]

(2) 3.14 (4)[pic]

35) Which number is rational?

(1) π (3)[pic]

(2) [pic] (4)[pic]

36) What is the sum of [pic] and [pic]

(1) [pic] (3) [pic]

(2) [pic] (4) [pic]

37) If [pic] is divided by [pic], the result is

(1) 1 (3) [pic]

(2) 0.01 (4) [pic]

38) What is the value of [pic]in scientific notation?

(1) [pic] (3) [pic]

(2) [pic] (4) [pic]

39) What is the quotient of [pic] and [pic]

(1) [pic] (3) [pic]

(2) [pic] (4) [pic]

40) If the number of molecules in 1 mole of a substance is [pic], then the number of molecules in 100 moles is

(1) [pic] (3) [pic]

(2) [pic] (4) [pic]

41) If U = {positive odd integers less than 19}, A = {1, 3, 5, 7, 9}, B = {7, 9, 11, 13}, C = {7, 9, 13, 15}

a) [pic] b) [pic] c) [pic]

d) [pic] e) T or F: B is a subset of C

42) A school newspaper took a survey of 100 students. The results of the survey showed that 43 students are fans of the Buffalo Bills, 27 students are fans of the New York Jets, and 48 students do not like either team. How many of the students surveyed are fans of both the Buffalo Bills and the New York Jets?

(1) 16 (3) 52

(2) 18 (4) 70

43) 80 students were surveyed about the foods they liked. Twenty students liked pizza, 10 students liked spaghetti, and 50 students liked tacos. If 10 students liked both pizza and tacos, 3 students liked both spaghetti and tacos, 4 students liked both pizza and spaghetti, and 3 students liked all three foods, how many students liked pizza or tacos?

44) A group of thirty-three students were surveyed about their favorite snack foods. 14 students like Doritos, 15 students like Lays Chips, and 12 students like Cheese Doodles. 4 students like Cheese Doodles and Lays Chips, 3 students like only Doritos and Cheese Doodles, 4 students liked all of these snack foods, and 5 students did not like any of these snack foods. How many students like Doritos and Lays Chips only?

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Hint: each set is made up of ordered pairs (x,y)

5

6

7

8

9

4

3

2

1

0

-1

-2

-3

-4

-5

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