2)
At the Bristol Racket Club tennis courts are rented by the hour. The spreadsheet shows the data for two monthly plans.
Plan A involves paying a one time monthly fee of $10 plus $9 per hour for court time.
Plan B involves a one time monthly fee of per hour for court time.
A B C
1 # of hours Plan A ($) Plan B ($)
2 1 19 74
3 2 28 78
4 3 37 82
5 4 46 86
How many hours would need to be rented during the month to make Plan B the best plan?
A)
13 or more hours
B)
10 or more hours
C)
11 or more hours
D)
14 or more hours
Solution:
Let the number of hours be x
70 + 4x < 10 + 9x
60 < 5x
x > 12
Answer: (A) 13 or more hours
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
3)
How are the symbols , 0.75, and 75% related?
Solution:
0.75 is in decimal form of 3/4 and 75% is in percentage formof 3/4.
Use inductive reasoning to predict the next number in the sequence. Explain your reasoning.
4)
21, 18, 15, 12, 9, . . .
.
Solution:
Next number is obtained by subtracting 3 from the previous number.
Next numbers will be 9 – 3 = 6.
Decide whether the argument is an example of inductive or deductive reasoning. Explain your reasons.
5)
23 + 3 = 26, 29 + 3 = 32, 41 + 41 = 82.
The sum of two prime numbers is even.
A)
Deductive
B)
Inductive
Solution:
(B) Inductive reasoning
Inductive reasoning is the method of deriving a general rule from a specific cases.
Write the statement indicated.
6)
Write the negation of the following:
The test is difficult.
The test is not difficult.
Decide whether the argument is an example of inductive or deductive reasoning. Explain your reasons.
7)
Practice makes perfect. Therefore, if I practice, I'll be perfect.
A)
A) Inductive
B)
Deductive
Answer: B) deductive; Deductive reasoning starts with a general case or facts and deduces specific instances.
8)
Form a conjunction from the following two statements and determine if the conjunction is true or false.
Two is an even number.
Two is a prime number.
Solution:
Two is an even and prime number.
Conjunction is true as 2 is prime as well as even number.
Solve the problem.
9)
A child's coin bank contains $ 2.58 in pennies and nickels. If the number of pennies is 36 less than 2 times the number of nickels, how many pennies are in the bank?
Solution:
Let the number of nickels be x then number of pennies will be 2x – 36.
5x + 2x – 36 = 258
7x = 258 + 36 = 294
x = 42
Number of pennies = 2*42 – 36 = 84 – 36 = 48
10)
A drink and a sandwich together cost $ 5.00. The sandwich costs $ 1.50 more than the drink. How much does the sandwich cost?
Solution:
Let the cost of sandwich be x then the cost of drink will be x - 1.5
x + x - 1.5 = 5.0
2x = 5.0 + 1.5 = 6.5
x = 3.25
Cost of sandwich = $3.25
List all the subsets of S.
11)
S = {Chocolate, Vanilla, Mint}
Solution:
Subsets = {ø, {Chocolate}, {Vanilla}, {Mint}, {Chocolate, Vanilla} , {Chocolate, Mint}, {Vanilla, Mint}, {Chocolate, Vanilla, Mint}}
12)
Explain why the sets {a,b,c} and {1,2,3} are equivalent sets but not equal sets.
Solution:
Since elements are not same.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
13)
Find A ? B, given A = { 6, 15, 3} and B = { 15, 3, 100}.
A) { }
B)
{6, 15, 15, 3, 3, 100}
C)
{6, 15, 3, 100}
D) {15, 3}
Answer: symbol did not appear between A and B.
But AUB = {6, 15, 3, 100}
A n B = {15, 3}
14)
Find (A n B) n C, given A = {s, e, t}, B = {m, e}, and C = {f, r, e, e}.
A
) {s, e, t, m, e, f, r, e, e}
B)
{s, e, t, m, f, r}
C)
{e}
D)
{ }
Solution: (A n B) = {e} (A n B) n C = {e}
Answer: C)
Name the property of addition that has been applied.
15)
( 8 + 2) + 2 = 8 + ( 2 + 2)
A)
Commutative
B)
Closure
C)
Identity
D
Associative
Answer: (D) Associative
Use the definition of subtraction to rewrite the subtraction equation as an addition equation.
16)
x - 64 = 80
Solution:
Add 64 to each side
x = 80 + 64
if we solve it, we will get x = 144
17)
Use the Associative and Commutative Properties of addition to simplify where a and b are whole numbers and
Question did not appear.
Use the Distributive Property to find the product.
18)
3 × (10 + 8)
= 3 × 10 + 3 × 8 = 30 + 24 = 54
Use the definition of division to rewrite the division equation as a multiplication equation.
19)
85 ÷ 5 = 17
Solution:
85 = 5 × 17
Use the distributive property of multiplication over addition to rewrite the sum as a product of two factors, where one of the factors is a sum.
20)
6yz - 54y
Solution:
6yz - 54y
Take 6y common out, we will get
= 6y(z – 9)