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MATH 208
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FINAL MOCK
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MATH 208 Final Exam Mock – EC SECTION – FALL 2022
MATH 208 FINAL MOCK EXAM – SECTION EC
𝑀=
0.6
0.4
0.4
0.1
𝐷=
6
4
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1) Assume that an economy is based on two industrial sectors, agriculture (A) and
energy (E). The technology matrix M and final demand matrices (in billions of
dollars) are shown below.
Find (𝐼 − 𝑀)−1 and the output for each sector X, that is needed to satisfy the final
demand, D.
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a. (𝐼 − 𝑀)−1 =
b. 𝑋 =
1
MATH 208 Final Exam Mock – EC SECTION – FALL 2022
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2) a) How many ways can a 4-person subcommittee be selected from a committee
of 9 people?
a. _____________ ways
b) How many ways can a president, vice-president, secretary and treasurer be
chosen from a committee of 9 people?
b. _______________ ways
2
MATH 208 Final Exam Mock – EC SECTION – FALL 2022
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3) From a standard 52-card deck, how many 6-card hands consist entirely of red
cards?
There are _________ possible hands
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MATH 208 Final Exam Mock – EC SECTION – FALL 2022
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4) A card is drawn from a well-shuffled deck of 52 cards. Find the probability that the
card is black or a 6.
The probability is _________
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MATH 208 Final Exam Mock – EC SECTION – FALL 2022
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5) A catering service offers 8 appetizers, 12 main courses, and 7 desserts. A banquet
committee is to select 2 appetizers, 7 main courses, and 4 deserts. How many ways
can this be done?
There are _________ possible ways this can be done.
5
MATH 208 Final Exam Mock – EC SECTION – FALL 2022
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6) An electronics store receives a shipment of 30 graphing calculators, 8 that are
defective. Four of the calculators are to be selected at random.
a. How many selections can be made?
_________ selections can be made
b. How many of these selections will contain no defective calculators?
________ selections will contain no defective calculators.
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MATH 208 Final Exam Mock – EC SECTION – FALL 2022
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7) A circular spinner is divided into 13 sectors of equal areas: 4 red sectors, 4 blue, 4
yellow and 1 green. Consider the experiment of spinning the spinner once. Find the
probability that the spinner lands on blue.
There is a probability of ______ that the spinner will land on a blue sector
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MATH 208 Final Exam Mock – EC SECTION – FALL 2022
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8) A standard 52-card deck has four 13-card suits: diamonds, hearts, clubs and
spades. The diamonds and hearts are red, and the clubs and spades are black.
Each 13-card suit contains cards numbered from 2 to 10, a jack, a queen, a king,
and an ace. An experiment consists of drawing 1 card from the standard deck. Find
the probability of drawing a black jack of diamonds.
the probability of drawing a black jack of diamonds is _______
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MATH 208 Final Exam Mock – EC SECTION – FALL 2022
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9) An experiment consists of dealing 5 cards from a standard 52-card deck. What is the
probability of being dealt 5 hearts?
The probability of being dealt 5 hearts is __________
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MATH 208 Final Exam Mock – EC SECTION – FALL 2022
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10) An experiment consists of rolling two fair dice and adding the dots on the two sides
facing up. Using the sample space provided below and assuming each simple event
is as likely as any other, find the probability that the sum of the dots is 9.
a. The probability of getting a sum of 9 is _____________
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MATH 208 Final Exam Mock – EC SECTION – FALL 2022
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11) In a family with 6 children, excluding multiple births, what is the probability of having
6 girls? Assume that a girl is just as likely as a boy at birth.
the probability of having 6 girls is _______
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MATH 208 Final Exam Mock – EC SECTION – FALL 2022
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12) Find the slope and x-intercept of the graph of the equation: 4x – y = 8
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MATH 208 Final Exam Mock – EC SECTION – FALL 2022
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13) A farmer buys a new tractor for $147,000 and assumes that it will have a trade-in
value of $87,000 after 10 years. The farmer uses a constant rate of depreciation to
determine the annual value of the tractor.
Find a linear model for the depreciated value V of the tractor t after it was purchased.
13
MATH 208 Final Exam Mock – EC SECTION – FALL 2022
14)
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A) Find the slop of the line that passes through the given points.
B) Find the standard form of the equation of the line.
C) Find the slope-intercept form of the equation of the line.
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(1,1) and (6,9)
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MATH 208 Final Exam Mock – EC SECTION – FALL 2022
Question 15
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How much interest will you have to pay for a credit card balance of $879 that is 1 month
overdue, if a 17% annual rate is charged?
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MATH 208 Final Exam Mock – EC SECTION – FALL 2022
Question 16
What is the APY for money invested at each rate?
a. 8% compounded quarterly
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b. 6% compounded continuously
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MATH 208 Final Exam Mock – EC SECTION – FALL 2022
Question 17
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What will a $120,000 house cost 4 years from now if the price appreciation for homes
over that period averages 8% compounded annually.
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MATH 208 Final Exam Mock – EC SECTION – FALL 2022
Question 18
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You can afford monthly deposits of $140 into an account that pays 4.5% compounded
monthly. How long will it be until you have $10,100 to buy a boat?
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MATH 208 Final Exam Mock – EC SECTION – FALL 2022
Question 19
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Recently, INVESTORS INC offered an annuity that pays 4.8% compounded monthly. If
$,1470 is deposited into this annuity every month, how much is in the account after 11
years? How much of this is interest?
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MATH 208 Final Exam Mock – EC SECTION – FALL 2022
Question 20
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A couple wishes to borrow money using the equity in their home for collateral. A loan
company will loan them up to 70% of their equity. They purchased their home 9 years
ago for $60,276. The home was financed by paying 20% down and signing a 30-year
mortgage at 8.4% on the unpaid balance. Equal monthly payments were made to
amortize the loan over the 30-year period. The net market value of the house is now
$100,000. After making their 108th payment, they applied to the loan company for the
maximum loan. How much (to the nearest dollar) will they receive?
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MATH 208 Final Exam Mock – EC SECTION – FALL 2022
Question 21
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Some friends tell you that they paid $27,419 down on a new house and are to pay $708
per month for 30 years. If interest is 6.6% compounded monthly, what was the selling
price of the house? How much interest will they pay in 30 years?
Question 22
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Find the inverse of the matrix
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MATH 208 Final Exam Mock – EC SECTION – FALL 2022
Question 23
Solve using Gauss-Jordan elimination.
2x1 + 6x2 – 15x3 = 1
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4x1 + 24x2 – 58x3 = 34
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x1 + 5x2 – 12x3 = 6
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MATH 208 Final Exam Mock – EC SECTION – FALL 2022
Question 24
Determine whether the statement is true or false.
There exist two nonzero 2 x 2 matrices A and B such that AB is the 2 x 2 zero matrix.
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Choose the correct answer below.
0 0
0 0
]and B = [0 𝑏], AB = [
]
𝑎 𝑎
0 𝑏
0 0
B) The statement is false because the product of two 2 x 2 matrixes is a 1 x 1
matrix.
C) The statement is false because the product of two 2 x 2 matrixes is a 4 x 2
matrix.
𝑎 0
0 0
0 0
]and B = [
], AB = [
]
D) The statement is true, because if A = [
𝑎 0
𝑏 𝑏
0 0
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A) The statement is true, because if A = [
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MATH 208 Final Exam Mock – EC SECTION – FALL 2022
Question 25
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A company produces foam mattresses in two sizes: regular and king size. It takes 2
minutes to cut the foam from a regular mattress and 3 minutes for a king mattress. If the
cutting department has 10 labour-hours available each day, how many regular and king
mattresses can be cut in one day? Express your answer as a linear inequality with
appropriate non-negative restrictions and draw its graph.
Let x be the number of regular mattresses cut per day and let y be the number of king
mattresses cut per day. Choose the correct inequality with appropriate non-negative
restrictions below.
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3x + 2y ≥ 10, x ≥ 0, y ≥ 0
2x + 3y ≤ 10, x ≥ 0, y ≥ 0
3x + 2y ≥ 600, x ≥ 0, y ≥ 0
3x + 2y ≤ 600, x ≥ 0, y ≥ 0
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A)
B)
C)
D)
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MATH 208 Final Exam Mock – EC SECTION – FALL 2022
Question 26
Determine where the finite series below is arithmetic, geometric, or neither. Find its sum
(only if possible with the given data)
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33 + 32.2 + 31.4 +… + 1.8
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MATH 208 Final Exam Mock – EC SECTION – FALL 2022
Question 27
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1) 𝑥𝑒 −𝑥 + 2𝑒 −𝑥 = 0
26