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MMW - Final Exam
Mathematics in the Modern World (Polytechnic University of the Philippines)
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E.E.
Mathematics in the Modern World (GEED 10053)
BSA1
Final Exam in GEED 10053
1. Which of the following best describes the true nature of mathematics?
(a) Mathematics consists of doing arithmetic operations and calculations.
(b) Mathematics sheds light to the nature of reality.
(c) Mathematics is the study of patterns and relationships.
(d) Mathematics is the study of the universe.
2. By ignoring the colors, which of the following logos is a cyclic rosette pattern?
(a)
(c)
(b)
(d)
3. If a frieze pattern only admits symmetries generated by one translation, one horizontal
reflection, and one glide reflection, which of the following classifies the pattern using the John
B. Conway naming system?
(a) Jump
(b) Hop
(c) Siddle
(d) Step
4. Which of the following equals the 10th Fibonacci number F10?
(a) 21
(b) 34
(c) 55
(d) 89
5. Leonardo Da Vinci named this ratio as the “divine proportion”. This ratio can be approximated
by taking a large positive integer n and divide Fn by Fn+1. What is the name of this ratio?
(a) Holy Ratio
(b) Bronze Ratio
(c) Silver Ratio
(d) Golden Ratio
6. If p and q are given true propositions, which of the following is also true?
(a) p −→ (¬ q)
(b) (¬ p) ∨ (¬ q)
(c) p ∧ (¬ q)
(d) (¬ p) −→ (¬ q)
7. Consider the conditional statement “If a pentagon has less than five sides, then an icosahedron
has at least fifteen faces.” Which of the following gives the contrapositive of the conditional
statement?
(a) An icosahedron has at least fifteen faces only if a pentagon has less than five sides.
(b) If an icosahedron has less than fifteen faces, then a pentagon has at least five sides.
(c) If an icosahedron has at least fifteen faces, then a pentagon has less than five sides.
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(d) If a pentagon has at least five sides, then an icosahedron has less than fifteen faces.
8. Which of the following collections is well-defined?
(a) the collection of all stars in the universe
(b) the collection of all real numbers whose square is irrational
(c) the collection of all sets
(d) the collection of all mathematicians 12 feet tall
9. Which of the following sets is equivalent to the set A = {4; 5; 6; 7; 8}?
(a) {1; 2; 3; 4}
(b) {x | x is prime and 1 < x < 12}
(c) {x ∈ R | 4 ≤ x ≤ 8}
(d) {n ∈ N | n < 9}
10. In a class of 50 students, sixty percent use neither an iPhone nor an iPad. Twenty percent use
an iPhone, while thirty percent use an iPad. How many students in this class are using both an
iPhone and an iPad?
(a) 5
(b) 10
(c) 15
(d) 30
11. Which of the following is a type of reasoning where we make conjectures based on
observable examples?
(a) inductive reasoning
(c) hyperactive reasoning
(b) deductive reasoning
(d) selective reasoning
12. The conjecture “If n is a positive integer, then n 2 + n + 1 is prime” is false. Which of the
following values of n is a counterexample?
(a) n = 3
(b) n = 5
(c) n = 2
(d) n = 4
13. Which of the following illustrates deductive reasoning?
(a) I’m going to be rich someday because everyone in my family who graduates in
college got rich and I just graduated college.
(b) On Christmas day, movie theaters and Chinese restaurants are always open.
Therefore, this Christmas, we can go to a movie and get some Chinese take-out food.
(c) My teacher usually gives surprise quizzes on Friday. Today is Thursday, so I must
review my lessons because my teacher might give a surprise quiz tomorrow.
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(d) Note that 9 2 = 81, 992 = 9; 801, and 9992 = 998; 001. Therefore, 99992 = 99; 980;
001.
14. Using inductive reasoning, determine which of the following is the sum of
(a) 49/50
(b) 50/51
(c) 99/100
(d) 100
15. A piece of rope is 48 inches long and is cut so that one piece is twice the as long as the other.
Which of the following is the length of the longer piece?
(a) 8 in
(b) 16 in
(c) 24 in
(d) 32 in
16. Which of the following is the type of sampling where every possible subsets of size n from a
population of size N has the same chance of being selected?
(a) purposive sampling
(b) simple random sampling
(c) quota sampling
(d) non-probability sampling
17. The totality of elements that we are interested to study in a statistical investigation is called
the
(a) population
(b) sample
(c) parameter
(d) statistic
18. This level of measure classifies data into categories which can be ranked; however, the
precise differences of these categories may not be clear. Which one is it?
(a) ratio level
(b) interval level
(c) ordinal level
(d) nominal level
19. Which of the following measures of central tendencies is most appropriate if the data can be
measured up to the nominal level only?
(a) mean
(b) median
(c) mode
(d) none of the other choices
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20. This measure of variability can be calculated by taking the average deviation from the mean.
Which one is it?
(a) range
(b) variance
(c) standard deviation
(d) mean
21. Vermae borrowed PhP 5,500 to her friend and agrees to repay it in 90 days with 5% annual
rate. If the amount of the interest is computed using the banker’s rule, how much does Vermae
need to pay?
(a) PhP 5,567.81
(b) PhP 5,568.75
(c) PhP 5,567.80
(d) PhP 68.75
22. Andrew deposited half of PhP 130,000 in a certificate of deposit (CD) paying 4% interest,
compounded quarterly. How much will Andrew have in his account after 7 and a half years if he
will not withdraw nor deposit into this account?
(a) PhP 175,220.35
(b) PhP 87,610.17
(c) PhP 175,220.36
(d) PhP 87,610.18
23. Kenneth wants to have PhP 5,000,000 in his account when he retires in 25 years. The
retirement account earns 5% interest convertible monthly. How much does he need to deposit
each month to meet his retirement goal?
(a) PhP 29,229.51
(b) PhP 29,229.50
(c) PhP 8,396.17
(d) PhP 8,396.16
24. A loan of PhP 75,000 with level payments to be made at the end of every month for 24
months with monthly rate of 3%. How much is the regular installment payment?
(a) PhP 4,428.56
(b) PhP 4,428.55
(c) PhP 3,223.59
(d) PhP 3,223.60
25. A loan of PhP 75,000 with level payments to be made at the end of every month for 24
months with monthly rate of 6% along with deposits to a sinking fund that earns a monthly rate
of 3%. How much is the amount in the sinking fund after 3rd payment?
(a) PhP 132.67
(b) PhP 6,733.71
(c) PhP 6,535.68
(d) PhP 68,266.29
26. The members of Math Club are to choose a representative among four candidates. The
following table shows the result of the election.
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Using Borda Count method, determine who is the winner of the election. By using this method,
was the majority criterion violated?
(a) Candidate A is the winner, the majority criterion is violated.
(b) Candidate B is the winner, the majority criterion is violated.
(c) Candidate C is the winner, the majority criterion is not violated.
(d) Candidate D is the winner, the majority criterion is not violated.
27. Consider the following preference table for the city that will host the Pambansang Palaro
2021. Using the Plurality-with-Elimination Method, which city wins the election?
(a) Manila
(b) Marikina
(c) Pasig
(d) None of the other choices
28. The following statements are true except
(a) The plurality method of voting satisfies the majority criterion.
(b) The Borda count method of voting always violates the majority criterion.
(c) The plurality-with-elimination method of voting satisfies the majority criterion.
(d) The pairwise comparison method of voting satisfies the head-to-head criterion.
29. If the standard quota of a certain district is 4, then what is its lower quota?
(a) 3
(b) 4
(c) 5
(d) 6
30. A school needs to assign 35 leaders to represent the students from Luzon, Visayas and
Mindanao. The distribution of the population of students (in thousands) is as follows:
Determine how many leaders should be assigned to represent students in Luzon, Visayas and
Mindanao using the Hamilton’s method.
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(a) Luzon: 19, Visayas: 14, Mindanao: 2
(b) Luzon: 19, Visayas: 13, Mindanao: 3
(c) Luzon: 20, Visayas: 12, Mindanao: 3
(d) Luzon: 20, Visayas: 13, Mindanao: 2
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