Modular Examination GED102 ( Final Exam) PDF

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Modular Examination GED102 The Perfect Sauce.

1. This is the branch of Mathematics that deals with the different designs in sociocultural groups. Graph Theory Fractal Theory ethnomathem atics Chaos Theory

2. Consider the following conditional statement: You can visit another city in Metro Manila only if you have a quarantine pass. What is the converse of the statement? If you have a quarantine pass, then you can visit another city in Metro Manila. If you can visit another city in Metro Manila, then you have a quarantine pass. If you cannot visit another city in Metro Manila, then you don’t have a quarantine pass. If you do not have a quarantine pass, then you cannot visit another city in Metro Manila.

3. Consider the following conditional statement: You can visit another city in Metro Manila only if you have a quarantine pass. What is the contrapositive of the statement? If you have a quarantine pass, then you can visit another city in Metro Manila. If you can visit another city in Metro Manila, then you have a quarantine pass. If you cannot visit another city in Metro Manila, then you don’t have a quarantine pass. If you do not have a quarantine pass, then you cannot visit another city in Metro Manila.

4. “All COVID-19 Patients have high fever”. This is an example of Biconditional Statement Conditional Statement Conjunction Disjunction

5. In the figure shown above. The perimeter of the outer regular pentagon (green) is 20 inches. If segment a makes a Golden Ratio with segment b and segment b makes a golden ratio with segment c. Find the Length of the segment MD. [Use the approximation of Φ at 3 decimal places] 7.64 inches

8.944 inches 6.472 Inches 2.472 Inches

6. In the language of mathematics, if we say “x is equal to 5” today, it will still be “x is equal to 5” even years after, we do not say “x was equal to 5”. The mathematical verb “=” will always be read “is equal to” regarding characteristics of the mathematical language? precise concise powerful nontemporal

7. This refers to the unique characteristics of the mathematical language being clear, exact and accurate in expressing information. precise concise powerful Nontemporal

8. Which of the following pairs of statements are logically equivalent? 1. Statement 1: it is not true that either I watch ‘crashlanding on you’ or you watched ‘Money Heist’. Statement 2: I did not watch ‘crashlanding on you’ and you watch ‘Money heist’. 2. Statement 1: Joe tells you that he is an engineer and he studied in Mapua. Statement 2: If Joe is lying then Joe is not an engineer or he did not study in Mapua. I and II II only

I only Neither I nor II

9. Which of the following pairs of statements are logically equivalent? 1. Statement 1: It is not true that both you have pneumonia and I got flu. Statement 2: Either you have no pneumonia or I have no flu. 2. Statement 1: it is not true that either I watch ‘crashlanding on you’ or you watched ‘Money Heist’. Statement 2: I did not watch ‘crashlanding on you’ and you watch ‘Money heist’. Neither I nor II I only II only I and II

10. In Fibonacci’s rabbit experiment, which assumptions were applied? I. A female rabbit always produces a pair of rabbits, one male and one female. II. A female rabbit is able to produce offspring one month after it was born. III. The gestation period for a female rabbit is one month. II and III I and II I, II and III. I and III

11. Which of the Following describe a function? I. y=x2+1 II. x=y2+1 Neither I nor II II only I only

I and II

12. II only Neither I nor II I and II I only

13. Under which conditions is the following compound statement “FALSE”?

P is true, q is true, r is true P is false, q is true, r is true p is true, q is true, r is false p is false, q is false, r is true. 14. Consider the following statements: P: You have high fever q: You have vovid-19 virus. Write the following statement in symbolic form: you have covid-19 virus but you don’t have high fever.

o o o o

q v~ p q ^p qvp q^~p

15. The following expression has the same meaning as the conditional statement “p  q” EXCEPT

o o o o

every q is p. p only if q not p or q q is a necessary condition for p

16. Using a truth table, identify which of the statements given below is equivalent to the compound statement: p v (q ^ ~ p). o ~p v q o p^q o ~p^q o pvq 17. Which of the following statements has a truth value of “Truth’? o 2 is an off number or 2 is an even number. o If 72=49 then 7 is an even number o The year 2020 is a leap year if and only if the number 1 is prime o (-1)33= 1 and (-1)27=-1. 18. Let m and n be two real number such that m > n. which of the following is equivalent to a Golden Ratio? o m+n/m o m+n/n o m-n/m o m-n/n 19. reciprocal of the Golden Ratio Φ is equal to which expression o o o o

Φ +2 Φ+1 Φ-1 Φ-2

20. Which of the following is an example of a noun in the mathematical language? o 3 o plus o x (as a variable)

o > o Parenthesis 21. Which of the following is a mathematical sentence?

22. Let Fn denotes nth Fibonacci number, where f1=f2=1. If F22=17,711 and f24 = 46 368, then what is f23? o 20,771 o 38, 057 o 26, 799 o 28,657 23. What is the contrapositive of the statement: If x ≠ y then x2 ≠ y2 . o If x2=y2 then x ≠ y. o If x2=y2 the x=y. o If x2=y2 then x = - y o If x2 ≠ y2 then x=y 24. Which of the following binary operation is not closed in the set of real numbers? o A*b= √ ab o A*b= 3 √ ab o A*b= ba o A*b= √a2 + b2 25. Let a, b be two real numbers and define a*b=ab+a+b. What is the identify element for this operation? o 0 o 1 o -a o Does not exist 26. Let a, b be two real numbers and define a*b=ab+a+b. What is the inverse element for 2? o -2/3 o -2 o 2/3 o Does not exist

27. Define the binary operation * on the set of the rational numbers as : a*b = ab+ a-b. what should be the value of x so that the equation 5*x =0 is true? o -5 o 5 o 5/4 o -5/4 Let a, b be two real numbers and define a*b=ab+a+b. What is the identity element for this operation? o 0 o 1

28. Let fn denotes the nth Fibonacci number, Where f1= f2= 1. Find f30. o o o o

832,040 132,050 75,025 67,025

29. A Fibonacci prime is a Fibonacci number that is also a prime number. Examples are F3=2, f4=3,f5=5, and f7=13. Which of the following is a Fibonacci prime? o o o o

233 461 997 113

30. Which of the following is an example of a verb in the mathematical language? o 3 o Plus o X (as a variable) o > answer o Parenthesis 31. Which of the following is a mathematical senctence? o 32=8 o √9 o x+2y o 3 less than twice a number

32. Define the binary operation * on the set of the rational numbers as : a*b = ab+ a-b. compute for the value of 2 * (3*4). o 24 o 13 o 21 o 9

33. The binary operation defined as a*b=3a – 2b is closed in all the given sets EXCEPT o Set of natural numbers o Set of integers o Set of real numbers o Set of rational numbers 34. A golden rectangle has width measuring 2.1 cm. what is the best estimate of its length? o 3.4 cm o 2.33cm o 2.8cm o 3.7 cm 35. Which of the following is a mathematical verb?

36. In the mathematical statement “25 ➗ o 10

12

≥ 10”, which is verb?

o ➗ o 12 o ≥ 37. Which of the following statement has a truth value of “true”? o

2 is an odd number or 2 is an even number.

38. What is the domain of the function f(x)=lxl ?...