Math Long Quiz 1 (pt 2)

Consider the following conditional statement: You can visit another city in Metro Manila only if you have a quarantine pass.

What is the inverse of the statement?

• A - If you do not have a quarantine pass, then you cannot visit another city in Metro Manila.

• B - If you have a quarantine pass, then you can visit another city in Metro Manila.

• C -If you cannot visit another city in Metro Manila, then you don't have a quarantine pass.

• D - 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.

Consider the following statements:

p: You have high fever.

q: You have COVID-19 virus.

Write the following statement in symbolic form: You have COVID-19 virus but you don't have high fever.

A. $q\lor\neg p$

B. $q\wedge p$

C. $q \wedge \neg p$

D. $q\lor p$

$$q \wedge \neg p$$

"AlI COVID-19 patients have high fever". This is an example of

A - Disjunction

B - Conditional statement

C - Conjunction

D - Biconditional statement

Conditional statement

Which of the following pairs of statements are logically equivalent?

1. Statement 1: It is not true that either I watched 'Crashlanding on You' or you watched 'Money

Heist.

Statement 2: I did not watch 'Crashlanding on You' and you watched 'Money Heist'.

II. 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.

• A - Il only.

• B - I and Il

• C - Neither I nor lI

• D - I only

Neither I nor lI

Consider the statements "Some engineers are fools" and "Some fools are rich"

Which of the following is a valid conclusion?

I. Some engineers are rich.

II. Some rich people are engineers.

Neither I nor II

Consider the statements "All ripe mangoes are colored yellow" and "No yellow fruit is cheap".

Which of the following is a valid conclusion?

I. All ripe mangoes are cheap.

Il. Yellow ripe mangoes are not cheap.

II only

Consider the statements "No math teacher can sing" and "Some math teachers can play musical instruments".

Which of the following statements can be concluded?

I. Non-math teachers who can play musical instruments can also sing.

II. Some people who can play musical instruments can also sing.

Neither I nor II

Let P(x) means "x is a freshman" and Q(x) means "x is a math major". Write the statement "Every math major is a freshman" in symbolic form.

$$\forall x (Q(x) \rightarrow P(x))$$

P(x) means "x is a freshman" and Q(x) means "x is a math major". Write the statement "Some freshmen are math majors" in symbolic form.

$$\exists x (P(x) \land Q(x))$$

In a small institute, parking spaces are reserved for the heads of the departments of Mathematics, Physics, Chemistry, Languages and Physical Education, with the spaces lined up in that order. The parking attendant can tell at a glance if the cars are parked correctly by looking at the color of the cars which are either yellow, green, purple, red, or blue. The department heads are Lilibeth, Dante, Aileen, Jonathan and Melchor.

- the car in the first space is red

- a blue car is parked between the red car and the green car

- the car in the last space is purple

- the secretary drives a yellow car

- Lilibeth's car is parked next to Jonathan's

- Melchor drives a green car

- Dante's car is parked between Aileen's and Merchor's cars

-Jonathan's car is parked in the last space

Who is the head of the Languages department?

Lilibeth

In a small institute, parking spaces are reserved for the heads of the departments of Mathematics, Physics, Chemistry, Languages and Physical Education, with the spaces lined up in that order. The parking attendant can tell at a glance if the cars are parked correctly by looking at the color of the cars which are either yellow, green, purple, red, or blue. The department heads are Lilibeth, Dante, Aileen, Jonathan and Melchor.

- the car in the first space is red

- a blue car is parked between the red car and the green car

- the car in the last space is purple

- the secretary drives a yellow car

- Lilibeth's car is parked next to Jonathan's

- Melchor drives a green car

- Dante's car is parked between Aileen's and Merchor's cars

-Jonathan's car is parked in the last space

Who is the head of the Math department?

Aileen

In Metro Manila, five cities were identified to be most flood-prone areas, namely Caloocan, Marikina, Navotas, Valenzuela and Manila. Having their locations in coastal areas, PAGASA has identified them as key floodgates, Gate 1, Gate 2, Gate 3, Gate 4, and Gate 5. This year, the recorded average volume of flood are 12 inches, 27 inches, 32 inches, 44 inches and 65 inches.

- The city at Gate 4 got the least floods; the city in Gate 2 has the most floods

- Navotas is in Gate 1

- Caloocan got more floods than Valenzuela

- Marikina got more flood than Manila, but lesser than Navotas

- Valenzuela recorded an average of 44 inches flood

- The city in Gate 1 got 32 inches of floods, the city in Gate 3 got 27 inches of flood.

Where is Valenzuela located?

Gate 5

In Metro Manila, five cities were identified to be most flood-prone areas, namely Caloocan, Marikina, Navotas, Valenzuela and Manila. Having their locations in coastal areas, PAGASA has identified them as key floodgates, Gate 1, Gate 2, Gate 3, Gate 4, and Gate 5. This year, the recorded average volume of flood are 12 inches, 27 inches, 32 inches, 44 inches and 65 inches.

- The city at Gate 4 got the least floods; the city in Gate 2 has the most floods

- Navotas is in Gate 1

- Caloocan got more floods than Valenzuela

- Marikina got more flood than Manila, but lesser than Navotas

-Valenzuela recorded an average of 44 inches flood

- The city in Gate 1 got 32 inches of floods, the city in Gate 3 got 27 inches of flood.

How much flood is recorded in Marikina?

27 inches

A number is a neat number if the sum of the cubes of its digits equals the number. Therefore, 153 is a neat number. What type of reasoning is used in this argument?

I. Inductive

Il. Deductive

II only

Find the domain of f(x)=x^2 for 0 ≤x≤5.

• A - [1,25)

• B - (1,25]

• C - (0,25)

• D - [0,25]

[0,25]

Let f(x)=x2 and g(x)=x-3. Find g(f(7)).

A - 38

B - 46

C - 18

D - 26

46

Let f(x)=3x2 + x - 5. Evaluate f(-2).

A 3

B 5

C 4

D 2

5

Which of the following is not a function?

• A - Equaion of a diagonal line.

• B - Equation of a parabola whose axis is parallel to the y-axis.

• C - Equation of circle

• D Equation of semi ellipse whose major axis lies along the x-axis.

Equation of circle

Let f(x)=x² and g(x)=x-3. Find g(f(x)).

A - x²-3

B - X-3

C - (x-3)²

D - 2x-3

x²-3

Let f(x)=x² and g(x)=x-3. Find f(g(x)).

A - X-3

B - (x-3)²

C - x²-3

D - (x²-3)²

(x-3)²

Harry found in a survey that 38 people liked product X, 36 liked product Y, and 39 liked product Z. If 24 people liked both products X and Y, 20 people liked products Z and X, 18 people liked product Y and Z, and 9 liked all the three products. Find how many people liked product Z only?

10

In a class containing 40 students, 10 students liked prune juice, 15 liked apple juice and 7 liked both prune and apple juice. Find how many students were taking neither prune juice nor apple juice.

22

Club of 40 executives, 33 like to smoke Marlboro and 20 like to smoke Philip Morris. How many like both?

13

Formal writing and communication, the common size of bond paper are the following:

Which paper type is nearest to the Golden Ratio in terms of width to length ratio?

Foolscap ---- 216mm by 343 mm

A4 --- 210mm by 297 mm

B4 ---- 250mm by 353 mm

А3 -- 297mm by 420 mm

• A B4

• B A4

• С АЗ

• D Foolscap

Foolscap

F, denotes the nth Fibonacci number, where F1= F2= 1. Find F19

4181

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 golden ratio at 3 decimal places)]

6.472 inches

Let Fn denotes the nth Fibonacci number, where F1 = F2=1. Find the sum F2 + F3 + F4 + F5.

11

B only

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 perimeter of the triangle EMA.

[Use the approximation of golden ratio at 3 decimal places)]

6.472 inches

B

The Golden Ratio may be exhibited in the following facial and body dimensions EXCEPT

• The width of the nose is a Golden Section of the length of the mouth.

• The width of the face forms a Golden Section of the length of the face.

• The ratio of the length of the middle finger to the length of the little finger is approximately equal to the Golden Ratio.

• The ratio of the weight of the lungs to the weight of the brain is approximately a Golden Ratio.

The ratio of the weight of the lungs to the weight of the brain is approximately a Golden Ratio.

Lan Stewart included the following as among the 17 equations that changed the world, EXCEPT

• A - Golden Ratio

• B - Calculus

• C - Normal Distribution

• D - Logarithms

Golden Ratio

Neither A nor B

I and II

Who is he?

He successfuly carried out the first wireless telegraphy (1895) and transmitted and received the first transatlantic radio signals (1901).

• A - Michael Faraday

• B - Heinrich Hertz

• C - Guglielmo Marconi

• D - James Clerk Maxwell

Guglielmo Marconi

A only

Define the binary operation in the set of rational numbers as: a*b=ab+a- b

Which of the following properties is satisfied?

I. Closure Property

II. Commutative Property

III. Associative Property

Closure Property

Logical statement is said to be ______

if all of its truth values are O's.

contradiction, tautology, negation, logical equivalence

contradiction

Let A be the statement "Alden is Asian" and B be the statement "Bernie is American". Which of the following is the simplest equivalent symbolism for the statement "Either Alden is Asian and Bernie is American, or neither Alden is Asian nor Bernie is American"?"

A <—> B

Let P(x) means "x is a freshman" and Q(x) means "x is a math major". Write the statement "Some freshmen are math majors" in symbolic form.

$$\exists x(P(x)\land Q(x))$$