Math Long Quiz 1

Define the binary operation * on the set of rational numbers as: ab= ab + a -b. Compute for the value of (23)*4.

A. 21

B. 9

C. 24

D. 13

21

The binary operation defined as a*b=3a - 2b is closed in all the given sets EXCEPT

A. set of real numbers

B. set of Natural numbers

C. set of integers

D. set of rational numbers

set of Natural numbers

Define the binary operation * on the set of rational numbers as: a*b = ab + a -b. What is the inverse element for 5 with respect to this operation?

A. -5/4

B. -5

C. 5

D. 5/4

-5/4

Which of the following is an example of a verb in the mathematical language?

A. 3

B. x (as a variable)

C. >

D. plus

E. parenthesis

>

Which of the following is an example of a noun in the mathematical language?

A. 3

B. x (as a variable)

C. >

D. plus

E. parenthesis

3

This refers to the unique characteristic of the mathematical language being brief and comprehensive in expressing information.

A. Concise

B. nontemporal

C. Precise

D. powerful

Concise

Which of the following is an example of a connective when stating a mathematical sentence? a) 3

b) Plus

c) X (as a variable)

d) >

e) Parenthesis

plus

In the mathematical statement 25 ÷ 12 ≥ 10 , which is the verb?

a) 10

b) ≥

c) 12

d) ÷

≥

Which of the following is a mathematical statement?

a) ( 2 x − 4 )+ 5 x = 3 x + 4

b) x² y − 4 x

c) √ x² + y ²

( 2 x − 4 )+ 5 x = 3 x + 4

The number sequence 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31 represents the number of days of the months of which calendar?

a) Gregorian Calendar

b) Hindu Calendar

c) Roman Calendar

d) Julian Calendar

Gregorian Calendar

This is known as the Golden Angle.

a) 137 °

b) 180 °

c) 45 °

d) 90 °

137

Consider a line segment of length L. it is always possible to divide the segment into two smaller segment of lengths L1 and L2 , where L1 > L2 such that LL1 = L1L2. Who is credited for this theorem?

a) Euclid

b) Des Cartes

c) Galileo

d) Newton

Euclid

Which of the following binary operation is not closed in the set of real numbers?

a) a* b = √ ab

b) a b = 3 √ ab

c) a b = ba

d) a * b = √ a 2 + b 2

a* b = √ ab

Let a,b be two real numbers are define a * b = ab + a + b. What is the identity element for this operation?

a) 0

b) 1

c) –a

d) Does not exist

0

A Fibonacci spiral is constructed by drawing semicircles in each square in a series of adjacent square in a series of adjacent squares, where a large square lies adjacent to a smaller one, and the sides of these squares are Fibonacci numbers.

a) True

b) False

False

Fibonacci spiral are claimed to appear in the arrangements and patterns of fruits, vegetables, pine cones, seed heads and shells. True or False

True

These are infinitely complex patterns that are self-similar across different scales

a) Honeycomb

b) Spirals

c) Water Waves

d) Fractals

Fractals

Which of the following pairs of statements are logically equivalent?

I. 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.

II. Statement 1: it is not true that either I watch ‘Crash landing on you’ or you watched ‘Money Heist’.

Statement 2: I did not watch ‘Crash landing on You’ and you watch ‘Money Heist’.

a) II only

b) I only

c) Neither I nor II

d) I and II

I only

Which of the following pairs of statements are logically equivalent?

I. 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.

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) I and II

b) I only

c) II only

d) Neither I nor II.

I only

Which of the following pairs of statements are logically equivalent? I. 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. 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) I and II

b) I only

c) II only

d) Neither I nor II.

I and II

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?

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

b) If you can visit another city in Metro Manila, then you have a quarantine pass.

c) If you cannot visit another city in Metro Manila, then you don’t have a quarantine pass.

d) If you do not have a quarantine pass, then you cannot visit another city in Metro Manila.

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

Under which conditions is the following compound statement “FALSE”? (~p^r)v(q^~r)

a) p is true, q is true, r is true

b) p is false, q is true, r is true

c) p is true, q is true, r is false

d) p is false, q is false, r is true

p is true, q is true, r is true

The following expression has the same meaning as the conditional statement “p--> q” EXCEPT

a) p only if q

b) q is a necessary condition for p

c) Every q is p

d) Not p or q

q is a necessary condition for p

Let Fn denotes the ntℎ Fibonacci number, where F 1 = F 2 = 1. Find F 19.

4181

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?

a) Precise

b) concise

c) powerful

d) nontemporal

nontemporal

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.

a) II and III

b) I and II

c) I, II and III.

d) I and III

II and III

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 v~p

b) q^p

c) qvp

d) q^~p

q^~p

Using a truth table, identify which of the statements given below is equivalent to the compound statement:

p v (q ^ ~ p).

a) ~p v q

b) p ^ q

c) ~ p ^ q

d) p v q

p v q

Reciprocal of the Golden Ratio Φ is equal to which expression

a) Φ + 1

b) Φ-1

c) Φ+2

d) Φ-2

Φ-1

Let Fn denotes nth Fibonacci number, where f1 = f2 = 1.

If F22=17,711 and f24 = 46,368, then what is f23?

A - 38,057

B - 26,799

C - 28,657

D - 20,771

28,657

A golden rectangle has width measuring 2 cm. what is the best estimate of its length?

a) 3 cm

b) 2

c) 2

d) 3 cm

3 cm

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

a) (-∞,∞)

b) (0, ∞)

c) [0, ∞)

d) (-∞,0)

(0, ∞)

Which of the following best defines the Golden Ratio?

a) The ratio of the circumference of a circle of a to its diameter.

b) The ratio of parts of a line segment such that the larger length divided by the smaller length is also equal to the whole length divided by the larger length.

c) The ratio of the width of a rectangle to its length

d) The ratio of two successive numbers in the Fibonacci sequence to its length

The ratio of parts of a line segment such that the larger length divided by the smaller length is also equal to the whole length divided by the larger length.

Consider the following conditional statement: you can visit another city in Metro Manila only if you have a quarantine pass is the inverse of the statement?

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

b) If you can visit another city in Metro Manila, then you have a quarantine pass.

c) If you cannot visit another city in Metro Manila, then you don’t have a quarantine pass.

d) If you do not have a quarantine pass, then you cannot visit another city in Metro Manila.

If you cannot visit another city in Metro Manila, then you don’t have a quarantine pass.

Which of the following is an example of a pronoun in the mathematical language?

a) 3

b) Plus

c) X(as a variable)

d) >

e) Parenthesis

X as a variable

This refers to the unique characteristic of the mathematical language being able to express complex ideas into simpler forms

a) Precise

b) Concise

c) Powerful

d) Nontemporal

powerful

He is one of the early mathematicians whose life testimony proved that computational skills are not required to grow and contribute to the mathematical field. He used abstraction, rather than explicit computations to prove and establish essential mathematical theories that led to breakthrough discoveries in both applied mathematics and sciences. His major influence in modern mathematics is the axiomatic treatment of geometry

a) Ian Stewart

b) Leonardo Pisano

c) David Hilbert

d) Rene Descartes

David Hilbert

Who said the following “what we know is a drop, what we do not know is an ocean”?

a) Isaac Newton

b) Galileo

c) Ian Stewart

d) Albert Einstein

Isaac Newton

Logically, “Not both” and “both not” mean the same. a) True b) False

false

The statement “The number 1 is neither an odd nor an even” is a disjunction. True or False?

false

In the argument " ~P → (Q v ~R ^ S) " which symbol is the "major connective" (the one from which the validity is based)?

A. v

B. ^

C. →

D. ~

→ (connective)