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Miscellaneous Mathematics Trivia Quiz

Mathematics is the foundation for science. Here are ten miscellaneous mathematics questions regarding calculus, algebra, statistics, trigonometry and vectors. Enjoy!

A multiple-choice quiz by Matthew_07. Estimated time: 5 mins.

Author
Matthew_07

Time
5 mins

Type
Multiple Choice

Quiz #
274,176

Updated
Jul 23 22

# Qns
10

Difficulty
Tough

Avg Score
6 / 10

Plays
2136

Last 3 plays: Guest 93 (3/10), Guest 107 (3/10), wycat (1/10).

One at a Time - Single Page - Timed Game

Question 1 of 10

1. We know that if we differentiate f(x) = e^x, we will get the function itself, namely e^x; and if we integrate the function f(x) = e^x, we will get e^x + c. The value of e, namely 2.71828... is an irrational number. It is also known as?
Hint

Fermat's number

Euler's number

Archimedes' number

Newton's number

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Question 2 of 10

2. In trigonometry, the sine of an angle theta is defined as the ratio of the length of the______ to the length of the ______.
Hint

opposite side; hypotenuse

adjacent side; hypotenuse

hypotenuse; opposite side

hypotenuse; adjacent side

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Question 3 of 10

3. M�bius strip is so-called after the German mathematician August Ferdinand M�bius. The amazing properties of the M�bius strip had also been discovered by another mathematician 2 months earlier in 1858. He was?
Hint

Edwin Thomson Jaynes

Edward Jan Habich

George Barker Jeffery

Johann Benedict Listing

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Question 4 of 10

4. In vectors, scalar products are also known as dot products. Let vector a = a1, a2, a3 and vector b = b1, b2, b3. The scalar product of a dot b is given by?
Hint

a1 + a2 + a3 + b1 + b2 + b3

a1 x a2 x a3 + b1 x b2 x b3

a1 x b1 + a2 x b2 + a3 x b3

a1 x a2 x a3 x b1 x b2 x b3

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Question 5 of 10

5. In mathematics, there are real numbers and imaginary numbers. An imaginary unit, i, is the square root of -1. Which of the following equations is the WRONG one?
Hint

i^3 = -i

i^2 = -1

i^4 = 1

i^5 = 1

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Question 6 of 10

6. In elementary linear algebra, the determinant of a 2x2 matrix is given by ad-bc. Meanwhile, the determinant of 3x3 or nxn matrix, where n is equal or greater then 4 can be found by using row or column cofactor expansion. What is the determinant for an 1x1 matrix that contains a single element of b?
Hint

surd b

1/b

b^2

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Question 7 of 10

7. In statistics and probability theory, the normal distribution (the bell-shaped curve) is also known as?
Hint

The Carl distribution

The Jouffret distribution

The Friedrich distribution

The Laplace-Gaussian distribution

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Question 8 of 10

8. In calculus, a very small difference between the real value of f(x) and c on the y-axis is represented by the symbol epsilon. On the other hand, the difference between the value x and c on the x-axis is represented by which symbol?
Hint

Kappa

Lambda

Delta

Theta

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Question 9 of 10

9. The Fourier series are used widely in many fields, such as optics, acoustics, signal and image processing, and spectroscopy. This series was first introduced by a French mathematician, Joseph Fourier in his work on heat conduction. This series is important in analyzing which of the following?
Hint

Linear functions

Periodic functions

Exponential functions

Quadratic functions

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Question 10 of 10

10. In mathematics, conjecture and theorem carry the same meaning.

Yes

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Oct 30 2024 : Guest 93: 3/10
Oct 10 2024 : Guest 107: 3/10
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Quiz Answer Key and Fun Facts

Answer: Euler's number

Euler's number is named after the famous mathematician, Leonhard Euler. The value e is the base of the natural logarithms, as in log (base e) x = In x.

2. In trigonometry, the sine of an angle theta is defined as the ratio of the length of the______ to the length of the ______.

Answer: opposite side; hypotenuse

The ratio of the length of the adjacent side to the length of the hypotenuse is the cosine of an angle. Meanwhile, the tangent of an angle is given by the ratio of the length of the opposite side to the length of the adjacent side.

Answer: Johann Benedict Listing

Johann was born in Frankfurt in 1808. His area of expertise in mathematics was topology. We can construct a M�bius strip ourselves by using a strip of paper. Give the strip of paper a half turn before attaching it end to end. Then, using a scissors, cut the paper into half along the strip of paper. Surprisingly, you will not get 2 rings, but what you get is a single larger ring.

A M�bius strip has only one surface and it is non-orientable, meaning that it has only one side. Other objects that are also non-orientable are Klein bottles and real projective planes.

4. In vectors, scalar products are also known as dot products. Let vector a = {a1, a2, a3} and vector b = {b1, b2, b3}. The scalar product of a dot b is given by?

Answer: a1 x b1 + a2 x b2 + a3 x b3

A scalar product is also known as a dot product. The result is a single number. They should not be confused with cross products, also known as vector products, where the results would be other new vectors.

5. In mathematics, there are real numbers and imaginary numbers. An imaginary unit, i, is the square root of -1. Which of the following equations is the WRONG one?

Answer: i^5 = 1

Actually, i^5 = i^4 x i = 1 x i = i. A very famous formula involving this imaginary unit would be Euler's formula, where it states that for any real number x, e^(ix) = cos x + i sin x.

Answer: b

Determinants are important in algebra as they are used in Cramer's rule to solve linear system of equations, as well as to find the eigenvalues for a matrix.

7. In statistics and probability theory, the normal distribution (the bell-shaped curve) is also known as?

Answer: The Laplace-Gaussian distribution

For a standard normal distribution, the value of the mean is 0 while the standard deviation's value is 1.

Answer: Delta

Delta is the fourth letter in the Greek alphabet while epsilon is the fifth letter. There are all together 24 letters in the Greek alphabet.

Answer: Periodic functions

Joseph Fourier, or his full name, Jean Baptiste Joseph Fourier was born in 1768 in France. He was also a great physicist. He made great contribution in the field of Fourier series. Example of periodic functions are trigonometric functions such as sine, cosine and tangent. For instance, the sine function repeats itself after a period of 2 pi. Therefore, f(x) = f(x + 2 pi).

10. In mathematics, conjecture and theorem carry the same meaning.

Answer: No

According to Wikipedia, a conjecture is a mathematical statement which appears likely to be true, but has not been formally proven to be true under the rules of mathematical logic. On the other hand, a theorem is a statement, often stated in natural language that can be proved on the basis of explicitly stated or previously agreed assumptions.

Source: Author Matthew_07

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