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Basic Math by the Definition Trivia Quiz

This quiz involves well known concepts from basic mathematics, but the actual definitions and theorems are probably not well known to non-mathematicians. I give the definition or theorem, you tell me what's being described. Good Luck!

A multiple-choice quiz by rodney_indy. Estimated time: 4 mins.

Author
rodney_indy

Time
4 mins

Type
Multiple Choice

Quiz #
267,517

Updated
Jul 23 22

# Qns
10

Difficulty
Average

Avg Score
7 / 10

Plays
1787

Awards
Top 35% Quiz

One at a Time - Single Page - Timed Game

Question 1 of 10

1. If a and b are positive integers, then there exists a positive integer d which satisfies the following properties:

1. a is divisible by d and b is divisible by d
2. Suppose D is another positive integer having the property a is divisible by D and b is divisible by D. Then d is divisible by D.

What is d known as? Hint

The least common multiple of a and b

The greatest common divisor of a and b

The product of a and b

The quotient of a and b

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Question 2 of 10

2. If a and b are positive integers, then there exists a positive integer m which satisfies the following properties:

1. m is divisible by a and m is divisible by b
2. Suppose M is another positive integer having the property M is divisible by a and M is divisible by b. Then M is divisible by m.

What is m known as? Hint

The least common multiple of a and b

The product of a and b

The greatest common divisor of a and b

The quotient of a and b

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Question 3 of 10

3. Let Q be the set of all numbers of the form a/b where a and b are both integers and b cannot be 0. What is the set Q called? Hint

The set of real numbers

The set of natural numbers

The set of complex numbers

The set of rational numbers

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Question 4 of 10

4. Let a and b be positive integers. Then there exist integers q and r which satisfy

a = b*q + r

with r greater than or equal to 0 and less than b. What is r called? Hint

The quotient

The remainder

The dividend

The divisor

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Question 5 of 10

5. Suppose a and b are real numbers (b positive) which satisfy a^2 = b. What is a called? Hint

The exponent of b

The square of b

A square root of b

The base 2 logarithm of b

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Question 6 of 10

6. Let a be a real number. Then there exists a real number b which satisfies:

a + b = 0.

Furthermore, if c is another real number which satisfies a + c = 0, then c = b.

What is this number b called?
Hint

The additive inverse of a

The square of a

The reciprocal of a

The square root of a

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Question 7 of 10

7. This is a type of sequence of numbers in which the difference between successive terms is constant. Hint

Geometric progression

Harmonic series

Geometric series

Arithmetic progression

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Question 8 of 10

8. Which function f has the following definition for a real number x?

If x is greater than or equal to 0, then f(x) = x, otherwise f(x) = -x. Hint

f(x) = -x

f(x) = the absolute value of x

f(x) = x^2

f(x) = the square root of x

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Question 9 of 10

9. A positive integer can be written uniquely (up to order of the factors) as a product of powers of distinct primes. What is this theorem called? Hint

The Fundamental Theorem of Galois Theory

The Fundamental Theorem of Algebra

The Fundamental Theorem of Arithmetic

The Fundamental Theorem of Calculus

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Question 10 of 10

10. What is the figure that is defined to be the set of all points in the plane that are equidistant from a single point? Hint

A circle

A line

A square

A parabola

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Quiz Answer Key and Fun Facts

1. If a and b are positive integers, then there exists a positive integer d which satisfies the following properties: 1. a is divisible by d and b is divisible by d 2. Suppose D is another positive integer having the property a is divisible by D and b is divisible by D. Then d is divisible by D. What is d known as?

Answer: The greatest common divisor of a and b

Part 1 of the definition says that d is a common divisor of a and b. Part 2 says that of all the divisors of both a and b, d is the greatest. I'll give an example. Let a = 12 and b = 20. The divisors of a are 1, 2, 3, 4, 6, and 12. The divisors of b are 1, 2, 4, 5, 10, and 20. The divisors of both a and b are 1, 2, and 4. 4 is the greatest common divisor of a and b by the definition since:

1. 12 is divisible by 4 and 20 is divisible by 4
2. The other divisors of both 12 and 20 are 1 and 2. 4 is divisible by 1 and 4 is divisible by 2.

2. If a and b are positive integers, then there exists a positive integer m which satisfies the following properties: 1. m is divisible by a and m is divisible by b 2. Suppose M is another positive integer having the property M is divisible by a and M is divisible by b. Then M is divisible by m. What is m known as?

Answer: The least common multiple of a and b

Part 1 of the definition says that m is a common multiple of a and b. Part 2 says that among all the common multiples of a and b, m is the least. I'll give an example: Let a = 12 and b = 20.

Multiples of a: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, ...
Multiples of b: 20, 40, 60, 80, 100, 120, 140, 160, 180, 200, ...
Multiples of both a and b: 60, 120, 180, ...

60 is the least common multiple of a and b by the definition since:
1. 60 is divisible by 12 and 60 is divisible by 20
2. Every common multiple of a and b is divisible by 60.

3. Let Q be the set of all numbers of the form a/b where a and b are both integers and b cannot be 0. What is the set Q called?

Answer: The set of rational numbers

The rational numbers include numbers such as 3/5 and 1 7/8 = 15/8. Note that any integer is also a rational number - for example, 3 = 3/1. The number (the square root of 3) is not a rational number. Any rational number can be expressed as a decimal that either terminates or has a repeating part.

4. Let a and b be positive integers. Then there exist integers q and r which satisfy a = b*q + r with r greater than or equal to 0 and less than b. What is r called?

Answer: The remainder

The statement above is actually a theorem called the division algorithm. It is just a mathematical statement of division of positive integers. For example, 23 divided by 7 has a quotient of 3 and a remainder of 2:

23 = 7*3 + 2

7 is the divisor, 23 is the dividend. Note that the remainder must be non-negative and smaller than the divisor.

5. Suppose a and b are real numbers (b positive) which satisfy a^2 = b. What is a called?

Answer: A square root of b

This is the definition of a square root. Note that any positive real number will have two square roots. For example, the number 49 has square roots 7 and -7 since 7^2 = 49 and (-7)^2 = 49.

6. Let a be a real number. Then there exists a real number b which satisfies: a + b = 0. Furthermore, if c is another real number which satisfies a + c = 0, then c = b. What is this number b called?

Answer: The additive inverse of a

For example, 3 is the additive inverse of -3 since -3 + 3 = 0. If x is a real number, the additive inverse of x is denoted -x.

The first part of the definition asserts the existence of an additive inverse (this is usually an axiom for certain algebraic structures such as Abelian groups, rings, or vector spaces). The second part states that the additive inverse is unique. Here is a proof of uniqueness:

Suppose c is another real number which satisfies a + c = 0. Then

c = 0 + c
= (b + a) + c since b + a = 0
= b + (a + c) by associativity
= b + 0
= b.

7. This is a type of sequence of numbers in which the difference between successive terms is constant.

Answer: Arithmetic progression

An example of an arithmetic progression is 2, 9, 16, 23, 30, 37, ... The difference between any two successive terms in the sequence is 7.

8. Which function f has the following definition for a real number x? If x is greater than or equal to 0, then f(x) = x, otherwise f(x) = -x.

Answer: f(x) = the absolute value of x

This is the actual definition of absolute value! Note that if x negative, -x is positive. By the definition, |-2| = -(-2) = 2.

9. A positive integer can be written uniquely (up to order of the factors) as a product of powers of distinct primes. What is this theorem called?

Answer: The Fundamental Theorem of Arithmetic

For example, 120 = (2^3) * 3 * 5. The above theorem states that this is in fact the only way you can write 120 as a product of powers of primes (we consider 3 * (2^3) * 5 to be the same factorization of 120). This theorem is not obvious! For a proof, consult a book on Number Theory.

10. What is the figure that is defined to be the set of all points in the plane that are equidistant from a single point?

Answer: A circle

The point in the definition is called the center and the distance from the center to a point on the circle is called the radius. Note that I said "the set of all points in the plane." In three dimensions, the set of all points equidistant from a single point is a sphere.

I hope you enjoyed my quiz! Thanks for playing!

Source: Author rodney_indy

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