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Math Trivia 4 Trivia Quiz

10 questions from 10 different areas of math! This time it's different - fill in the blank! Good luck!

A multiple-choice quiz by rodney_indy. Estimated time: 7 mins.

Author
rodney_indy

Time
7 mins

Type
Multiple Choice

Quiz #
290,468

Updated
Dec 03 21

# Qns
10

Difficulty
Tough

Avg Score
5 / 10

Plays
1797

One at a Time - Single Page - Timed Game

Question 1 of 10

1. Arithmetic:

What is the product of 8 and 5?

Answer: (a number)

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Question 2 of 10

2. Basic Algebra:

Let x = 7 and y = 2. What is the value of x + y^2 ?

Answer: (Use the correct order of operations)

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Question 3 of 10

3. Geometry:

In the plane, the sum of the measures of the three angles in a triangle is how many degrees?

Answer: (a number)

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Question 4 of 10

4. Trigonometry:

Which trigonometric function is the reciprocal of secant?

Answer: (One Word)

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Question 5 of 10

5. Analytic Geometry:

What is the radius of the circle whose equation is given by

(x-3)^2 + (y+1)^2 = 64 ?

Answer: (a number)

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Question 6 of 10

6. Calculus:

Is the function f(x) = x^3 + x increasing, decreasing, or neither for all real numbers x?

Answer: (One Word)

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Question 7 of 10

7. Sets:

How many subsets does the empty set have?

Answer: (a number)

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Question 8 of 10

8. Probability:

An experiment consists of flipping a fair coin 5 times and noting the result of each flip. How many of the 32 possible outcomes have exactly 3 heads?

Answer: (a number)

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Question 9 of 10

9. Number Theory:

What is the remainder when 17^(2008) is divided by 15?

Answer: (a number from 0 to 14)

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Question 10 of 10

10. Linear Algebra:

True or False: It is possible to have 4 linearly independent vectors in R^3.

True

False

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Quiz Answer Key and Fun Facts

1. Arithmetic: What is the product of 8 and 5?

Answer: 40

8 times 5 is 40. The word "product" always refers to multiplication.

2. Basic Algebra: Let x = 7 and y = 2. What is the value of x + y^2 ?

Answer: 11

You must square y before you add it to x. So 7 + 2^2 = 7 + 4 = 11.

3. Geometry: In the plane, the sum of the measures of the three angles in a triangle is how many degrees?

Answer: 180

Note that this is true for triangles in the plane (Euclidean geometry). If you have a triangle on a sphere, it's angles would sum to more than 180 degrees.

4. Trigonometry: Which trigonometric function is the reciprocal of secant?

Answer: cosine

By definition, sec(theta) = 1/cos(theta), hence the reciprocal of secant is cosine. The other reciprocal functions are cosecant (reciprocal of sine) and cotangent (reciprocal of tangent).

5. Analytic Geometry: What is the radius of the circle whose equation is given by (x-3)^2 + (y+1)^2 = 64 ?

Answer: 8

The general form for the equation of a circle with center (h,k) and radius r is given by

(x-h)^2 + (y-k)^2 = r^2.

The circle in the question is a circle of radius 8 (since the square root of 64 is 8) with center (3,-1).

6. Calculus: Is the function f(x) = x^3 + x increasing, decreasing, or neither for all real numbers x?

Answer: increasing

The derivative of f(x) is 3x^2 + 1, which is always positive. Therefore f(x) is strictly increasing for all x.

7. Sets: How many subsets does the empty set have?

Answer: 1

The empty set is a subset of every set, including itself.

8. Probability: An experiment consists of flipping a fair coin 5 times and noting the result of each flip. How many of the 32 possible outcomes have exactly 3 heads?

Answer: 10

The number of outcomes with exactly 3 heads is C(5,3) = 10 where C(5,3) is the number of combinations of 5 objects taken 3 at a time. To see why this is the case, think of each of the 32 outcomes as 5 letter words consisting of H's and T's. Let's count the number of 5 letter words of this sort with exactly 3 H's:
The number of ways to place the 3 H's in the word is C(5,3) (the number of 3 element subsets of a 5 element set), leaving only one way to place the 2 T's.

9. Number Theory: What is the remainder when 17^(2008) is divided by 15?

Answer: 1

First note that 17 is congruent to 2 (mod 15). This means that (17 - 2) is divisible by 15, or in other words, the remainder we obtain when we divide 17 by 15 is 2. So 17^4 is congruent to 2^4 = 16 which is congruent to 1 (mod 15). Now 2008 is divisible by 4 (2008 = 4 * 502), so if 17^4 is congruent to 1 (mod 15), then raising both sides to the 502nd power gives 17^(2008) is congruent to 1 (mod 15), thus 1 is the remainder.

10. Linear Algebra: True or False: It is possible to have 4 linearly independent vectors in R^3.

Answer: False

R^3 has dimension 3, so any basis of R^3 consists of 3 linearly independent vectors. A basis is a maximal independent set, so any 4 vectors in R^3 would necessarily have a linear dependence. I hope you enjoyed this quiz! Thanks for playing!

Source: Author rodney_indy

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