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Quiz about Math Quiz
Quiz about Math Quiz

Math Quiz


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A multiple-choice quiz by quotidiantrivia. Estimated time: 7 mins.
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Time
7 mins
Type
Multiple Choice
Quiz #
82,256
Updated
Dec 03 21
# Qns
10
Difficulty
Very Difficult
Avg Score
4 / 10
Plays
6591
- -
Question 1 of 10
1. Without using a calculator or a pencil and paper, which of these is a perfect square? Hint


Question 2 of 10
2. What is the sum of the infinite series 1 + 0.5 + 0.25 + 0.125 + 0.0625 + ... ?

Answer: (A number, not a word)
Question 3 of 10
3. Let f(x) = 3x/2. Let g(x) = 2x + 3. What is f(g(f(g(f(g(f(2)))))))? Write your answer as a fraction, not a decimal.

Answer: (Type in a common fraction in the form x/y.)
Question 4 of 10
4. An ant starts at the origin and moves one unit to the right, 1/2 unit up, 1/4 unit left, 1/8 unit down, 1/16 unit right, and so on. If it continues infinitely, on what point is it converging? Hint


Question 5 of 10
5. I am somewhere on earth. I go one mile south, one mile east, and one mile north and I am back where I started. Where must I be? Hint


Question 6 of 10
6. An easy one. Solve for x:

7x - 2 = 4x + 1

Write your answer as a number.

Answer: (A number)
Question 7 of 10
7. Another easy one:
Factor:
x^3 - y^3
Hint


Question 8 of 10
8. What is the slope of the line tangent to the parabola f(x) = x^2 + 1 at x = 2? Hint


Question 9 of 10
9. Find the sum:

1 + 2 + 3 + 4 + 5 + ... + 100

Answer: (A number)
Question 10 of 10
10. What is the maximum number of regions into which 100 straight lines can divide a plane?

Answer: (A number)

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Most Recent Scores
Mar 09 2024 : Guest 75: 5/10
Mar 03 2024 : Guest 85: 4/10

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quiz
Quiz Answer Key and Fun Facts
1. Without using a calculator or a pencil and paper, which of these is a perfect square?

Answer: 79242972893648656

This may seem impossible to do, but three of these choices can be eliminated based on the digits. 2893467827688677 and 9134751098236810 can both be eliminated because a square number must end in a 1, 4, 5, 6, 9, or 00. Finally, 5916378240699596 is eliminated because a square number's digital root must be 1, 4, 7, or 9.

A digital root is calculated by adding the digits of the number and then adding the digits of the resulting number and repeating the process until we are left with a 1-digit number (e.g. to find the digital root of 89...8+9=17, 1+7=8).

This leaves us only one choice.
2. What is the sum of the infinite series 1 + 0.5 + 0.25 + 0.125 + 0.0625 + ... ?

Answer: 2

The formula for finding an infinite sum is A/(1-R), where A is the first term and R is the common ratio, or the number by which you have to multiply the first term to get the second term. In this case, A = 1 and R = 0.5. A/(1-R) = 1/(1-0.5) = 1/0.5 = 2.
3. Let f(x) = 3x/2. Let g(x) = 2x + 3. What is f(g(f(g(f(g(f(2)))))))? Write your answer as a fraction, not a decimal.

Answer: 279/2

It just takes some work to do this one. Start like this: f(2) = 3(2)/2 = 3. g(3) = 2(3) + 3 = 9, and so on.
4. An ant starts at the origin and moves one unit to the right, 1/2 unit up, 1/4 unit left, 1/8 unit down, 1/16 unit right, and so on. If it continues infinitely, on what point is it converging?

Answer: (4/5, 2/5)

Take the coordinates separately. First, the x-coordinate. The x-coordinate of where the ant converges can be expressed as an infinite sum 1 - 1/4 + 1/16 - 1/64 + .... Using the formula given earlier, the sum is 1/(1-(-1/4)) = 4/5, so the x-coordinate is 4/5. Similarly solving for the y-coorindate of the point, we get 2/5.
5. I am somewhere on earth. I go one mile south, one mile east, and one mile north and I am back where I started. Where must I be?

Answer: Cannot be determined with the information given.

Yes, the North Pole is one possible place, but there are others. The "widest" part of the Earth is at the equator. However, if you go far enough north or south, the "circumference" of the earth will get smaller, eventually, near the poles, the circumference is only a mile. If you are one mile above such a place, then you can go one mile south and one mile east, circling the earth to end up right where you were, and then one mile north to end up back where you started.

This is sort of hard to explain without a diagram.
6. An easy one. Solve for x: 7x - 2 = 4x + 1 Write your answer as a number.

Answer: 1

Subtract 4x from both sides and you get 3x - 2 = 1. Then, add 2 to both sides to get 3x = 3. Finally, divide both sides by 3 and you get x = 1.
7. Another easy one: Factor: x^3 - y^3

Answer: (x - y)(x^2 + xy + y^2)

If you do not already know how to factor the difference of two cubes, then just multiply all of the choices and you will get the right answer.
8. What is the slope of the line tangent to the parabola f(x) = x^2 + 1 at x = 2?

Answer: 4

To find the slope of the line tangent to a curve at x = a, you use limits. The expression is the limit as h approaches 0 of the expression (f(a + h) - f(h))/h. Evaluating the limit, we get 4.
9. Find the sum: 1 + 2 + 3 + 4 + 5 + ... + 100

Answer: 5050

There is a formula for the sum of 1 + 2 + 3 + 4 + 5 + ... + n. It is n(n+1)/2. Substituting 100 for n, we get 5050. If you don't know this formula, you can find the sum quickly by grouping the numbers like this:
1 + 2 + 3 + 4 + ... + 100 = 1 + 100 + 2 + 99 + ... + 50 + 51. This is equal to 101 + 101 + 101 + 101 + ... 50 times. Multiplying, 50 x 101 = 5050.
10. What is the maximum number of regions into which 100 straight lines can divide a plane?

Answer: 5051

The formula for finding the number of regions that n lines can divide a plane into is (n(n+1)/2) + 1. Substituting 100 for n, we get 5051.
Source: Author quotidiantrivia

This quiz was reviewed by FunTrivia editor crisw before going online.
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