FREE! Click here to Join FunTrivia. Thousands of games, quizzes, and lots more!

# High school math Trivia Quiz

### These are all questions that a high school student would have the knowledge to figure out. The questions are a little trickier than simply numbers and variables.

A multiple-choice quiz by bfguitarhero. Estimated time: 6 mins.

Author
Time
6 mins
Type
Multiple Choice
Quiz #
305,455
Updated
Dec 03 21
# Qns
10
Difficulty
Very Difficult
Avg Score
4 / 10
Plays
691
- -
Question 1 of 10
1. A triangle is formed by connecting the vertices of three points; (0,0), (3,2), and (4m,-1). The line y = mx is then drawn through the triangle, splitting it into two equal parts. What is the sum of all possible values of m? Hint

#### NEXT>

Question 2 of 10
2. How many positive integers are there that are meet all of the following conditions?
-Less than 1,000,000
-Perfect cube
-Multiple of 72
Hint

#### NEXT>

Question 3 of 10
3. Since our economy is so bad, we've decided to implement a new coin system, where each coin has a different value. There are five different coins of five different colors: red, blue, green, yellow, and white. The way the system works is that 1 red coin = n blue coins, 1 blue coin = n green coins, 1 green coin = n yellow coins, and 1 yellow coin = n white coins. In a transaction, someone with 12 blue coins and 168 white coins receives 1 red coin, 33 green coins, and 38 yellow coins. What is the sum of all possible values of n? (Note: n can NOT have a negative value OR a value of zero) Hint

#### NEXT>

Question 4 of 10
4. Two cogs, one bigger than the other, both start out pointing due north. One cog spins at a rate of 80 revolutions per minute, while the other spins at a rate of 67 1/2 revolutions per minute. After how many seconds will both cogs be pointing due north again for the first time? Hint

#### NEXT>

Question 5 of 10
5. Assume N(z) = 10...064, where z is the number of zeros between the 1 and the 6. The value of N(z) can then be put into the form 2^n * k, where k is any positive whole number not divisible by 2. What is the maximum value of n for any value of z? Hint

#### NEXT>

Question 6 of 10
6. Three circles are drawn tangent to each other so that each circle touches each other circle once. Each circle has a radius of 1. A fourth circle is then drawn around these three circles so that it is internally tangent to all three circles. The radius of this circle can be represented as (a + b * sqrt(c)) / d, where a, b, c, and d are all in their simplest forms. What is the value of a + b + c + d? Hint

#### NEXT>

Question 7 of 10
7. Any integer can be expressed as the difference of the squares of two different integers.

#### NEXT>

Question 8 of 10
8. What is the sum of all solutions to the following problem?

49^x + 7^(1-2x) = 8
Hint

#### NEXT>

Question 9 of 10
9. The first three terms of an arithmetic sequence are 3x - 5, 2x + 3, and 5x - 1, respectively. What is the 100th term of this sequence? Hint

#### NEXT>

Question 10 of 10
10. 30 people are in the same room with one another. Assuming no one was born on February 29th, what is the probability that at least two people in the room have the same birthday? Hint

 (Optional) Create a Free FunTrivia ID to save the points you are about to earn: Select a User ID: Choose a Password: Your Email:

Quiz Answer Key and Fun Facts
1. A triangle is formed by connecting the vertices of three points; (0,0), (3,2), and (4m,-1). The line y = mx is then drawn through the triangle, splitting it into two equal parts. What is the sum of all possible values of m?

Because the line y = mx goes through the point (0,0), it must also go through the midpoint of (3,2) and (4m,-1) in order to split the triangle in half. To find the midpoint, simply find the average of the x- and y-coordinates, which would be ((4m + 3)/2, 1/2). Substituting that point into the line equation, we get that 1/2 = m(4m + 3)/2. Simplified, we get that 4m^2 + 3m - 1 = 0, which factors to (m + 1)(4m -1) = 0.
Our two answers for m are -1 and 1/4, the sum of which is -3/4.
2. How many positive integers are there that are meet all of the following conditions? -Less than 1,000,000 -Perfect cube -Multiple of 72

Let n represent the highest number (not integer) that can meet these three conditions. In order to meet the first condition, n must equal 1,000,000. In order to meet the second condition, n^3 must equal 1,000,000. In order to meet the last condition, we must find the lowest perfect cube that is a multiple of 72. Since 72 breaks down to 2^3 times 3^2, we must multiply it by 3 to get a perfect cube of 216. So, the final equation is:

216n^3 = 1,000,000

This, when you find the cubic root of each side, simplifies to:

6n = 100
n = 16.666

Since n is equal to 16.6666, there are 16 numbers that meet all three conditions.
3. Since our economy is so bad, we've decided to implement a new coin system, where each coin has a different value. There are five different coins of five different colors: red, blue, green, yellow, and white. The way the system works is that 1 red coin = n blue coins, 1 blue coin = n green coins, 1 green coin = n yellow coins, and 1 yellow coin = n white coins. In a transaction, someone with 12 blue coins and 168 white coins receives 1 red coin, 33 green coins, and 38 yellow coins. What is the sum of all possible values of n? (Note: n can NOT have a negative value OR a value of zero)

The way that the system works is that the value of coins increases exponentially. So, if a white coin has a value of 1, then a yellow coin has a value of n, a green coin has a value of n^2, and so on and so forth.

So, the transaction tells us that n^4 + 33n^2 + 38n = 12n^3 + 168. Moving it all to one side, you get that n^4 - 12n^3 + 33n^2 + 38n - 168 = 0. When factored, you get that (n - 3)(n - 4)(n - 7)(n + 2) = 0, so the only possible positive values of n are 3, 4, and 7, the sum of which is 14.

I have no idea how this system would help a struggling economy, but oh well.
4. Two cogs, one bigger than the other, both start out pointing due north. One cog spins at a rate of 80 revolutions per minute, while the other spins at a rate of 67 1/2 revolutions per minute. After how many seconds will both cogs be pointing due north again for the first time?

The first cog revolves at a rate of 80 revolutions per 60 seconds, or 4 revolutions every 3 seconds. The second cog revolves at a rate of 67 1/2 revolutions per 60 seconds, or 9 revolutions per 8 seconds. The lowest common multiple of the 3 seconds it takes the first cog to point in the same direction and the 8 seconds it takes the second cog is 24 seconds.
5. Assume N(z) = 10...064, where z is the number of zeros between the 1 and the 6. The value of N(z) can then be put into the form 2^n * k, where k is any positive whole number not divisible by 2. What is the maximum value of n for any value of z?

If l represents any whole number, then N(z) can be broken down to 10^l + 64, where l depends on the value of z. First, factor out the highest possible power of two from the equation. This leaves us with 2^6 * (10^l/64 + 1). To get the highest possible value of n, we must find what the greatest possible value of n is in 10^l/64 + 1. To get this to be an even number, 10^l/64 must be odd, and the only possible number it could be ends in 25. Once the 1 is added, the number ends in 26, leaving us with only one more factor of 2.

Therefore, the highest possible value of n is 6 + 1, or 7.
6. Three circles are drawn tangent to each other so that each circle touches each other circle once. Each circle has a radius of 1. A fourth circle is then drawn around these three circles so that it is internally tangent to all three circles. The radius of this circle can be represented as (a + b * sqrt(c)) / d, where a, b, c, and d are all in their simplest forms. What is the value of a + b + c + d?

First, draw three circles tangent to one another so that they resemble a triangle. It is more convenient if one is placed above the other two. Next, draw the fourth circle around the smaller circles. Connect all of the centers of the circles to one another, and you'll notice that an equilateral triangle is formed, with each side having a length of 2. This is the main diagram used to find the radius.

Draw a dot to represent the center of the larger circle and draw a radius to the circumference of the larger circle through one of the centers of the smaller circles, preferably the one above it. You'll notice that the radius is equal to the radius of the smaller circle plus the distance from the center of the larger circle to the center of the smaller circle. This distance can be calculated by finding the location of the point in relation to the endpoints of the equilateral triangle.

The easiest way to do this is to find where the center is the same distance from all 3 endpoints. In order to find this, treat the points as if they were on the coordinate plane (This where drawing the circle above the center comes in handy). To find the height of the triangle, simply draw in an altitude and use Pythagorean Theorem. You end up with points (0,0), (2,0), and (1,sqrt(3)). Next, find the midpoints of all three lines. You end up with (1,0), (1/2,sqrt(3)/2), and (3/2,sqrt(3)/2). Next, connect each endpoint to the opposite midpoint, and find the equations of those lines. You get x = 1, y = sqrt(3)x/3, and y = (2 - x)sqrt(3)/3. If you find the point where all three lines intersect, you get the point (1,sqrt(3)). If you check, you will notice that the distance from this point to each of the triangle's endpoints is sqrt(4/3). Since the point lies on the triangle's altitude, simply subtract the y-coordinate of the point by the altitude of the triangle, and you get 2sqrt(3)/3.

Add this to the radius of the smaller circle and you get 1 + 2sqrt(3)/3, or (3 + 2sqrt(3))/3. 3 + 2 + 3 + 3 is 11. If you find the decimal value of this solution, you'll notice that it is slightly higher than 2.
7. Any integer can be expressed as the difference of the squares of two different integers.

The difference of two squares can be represented by a^2 - b^2, which factors out to (a - b)(a + b). If both a and b are even or both a and b are odd, then both (a - b) and (a + b) must be even, meaning a^2 - b^2 must be a multiple of 4. If a and b are not both even or both odd, then (a - b) and (a + b) both must be odd, meaning that a^2 - b^2 must be odd.

Therefore, a^2 - b^2 cannot be an even integer that is not a multiple of 4, proving the statement to be false.
8. What is the sum of all solutions to the following problem? 49^x + 7^(1-2x) = 8

To solve the equation, you first need to simplify 7^(1 - 2n). First, find the inverse of the term, so you get 1/7^(2n - 1). Then, multiply the top and bottom by 7^1 (or 7), and you get 7/7^(2n). Then, square the 7 in the denominator to get 7/49^n. The equation now looks like the following:

49^n + 7/49^n = 8

Multiply each side by 49^n, and move the term on the right over, and you get:

(49^n)^2 - 8(49^n) + 7 = 0

Factor this and you get:

(49^n - 7)(49^n - 1) = 0

This means that 49^n equals either 1 or 7, meaning n equals either 0 or 1/2, the sum of which is 1/2.
9. The first three terms of an arithmetic sequence are 3x - 5, 2x + 3, and 5x - 1, respectively. What is the 100th term of this sequence?

If the numbers are in an arithmetic sequence, then the difference between the first and second term must be the same as the difference between the second and third term. Therefore:

(2x + 3) - (3x - 5) = (5x - 1) - (2x + 3)
-x + 8 = 3x - 4
12 = 4x
x = 3

By substituting, we know that the first three terms are 4, 9, and 14, which represent the sequence a(n) = 5n - 1. Therefore, the 100th term is 5(100) - 1, or 499.
10. 30 people are in the same room with one another. Assuming no one was born on February 29th, what is the probability that at least two people in the room have the same birthday?