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Math is for Squares Trivia Quiz

OK, so someone in the Author's Challenge wanted a quiz about squares. Here's a quiz about squares. Warning: your calculator might not help you very much!

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

Author
Tchochkekop

Time
5 mins

Type
Multiple Choice

Quiz #
318,480

Updated
Dec 03 21

# Qns
10

Difficulty
Difficult

Avg Score
5 / 10

Plays
780

One at a Time - Single Page - Timed Game

Question 1 of 10

1. Which of the following represents the square of ANY number n? Hint

n*2

n*n

2^n

All of these

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Question 2 of 10

2. What is i^2 (i squared)? Hint

-1

Undetermined

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Question 3 of 10

3. Solve n^2 = n. Note: There are two answers.

Answer: (Enter two numbers, separated by a space)

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Question 4 of 10

4. Which of the following can be made into a square with changes to its angles only? Hint

Parallelogram

All of these

Rectangle

Rhombus

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Question 5 of 10

5. Everybody knows that each angle of a square is 90 degrees, right? Well, I just drew a square whose angles are each 120 degrees. Where did I draw it?
Hint

In a bar, after having too much to drink

On a sphere

In Euclidian space

Around a plane circle

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Question 6 of 10

6. A number raised to the second power is a square, and a number raised to the third power is a cube. What term can be used for a square of squares, or a number raised to the fourth power?
Hint

Quadratic

There is no such term

Prismatic

Quartic

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Question 7 of 10

7. If a solid object undergoes a proportional increase in size, which measure increases by the square of the multiplier?
Hint

All of these

Perimeter

Surface area

Volume

8. Using only a compass and a straightedge, you try, in a finite number of steps, to make a square with the same area as a given circle. Don't try too long, because it can't be done! That this is a futile exercise was proven in 1882 with the Lindemann-Weierstrass theorem. What's the name of this famous problem?
Hint

Squaring the circle

Compassing the straightedge

Circling the square

Straighttedging the compass

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Question 9 of 10

9. In rectangular coordinates, what is the fourth vertex of a square whose other vertices are (1,1) (3,-1) (1,-3)?
Hint

(-3,1)

(-1,-1)

(-3,-3)

(-1,-3)

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Question 10 of 10

10. Finally, you have 1475.366 feet of fencing and want to use it to enclose a quadrilateral fish farm for vermillion Clupea pallasii. The fish farm is to have the maximum possible area. What shape will the farm be?
Hint

Circular

Trapezoidal

Rectangular, with sides of ratio 1:38.41 (square root of 1475.366)

Square

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Quiz Answer Key and Fun Facts

1. Which of the following represents the square of ANY number n?

Answer: n*n

A square is a number multiplied by itself. n*2 would be correct only for "two squared". 2^n usually means "two to the nth power."

2. What is i^2 (i squared)?

Answer: -1

i is the base of the imaginary numbers, or the square root of -1. Therefore, i^2 = -1.

3. Solve n^2 = n. Note: There are two answers.

Answer: 0 1

The only numbers that are the squares of themselves are 0 and 1 (0*0=0, 1*1=1). Infinity is not correct because infinity squared is a higher infinity (greater aleph), a concept that is way beyond the scope of this quiz!

4. Which of the following can be made into a square with changes to its angles only?

Answer: Rhombus

A rhombus is a quadrilateral with equal sides, so changing the angles to 90 degrees makes it a square. For rectangles and parallelograms, you might also have to change the lengths of the sides.

5. Everybody knows that each angle of a square is 90 degrees, right? Well, I just drew a square whose angles are each 120 degrees. Where did I draw it?

Answer: On a sphere

A square's angles are, indeed, 90 degrees in Euclidian geometry. In non-Euclidian systems, however, other sizes are possible. In spherical geometry, a square can have angles of 120 degrees. In a hyperbolic plane, the angles are 72 degrees each.

6. A number raised to the second power is a square, and a number raised to the third power is a cube. What term can be used for a square of squares, or a number raised to the fourth power?

Answer: Quartic

"Quadratic" actually relates to equations or terms of the second degree, and "prismatic" I just made up. While "quartic" is sometimes used for numbers of the fourth degree, it is not very common.

7. If a solid object undergoes a proportional increase in size, which measure increases by the square of the multiplier?

Answer: Surface area

When you expand a solid object, its surface area increases by the square of the multiplier, and its volume increases by the cube of the multiplier. This is known as the "square-cube law".

Answer: Squaring the circle

Squaring the circle can't be done because pi is a transcendental irrational number rather than an algebraic irrational number, which is what the Lindemann-Weierstrass theorem proved. Aren't you glad I saved you hundreds of years of wasted work?

9. In rectangular coordinates, what is the fourth vertex of a square whose other vertices are (1,1) (3,-1) (1,-3)?

Answer: (-1,-1)

An easy way to solve this is to draw it. This square is not "flat"; it looks like a diamond. The slope of each side is 1 (or -1).

Answer: Square

The length is a red herring (or a vermillion Clupea pallasii). The maximum area you can enclose with a given perimeter is a circle, but that's not a quadrilateral. For a quadrilateral, a square gives the maximum area. Too tricky? Remember what the theme of this quiz is!

Source: Author Tchochkekop

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