Math quiz answers
Mar. 15th, 2007 06:00 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
emmagrant01The quiz is here.
1. 1 is a prime number.
Answer: False. Prime numbers are defined to be those that have exactly two divisors: themselves and 1. So 1 only has one divisor and doesn't meet the criteria for a prime. But more importantly, the main reason that we're interested in prime numbers is that they are the building blocks of other numbers. Every integer can be written in a unique way as a product of prime numbers; so 24 = 23 ⋅ 3. (This is called the Fundamental Theorem of Arithmetic.) But if we let 1 be a prime, we would lose that uniqueness -- so we could write 24 = 12 ⋅ 23 ⋅ 3 = 145 ⋅ 23 ⋅ 3, and so on. (More on this topic here.)
2. A square is a:
Answer: all of them. A square is a quadrilateral (a closed four-sided figure), a rectangle, a rhombus (an equilateral parallelogram), a parallelogram (opposite sides are parallel), and a regular polygon (a closed figure with all sides and angles equal).
3. Circumference is a measure of:
Answer: perimeter; specifically the perimeter of a circle.
4. If x squared is 9, then x is:
Answer: 3 or -3. In the equation x2 = 9, what we are looking for are all the numbers that when substituted for x would make the equation true. 32 = 9 and (-3)2 = 9, so both answers are correct.
5. If the square root of x is 9, x is:
Answer: 81. This is the only integer whose square root is 9. -81 doesn't have a real square root, and its complex square root is 9i.
6. 1/3 is
Answer: a rational number. Any number that can be written as a ratio (fraction) of two integers is rational. And contrary to what many of my students seem to think, 1/3 ≠ 0.3. Those two numbers are close, but not equal.
7. The number 1 is equal to the number 0.9999999999...
Answer: true! Just like we can write 1/3 = 0.3333..., we can write 1 = 0.99999... There are several interesting ways to prove this fact, but I'll direct anyone interested to a good explanation here.
8. If you draw a large triangle on a globe connecting three cities, what can say say about the sum of the angles inside the triangle?
Answer: The sum is greater than 180 degrees. To demonstrate this to yourself, draw three dots on an orange and then draw straight lines on the surface of the orange between them. You can probably see it by looking, but you can measure the angles to check. More info is here.
9. 0.555555555... is:
Answer: a rational number, also equal to 5/9. Decimal numbers that either terminate or repeat infinitely are rational numbers. I won't go into the technical details of why, but if you want to know more, go here (and scroll halfway down until you see "Rational Numbers").
10. A trapezoid is mathematically defined as:
Answer: both! This is a weird case where one mathematical definition wasn't agreed upon, and so both are considered valid. They have different consequences, so you have to specify which one you're using. For example, under the first definition, a parallelogram is not a trapezoid, but under the second, it is a trapezoid.
11. Which of the following situations represents 3 divided by 1/2?
Answer: I have 3 pizzas, and I want to give 1/2 pizza to each of my friends. How many friends can I feed? People often mistranslate the problem as "divide three into two halves", but the question really is "how many halves are in 3?" There are 6 halves in 3, 2 in each whole.
12. If a number is divisible by 24, is it divisible by 8?
Answer: Yes. If the number is divisible by 24, then it is divisible by the factors of 24, so it is also divisible by 2, 3, 4, 6, 8, and 12.
So, how'd you do?
1. 1 is a prime number.
Answer: False. Prime numbers are defined to be those that have exactly two divisors: themselves and 1. So 1 only has one divisor and doesn't meet the criteria for a prime. But more importantly, the main reason that we're interested in prime numbers is that they are the building blocks of other numbers. Every integer can be written in a unique way as a product of prime numbers; so 24 = 23 ⋅ 3. (This is called the Fundamental Theorem of Arithmetic.) But if we let 1 be a prime, we would lose that uniqueness -- so we could write 24 = 12 ⋅ 23 ⋅ 3 = 145 ⋅ 23 ⋅ 3, and so on. (More on this topic here.)
2. A square is a:
Answer: all of them. A square is a quadrilateral (a closed four-sided figure), a rectangle, a rhombus (an equilateral parallelogram), a parallelogram (opposite sides are parallel), and a regular polygon (a closed figure with all sides and angles equal).
3. Circumference is a measure of:
Answer: perimeter; specifically the perimeter of a circle.
4. If x squared is 9, then x is:
Answer: 3 or -3. In the equation x2 = 9, what we are looking for are all the numbers that when substituted for x would make the equation true. 32 = 9 and (-3)2 = 9, so both answers are correct.
5. If the square root of x is 9, x is:
Answer: 81. This is the only integer whose square root is 9. -81 doesn't have a real square root, and its complex square root is 9i.
6. 1/3 is
Answer: a rational number. Any number that can be written as a ratio (fraction) of two integers is rational. And contrary to what many of my students seem to think, 1/3 ≠ 0.3. Those two numbers are close, but not equal.
7. The number 1 is equal to the number 0.9999999999...
Answer: true! Just like we can write 1/3 = 0.3333..., we can write 1 = 0.99999... There are several interesting ways to prove this fact, but I'll direct anyone interested to a good explanation here.
8. If you draw a large triangle on a globe connecting three cities, what can say say about the sum of the angles inside the triangle?
Answer: The sum is greater than 180 degrees. To demonstrate this to yourself, draw three dots on an orange and then draw straight lines on the surface of the orange between them. You can probably see it by looking, but you can measure the angles to check. More info is here.
9. 0.555555555... is:
Answer: a rational number, also equal to 5/9. Decimal numbers that either terminate or repeat infinitely are rational numbers. I won't go into the technical details of why, but if you want to know more, go here (and scroll halfway down until you see "Rational Numbers").
10. A trapezoid is mathematically defined as:
Answer: both! This is a weird case where one mathematical definition wasn't agreed upon, and so both are considered valid. They have different consequences, so you have to specify which one you're using. For example, under the first definition, a parallelogram is not a trapezoid, but under the second, it is a trapezoid.
11. Which of the following situations represents 3 divided by 1/2?
Answer: I have 3 pizzas, and I want to give 1/2 pizza to each of my friends. How many friends can I feed? People often mistranslate the problem as "divide three into two halves", but the question really is "how many halves are in 3?" There are 6 halves in 3, 2 in each whole.
12. If a number is divisible by 24, is it divisible by 8?
Answer: Yes. If the number is divisible by 24, then it is divisible by the factors of 24, so it is also divisible by 2, 3, 4, 6, 8, and 12.
So, how'd you do?
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Date: 2007-03-16 03:03 am (UTC)