Math Concepts

Question 1

What is the mathematical term for the distance from one side of a circle to the other measured in a straight line through the center?

Answer 1

1.

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Half of the diameter is the radius.

Question 2

What is the term for the perimeter of a circle?

Answer 2

circumference

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The circumference of a circle can be calculated using radius or diameter:

C = 2 * π * r
or
C = π * d

Question 3

What is the mathematical term for the measure of space occupied by a 2-D surface?

Answer 3

area

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Common area equations include:

• Circle: A = π r^2
• Triangle: A = 1/2 b * h
• Rectangle: A = s1 * s2
• Parallelogram: A = b * h

Question 4

What is the name for the amount of space within a three-dimensional figure?

Answer 4

volume

Common volume equations include:

Sphere: (4/3) * π * r3
Cylinder: V = (π * r * r) * h
Square Pyramid: V = (l * w * h) / 3
Rectangular Prism: V = l * w * h

Volume can also be thought of as the amount of water that would fit inside of something.

Question 5

How many sides does a pentagon have?

Answer 5

five

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Polygons are made using the Greek prefix for the number + the suffix “gon”. The other main polygons are:

• hexagon (6 sides)
• heptagon (7 sides)
• octagon (8 sides)
• nonagon (9 sides)
• decagon (10 sides)

See this article for more information about polygons.

Question 6

________ data includes numerical measurements and ________ data includes descriptive words.

Answer 6

quantitative (or empirical); qualitative

Question 7

If a shirt was originally $4, and now it costs $5, by what percent did the price increase?

Answer 7

25%

Percent change is calculated by dividing the difference between the two numbers by the original number, then multiplying by 100 to convert to percentage.

For example: A shirt was originally $4, but is now $6. What is the percent change?

1. 6 - 4 = 2
2. 2 / 4 = 0.5
3. 0.5 * 100 = 50%

Question 8

What mathematical theorem is depicted below?

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Answer 8

Pythagorean Theorem

Discovered by the Greek philosopher and mathematician Pythagoras (570 - 495 BC), this theory is commonly used to deduce the missing side of a right triangle when the length of the other two sides are known.

Question 9

What type of statistical distribution is shown below?

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Answer 9

normal distribution

(bell curve) (your image)

Saying that some phenomenon is “normally distributed” means that there is an “average” amount of variation within a population.

For example, the frequency of birth weights are quite normally distributed (around a mean and median of about 7 lbs for male babies).

Meanwhile, wealth is quite unevenly distributed, with the richest earning disproportionately more than the poor. This is said to be a skewed distribution.

Question 10

What is the mathematical term for lines that form at a 90-degree angle at their intersection?

Answer 10

perpendicular

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Question 11

What is the mathematical term for lines that are the same distance apart at every point along their length and never touch?

Answer 11

parallel

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Parallels are important in math because they allow the understanding of relationships between paths of objects and sides of various shapes.

Some examples of parallel lines are the following:
* Railway tracks
* Zebra crossings
* Electrical wires

Question 12

What is the mathematical term for a number that when squared, results in a negative number?

Answer 12

imaginary number

Imaginary numbers were once mocked and thought to be useless, but have since been applied to serious mathematics applications.

One such example is in electronics, where imaginary numbers are used to calculate current.

Question 13

Because 6 can be divided neatly by 2 and 3 without remainder, it is said that 2 and 3 are ________ of 6.

Answer 13

factors

For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.

We can also say that 6 is “divisible” by 3. Being able to quickly remember a number’s factors is a helpful skill for many everyday math activities, like dividing a bill.

Question 14

What is the mathematical term for the average of a group of numbers?

Answer 14

mean

For example, the mean of 1, 2, 3, 4, and 100 is 22.

With a mean, one huge outlier can skew the “average” and present a different picture than most of the population’s actual stats.

Meanwhile, for something like your grades, one 0 can similarly bring down your mean class grade significantly.

Question 15

What is the mathematical term for the middle number in a set of numbers when they are ordered from least to greatest?

Answer 15

median

For example, the median of 1, 2, 4, 7, and 9 is 4.

The median can be used to determine an approximate average. It represents the middle value in a dataset.

Question 16

What is the mathematical term for the number that occurs most often in a group of numbers?

Answer 16

mode

For example, the mode of 9, 4, 3, 9, 62, and 8 is 9.

Question 17

The numbers 6, 9, 12, and 15 are all ________ of 3.

Answer 17

multiples

For example, the multiples of 3 include 3, 6, 9, 12, etc.

Being able to mentally calculate the multiples of an integer is an important skill in common daily activities, like making forecasts or estimates.

Question 18

In a circle, what is the mathematical term for the ratio of its circumference to diameter?

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Answer 18

π

(pi)

The constant π appears in countless natural phenomena and common trigonometric equations.

Pi is usually rounded to 3.14, but is actually an infinite decimal that never repeats or ends.

The first 15 digits of pi are: 3.14159265358979

Question 19

What is the mathematical formula to calculate an average (or mean)?

Answer 19

sum of terms / number of terms

For example, the average of 10, 13, 7, 3, and 17 is 10.

The equation for that would be (10 + 13 + 7 + 3 +17) / 5 = 10

Question 20

What is the mathematical formula to calculate the chances of something occuring from a set of possible outcomes?

Answer 20

target outcomes / total number of outcomes

For example, the probability of drawing an ace on your first attempt out of a deck of cards would be 7.7%.

The equation for that would be (4 / 52) * 100 = 7.7%

The reason you multiply by 100 is so you turn the decimal into a percentage.

Question 21

What is the mathematical formula to calculate the distance between two points on a coordinate plane?

Answer 21

d = √(x₁ – x₂)² + (y₁ – y₂)²

Distance equals the square root of x₁ – x₂ squared, plus y₁ – y₂ squared

For example, the distance between the point (1, 8) and (4, 5) is √18.

The equation for that would be √(1₁ – 4₂)² + (8₁ – 5₂)² = √18

Question 22

What is the mathematical formula to calculate the slope of a line that connects two points on a plane?

Answer 22

y₂ – y₁ / x₂ – x₁

For example, the slope of a line connecting the points (3, 9) and (2, 7) is 2.

The equation for that would be ( 7 – 9 / 2 – 3 ) = 2

Question 23

What is the mathematical formula for a slope intercept?

Answer 23

y = mx + b

For example, the slope intercept of a line connecting the points (4, 8) and (2, 6) is y = 1x + 4.

The equation for that would be ( 6 – 8 / 2 – 4 = 1 (slope), 8 = 1(4) + b ) = y = 1x + 4

Question 24

What is the mathematical formula for finding the midpoint between two pionts on a plane?

Answer 24

(x₁ + x₂) / 2, (y₁ + y₂) / 2

For example, the midpoint between the points (6, 2) and (4, 8) is (5, 5).

The equation for that would be ( (6₁ + 4₂) / 2, (2₁ + 8₂) / 2 ) = (5, 5)

Question 25

What is the mathematical formula to calculate the area of a triangle?

Answer 25

1/2 * base * height

For example, the area of a triangle with a base of 7 and a height of 4 is 14.

The equation for that would be 1/2 * 7 * 4 = 14

Question 26

What is the mathematical formula to calculate the area of a rectangle?

Answer 26

length * width

For example, the area of a rectangle with a length of 8 and a width of 5 is 40.

The equation for that would be 8 * 5 = 40

Question 27

What is the mathematical formula to calculate the volume of a rectangular prism?

Answer 27

length * width * height

For example, the volume of a rectangular prism with a length of 4, a width of 8, and a height of 5 is 160.

The equation for that would be 4 * 8 * 5 = 40

Question 28

What are the qualifications for a number to be considered prime?

Answer 28

if it is divisible by only 1 and itself

For example, 11 is prime, since its only factors are 1 and 11.

The opposite of a prime number is called a composite number. 10 is not prime, and would therefore be categorized as composite, since its factors include 1, 2, 5, 10.

Exceptions:

• 0 is neither prime nor composite.
• 1 is neither prime nor composite.
• A common misconception is that 1 is prime, but it is not technically divisible by 1 AND itself.

Question 29

The numbers MCXV, III, XVII are made up of ________ numerals

Answer 29

Roman numerals

Roman numerals are still used today, for things like book outlines, architectural blueprints, and serial items like events (e.g. Super Bowl XLVIII = Super Bowl 48).

Roman numerals are written largest to smallest. If a smaller number is placed before a larger one, that value should be subtracted from the larger one. For example: IX is 9 (10-1).

Question 30

Which French philosopher and mathematician is famous for his creation of the Cartesian coordinate system, still used today in algebra and geometry?

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Answer 30

René Descartes

(1596-1650)

You may remember the Cartesian coordinate system as a plot of X, Y on a two-dimensional axis.

This changed the way mathematicians were able to describe functions (correlational relationships).

Question 31

Which Greek mathematician was known as the Father of Geometry and also wrote Elements?

Answer 31

Euclid

(Lived around 300 B.C.)

Euclid’s findings still influence the study of geometry to this day.

Euclidian Geometry is still the title of many high school and college classes.