Math & Measurements Flashcards
Get over your fear of math with this comprehensive review of math vocabulary, concepts, and conversions. Special thanks to Khan Academy and Wolfram Alpha for helping us learn some of the concepts in this deck! (34 cards)
In geometry, what is the mathematical term for the perimeter of a circle?
circumference
The circumference of a circle can be calculated using radius or diameter:
C = 2 * π * r or C = π * d
How many sides does a pentagon have?
five
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)
Which French philosopher and mathematician is famous for creating the Cartesian coordinate system, still used today in algebra and geometry?
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).
__________ data includes numerical measurements and __________ data includes descriptive words.
Quantitative (or empirical); qualitative
If a shirt was originally $4, and now it costs $5, by what percent did the price increase?
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 $5. What is the percent change?
- 5 - 4 = 1
- 1 / 4 = .25
- .25 * 100 = 25%
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?
diameter
What is the name for the amount of space within a three-dimensional figure?
volume
Common volume equations include:
- Sphere: (4/3) * π * r3
- Cylinder: V = π x r² x 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.
What type of statistical distribution is shown below?
normal distribution
(bell curve)
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.
What is the mathematical term for lines that form a 90-degree angle at their intersection?
perpendicular
What is the mathematical term for a number that, when squared, results in a negative number?
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.
What area measurement equals exactly 43,560 square feet?
acre
(hectare)
Some things that are often measured in acres are properties or forest land.
What mathematical term measures the space occupied by a two-dimensional surface?
area
Common area equations include:
- Circle: A = π r^2
- Triangle: A = 1/2 b * h
- Rectangle: A = s1 * s2
- Parallelogram: A = b * h
Because 6 can be divided neatly by 2 and 3 without remainder, it is said that 2 and 3 are _____ of 6.
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.
What is the mathematical term for the average value of a group of numbers?
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.
What is the mathematical term for the middle number in a set of numbers when they are ordered from least to greatest?
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.
The numbers 6, 9, 12, etc. are all _____ of 3.
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.
What is the mathematical term for lines that are the same distance apart at every point along their length and never touch?
parallel
Parallels are important in maths 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
In a perfect circle, what is the mathematical constant for the ratio between its circumference and diameter?
pi
(π)
What are the qualifications for a number to be considered prime?
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.
What is the mathematical term for the distance from the center of a circle to its circumference?
radius
Radius is often used when citing the distance of some phenomenon from a central location.
Ex: “There is earthquake damage for a 10-mile radius from the epicenter.” Or “The fugitive is expected to still be within a 5-mile radius from here”.
Which numerical system uses letters from the Latin alphabet to represent numbers, for example, MCXV, III, and XVII?
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).
Which Greek mathematician, known as the Father of Geometry, wrote Elements?
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.
What mathematical theorem is depicted below?
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.
Convert:
1 gallon to liters
1 gallon = 3.785 liters
For a quicker (although less accurate) calculation, multiply the number of gallons by 3.8 liters.
