Foundations of College
Mathematics
◉ real numbers. Answer: Nearly any number you could think of
Ex: 2, -5, 0, 6.7, 9/200, 3.14..., etc
◉ rational number. Answer: Any number that can be expressed as a ratio
of two integers (fraction) or a repeating decimal
◉ irrational number. Answer: Numbers that cannot be expressed as a
ratio of two integers. Their decimal expansions are non-ending and non-
repeating.
◉ Compound Intrest Formula. Answer: A=P(1+r/n)^nt
◉ Similar Triangles. Answer: Similar triangles have the same shape:
corresponding angles are equal and corresponding sides are proportional
◉ congruent angles. Answer: angles with the same measure
◉ Triangle Area Formula. Answer: A=1/2bh
,◉ Area of similar triangles. Answer: In two similar triangles, the ratio of
their areas is the square of the ratio of their sides.
Example: What is the area of triangle DEF?
Side AB = 7.4
Side DE = 3.7
Area Triangle ABC = 9.2
7.4/3.7 = 2
2^2=4
So we can make the equation x/9.2 = 4
(What divided by 9.2 = 4? That is your area.)
◉ Is the follow true for all real numbers A and B? How would you solve
it?
A^3 - B^3 = ( A + B^2 ) x ( A^2 - B ). Answer: Pick simple low
numbers for both A and B, then solve to see if the statement is true.
Ex: A=1 and B=2
, ◉ Integer. Answer: Whole numbers and their opposites (. . . -3, -2, -1, 0,
1, 2, 3. . .)
◉ standard deviation. Answer: the square root of the variance and
provides a measure of the standard, or average, distance from the mean
◉ mean. Answer: the arithmetic average of a distribution, obtained by
adding the scores and then dividing by the number of scores
◉ Mode. Answer: The value that occurs most frequently in a given data
set.
◉ How is a factorial written?. Answer: Ex: 2!, 5!, 13!
◉ What is a factorial?. Answer: A factorial is the product of itself with
all positive integers less than it.
Ex: 4! = 4x3x2x1 = 24
◉ What combinatoric equation do you use when order doesn't matter?.
Answer: Binomial coefficient
◉ What combinatoric equation do you use when order does matter?.
Answer: n!/(n-k)!
Mathematics
◉ real numbers. Answer: Nearly any number you could think of
Ex: 2, -5, 0, 6.7, 9/200, 3.14..., etc
◉ rational number. Answer: Any number that can be expressed as a ratio
of two integers (fraction) or a repeating decimal
◉ irrational number. Answer: Numbers that cannot be expressed as a
ratio of two integers. Their decimal expansions are non-ending and non-
repeating.
◉ Compound Intrest Formula. Answer: A=P(1+r/n)^nt
◉ Similar Triangles. Answer: Similar triangles have the same shape:
corresponding angles are equal and corresponding sides are proportional
◉ congruent angles. Answer: angles with the same measure
◉ Triangle Area Formula. Answer: A=1/2bh
,◉ Area of similar triangles. Answer: In two similar triangles, the ratio of
their areas is the square of the ratio of their sides.
Example: What is the area of triangle DEF?
Side AB = 7.4
Side DE = 3.7
Area Triangle ABC = 9.2
7.4/3.7 = 2
2^2=4
So we can make the equation x/9.2 = 4
(What divided by 9.2 = 4? That is your area.)
◉ Is the follow true for all real numbers A and B? How would you solve
it?
A^3 - B^3 = ( A + B^2 ) x ( A^2 - B ). Answer: Pick simple low
numbers for both A and B, then solve to see if the statement is true.
Ex: A=1 and B=2
, ◉ Integer. Answer: Whole numbers and their opposites (. . . -3, -2, -1, 0,
1, 2, 3. . .)
◉ standard deviation. Answer: the square root of the variance and
provides a measure of the standard, or average, distance from the mean
◉ mean. Answer: the arithmetic average of a distribution, obtained by
adding the scores and then dividing by the number of scores
◉ Mode. Answer: The value that occurs most frequently in a given data
set.
◉ How is a factorial written?. Answer: Ex: 2!, 5!, 13!
◉ What is a factorial?. Answer: A factorial is the product of itself with
all positive integers less than it.
Ex: 4! = 4x3x2x1 = 24
◉ What combinatoric equation do you use when order doesn't matter?.
Answer: Binomial coefficient
◉ What combinatoric equation do you use when order does matter?.
Answer: n!/(n-k)!
