Studied by 82 peopleFor difficult multiplying radical questions…
Simplify radical to get similar bases between the factors
Convert to rational exponential form
Use exponent rules to combine exponents
Area of a prism
bh
If two pairs of corresponding angles in a pair of triangles are congruent, then the triangles are…
similar.
Triangle similarity theorems
AA, SAS, SSS (angles are congruent, but sides are proportional)
In order to prove triangles are similar, you need __ sides or _ sides to be IN PROPORTION
2; 3 (2 sides needs a congruent angle)
quadratic formula
[-b ± √(b² - 4ac)] / (2a)
remainder theorem
when f(x) is divided by (x-c), the remainder is f(c)
For a poly p(x), the value of p(3) is -2. Which of the following must be true for p(x)?
The remainder when p(x) is divided by x-3 is -2
Factor theorem
A polynomial f(x) has a factor (x-k) if f(x)/x-k = 0
xⁿ × yⁿ =
(xy)ⁿ
2ⁿ × bⁿ = 10ⁿ, b =
5
integers
all the whole numbers together with their opposites (3, -2, -1, 0, 1, 2, 3)
rationals
fractions (anything expessable as a ratio of integers)
reals
integers, rationals, plus special #s (like √2 or pi)
percentages
part = (percent / 100) x whole
mode
value in the list that appears most often
median
middle value in the list
x^a · x^b =
x^(a+b)
x^a / x^b =
x^(a-b)
x^(-b) =
1 / x^b
(x^a)^b =
x^(a·b)
x^0
1
√(xy) =
√x · √y
Factor x²-9x+14
(x-7)(x-2)
distance formula
√[(x₂-x₁)² + (y₂-y₁)²)]
mid-point formula
[(x₁+ x₂)/2 , (y₁+ y₂)/2]
angles of triangle add up to...
180 degrees
similar triangle definition
same shape, corresponding angles are equal, corresponding sides are in proportion
arc length (degrees)
(n degree / 360 degrees) · 2πr OR (n degree / 360 degrees) · C
area of sector (degrees)
(n degree / 360 degrees) · πr²
arc length (radians)
rθ
area of sector (radians)
(½)r²θ
prime numbers
2, 3, 5, 7, 11, ... (not 1)
circle equation
(x - h)² + (y - k)² = r²
Slope intercept form
y=mx+b
Point-Slope form
y - y₁= m(x - x₁)
Linear standard form
Ax + By = C (A, B, and C are not decimals or fractions, A and B are not both zero, and A is not a negative)
Vertex form
y = a(x-h)²+k
Vertex
(h, k)
When dividing by a negative number in an inequality
You must flip the sign
Graphing < or > on a coordinate plane
dotted line
Graphing ≥ or ≤ on a coordinate plane
solid line
Graphing ≥ or > on a coordinate plane
shade upwards
Graphing ≤ or < on a coordinate plane
shade downwards
steps to convert a parabola to vertex form by completing the square
gcf 2. (b/2)²=c 3. Multiply c by gcf and add opposite to the constant outside the parentheses
exponential equation
y = ab^x
b in exponential equations
growth/decay factor
exponential growth equation
y = a(1+r)^x
exponential decay equation
y = a(1-r)^x
a in exponential equations
initial amount
r in exponential equations
growth/decay rate
In order for two lines in a system of equations to have no solution, they have to be...
parallel
In order for two lines in a system of equations to have infinite solutions, they have to be...
the same line
When data has a symmetrical distribution, the mean and median are...
about equal
Extreme values have less effect on the _____ than on the _____ of a data set
median; mean
Compound interest formula
A = P(1 + r/n)^nt
Principal square roots only yield the _____ answer
positive
cos(90°-x) =
sinx
If there must be at least one x for every 2000 y, then the equation is...
x ≥ y/2000
Find the maximum number of x
x ≤ ...
The slope of a vertical line is...
undefined
The slope of a horizontal line is...
0
√-1 =
i
√-16 x √-16 =
√16i x √16i = 4i x 4i = 16i² = -16
i³ =
-i
Factor m⁵-81m
m(m⁴-81) = m(m²+9)(m²-9) = m(m3)(m-3)(m²+9)
(x^1/6)/(x^1/3) =
(x^1/6)/(x^2/6) = x^-1/6
x^z/y =
^y√x^z (y is index of radical)
Percent change formula
|final-initial|/initial x 100
What is sum of solutions to the equation |x+11| = 24
x+11=24 x=13 x+11=-24 x=-35 13-35 = 22
The more people in your sample the lower the...
margin of error
There is an inverse relationship between number of people in sample and...
margin of error
If you say the median is between two numbers, the larger the range between these numbers, the larger your...
confidence level
Confidence level and range have a _______ relationship
direct
Zero of a function with even multiplicity
When the graph bounces off the x-axis
Zero of a function with odd multiplicity
When the graph crosses through the x-axis
Quadratic standard form
ax²+bx+c
In a quadratic, if a is 4 the graph will be..
skinny and happy
If a is -1/2 the graph will be...
fat and sad
Formula for x value of quadratic vertex
-b/2a
c is the...
y-intercept
In a triangle, the length of the two line segments created on the hypotenuse by the altitude can be multiplied together to get the length of the...
altitude squared
The cost of renting a bicycle is $10 for the first hour, plus $5 for each additional hour. If h represents the number of hours the bicycle is rented, which of the following functions gives the cost C(h), in dollars, of renting the bicycle for h hours?
C(h) = 5h + 5
When looking at scatterplots and graphs, keep in mind that the origin of the graph often is NOT at...
(0,0)
Population density
Number of people/land area
A community center offers a Spanish course. This year, all students in the course were offered additional audio lessons they could take at home. The students who took these additional audio lessons did better in the course than students who didn't take the additional audio lessons. Based on these results, which of the following is the most appropriate conclusion?
No conclusion about cause and effect can be made regarding students at the community center who took the additional audio lessons at home and their performance in the Spanish course. (because there are outside variables the could have influenced the students doing better)
Standard deviation
A measure of how dispersed the data is in relation to the mean
Low standard deviation indicates that the data is...
close to the mean
High standard deviation indicates that the data is...
spread out far away from the mean
Researchers expect the deer population to decline by 6% every year. If the current deer population is 12,000, what is the approximate expected population size 10 years from now?
y = 12000(1-0.06)^10 y = 6463
Solve (9^1/2 + 16^1/2)²
DONT DISTRIBUTE SQUARE (3+4)² = 7² = 49
How many solutions does y+3x=8 and 2y-6x=16 have?
One
Shortcut for finding the product of solutions to a quadratic
c/a
Shortcut for finding the sum of solutions to a quadratic
-b/a
Formula for sum of interior angles in polygon with n sides
180(n-2)
logarithm form of b^y = x
log(base b)x = y
How to calculate the range
max-min
The line in the center of a box plot is the...
median
In order for a parabola to only have one solution, the graph has to...
have a minimum vertex ON the x-axis (can only touch the x-axis once)
cf(x)
Vertical stretch or shrink
Note
Flashcard