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Math
Math Foundations
SAT Math Terms & Formulas
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Terms in this set (74)
quadratic formula
[-b ± √(b² - 4ac)] / (2a)
slope formula
(y₂- y₁) / (x₂- x₁)
integers
..., -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)
order of opperations
PEMDAS (Parentheses / Exponents / Multiply / Divide / Add / Subtract)
Arithmetic Sequences
t₁, t₁+ d, t₁+2d, ...
Geometric Sequences
t₁, t₁· r, t₁· r², ...
Factors
ex. factors of 52 are 2, 4, 13, and 26
Multiples
ex. multiples of 20 are 40, 60, 80, 100, ...
percentages
part = (percent / 100) x whole
average
average = sum of terms / number of terms
average speed
average speed = total distance / total time
sum
sum = average x (number of terms)
mode
mode = value in the list that appears most often
median
median = middle value in the list
fundamental counting principle
if an event can happen in N ways, and another, independent event can happen in M ways, then both events together can happen in N x M ways.
probability
probability = number of desired outcomes / number of total outcomes
adding exponents
x^a · x^b = x^(a+b)
subtracting exponents
x^a / x^b = x^(a-b)
negative exponents
1 / x^b = x^(-b)
multiplying exponents
(x^a)^b = x^(a·b)
x^0
1
roots
√(xy) = √x · √y
FOIL
(x+a)(x+b) = x^2 + (b+a)x + ab
difference of squares
a^2 -b^2 = (a+b)(a-b)
a^2 + 2ab + b^2
(a+b)^2
a^2 - 2ab + b^2
(a-b)(a-b)
distance formula
√[(x₂- x₁)^2 + (y₂- y₁)^2)]
mid-point formula
[(x₁+ x₂)/2 , (y₁+ y₂)/2]
intersecting lines
opposite angles are equal (each pair of angles along the same line add to 180 degrees)
area of triangle
area = (1/2)bh
angles of triangle
add up to 180 degrees
length of triangle sides
length of 1 side is always less than the sum of the other 2
equilateral
three equal sides, all angles = 60 degrees
isosceles
2 equal sides, 2 equal angles
similar
same shape, corresponding angles are equal, corresponding sides are in proportion
circle area
pi · r^2
circle circumference
2 · pi · r
full circle
= 360 degrees
length of arc
(n degree / 360 degrees) · 2 · pi · r
area of sector
(n degree / 360 degrees) · pi · r^2
rectangle area
area = lw
parallelogram area
area = lh
rectangular solid volume
volume = lwh
right cylinder volume
volume = pi · r^2 · h
prime factors
2, 3, 5, 7, 11, ...
Greatest Common Factor
ex. GCF of 200 and 60 is 20
Least Common Multiple
ex. LCM of 200 and 60 is 600
equation of circle
with midpoint (h,k) ... (x - h)^2 + (y - k)^2 = r^2
logarithms
y = log(little b)x asks b^y = x
complex numbers
i^0 = 1; i^1 = i; i^2 = -1; i^3 = -i; i^4 = 1; i^5 = i; i^6 = -1; i^7 = -i
sin of an angle
opp / hyp
cos of an angle
adj / hyp
tan of an angle
opp / adj
special sin cos relationship
sin^2(angle) + cos^2(angle) = 1
degree to radian
degree# · (pi / 180 degrees)
radian to degree
radian# · (180 degrees / pi)
trapezoid area
area = [(base1 + base2) / 2] · h
Direct Variation
y=kx
Inverse Variation
y=k/x
Slope intercept form
y=mx+b
Point-Slope form
y - y₁= m(x - x₁)
standard form
Ax + By=C, where A, B, and C are not decimals or fractions, where A and B are not both zero, and where A is not a negative
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 or to the right
Graphing ≤ or < on a coordinate plane
shade downwards or to the left
circle perimeter
2 pi r
Chord
The distance from one point on the circle to another point on the circle.
Sector
The part of a circle that looks like a piece of pie. A sector is bounded by 2 radii and an arc of the circle.
arc
Part of a circle connecting two points on the circle.
Central Angle
An angle whose vertex is the center of the circle
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Verified questions
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Greg took a trip for 21 days. He took an average of 36 black-and-white photos and 60 color photos every day. How many more color photos than black-and-white photos did Greg take on this trip? A 504 B 756 C 1,116 D 2,016
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Kevin has 5 fish in his fish tank. Jasmine has 4 times as many fish as Kevin. How many fish does Jasmine have?
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Joanna has 70 beads. She uses 8 beads for each bracelet. She makes as many bracelets as possible. How many beads will Joanna have left over?
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Suppose that the domain of g includes all real numbers, that g is an odd function, and that g(1) = 2. Evaluate g(-1). Justify your answer.
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