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NMAT Review: Quantitative Reasoning
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Terms in this set (14)
Solving fractions in fractions
Resolve the innermost fraction first, then work your way out.
imaginary numbers
i x i = -1
Sum of infinite sequence formula
S(infinity) = a/(1-r)
Where -1 < r < 1, and stands for the common ratio
a - first term
Inverse functions
Switch the x and y variables and solve for y.
Trig identities (sin, tan, cos, csc, sec, cot)
sin - y/r
cos - x/r
tan - y/x
csc - 1/sin
sec - 1/cos
cot - 1/tan
Volume formulas
Cube - l x w x h
Cylinder - (pi) x r^2 x h
Cone - (1/3) x pi x r^2 x h
Sphere - (4/3) x pi x r^3
Pyramid - (1/3) x b x h
r is radius
h is height
b is base
l is length
w is width
Surface area formulas
Cube - 6s^2
Cylinder - (2 x pi x r) + (r+h)
Cone - pi x r x (l+r)
Sphere - 4 x pi x r^2
s is sides
r is radius
h is height
l is length
Work equation
Work = rate x time
Density formula
Density (p) = mass (m)/volume (V)
Finding lengths of right triangles
30-60-90 triangle
-hypotenuse is twice the length of the side across the 60 degree angle
-the side adjacent to the hypotenuse across the 30 degree angle is the same size the other length multiplied by square root of 3.
Finding the angles of right triangles
Use trig identities
Probability formulas
Probability of an event A is symbolized by P(A). Probability of an event A is lies between 0 ≤ P(A) ≤ 1. 0 being never gonna happen and 1 being it is 100% going to happen.
P(A) = (number of favorable outcomes)/(total number of possible outcomes)
Addition rule:
-In mutually exclusive events, where the events can't happen at the same time/overlap
P(A or B) = P(A) + P(B)
ex. flipping a coin and getting heads or tails
-In NOT mutually exclusive events, where the events may overlap/affect each other
P(A or B) = P(A) + P(B) - P(A and B)
ex. pulling a card from a deck and getting a heart or a King; there's the possibility of getting the King of hearts
Multiplication rule:
-In independent events, where the events do not affect one another
P(A and B) = P(A) x P(B)
ex. rolling a die to get a 3 and then a 5
-In dependent events, where the events do affect the probability of the next event
P(A and B) = P(A) x P(B/A)
(B/A) being that A is assumed to have happened.
ex. Pulling a King from a deck and then pulling a Queen without returning the King card.
Combination formula
Where the order of the choices doesn't matter.
n - total number of choices
r - number of available spots
Permutation formula
Where the order of the choices do matter.
n - total number of choices
r - number of available spots
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