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98 Cards in this Set
- Front
- Back
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What is the value of tan(45 degrees)?
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Tan x = sin x / cos x
Tan (45) = sin (45) / cos (45) = [(square root 2)/2] / [(square root 2)/2] = 1 |
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Zero degrees equals what in radians? sin? and cos?
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0 degrees = 0 radians
sin (0) = 0 cos (0) = 1 |
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30 degrees equals what in radians? sin? and cos?
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30 degrees = pi/6 radians
sin (30) = 1/2 cos (30) = (square root 3)/2 |
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45 degrees equals what in radians? sin? and cos?
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45 degrees = pi/4 radians
sin (45) = (square root 2)/2 cos (45) = (square root 2)/2 |
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60 degrees equals what in radians? sin? cos?
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60 degrees = pi/3 radians
sin (60) = (square root 3)/2 cos (60) = 1/2 |
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90 degrees equals what in radians? sin? cos?
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90 degrees = pi/2 radians
sin (90) = 1 cos (90) = 0 |
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what does SOH-CAH-TOA mean?
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SOH: Sin = Opposite/Hypotenuse
CAH: Cos = adjacent/hypotenuse TOA: Tan = opposite/adjacent |
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1 gallon = how many quarts? pints? and ounces?
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1 gallon = 4 quarts = 8 pints
1 pint = 16 fluid ounces 1 gallon = 128 ounces |
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What is the Order of Operations?
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PEMDAS : "Please Excuse My Dear Aunt Sally"
Parentheses Exponents Multiplication Division Addition Subtraction |
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What does cotangent equal?
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cotangent = 1/tangent
or = cosine/sine |
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What does tangent equal?
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tangent = sine/cosine
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square root of 3 =
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1.7
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square root of 2 =
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1.4
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Calculate Radian Measure
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Radian = Degrees x [(2 pi)/360]
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Calcuate Degree Measure
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Degrees = Radians x [360/(2 pi)]
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cos (-X) =
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cos (x)
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sin (-X)
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- sin x
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Calculating Total Time
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Total Time = (T1 x T2) / (T1 +T2)
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36% of 18 is 18% of what number?
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36%(18) = 18%(x)
36/100(18) = (18/100)(x) x = (36/100)(18)(100/18) = 36 |
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cosecant
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1/sine
cosecant = hypotenuse/opposite |
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secant
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1/cosine
secant = hypotenuse/adjacent |
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cotangent
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1/tangent
cotangent = adjacent/opposite |
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Slope Intercept Equation
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y = mx + b
m = slope b = y-intercept parallel lines have same slope perpendicular lines have negative reciprocal slopes |
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Distance Formula
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Finds the distance between two points.
distance = square root of [(x1 - x2)^2 + (y1 - y2)^2] |
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Midpoint of a segment
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average the x-coordinates and y-coordinates
midpoint = [(x1 + x2)/2], [(y1 + y2)/2] |
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Volume of a Cylinder
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Given base radius r and height, the area of base is pi(r^2)
Volume of a cylinder = pi(r^2)h |
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Volume of a Cube
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l, w, and h are all equall.
If e = length of each cube Volume of a Cube = e^3 |
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Volume of Rectangular Solid
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Volume of Rectangular Solid = lwh
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Volume of Any Solid
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Volume = (base)(height)
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Calculating diagonal distance from one vertices to another on a solid.
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distance = square root of (l^2 + w^2 + h^2)
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Surface area of a rectangular solid
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Official geometric term for a box.
Surface area of rectangular = 2lw + 2wh + 2lh |
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Volume of a Pyramid
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Given area of base and h,
Volume of a Pyramid = 1/3(area of base)(height) |
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Volume of a Sphere
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Given radius r =
Volume of a Sphere = 4/3(pi(r^3)) |
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Surface Area of Sphere
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Given radius r,
Surface area of a sphere = 4(pi)(r^2) |
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Volume of a Cone
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Given base radius r and height h,
Volume of Cone = 1/3(pi)(r^2)(h) |
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Lateral Area of a Cone
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Lateral area of a cone = (1/2)cl
c = circumference l = slant height |
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Area of a sector
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Sector is a piece of the area of a circle.
If n = central angle of sector, Area of sector = (n/360) x (pi(r^2)) |
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Area of a Circle
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Area of Circle = pi(r^2)
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Length of an Arc
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An arc is a piece of circumference.
Length of an Arc = (n/360) x (2 pi r) |
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Circumference
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2 x pi x r
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Area of a Hexagon or Polygon
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Area = [3 s^2 (square root of 3)]/2
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Area of a Square
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Area = side^2
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Percent Formula
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Percent = Part/Whole
e.g. If part = 3, whole = 4, then percent = 3/4 x 100 = 75% |
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Percent Increase
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Percent increase = Amount of increase/Original Whole
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Percent Decrease
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Percent Decrease = Amount of Decrease / Original Whole
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Average
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Average = Sum of terms / number of terms
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Find the average of 12, 15, 23, 40, and 40.
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(12 + 15 + 23 + 40 + 40)/5 = 130/5 = 26
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Probability of one event
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Probability = Possible # of desired outcomes / total # of possible outcomes
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Probability of two events occurring
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P = Product of the two events
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Absolute Values
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If n > 0,
1. [whatever] < n, then -n < whatever < n 2. [whatever] > n, then whatever < -n OR whatever > n |
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Rules of Triangles
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1. Sum of three interior angles = 180
2. Measure of an exterior angle = sum of remote interior angles. 3. Measure of all 3 exterior angles = 360 4. Area = 1/2 (base)(height) 5. Each side is greater than difference and less than the sum of the other two sides. |
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Isosceles Triangle
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Triangle that has two equal sides.
Not only are sides equal, but the angles opposite are equal (base angles) |
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Equilateral Triangle
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1. Triangle with 3 equal sides.
2. Since all sides are equal, the angles are equal. 3. All angles measure 60 degrees. |
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Area of Equilateral Triangle
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Area = [s^2(square root of 3)]/2
s = length of one side |
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Right Triangle
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1. Triangle with a right angle.
2. Two sides forming Right angle = legs (can be used as base and height to find area) |
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Area of Right Triangle
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Area = 1/2 (leg1) (leg2)
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Pythagorean Theorem
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For ALL right angles:
(leg1)^2 + (leg2)^2 = (hypotonuse)^2 |
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Pythagorean Triplets
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Set of Integers that fit the theorem:
(3,4,5) (9,40,41) (5,12,13) (8,15,17) (7,24,25) |
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45 - 45 - 90 triangle
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sides = 1 : 1 : (square root of 2)
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30 - 60 - 90 triangle
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sides = 1 : (square root of 3) : 2
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Area of Trapezoid
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Area = [(base 1 + base 2)/2] x height
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Parallelograms
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1. 4-sided figure with 2 pairs of parallel sides
2. Opposite sides are equal and opposite angles are equal. 3. Consecutive angles add up to 180. |
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Area of Parallelogram
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Area = (base) x (height)
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Rectangles
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1. 4-sided, four right angles
2. Opposite sides are equal 3. Perimeter = Sum of 4 sides = 2l + 2w |
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Area of Rectangles
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Area = length x width
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Rhombus
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1. 4-sided figure with four equal sides.
2. Also a parallelogram 3. Area is same as square 4. Just a square leaning over |
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Area of Rhombus
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Area = length x width
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If A is 40% C and B is 60% C, what percent is A of B?
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A = 40/100C, B = 60/100C
(A/B)100% = 100% (40C/100)(60C/100) = 100%(40/60) = 100% (2/3) = 66 2/3% |
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9-8-6-3
If the lock above has the combination above, and the numbers range from 1-9, how many different combinations will not open the lock? |
(9 x 9 x 9 x 9) - 1 = 6561 - 1 = 6560
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Factor 13! + 14!
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13! + 14! = 13! + 14!(13!) = 13! (1+14) = 13!(15)
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How many different ways can 5 people be arranged in a line?
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Answer = 5 x 4 x 3 x 2 x 1 = 120
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How many different ways can 9 people be arranged in a line of 4 people?
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Answer = 9 x 8 x 7 x 6 = 3024
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Little poor timmy has 9 trees of a different type. How many different combinations of 3 trees can be planted in front of richie rich's house?
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Use combination formula:
N!(K!(N-K)!) Where N = large Group = 9 K = small group = 3 9!(3!(9-3)!) = 9!/(3!6!) = (9x8x7x6x5x4x3x2x1)/[(3x2x1)((6x5x4x3x2x1) = 3 x 4 x7 = 84 combinations |
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Of one of the three tree combinations above, how many different ways can they be arranged in a line.
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3! = 3 x 2 x 1 = 6 ways
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2^(3x) = 8^24, what is x?
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= (2^3)x = 8^24......8^x = 8^24
thus x must equal 24 in order for both sides of the equation to be equal. |
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LOG 1 = ?
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0
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LOG 10 = ?
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1
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Ln(e) = ?
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1
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If 10 = 100^x, what is x?
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10 = 10^(2x)
LOG 10 = LOG (10^(2x)) LOG 10 = 2X (LOG10) 1 = 2X, thus X = 1/2 |
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If 4a = (square root 8)(square root 2), what is a?
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4a = square root (8 x 2)
4a = square root (16) 4a = 4, thus a = 1 |
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What percent of X is Y?
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If the wording seems confusing then just think of a familiar example and use the wording as a framework such as "what percent of 100 is 10" is in the form 10/100 x 100%, so pretend 10 = y and 100 = x and substitute in the appropriate fashion:
(Y/X)100% |
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What is the volume of a cube with one side of length (Square root 2)?
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Volume of a cube = s^3
(Square root 2)^3 = 2 (Square root 2) |
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What is the volume of a sphere with diameter = 18?
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Volume o a sphere = 4/3 (pi(r^3))
Volume = 4/3 (pi)(9^3) |
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If you have 3 different pairs of shoes, 2 different ties, and 3 different shirts, how many different ways can you put on a pair of shoes, then a tie, then a shirt in that order?
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3 x 2 x 3 = 18
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If 0 < x < 1, for which of the following must y > x?
I. y = 1 - x II. y = x -1 III. y = 1/x |
III only
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If one woodchuck can chuck wood at a rate of 1 hour/piece of wood, and another woodchuck can chuck at a rate of 2 hours/piece of wood, then how long would it take both of the woodchucks to church a piece of wood if they chucked wood together?
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(T1 x T2) / (T1 + T2) = Total time
Total time = (2 x 1) / (2 + 1) = 2/3 hours = 40 minutes |
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If it takes 5 people 20 minutes to paint a cow, how long would it take 6 people to paint 1.5 cows?
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Answer = 150/6
1. Determine how long it would take one person to paint a cow: (20 min/cow)(5 people) = 100 min/cow per person. 2. Then find out how long it would take one person to paint 1.5 cows: (100 min/cow)(1.5 cow) = 150 minutes 3. Since it would take 150 minutes for one person to paint 1.5 cows, the time would be reduced by 6 times if 6 people were to work together, thus divide the answer by 6. |
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If Israel is inviting 4 guests over, two of whom which are girls and two of whom which are boys, how many ways can he seat the guests along with himself onto a round table if no two guests of the same sex are to be seated next to each other?
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2 x 2 = 4 possible seating arrangements
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If 55% of 9t/5 = 33, then t must equal?
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Answer = 100/3
(55/100)(9t/5) = 33 (9t/5) = 33(100/55) (9t/5) = (300/5) 9t = 300 t = 100/3 |
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A certain number is larger than 5 by the same amount that it is smaller than 3 more of 14. What is this number?
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11
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If a heart beats 144 beats per minute, how many times does it beat every second?
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2.4 times
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Enoch owns 2/3 of the stock at Heald College. If Enoch sells 1500 of his 2000 shares, approximately what percent of the college's stock does Enoch have left?
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Answer = 1/6 or 16.67%
2/3 of total stock = 2000 total stock = 3000 2000 - 1500 = 500 500/3000 = 1/6 or 16.67% |
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Inscribed angles
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Defined by two chords of the circle sharing an endpoint.
An inscribed angle is HALF the measure of the central angle intercepting the same arc. angle BAC IIA) = (1/2) angle BOC Formed when two secant lines of a circle intersect on the circle. |
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Chords
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A chord of a curve is a geometric line segment whose endpoints both lie on the the curve.
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Permutation
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Mapping the elements of a set to other elements of the same set. "exchanging" elements of a set.
n = size of the set (the number of elements available for selection), then the total number of possible permutations is equal to n!, where ! is the factorial operator. Once n has been chosed, n - 1 elements are left, so for the second element there are only n - 1 possible choices. |
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How many arrangements can 6 people be seated around a circular table?
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n - 1, where n = 6.
Therefore, (6 - 1)! = 5 x 4 x 3 x 2 x 1 = 120 ways |
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Probability for "r" successes out of "n" attempts equation
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p = probability of successes in a single trial
q = probability of failure (1 - p) Probability of r successes out of n attempts formula = (nCr)x(p^r)x(q^n-r) |
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Quadratic equation
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x = [- b (+/-) (square root of b^2 - 4ac)] / 2ac
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