Section 1
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Volume of cylinder
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Cards (126)
Section 1
(50 cards)
Volume of cylinder
V = (pi) r^2 h
Isosceles Right Triangle
*A right triangle with the two legs (and their corresponding angles) equal.* (short leg : long leg : hypotenuse) x : x : x square root of 2 has angles 45-90-45
Pi or π
circumference : diameter ratio
Circumference of a circle
C = 2(pi)r Or C = (Pi)D
Percent Decrease
amount of decrease/original whole X 100%
Percent Increase
Amount of Increase/Original Whole X 100%
Area of a circle
Area = (Pi)r^2
Pythagorean Theorem
Finding the sides of a right triangle a^2 + b^2 = c^2
Range
put in order from least to greatest and subtract smallest from largest number in set
Solving for # of variables
Determine number of unique values per variable and multiply them by each other
common multiple of 2 numbers
prime factor both numbers; multiply each factor the greatest number of times it appears in factorization.
Central angle/Arc length/Sector area
central angle/360 = arc length/circle circumference = sector area/circle area
Surface area of a cube
SA = 6a^2
Surface Area of a Cylinder
A=2πrh+2πr2
Determining slope direction
Coefficient of x (neg. or pos.) shows the direction of the slope. Negative slopes down left to right, while positive slopes up left to right.
Percent
part = percent X whole
Determining Slopes with 2 Sets of Coordinates
(y2 - y1) / (x2 - x1)
Sum of consecutive EVEN integers
Sum=n∗(n+2)/4 Ex: sum of even integers from 1 to 200 =200∗(202)/4=10100 sum of even integers from 1 to 10 =10∗(12)/4=30
Simplifying exponential equations
·When comparing expressions to find which is greater find a common root using prime factorization Ex: 64^5 & 16^8 = (4^3)^5 & (4^2)^8 or 4^15 & 4^16
Simple probability
Probability = # of desired outcomes/# of total possible outcomes
Surface area of sphere
SA=4(pi) r^2
Sum of consecutive ODD integers
Sum=(n+1)∗(n+1)/4 = (n+1)2/4 Ex: sum of odd integers from 1 to 199 = 200∗(200)/4=10000 sum of odd integers from 1 to 9 = 10∗(10)/4=25
Area of a Parallelogram
A= bh
Quadratic Formula
30º, 60º, 90º Triangle
*long leg is opposite 60 degree angle
Area of a Trapezoid
Area = Average of parallel sides X Height OR A=1/2 (b1 + b2) h
Quadratic Inequalities
· Remember a quadratic formula = a parabola · You're looking for the two x axis intersections and the direction of the remaining · When you divide both sides by a negative you must switch the direction of the inequality sign
Slope of a Line
Slope = Rise/Run = change in Y/Change in X Example: slope of line with (1, 2) and (4, -5) = (-5-2)/(4-1) = -7/3
Sum of Consecutive integers
Sum=n*(n+1)/2 Ex: sum of first 200 integers=200∗(201)/2=20100 sum of first 10 integers = 10∗(11)/2=55
Ratio of boys to girls is 3/4. If there are 135 boys, how many girls?
3/4 = 135/g *cross multiply and divide
Volume of a sphere
V = (4/3) (pi) r^3
Average
Average = Sum of terms/number of terms
Graphing Quadratic Equations
· Factor equation · Set each factor = 0 · Solve for x · xV = (x intersect 1 + x intersect 2) / 2 · To find yV, plug in xV into original equation · To find y intercept, make x=0 into original equation and solve for y
Combinations
A permutation where you DON'T care about the order nCr = (n!/(n-r)!)/r!
Revenue Formula
Profit = Revenue - Cost
Quadratic Equation
ax^2 + bx + c = 0
Ratio
Ratio= Of/To 20 oranges to 12 apples = 20/12 = 5/3
Improper fractions to mixed numbers
e.g. 18/7 = 2 R4 or 2 4/7
Count consecutive numbers (inclusive)
B-A +1 (how many integers from 73-419 = 419-73 + 1
Rate
R=D/T *identify quantities and units to be compared. Keep units straight. If question gives you a rate in hours, but wants an answer in minutes, then convert the hours in the problem to minutes to solve.
Solve for both or neither (venn diagram)
Group1+group2+ neither - both= total
Average of Consecutive numbers
Add the two numbers and divide by 2 (ave. of integers from 13 to 77 = 13 + 77/2)
Area of a Triangle
A= bh/2
Area of a Hexagon Equation when side length is known
A = (3√3)/2 * known side squared
distance formula
d= rt
surface area of rectangular cube
A=2(wl+hl+hw)
Mixed number to improper fractions
numerator = denominator x integer + original numerator denominator remains the same Ex: 2 4/7 7 x 2 + 4 = 18 18/7
Median
Middle number
Mode
number that appears most often
special right triangle (half of an equilateral triangle)
has angles 30-60-90 (short leg : long leg : hypotenuse) x : x square root of 3 : 2x
Section 2
(50 cards)
(a^-x)(b^y)
(b^y)/(a^x)
a^0
1
multiplying exponents
*must have same base
exponent is a fraction 25^(1/2)
squar root 25 = 5 or -5
If a lamp decreases to $80, from $100, what is the decrease in price?
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
How many different ways can 5 people sit in 3 chairs?
· Written, 5P3 · Equation for solving 5!/(5-3)! · Because 5x4x3x2x1/2x1, the "2x1" cancel out from both the numerator and denominator, you only solve for: 5 x 4 x 3 = 60 different possibilities
Probability
P is probability, m is # of favorable ways, n is total # of ways P = m / n when combining probability of two mutual exclusive events Pa x Pb
Finding the vertex of a quadratic equation
-b/2a
Permutations
When you DO care about the order. For instance, if there are 5 people, how many different ways can they sit in 3 chairs. When a person sits down, it removes the possibility of sitting in any other chair. nPk = n!/(n-k)!
even^odd
even always
(12sqrt15) / (2sqrt5) =
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
find value for x & y for: x - 2y = 2 & 2x +y = 4
· Add Equations · Find common factor for x to cancel it out (2x + y = 4) + -2(x - 2y = 2) · Solve for y 5y = 0 so, y = 0 · Replace y value into either one of the original equations and solve for x x - 2(0) = 2 so, x = 2
(6sqrt3) x (2sqrt5) =
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
(ab)^x
(a^x)(b^x)
-4 < -x, then +4 > +x
Always
xy + xz =
x(y+z)
If a>b then
-a<-b
dividing exponents
*must have same base
x^2 + 2xy + y^2 =
(x+y)(x+y) = (x+y)^2
negative exponents
10^5 how many zeros?
100,000 10^5 means 5 zeros
0^0
undefined
Integer divisible by 6
If sum of the digits are divisible by 3 and the last digit is even Ex: 1,458: 1 + 4 + 5 + 8 = 18
value of x for: x + 4y = 7 & x - 4y = 8
· Add Equations · No need for a common factor since 4y & -4y cancel each other out 2x = 15 x = 15/2
1ⁿ
1
(2a^m)(1/3a^-n)
= (2/3a^m)(a^-n) = 2a^m / 3a^n
inscribed angle whose triangle base = diameter
*When the base of triangle is the diameter of the circle, triangle must be a right triangle
x^2 - y^2 =
(x + y)(x - y)
(x-y)/xy=
1/y - 1/x x,y≠0
Integer divisible by 9
Add up digits, If the result is divisible by 9, then the original number is divisible by 9. Ex: 2,880: 2 + 8 + 8 + 0 = 18: 1 + 8 = 9
Equilateral Triangle
60-60-60 all sides are equal
what is c if, 200 = (a+b+c)/2 & 80 = (a+b)/3
· Get rid of the denominator in each equation by multiplying both sides by the denominator value · Now subtract both equations by each other (400 = a+b+c) - (240 = a+b) · Therefore, 160 = c
y^2 = x
y = ±√x e.g. y^2 = 4 so, y = ±√4 = ±2
Odd and even number operations (addition and multiplication)
Odd + Odd = Even Even + Even = Even Odd +Even = Odd Odd x Odd = Odd Even x Even = even (and divisible by 4) Odd x even = even
Inscribed angle
1/2 of central angle
Vertex
· The minimum or maximum of a parabola · Equal distance from the two points intersecting the x-axis.
7/12 + 3/5
· Cross multiply & add both products together 7x5 + 12x3 = 71 · Multiply both denominators 12x5 = 60 · So, 71/60, then simplify to a mixed number 1 11/60 or · Find a multiple that makes the denominators equal 60 is the lowest common denominator · Multiply each fraction by their respective multiple 5(7/12) + 12(3/5) = 35/60 + 36/60 · Add the two numerators 71/60 or 1 11/60
Formula to calculate arc length?
Arc length = (n/360)(2πr) where n is the number of degrees.
if a/b = 1/4, where a is a pos. integer, which of the following is possible for the value a^2/b?: 1/4, 1/2, 1
All · cross multiply 4a=b · substitute b in equation a^2/4a · square root both nominator and denominator a/4 · looking at the options, plug in values to see if they equal any of the possible answers
a/∅
undefined
Integer divisible by 4
The last 2 digits are a multiple of 4. Ex: 144 .... 44 is a multiple of 4, so 144 must also be a multiple of 4
odd^odd
odd always
Integer divisible by 3
Add all the digits, If that digit is a 3,6 or 9, the number is a multiple of 3 Ex: 314159265 3 + 1 + 4 + 1 + 5 + 9 + 2 + 6 + 5 = 36 Then, 3 + 6 = 9
How many more times is 17% than 3%
17/3 or 5 2/3 how many more times is m than n? x = m/n
xy - xz =
x(y-z)
(x+y)/xy =
1/x + 1/y x,y≠0
Integer divisible by 8
Examine the last three digits Ex: 34152: Examine divisibility of just 152: 19 × 8
Solve for x, x^2 + 2xy + y^2 = 25, with x + y > 0 & x-y=1
· factor the equation (x+y)(x+y) = 25 or, (x+y)^2 = 25 · Square root both sides x + y = ±5 · Since it is stated that "x + y > 0" we know that 5 can only be positive · add the remaining equations together (x+y=5) + (x-y=1) · Because the y value cancels it's self out, there's no need to multiply by a common factor 2x = 6, x = 3
(a/b)^x
a^x/b^x
x^2 - 2xy + y^2 =
(x-y)(x-y) = (x-y)^2
Section 3
(26 cards)