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61 Cards in this Set
- Front
- Back
- 3rd side (hint)
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Circular permutations. |
I have to fix one spot and factorial the rest. If 5 noble knights are to be seated in a round table, then how many different ways ut can be seated? |
24. I fix 1 and have 4! Left. |
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Circunference |
Pi por diametro |
Revoluciones es igual a circunferencia |
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(X’2-Y’2)= (X - Y) . (X + Y) |
Quadratic expression |
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X’2 + 2xy + Y’2 |
(X+Y)’2 o (x+y) (x+y) |
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(X-Y)’2 |
X’2-2xy+Y’2 |
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Three men hace 4 coats, 5 waist coats and 6 caps. In how maby ways can they wear them? |
4!/1!= 24 ways of using coats (4*3*2) 5*4*3= 60 ways of using waist 6*5*4= 120 ways of using caps 120*60*24 ways |
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In permutations, the number of places I need to ocupy is the _ I write! Then the numbers up these _ are the total possibilities. If I want to sit 4 people out of a total of 8. |
_ _ _ _ = number of people I want to seat. 8*7*6*5= arrangements! |
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If 20 persons were invited for a party, in how many ways can 2 particular persona be seated on either side of the host. |
Consider the 2 persons and host as 1. 18! But the two persons can be seated in either side so is 18! X 2 |
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If -3 < x < 5 and -7 < y < 9. Which one represents the range of all posible values of y-x ? |
To get max value of y-x take max value of y and min value of x : 9 - (-3) = 12 To get min value of y-x take min value of y and max of x: -7 - (5) = -12 |
Max value is the higher of the 1st one and smaller of the second one. Min value is the smaller of the first one and higher of the second one. |
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How many is the growth rate of a population that was 3600 in 1990 and is 4800 in 1993? |
Is 33% |
4800 (actual number) - 3600 (first number) / first number (3600) = 1200/3600 = 33% |
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If 2 different numbers are selected from the set (1,2,3,4,5). What is the probability it would be greater than 4? |
Only cases would be if I get a 1 in the first case 1/5 and a 2 or 3 in the second one 2/4. BUT THEN I JAVE TO ADD THE OTHER SCENARIO. Where I get a 2 or 3 in the first one and a 1 in the second one. |
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Volume of a cylinder |
Pi * r2 * h |
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Percentage increase |
Don’t count the first 100% |
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X intercept of the line |
Value when y=0 |
Ax+by+C=0 . The x intercept would be X= -C/A. If they have different signs would be positive, jd not negative. |
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Rectangular Solid |
All angles are right angles, opposite faces are equal. Can have maximum 3 different areas (or just 1 in case is it a cube) |
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A right triangle inscribed in a circle |
Must have its hypotenuse as the diameter of the circle. The reverse is algo true: if the diamrter of the circle is also the triangle hypotenuse, then its a right triangle |
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Perpendicular to the hypotenuse will always divide the triangle into two triangles with the same properties as the original. |
With 2 values of the sides you can find the 6 values of the sides |
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When probability doesn’t ask for a certain order to get the results |
There is no need to sum the different outcomes order, its not a permutation question. On the other side, if it matters who attemps to resolve 1st, 2nd or 3rd it does matter |
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Finding the number of powers of a prine number k, in the n! If p is the product of integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of p? |
The formula is n/k + n/k^2 + n/k^3 |
14. 30/3+ 30/9 + 20/27 |
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When positive integer x is divided by positive integer y, the remainder is 9. If x/y= 96.12. What is the value of y? |
X/Y= 96.12 = 96 + 12/100. = 96 + 3/75. This means when x is divided by y, quotient is 96 and remainder is 3 if Y is 25. So if remainder is 9, y must be 75. |
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Perfect squares of a number. If y is the smallest positive integer such that 3150 multiplied by y is the square of an integer, then y must be: |
Has even powers of it primes. |
14 |
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Sum of first consecutive positive integers Sum of consecutive integers from 1 to 30 |
N(n+1) /2 |
30.31 /2 = 465 |
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A welder received an order to make a 1 million liter cube-shaped tank. If he has only 4x2 meter sheets of metal that can be cur, how many metal sheets will be required for this order? (1 cubic meter= 1000 liters) |
A cube has 6 sides. Each side will have a surface of 10m. (10m3 = 100 cubic meters). Each side will be able to contain 12 sheets (100 / 8) and 2x2 will remain. That’s why we could use 12*6=72 + 3 from the remainings of each sheets that are adjacent. |
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A train traveling at a certain constant speed takes 30 seconds longer to travel 2 kilometers than it would take to travel 4 kilometers at 120 km p/hour. At what speed, in kilometers per hour, is the train traveling? |
Tarda 30 segundos mas en hacer 2km que lo que el otro tarda en hacer 4, entende bien lo que dice. |
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When triangle is inscribed in a circle |
Height = shorter side Base = Hypothenuse |
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Cualquier numero mayor a 1 elevado a un numero positivo |
Es mayor a 1 |
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10 competitors, three medals, in how many ways can these be awarded? |
Ways! Permutation, order matters. 10*9*8 = 720 |
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Area of a Right Triangle |
Los 2 lados mas chicos multiplicados y divido por 2. La hipotenusa no juega |
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Triangle. Lenght of the longest side? |
Must be smaller than the sum of the other two sides. |
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Area of a shape is |
X = (d+1) * (d+2) |
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For which of the following functions is f(a + b) = f(a) + f(b) for all positive numbers a and b ? |
Resolve para cada uno de los f para ver si da el mismo resultado. |
Choose values and try them |
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Population double |
Population = S. 2 ^ (t\i) |
If a population of rabbits doubles every 7 months and the starting population is 100. What will. Be the population in 7 months?
P= 100. 2 ^ (21/7) P= 100. 2^3 = 800 |
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Combined ratios ( 3 terms) |
If C:A = 3:2 and C:L = 5:4 then? |
C A L 3 2 5 4 Multiply by 5 15 10 12 |
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Glue method |
In combinations or permutations when having a restriction : First :calculate the total Then : calculate as if there were 1 person BUT multiply by 2 if the restriction apply for both sides. |
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Glue method |
In combinations or permutations when having a restriction : First :calculate the total Then : calculate as if there were 1 person BUT multiply by 2 if the restriction apply for both sides. |
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Six friends want to sit in a row but jane won’t sit behind paul |
Total would be 720, and behind would be half the possibilities. So 360. |
Behind usually means half |
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Standard deviation. If each data point is increased by a number, the SD won’t be affected. If each data point is multiply by a factor, the sd will increase by that factor |
Remember this |
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Residual |
Difference from any data point and it’s average. If we know a the n number of terms and the average we can calculate kt easy. |
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Is the product of prime numbers is even or if the sum is odd it means |
That one of them is a 2. |
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Evenly spaced sets (consecutive integers) |
Mean and median are ALWAYS EQUAL Mean and median are equal to the average of the 1st and last term The sum of all elements is equal to the mean*numbers of terms |
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Different prime factors |
No need to count the power of primes |
Total prime factors. Need to count total |
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In fractions |
The denominator is NEVER SPLITTED |
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75% of what number is 21? |
75/100=21/x es mas rapido |
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75% of what number is 21? |
75/100=21/x es mas rapido |
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90 is what percent of 40? |
90/40 = x/100 |
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Arithmetic Sequence formula |
S= kn + x |
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Arithmetic Sequence formula |
S= kn + x |
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Exponential sequence formula |
S = x (k^n) |
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Linear growth |
Y= mx + b |
Baby is born with 9 pounds and increase 1.2 each month.
Y= 1.2n + 9 |
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X^2+x |
X ( x + 1) |
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X^2+x |
X ( x + 1) |
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X^5 - x ^ 3 |
X^3 ( x^2 - 1) o X^3 (x+1) (x-1) |
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A^b + a ^b+1 |
A^b(1+a) |
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Average Speed |
= 2*a+b\a+b |
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Time , speed and distance |
Time = Distance / speed |
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Area of parallelogram |
Base x Height. The height will always be less than one side of the parallelogram. Thus, the area would always be less than the area lf if it were a rectangle. |
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Angles in triangles |
Is bigger than a Isosceles or than half an equilaterus? So it’s bigger than 60. |
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Circunference of a circle |
Pi por diametro |
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(a^n)^m |
a^n.m |
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Overlapping. Exactly 2 |
2. All three. |
Not exactly 2 means that I dont need to multiply by 2 |
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When given statements that might look like having only 1 solution. |
Check if an upper limit is stated in the problem. If this is the case the statement might he sufficient. If not is very likely that there is more than 1 solution. |
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