Quant Flashcards
counting the sum of intergers form x to y
https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-solving-equations/linear-equations-word-problems/v/sum-consecutive-integers
2.5/3
is not a fraction, fraction must have an integers as a nominator and denominator
To reproduce an old photograph, a photographer charges x dollars to make a negative, 3x53/5 dollars for each of the first 10 prints, and 5x/5 dollars for each print in excess of 10 prints. If $45 is the total charge to make a negative and 20 prints from an old photograph, what is the value of x [x=5]
x + 3x/5 (n - first 10) + 5x/5 (x - 10) = 45
https://greprepclub.com/forum/to-reproduce-an-old-photograph-a-photographer-3x-charges-x-8710.html
long polynomial division
https://www.youtube.com/watch?v=RPXMBIFG_W4
finding the two different values (quadratic equation-parabola) that will resut the same output
f(x)=x^2 - 8x +12
- find the roots of the equation
(x+-a)(x-+b) - finding vaules by symetry e.x x=6 and x=2 lower point = 4 (6+2=8, 8/2=4); next point 3 & 5
- there are infinite number of pairs
ratio
The ratio of men to women is 9 to 20. The total number of people of 58
Ratio does not give any information about actual number of things, people ect. e.x the ratio of apples to oranges is 3:5 = the actual number of fruit might be 8, 16, 24, 32, 40 - all depends on the multiplier
- make the equation 9x/20y=9/20 M+W=58
2. find the multiplier (x) that will give you the right number
2x^2=(2x)^2
2x^2=4x^2
0=2x^2
x=0
(x-1)(x+1)=
(x^2-1)
number of multiples of 7 from 1 to 1000
counting the last multiple of 7 1000/7=142.85
ignore the desmo
142*7=994
last - first/# +1
994-7/7+1 = 142
angle bisector inside a triangle
https://www.youtube.com/watch?v=6WZRypy7ry0
slope = -1/2
y=-1/2x + 1 the slope will be one down the y-axis and 2 right the x-axis
https://www.wolframalpha.com/input/?i=y%3D-1%2F2x+%2B+1
the same line ex y=x+3 and y=x+3
- inifnite number of solutions
- the slope is the same (pararell lines)
- the y-intersept is the same
1
factor and divisior of every numer
is not a prime number
1/3 + 1/3
=2/3
7/11*2/9
=14/99
k^2=m^2
I k I = I m I
agebraic term
3x^2 - 1 term
3x^2 + 5 - 2 terms
the number (only) next to the letter is called coefficient, the number without the letter is called constant
4x^2 - 36
= (2x-6)(2x+6)
if n=33^43 + 43^33 what is the unit digit of n
- pattern for 3 is 3, 9, 27, 81
the pattern repeat itself every 4 numbers so look for multiples of 4
the closest multiple of 4 is 40 (unit digit=1) therefore the unity digit of 33^43 is 7
the colosest multiple of 4 in 43^33 is 32 (unit digit=1) therefore unit digit is 3
the unit digit of n = 0
final exam grade = 70% of final grade, John got 75%
midterm exam grade = 30% of final grade, John got 40%
total = 70 + 30 = 100
0.75 * ( 70 ) + 0.40 * ( 30 ) / 100 = 52.5 + 12 / 100 = 64. 5
Kim’s midtem exam is worth 20% of final grade and she got 35/50 = 0.70 * 20 = 14
solution A, consisting of 40% bleach and 60% orange juice, is mixed Solution B consisting of 20% and 80% orange juice. The resulting mixture contains 24% bleach. Solution A accounts for what percentage of the mixture.?
bleach
20 (B) 24 40(A)
ratio is 16:4 = 4(B):1(A) B is more to 24 so the ratio is going to be bigger is B side
answer 1/5 = 20% (A accounts for 1, the total is 4+1=5)
y > 2x + 1
https://www.wolframalpha.com/input/?i=y+%3E+2x+%2B+1
y=x^2
parabola
https://www.wolframalpha.com/input/?i=y%3Dx%5E2
https: //www.wolframalpha.com/input/?i=y%3Dx%5E2+%2B1 (y=x^2 + 1)
https: //www.wolframalpha.com/input/?i=y%3Dx%5E2+-2 (y=x^2 - 2)
https: //www.wolframalpha.com/input/?i=y%3D%28x%2B1%29%5E2 (y=(x+1)^2)
https: //www.wolframalpha.com/input/?i=y%3D%28x-1%29%5E2+%2B+3 (y=(x-1)^2 + 3)
y=-x+2, y=x^2
https://www.wolframalpha.com/input/?i=y%3D-x%2B2%2C+y%3Dx%5E2
-x+2=x^2
(x-1)(x+2)=0
x=1, x=-2 | points (1,1) and (-2,4)
interior vs. exterior volume
the volume of a box is 2688 but the box is 1/4 thick all around. 12-1/4-1/4 = 11.5 interior volume = 11.5 * 13.5 * 15.5 = 2406.375
- numbers form 1 to 10, what’s the probability of getting first 1 and then 3 (order matter)
- numbers form 1 to 10, what’s the probability of getting first 1 and then 3 (order does not matter)
1/10 * 1/9 = 1/90
1/90 * 2
permutation
order does matter (10) = 10 * 9 * 8
order does not matter (10) = n! / (n-r)! * r!
- the value of overall change in graphs
2. the average of x changes in graphs
- = range
2. = first - last / x
standard deviation
adding/multiplying numbers by the same number
how far apart are the numbers (from the mean) e.x 1, 3 = the mean is 2 = the s.d is 1
if all numbers are the same, the s.d = 0
an equation with the biggest slope has the biggest s.d ( the bigger the slope - the bigger the s.d )
adding/subtracting = s.d stays the same
multiplying/dividing = s.d will be mutiplied by the number ( 0 is the exeption )
normal distribution: properties
- mean, median mode are nearly equal
2. 2/3 of the data are within 1 s.d of the mean
