Quantitative Reasoning Basic Knowledge
Specifically, what is the area of a triangle?
(0.5)bh. Any side can be the base, and the height is perpendicular to this side
a²-b²=?
(a+b)(a-b)
(ab)^n = ?
(a^n)(b^n)
(a/b)^n = ?
(a^n)/(b^n)
Formula for the sum of the interior angles of an n-sided polygon.
(n-2)180°
Equation of a circle?
(x-a)²+(y-b)² = r² center = (a,b)
What is the difference between and odd root (such as cube root) and an even root (such as square root)?
- We can take any even root of a positive number, which results in a positive output, but we can't take any even root of a negative number - We can take any odd root of any number on the number line, positive, or zero or negative. Any odd root of a positive number is positive, and any odd root of a negative number is a negative.
n root of 0 = ?
0
√0 = ?
0
0^n = ?
0 if n>0
What are the possible number of time a circle can intersect a square?
0-8
What is 1/8 in decimal form?
0.125
2. What is 1/6 in decimal form?
0.166666....
What is 3/8 in decimal form?
0.375
What is 5/8 in decimal form?
0.625
What is 5/6 in decimal form?
0.83333333.....
What is 7/8 in decimal form?
0.875
What is the percentile of the lowest score?
0th percentile
The higher the order of a root, the closer the result is to ___?
1
n root of 1 = ?
1
12. What is the complement rule? i.e. P(not A) = ?
1 - P(A)
a⁰ = ?
1 as long as a does not equal 0
7. 1^n = ?
1 for all n
What are the 4 Pythagorean triplets?
1. 3,4,5 2. 5,12,13 3. 8,15,17 4. 7,24,25
2. How to quickly compare 2 fractions that are relatively close?
1. 7/11 ?? 5/8 2. (7)(8) ?? (11)(55) 3. 56 > 55 4. So, 7/11 > 5/8
What are the 4 special lines that can occur in an isosceles triangles spontaneously?
1. Angle bisector 2. Perpendicular bisector of a side 3. Median 4. Altitude (height)
How to calculate the standard deviation?
1. Calculate the mean of values 2. Find the difference of the mean from every number to produce a second list, the list of deviations 3. Square every deviation to produce a third list, a list of the squared deviations. 4. Find the average of the third list, the average squared deviation; this is called the variance 5. Take the square root of the variance; this is the standard deviation. MDSAR
2. How to multiply with decimals?
1. Count the number of digits to the right of the decimal of each number. The sum of these is the amount of decimal places in your product 2. Find the product without worrying about the decimals 3. Put the correct number of decimal places into the final produce
Rules of multiplying evens and odds
1. E x E = E 2. O x O = O 3. E x O = E
Rules of subtracting evens and odds
1. E+/- E = E 2. O+/- O = E 3. E+/- O = O
What type of list must you have in order for the mean = median
1. Evenly spaced lists (such as consecutive integers or multiples) 2. Symmetrically distributed lists. {4, 8, 13, 23, 25, 27, 37, 42, 46} - median = 25 - 23 = 25 -2, 27 = 25 +2 - 13 = 25 - 12, 37 = 25 +12 - 8 = 25 - 17, 42 = 25 +17 - 4 = 25 - 21, 46 = 25 + 21
5. How to go from an absolute value inequality to an ordinary inequality?
1. Find out the median, which is the number being subtracted from x. 2. Figure the maximum distance between the median and the endpoints, which is the number that the absolute value is related to 3. Figure out the end points by subtracting/adding the distance from the median. 4. Your x is in that range
5. How to go from a given region of numbers to an absolute value inequality.
1. Find the median of the region 2. Find the endpoints 3. Find the distance from the median to the endpoint. 4. Put answer in following format |x-median|</>/≤/≥ distance between median and endpoints
How to find the least common multiple?
1. Find the prime factorization of each number 2. Find the GCF of the 2 numbers 3. Write each number in the form (GCF) times (another factor) 4. The LCM is the product of these 3 factors or use the formula LCM = P*Q/GCF
how to find the number of even factors of a large number.
1. Find the total number of factors 2. Find the total number of odd factors 3. subtract them
How to find the last digit of an integer raised to a large power? (ex: 57^123)
1. Focus on single-digit multiplication only 2. Look for the repeating pattern, and determine the period of the pattern (period is often 4) 3. Extend the pattern, using multiples of the period o 71 =7 o 72 = 49 o 73 = ....3 (9x7=63) o 74 = .... 1 (3x7 =21) o 75 = .....7 (1x7 =7) o 76 = ....9 (7x7 =49) o 78 = ....3 • Period of 4. So all exponents that are a multiple of 4 will end in 1. 120 is a multiple of 4 • 7120 = ...1 • 7121 = ...7 • 7122 = ...9 • 7123 = ...3
What are the properties of a trapezoid?
1. Has exactly one pair of parallel sides 2. The two angles on a leg ( the non-parallel sides) are supplementary
What are the big 4 properties of parallelograms?
1. Opposite sides are parallel 2. Opposite sides are equal 3. Opposite angles are equal 4. The diagonals bisect each other OSP OSE OAE DIA
How to square a number ending in 5.
1. Remove the 5, leaving the remaining digit(s) 2. Add 1 to the remaining digit(s) 3. Multiply the numbers (n)(n+1) 4. Put this product in front of 25.
5. How to use the difference of 2 squares to help simplify decimals just less than 1?
1. Simplify .99951/.993 1-.000049/1-.007 = 1²-.007²/1-.007 = (1+.007)(1-.007)/(1-.007)= 1+.007 = 1.007
What are the 2 equations that we have to set up if the amount of 2 mixtures are initially unknown?
1. The "total" equation: total volume or total mass/weight 2. The amount of solute
What is the binomial situation?
1. The probability of "success" in an individual trial is given or obvious from context. (usually with dice or coins) 2. The number of trials, n, is decided before hand. Trials are independent 3. For some r≤n, what s the probability of exactly r successes in n trials
What operations can we do with inequalities that preserve the order of the inequality? (i.e not change the relationship)
1. We can always add or subtract any number to both sides of an inequality 2. We can multiply or divide both sides of an inequality by the same POSITIVE number. This includes cross-multiplying, as long as all fractions are positive.
How to find the total number of factors of a large number?
1. find prime factorization 2. Make a list of the exponents of the prime factors 3. Add 1 to every number on the list 4. Multiple all the numbers together and that is the number of factors
How to find the number of odd factors of a large number
1. find prime factorization 2. Make a list of the exponents of the prime factors, excluding the factors of 2 3. Add 1 to every number on the list 4. Multiple all the numbers together and that is the number of factors
√ 2 = ? (approximately)
1.4
√ 3 = ? (approximately)
1.7
b^-n = ?
1/b^n
3. The equation for finding the % increase/decrease.
100 (difference)/ original value
12 x 9
108
5! =
120
11^2?
121
2^7 =?
128
12 x 11
132
12^2?
144
2^4 = ?
16
13^2?
169
14^2?
196
What is enough to establish that 2 triangles are similar?
2 angles in one triangle equal 2 angles in another triangles.
What 2 new numbers added onto a list will not change the SD?
2 new numbers that are the same distance from the mean as the SD
What 2 new numbers added onto a list will decrease the SD the most?
2 numbers that equal the mean
4. What are the first prime numbers under 60?
2,3,5,7,9,11,13,17,19,23,29,31,37,41,43,47,53,59
√ 5 = ? (approximately)
2.2
6^3 = ?
216
15^2?
225
4! =
24
2^8 = ?
256
4^4 = ?
256
2^5 = ?
32
7^3 = ?
343
What is the sum of interior angles of a quadrilateral?
360°
8! =
40320
6 x 7
42
Lines with slopes of +/- 1 make ____ with the axes.
45°
6 x 8
48
7! =
5040
2^9 = ?
512
8^3 = ?
512
7 x 8
56
3! =
6
12 x 5
60
Each angle of an equilateral triangle is what?
60 degrees
5^4 = ?
625
2^6 = ?
64
4^3 = ?
64
12 x 6
72
6! =
720
9^3 = ?
729
3^4 = ?
81
12 x 7
84
12 x 8
96
What is the percentile of the highest score?
99th percentile
What is an arc of a circle?
A piece of the curve of a circle
What is created when we draw a radius to the point of tangency?
A right angle
What is a chord of a circle?
A segment with two endpoints on the circle
What is a transversal line and how do the angles it forms relate to one another?
A transversal is a line that cuts across 2 parallel lines. Of the 8 angles formed, the four "big" angles are all equal, and the four "little" angles are all equal. - a=d=e=h and b=c=f=g - Any "big" angle and any "little" angle are supplementary
What is the work equation?
A= RT • A= amount of work done • R= the work rate • T= time
1. If we know the value of n², then how can we get the next square up (n+1)²?
Add n and (n+1) to n²
12. In probability: - "Or" means _______ -"And" means _______
Add, multiply
What does it mean to be a regular polygon?
All sides are equal and all angles are equal.
How do we find the combined output of 2 machines working side by side?
Always add rates. If one machine takes 3 hrs for a job, and the other takes 6 hrs, we can't add or subtract times. We have to change those to rates, (1 job)/(3 hr) and (1 job)/(6hr), and add those.
What is the equation for concentration?
Amount of solute/ total amount of solution x 100
What is a central angle of a circle?
An angle with its vertex at the center of the circle
What is an inscribed angle on a circle?
An angle with its vertex on the circle
What is a sequence?
An ordered list of numbers
How can we use proportions to find weighted averages?
Average of whole = A1p1+ A2p2+ A3p3 - A = average of that group - p = percentage of the whole - p1+ p2+ p3 =1
Equation for average velocity?
Average velocity = total distance/total time
How to find the common factor(s) of 2 integers?
Break both numbers down to their prime factors to see which they have in common. Then multiply the shared prime factors in every possible combination.
4. How to determine the greatest common factor (GCF) of a pair of integers?
Break down both integers into their prime factorizations and multiple all the prime factors they have in common to get your GCF. EX: GCF of 36 and 48. 36 = (2)(2)(3)(3) 48 = (2)(2)(2)(2)(3) GCF = (2)(2)(3) = 12
6. How to solve age problems?
Choose variable to represent the ages now, and use addition and subtraction to create expressions for ages at other times.
2 equations relating the dividend (D), divisor (S), Quotient (Q) and Remainder (r)
D/S = Q + r/S D = S*Q +r
What is the equation that relates distance, rate(speed) and time?
Distance = Rate(or speed) * Time
How to divide any number by 5.
Double the number and divide it by 10 in either order
What does it mean to say events A and B are mutually exclusive?
Events A and B are mutually exclusive if it is absolutely impossible for them both to happen at the same time. For example, in a single coin toss, head & tails are mutually exclusive --- you get one or the other. If you draw a single card from a deck, the suits are mutually exclusive --- if that card is a spade, then it cannot possibly be a diamond as well.
What is usually the simplest way to solve a shrinking/expanding gap?
Figure out the speed at which the gap is shrinking or expanding and then relate it to the 2 individual speed by subtraction or addition
5. How to use the difference of 2 squares to help find the prime factorization of a large number?
Find the prime factorization of 1599 1600-1 = (40²)-(1²) = (40+1)(40-1) = (41)(39) = 41 * 3 * 13
What is the median if N (the amount of values) is odd? is even?
If N is odd, the median is the middle number on the list. If N is even, the median is the average of the 2 middle numbers.
What determines if a parabola opens upwards or downwards?
If a is the quadratic coefficient, then a > 0 means the parabola opens upward; when a < 0, it opens downward
What determines how wide a parabola is?
If a is the quadratic coefficient, |a| > 1, the then the parabola is skinny; if |a| < 1, then the parabola is wide
When does SD =0?
If all the numbers on a list are identical
If events A and B are mutually exclusive, then P(A and B) =
If events A and B are mutually exclusive, then P(A and B) = ? Click to see back → LEARNING For mutually exclusive events, P(A and B) = 0 because, by definition, it's impossible for them to happen at the same time.
How to determine if an integer is divisible by 6?
If it is divisible by 2 and 3, then it divisible by 6.
How to determine if an integer is divisible by 9?
If its digits add up to a multiple of 9, then it is divisible by 9.
How to determine if an integer is divisible by 4?
If its last 2 digits are a multiple of 4 then it is divisible by 4. Ex: 6,932 is a multiple of 4, since 32 is a multiple of 4.
4. How to determine if an integer is divisible by 3?
If the sum of the digits are a multiple of 3, then it is divisible by 3.
11. What's the difference between a permutation and a combination?
In a permutation, order of the selection matters: {A, B, C} and {C, A, B} are two different permutations. Use factorials In a combination, only the result matters, not the order of selection: {A, B, C} and {C, A, B} count as the same combination. nCr
What is a recursive sequence?
In a recursive sequence, each term a,n is defined in terms of one or two previous terms (an-1 and maybe an-2)
What is the general structure of a percentile?
In general, if a score is the pth percentile of a distribution, that score is larger than p% of the score in the distribution.
How to multiply 2 powers with the same base (a²*a⁵)?
Keep the base and add the exponents together (a⁷)
How to divide 2 powers with the same base?
Keep the base and subtract the exponent of the denominator from the exponent of the numerator.
Equation for the LCM of P &Q
LCM = P x Q/GCF, make sure to cancel before multiplying
2. How to find the power of a decimal?
Multiply the amount of digits to the right of the decimal with the exponent and that is the amount of decimal places will be in your answer. (.03)³=.000027
How to multiply 2 powers with different bases but the same power? (x⁴*y⁴)
Multiply the bases together and keep the power the same (xy⁴)
How to raise a power to another power?
Multiply the exponents
2. How to simplify a complex fraction?
Multiply the numerator and denominator of the big fraction by each denominator of the inner fractions.
If, in a set of n items, b are identical, a different c are identical, and another group of d are identical, then what is the total of distinct arrangements?
N = n!/((b!)(c!)(d!))
10. If N is the number of values and M is the mean of N values, then the sum of N values = ?
N*M
If we add the same number to every number on a list, or subtract the same number from every number on the list, does the SD change? If so, how?
No, it does not change the SD
What pulls the mean away from the median and what direction does it pull it towards?
Outliers pull the mean away from the median and it pulls it towards the outlier's direction.
What is the probability of 2 independent events?
P(A and B) = P(A) * P(B)
What is the generalized "and" rule (i.e when there are conditional probabilities)?
P(A and B) = P(B) x P(A|B) P(A and B) = P(A) x P(B|A)
What is the probability of 2 non-mutually exclusive events and it could also be for independent events (i.e. the general "or" rule?
P(A or B) = P(A) + P(B) - P(A and B)
What is the probability of 2 mutually exclusive events?
P(A or B) = P(A) +P(B) It uses "or" because it is impossible for both to occur at the same time
What is the complement rule for "at least one"?
P(at least one success)= 1- P (no successes)
If we know the lengths of 2 of the 3 sides of a triangle, P and Q, then what is the range of the 3rd side?
P-Q < 3rd side < P+Q
What is the binomial situation formula?
P= (nCr)(p^r)[(1-p)^n-r] p= probability of success on one trial n= # of trials r= # of successes (p^r)= success happening r time [(1-p)^n-r] = nonsuccesses happening n-r times (nCr) = how many different ways can those r successes be distributed among n trials
What is the first quartile?
Q1, the first quartile, is the median of the "lower list." It divides the bottom 25% of the list from the rest.
What is the third quartile?
Q3, the third quartile, is the median of the "upper list." It divides the lower 75% from the upper 25%.
What are the values that standard deviation can never be and why?
SD can never be negative because SD is distance and distance can never be negative
What is a symmetrical/isosceles trapezoid and what are its properties.
Same as a regular trapezoid 1. Has exactly one pair of parallel sides 2. The two angles on a leg ( the non-parallel sides) are supplementary PLUS 3. 2 equal legs 4. Adjacent angles along the parallel lines are equal
What do you do to find the point reflected over the x-axis?
Same x, Change the sign of y
What do you do to find the point reflected over the y-axis?
Same y, changes the sign of x
8. What is a bisector?
Something that cuts another thing into two congruent pieces.
Area of a trapezoid
Sometimes, we can find the area of a trapezoid by subdividing the trapezoid into a central rectangle and two side right triangles
How to square a multiple of 10.
Square the digits without the zeros, then put 2 zeros after the nonzero numbers.
What operations can we do if we know that both values of the inequality are positive?
Squaring and taking the square root
What must we do if we multiply or divIde by a negative number to both sides of the inequality?
Switch the inequality sign Ex: 7>3 --> -7<-3
What is the interquartile range (IQR) and how do we calculate it?
The IQR is the size of the middle 50% of the population. This is represented by the box of the box plot. IQR = Q₃-Q₁
What is does the Triangle Inequality state?
The Triangle Inequality states that the sum of any two sides of a triangle must be bigger than the third side. If we can identify which side is the largest, then the other two sides must have a sum larger than that largest side in order for the triangle to be possible.
Define |x-c| < b
The absolute value |x-c| is the distance between point x and point c c is the median of the range of values b is how far the range can go from the median
How are similar triangles and area related?
The area of the bigger triangle is the area of the smaller triangle multiplied by k2. When lengths are multiplied by k, area is multiplied by k2.
What are the properties of rectangles?
The big four of parallelograms 1. Opposite sides are parallel 2. Opposite sides are equal 3. Opposite angles are equal 4. The diagonals bisect each other PLUS 5. All four angles equal 90° 6. Diagonals are congruent
What are the properties of rhombuses?
The big four of parallelograms 1. Opposite sides are parallel 2. Opposite sides are equal 3. Opposite angles are equal 4. The diagonals bisect each other PLUS 5. All four sides are equal 6. Diagonals are perpendicular
What are the properties of a square?
The big four of parallelograms 1. Opposite sides are parallel 2. Opposite sides are equal 3. Opposite angles are equal 4. The diagonals bisect each other PLUS 5. All four sides are equal 6. Diagonals are perpendicular 7. All four angles equal 90° 8. Diagonals are congruent
How to find the total weighted average if there are only 2 groups using proportions and distance of group average to the total average?
The bigger portion of the whole/the smaller portion of the whole = the bigger distance of group average to the total average/the smaller distance of group average to the total average
Area of a rhombus and for a parallelogram
The formula A = bh works for rhombuses and parallelograms, and any side can be the base, but the height has to be perpendicular to the base, so it will not lie along a side. If the length of the height is not given, then almost always one can find it from the Pythagorean theorem
What do the gaps from one bar on a box plot to another bar represent?
The gaps from one bar to the next represent difference in score, not difference in number of people or data points
For powers of 10 less than 1, the negative exponent next to the 10 equals what?
The number of decimal places to the right of the decimal. (10^-2 =.01)
2. When a multiple of 10 greater than 1 is written in standard form, the exponent next to the 10 equals what?
The number of zeros after the 1. (10,000 = 10⁴)
When dealing with shrinking and expanding gap problems, subtracting/adding the speeds of the 2 objects gives us what?
The rate of the gap shrinking/expanding
What are the x intercepts of a parabola?
The solution(s) of the quadratic set equal to zero
What does the vertical axis of a histogram always represent?
The vertical axis is always "frequency," that is, number of people or occurrences
What is the relationship between the central angle and the arc it intersects?
They are equal
5. What are the roots of an algebraic expression?
They are the x-values that make the expression equal to zero.
What does it mean to say events A and B are independent?
They have absolutely no effect on each other. The outcome of one has absolutely no bearing or influence on the outcome of the other.
What are supplementary angles?
Two angles that add up to 180 degrees
3. What is the equation for compound interest?
V=P[1+(r/100n)]^nt
How can we add 2 inequalities?
We can add inequalities with the same direction. ex: a > b , c > d = (a+c) > (b+c)
How can we simplify a complex fraction?
We can simplify a complex fraction by multiplying the numerator and denominator of the big fraction by the LCM of all the denominators of the little fractions
How can we subtract 2 inequalities?
We can subtract inequalities that have opposite directions. ex: a>b, d<c = (a-d) > (b-c)
What do we do when we raise a radical expression to a power?
We distribute the exponent to each factor; any even power of a radical is a power of a whole number
How do we multiply and divide radical expressions? [Ex: (3√5)*(7√2)]
We multiply/divide whole numbers by whole numbers, and radicals by radicals [21√10]
How do we solve |A| = B
We split it into 2 equations 1. A = B 2. A = - B
What is a perpendicular bisector?
When a line bisects a segment at a 90 degree angle.
When can an absolute value of an expression give us extraneous solutions ( solutions that result correctly from the math, but which don't work in the original equation.)
When an absolute value of an expression equals, not a single number, but another expression. So, we must check our work
When dealing with shrinking and expanding gap problems, when do we add the speeds of the 2 objects?
When the objects are traveling in opposite directions
When dealing with shrinking and expanding gap problems, when do we subtract speeds of the 2 objects?
When the objects are traveling in same directions.
What are vertical angles and how are they related?
When two lines cross, four angles are formed. The pairs of angles opposite each other, sharing only the vertex in common, are called vertical angles. Vertical angles are congruent.
How do we add and subtract radical expressions?
When we have a sum or difference of radicals, we have to simplify each radical separately, and then we can add the ones that have the same radical factor.
In any counting question that is asking about 2 terms to be in one order and not another, what should you think about?
Whether the 2 groups are related by symmetry
In an obtuse triangle, what may you have to do in order to find the height of a triangle?
With an obtuse triangle, we may have to extend a line of a side, and then draw a segment from the vertex that is perpendicular to this extended segment. The height would be PR and the base would be MN.
If we multiply every number on a list by positive number K, does the SD change? If so, how?
Yes, the SD is also multiplied by K
5. How do you know when a two equation/two unknown problem has an infinite number of solutions?
Your solution will wind up with an ALWAYS TRUE equations, such as 7=7, and that's the indication that the system of equations is also ALWAYS TRUE for x & y.
How do you know when a two equation/two unknown problem has zero solutions?
Your solution will wind up with an NEVER TRUE equations, such as 15=7, and that's the indication that the system of equations is also NEVER TRUE for x & y.
Equation for sum of a sequence.
[N*( a1 + an)]/2 N = the number of items
What is a histogram?
a graphical way to display the data in a set. They visually display data and allow us to see the distribution at a glance.
4. If an unknown number is in its prime factorization form and it has all even exponents, then we know that the number must be a what?
a perfect square
What is an arithmetic sequence?
a sequence in which we add the same constant to get from each term to the next. The terms have a common difference.
For a circle in the x-y plane, each slanted radius is what?
a slope triangle with an equal hypotenuse
If a segment across a triangle is parallel to one of the sides, it automatically creates a what?
a smaller, similar triangles
What is the median of a triangle?
a special line that goes from a vertex to the midpoint of the opposite side. In a general triangle, the median divides the opposite side in half, but does NOT divide the angle into half.
At least 2 of the angles in any triangle have to be what?
acute
Any factorial n! is divisible by what?
all the integers less than n and all the factorials less than n!
The equation for the nth term of an arithmetic sequence with an initial term a1 and a common difference d is
an = a1 + (n-1)d
Equation to switch from arc length to arc angle.
arclength/2πr = arc angle/360°
Equation to switch from area of sector to arc angle.
area of sector/πr² = arc angle/360°
When you see the words " __ ______" in a probability question, use the complement rule as a shortcut.
at least
5. (a+b)²=?
a²+2ab+b²
(a-b)²=?
a²-2ab+b²
(a+b)³=?
a³+3a²b+3ab³+b³
(a-b)³=?
a³-3a²b+3ab³-b³
For a base between 0 and 1, taking a square root of it makes it ________ (smaller/bigger)
bigger
How to test whether any number less than 100 is prime?
check whether it is divisible by one of the prime numbers less than 10. If a number less than 100 is not divisible by any prime divisor less than 10, then the number has to be prime.
The ______ (closer/further) the points are to the mean, the smaller the SD is.
closer
A small group drawn from a large group is a ______
combination
If the 2 new numbers are added to a list and are closer to the mean than the SD, then they will __________(decrease/increase) the SD
decrease
Parallel lines have _____ slopes.
equal
Similar figures have _____ angles
equal
Every point on the perpendicular bisector of a segment is __________ from the 2 endpoints of the segment.
equidistant
Every special fact about isosceles triangles also applies to what kind of triangles?
equilateral
What do you use when you want to calculate the different ways n objects can be ordered from 1st to nth? (o For the permutation of n different items, # of permutations is found by how?)
factorials
The ______ (closer/further) the points are to the mean, the larger the SD is.
further
The measure of the inscribed angle of a circle is ______ the measure of the arc it intercepts
half (If angle ABC = 40°, then arc AC = 80°)
If the 2 new numbers are added to a list and are further from the mean than the SD, then they will __________(decrease/increase) the SD
increase
How to divide with decimals?
move the decimals of both numbers one place to the right until the denominator is a whole number.
nC1 = ?
n
11. What equation do you use when you want to calculate the number of ways to select AND order k objects out of n objects?
n!/(n-k)!
What equation do you use when you want to calculate the number of ways to select but not order k objects out of n objects?
n!/k!(n-k)! = nCr ex: 10C2= 10*9/2*1
If Task #1 can happen in m ways, and Task #2 can happen in n ways, and Task #3 can happen in p ways, and if all three tasks are independent, then the number of outcomes is
n*m*p. This is called the Fundamental Counting principle.
Formula for the sum of the diagonals in a n-sided polygon
n-3
What other value of "r" in nCr can give you the same answer as nCr? (Ex 10C4 =?)
nC(n-r) 10C6
a²+b²=?
not factorable
4. A perfect square always has an ____ number of factors.
odd
Perpendicular lines have what kind of slopes?
opposite-signed reciprocals of each other
The mean is heavily influenced by _____, while the median is entirely unaffected by them.
outliers
The sides in similar figures are ________
proportional
Any inscribed angle that intercepts the endpoints of a diameter has to be a what?
right angle
The pythagorean theorem only works for what?
right triangles
Slope formula
rise/run = (y2-y1)/(x2-x1)
Most of the cases in which you will have to use the generalized AND rule involves what? [i.e. P(A and B) = P(B) * P(A|B)]
selection without replacement
Two geometric figures with the same shape and different sizes are called______
similar
Mutually exclusive event are most useful for ______ systems, such as what?
simple; dice, coins and cards
What do you do to find the point reflected over y = x
switch x and y
What do you do to find the point reflected over y = - x
switch x and y, and make each the opposite sign
Diagonal of a square
s√2
Space diagonal of a cube
s√3
If all the numbers on a list are the same distance from the mean, then SD = ?
that distance
What is the longest chord of a circle?
the diameter
The longest angle of a triangle is always opposite of what?
the longest side
What does the horizontal axis of a histogram always represent?
the quantitative variable in question
If the sides of the bigger triangle are written in the numerator, then these fractions are greater than one, and this quantity is known as what?
the scale factor (k)
If we know any length in the smaller similar triangle (including altitude), the corresponding length in the larger similar triangle is that original length times what?
the scale factor (k)
The shortest angle of a triangle is always opposite of what?
the shortest side
What is the slope of vertical lines?
undefined
9. How to find the vertex of the parabola?
vertex:(h,k) h=-b/2a then plug in h for x in the equation to find the k
General form for vertical lines
x = K
General form for horizontal lines.
y = K
Standard form of a quadratic equation
y = ax²+bx+c
What is the slope intercept form?
y = mx + b m = slope b = y-intercept
How do you find the number of integers from x to y inclusive?
y-x+1
How do you find the number of integers from x to y exclusive?
y-x-1
What is the slope for horizontal lines?
zero
4. If the divisor is larger than the dividend the integer quotient = ______ and the remainder = _______
zero, the dividend
What is 1/7 in decimal form?
~0.143
Circumference of a circle
πd = 2πr
Area of a circle?
πr²
When to include or not include the negative square root in the GRE?
• If the √ sign is written by the test-maker, written as part of the way the question is asked, then this means: consider positive roots only • If the problem contains a variable squared, or if your calculations lead you to a variable squared, an you yourself have to take a square root as part of solving the equation, then always consider both positive and negative square roots.
Space diagonal of a rectangular solid
√(h²+w²+d²)
