1,141 terms

GRE - MATH

a combination of various GRE quizzes from different Quizlet users whom I find authoritative
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Time per question: Sentence Equivalence
45 seconds
Time per question: Text Completion
30-90 seconds, depending on the number of blanks
Time per question: Reading Comprehension
1 min 30 seconds; plan to complete a short passage (2 questions) in about 3 minutes and a long one (3 questions) in about 4.5 minutes.
Time per question: Quantitative Comparisons
1 min 15 seconds
Time per question: Discrete Quant
2 min
Time per question: Data Interpretation
2 min
Last 30 seconds
Guess the last few questions, leave nothing blank
If you mark a question (to come back) remember to...
Always choose an answer, you can change it later. If you run out of time, at least it isn't left blank.
When taking a practice test...
Always use a timer. Use scrap paper. Take practice tests under standard testing conditions. Never hit the "pause" button.
Study session length of time
Study for no more than 2 hours at a time. Take a break and do something that doesn't require you to learn something new during that time.
Log your mistakes...
Keep a running log of the problems you got wrong. Not the type of problem and why you got it wrong. Find the relevant content in your study guide(s) and note the page # in your log. Try similar problems. Periodically go back through your error log to make sure you learn from your mistakes.
How to read RC Passages
1) Know the point/thesis statement. 2) Keep an eye out for contrast language such as: but, however, although, yet, despite. 3) Understand the purpose of each paragraph 4) Know where to find the details (but you don't need to know them) 5) Take heavily abbreviated notes while you read 6) Include the point, changes in direction, point of paragraphs
Verbal sections: When you have 15 minutes left...
You should be on question 11
Verbal sections: When you have 5 minutes left...
You should be on question 17
Quant sections: When you have 25 minutes left...
You should be on question 7
Quant sections: When you have 15 minutes left...
You should be on question 13
Quant sections: When you have 5 minutes left...
You should be on question 19
Quant sections: Only one math function in your head at a time
As soon as you get to your second function, write it on your scratch paper. Gives you a fighting shot on the hard questions. When your brain is tired, which it will be, you have a better chance at getting the easier questions right.
GRE Helpful Habit # 1
Write down everything! Ex: as soon as you see a Quant Comparison, write: A a b c d B, Write down everything! Ex: as soon as you see a Quant Comparison, write: A a b c d B
GRE Helpful Habit # 2
Don't skip steps! Write out every step. Go slow. Work for accuracy. The GRE is filled with answers which will look correct if you skip steps/writing things out.
GRE Helpful Habit # 3
Read the question (carefully)! The GRE questions are often worded in a tricky way. Be sure your answer actually answers the question.
GRE Helpful Habit # 4
Ballparking- estimate the answer and use POE to get rid of wrong answers. The answer choices are part of the question. Sometimes you don't need an exact answer, you just have to be in the ballpark.
GRE Helpful Habit # 5
Start with the end in mind. For example, if the answer choices are written as fractions, do the math as fractions. Convert percentages, etc to fractions before you do the math. Instead of getting a perfect answer and try to convert into a fraction.
GRE Helpful Habit # 5
Skip early and skip often. Remember you can mark questions (always guess before moving on). Take the "easy" test first, then come back and answer the hard questions.
GRE Helpful Habit # 6
Don't be intimidated! Questions/equations can look large and/or complicated, but often easily broken down into easier parts.
Perfect Squares 1-15
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225
How to recognize if a # is a multiple of 12
The sum of the digits it a multiple of 3 and the last two digits is a multiple of 4. (i.e 144: 1+4+4=9 which is a multiple of 3, and 44 is a multiple of 4, so 144 is a multiple of 12.)
Area of a rectangle
A = length x width
How to recognize a # as a multiple of 9
The sum of the digits is a multiple of 9.
Slope given 2 points
m= (Y1-Y2)/(X1-X2)
Circumference of a Circle
c=2 x pi x r
OR pi x D
Area of a circle
A=pi*(r^2)
Perimeter of a rectangle
P= 2L + 2w
How to recognize a multiple of 6
Sum of digits is a multiple of 3 and the last digit is even.
Volume of a rectangular box
V=Lwh
How to recognize a # as a multiple of 4
The last 2 digits are a multiple of 4. (i.e 144 .... 44 is a multiple of 4, so 144 must also be a multiple of 4.)
How to recognize a # as a multiple of 3
The sum of the digits is a multiple of 3
(i.e. 45 ... 4 + 5 = 9 so the whole thing is a multiple of 3)
Area of a triangle
A= (1/2) b*h
When dividing exponential #s with the same base, you do this to the exponents...
Subtract them.
i.e (5^7)/(5^3)= 5^4
When multiplying exponential #s with the same base, you do this to the exponents...
Add them.
i.e. (5^7) * (5^3) = 5^10
First 10 prime #s
2, 3, 5, 7, 11, 13, 17, 19, 23, 29
A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself
Find distance when given time and rate
d=rt so r= d/t and t=d/r
binomial product of (x+y)(x-y)
x²-y²
factored binomial product of (x+y)²
x²+2xy+y²
factored binomial product of (x-y)²
x²-2xy+y²
binomial product of (x+y)²
(x+y)(x+y)
binomial product of (x-y)²
(x+y)(x-y)
the measure of a straight angle
180°
the slope of a line in y=mx+b
m
Pythagorean theorem
a²+b²=c²
If a is inversely porportional to b, what does it equal?
ab=k
(k is a constant)
#1 What is the relationship between lengths of the sides of a triangle and the measure of the angles of the triangle?
• The longest side is opposite the largest (biggest) angle.
#2 What is the relationship between lengths of the sides of a triangle and the measure of the angles of the triangle?
• The shortest side is opposite the smallest angle.
#3 What is the relationship between lengths of the sides of a triangle and the measure of the angles of the triangle?
• Sides with the same lengths are opposite angles with the same measure.
If y is directly proportional to x, what does it equal?
y/x is a constant
What is a percent?
A percent is a fraction whose denominator is 100.
#1 What is an important property of a 30-60-90 triangle?
• The triangle is a right triangle.
#2 What is an important property of a 30-60-90 triangle?
• The hypotenuse is twice the length of the shorter leg.
#3 What is an important property of a 30-60-90 triangle?
• The ratio of the length of the three sides is x:x√3:2x
The negative exponent x⁻ⁿ is equivalent to what?
1/xⁿ
i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
formula for area of a triangle
A=½bh
formula for volume of a rectangular solid
V=l×w×h
formula for the volume of a cube
V=side³
#1 What are the important properties of a 45-45-90 triangle?
• The triangle is a right triangle.
#2 What are the important properties of a 45-45-90 triangle?
• The triangle is isosceles (AC=BC).
#3 What are the important properties of a 45-45-90 triangle?
• The ratio of the lengths of the three sides is x:x:x√2.
formula for distance problems
distance=rate×time or d=rt
The sum of the angles in a quadrilateral is
360°
The sum of the measures of the n angles in a polygon with n sides
(n-2) x 180
In any polygon, all external angles equal up to
360°
In a Regular Polygon, the measure of each exterior angle
360/n
The consecutive angles in a parallelogram equal
180°
A quadrilateral where two diagonals bisect each other
Parallelogram
In a rectangle, all angles are
Right
In a Rectangle, each angles measures
90°
The Perimeter of a rectangle
P=2(l+w)
The Perimeter of a Square
P=4s (s=side)
Area of a Parallelogram:
A=(base)(height)
(x-y)(x+y)
x²-y²
(x-y)²
x²-2xy+y²
(x+y)²
x²+2xy+y²
An Angle that's 180°
Straight Angle
The sum of all angles around a point
360°
If a pair of parallel lines is cut by a transversal that's not perpendicular, the sum of any acute angle and any obtuse angle is
180
Acute Angle an angle that is less than 90°
Obtuse Angle:angle that is greater than 90° but less than 180°
Distance
(rate)(time) d=rt
Rate
d/t (distance)/(time)
Time
(distance)/(rate) d/r
How do you solve proportions?
a/b=c/d
Cross multiplication
a/b=c/d
4/6=10/15
4(15)=6(10) 60=60
If a lamp increases from $80 to $100, what is the percent increase?
= 25%.
= (actual increase/original amount) x 100%
= 20/80 x 100% = 1/4 x 100% = 25%
The percent decrease of a quantity
= (actual decrease/Original amount) x 100%
If a lamp decreases to $80, from $100, what is the decrease in price?
= (actual decrease/Original amount) x100%
= 20/100x100% = 20%
To increase a number by x%
multiply by 1+x%
i.e. 100 x (1+50%)=100x1.5=150
To decrease a number by x%
multiply by 1-x%
i.e. 100 x (1-50%)=100x.5=50
THE DENOMINATOR CAN NEVER
BE ZERO! 1/∅=null
If a>b then
-a<-b
The reciprocal of any non-zero number is
1/x
Probability of an Event
P(E) = number of favorable outcomes/total number of possible outcomes
If Event is impossible
P(E) = ø
If E is certain
P(E) = 1/1 = 1
Probability of Event all cases
∅≤P(E)≤1
Probability of E not occurring:
1 - P(E)
Circumference of a circle
pi(diameter)
Circumference of a circle
2(pi)r
Area of a circle
(pi)r²
Volume of a rectangular solid
(length)(width)(height)
Volume of a cube
edge³
Vertical lines
Do not have slopes!
Any Horizontal line slope
zero
Slope of any line that goes up from left to right
Positive
Slope of any line that goes down as you move from left to right is
Negative
Slope
y₂-y₁/x₂-x₁
For any number x
Can be negative, zero, or positive
X is the opposite of
-X
3 is the opposite of
-3
The only number that is equal to its opposite
∅ ∅=∅
Product of any number and ∅ is
If a product of two numbers is ∅, one number must be
7 divided by ∅
Null
∅ divided by 7
The product of odd number of negative numbers
Negative
The reciprocal of any non-zero #x is
1/x
The product of any number x and its reciprocal
1
Dividing by a number is the same as multiplying it by its
Reciprocal
∅ Is neither
Positive or Negative
Consecutive integers
x, x+1, x+2
One is (a prime or not?)
NOT A PRIME
Positive integers that have exactly 2 positive divisors are
Prime numbers (2, 3, 5, 7, 11, 13, 17, 19, 23)
∅ Is
EVEN
∅ is a multiple of
Two (∅×2=∅)
∅ is a multiple of
Every number
2 is the only
Even prime number
1
bⁿ
b∧b∧b (where b is used as a factor n times)
2⁵×2³
2⁸
2⁵/2³
(2²)³
2⁶
2³×7³
(2x7)³
∅²
If a is positive, aⁿ is
Positive
If a is negative and n is even then aⁿ is (positive or negative?)
aⁿ is positive
-3²
9
-3³
-27
a(b+c)
ab+ac
a(b-c)
ab-ac
a>b then a - b is positive or negative?
a-b is positive
a<b then a - b is positive or negative?
a-b is negative
If a<b, then
a+c<b+c
∅ is
Even
∅ is
A multiple of every integer
a/∅
Null
1ⁿ
1
1 is a divisor of
every number
1 is the
smallest positive integer
1 is an
ODD number
30 60 90
x, x(SR3), 2x
30 60 90
3, 4, 5
30 60 90
5, 12, 13
30 60 90
3x, 4x, 5x
25^(1/2) or sqrt. 25 =
5 OR -5
Number of degrees in a triangle
180
What are the real numbers?
All the numbers on the number line (negative, rational, irrational, decimal, integer). All the numbers on the GRE are real. (-2, 1, .25, 1/2, pi)
What are the rational numbers?
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2, 1, .25, 1/2)
What are the irrational numbers?
All real numbers which can't be expressed as a ratio of two integers, positive and negative (pi, -sqrt3)
What are the integers?
All numbers multiples of 1.
1/2 divided by 3/7 is the same as
1/2 times 7/3
A number is divisible by 3 if ...
the sum of its digits is divisible by 3.
A number is divisible by 4 is...
its last two digits are divisible by 4.
A number is divisible by 6 if...
its divisible by 2 and by 3.
A number is divisible by 9 if...
the sum of digits is divisible by 9.
10<all primes<20
11, 13, 17, 19
20<all primes<30
23, 29
30< all primes<40
31, 37
40 < all primes<50
41, 43, 47
50 < all primes< 60
53, 59
60 < all primes <70
61, 67
70 < all primes< 80
71, 73, 79
1/8 in percent?
12.5%
1/6 in percent?
16.6666%
3/8 in percent?
37.5%
5/8 in percent?
62.5%
7/8 in percent?
87.5%
5/6 in percent?
83.333%
x^4 + x^7 =
x^(4+7) = x^11
x^6 / x^3
x^(6-3) = x^3
(x^2)^4
x^(2(4)) =x^8 = (x^4)^2
a^0 =
1
0^0
undefined
Can you add sqrt 3 and sqrt 5?
No, only like radicals can be added.
Can you subtract 3sqrt4 from sqrt4?
Yes, like radicals can be added/subtracted.
(6sqrt3) x (2sqrt5) =
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
(12sqrt15) / (2sqrt5) =
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
Can you simplify sqrt72?
Yes, because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
10^6 has how many zeroes?
6
To multiply a number by 10^x
move the decimal point to the right x places
What does scientific notation mean?
Expressing a number as the product of a decimal between 1 and 10, and a power of 10.
Define a "term",
A term is a numerical constant or the product (or quotient) of a numerical constant and one or more variables. (3x, 4x^2 and 2a/c)
Define an "expression".
An algebraic expression is a combination of one of more terms. Terms in an expression are separated by either addition or subtraction signs. (3xy, 4ab, -5cd, x^2 + x - 1)
Define a "monomial"
An expression with just one term (-6x, 2a^2)
a^2 - b^2 =
(a - b)(a + b)
a^2 + 2ab + b^2
(a + b)^2
Solve the quadratic equation ax^2 + bx + c= 0
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
If an inequality is multiplied or divided by a negative number....
the direction of the inequality is reversed.
What is the "domain" of a function?
The set of input values for a function.
What is the "range" of a function?
The set of output values for a function.
What is the order of operations?
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
What is the sum of the angles of a triangle?
180 degrees
Factor a^2 + 2ab + b^2
(a + b)^2
a^2 - 2ab + b^2
(a - b)^2
a^2 - b^2
(a - b)(a + b)
What is the "range" of a series of numbers?
The greatest value minus the smallest.
How to determine percent decrease?
(amount of decrease/original price) x 100%
Area of a triangle?
(base*height) / 2
What is an isoceles triangle?
Two equal sides and two equal angles.
Circumference of a circle?
Diameter(Pi)
How to find the circumference of a circle which circumscribes a square?
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
When does a function automatically have a restricted domain (2)?
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
The larger the absolute value of the slope...
the steeper the slope.
What is the slope of a horizontal line?
0
What is the slope of a vertical line?
Undefined, because we can't divide by 0.
What are "supplementary angles?"
Two angles whose sum is 180.
If the two sides of a triangle are unequal then the longer side.................
lies opposite the greater angle
What is a chord of a circle?
A chord is a line segment joining two points on a circle.
What is a central angle?
A central angle is an angle formed by 2 radii.
What is a tangent?
A tangent is a line that only touches one point on the circumference of a circle.
Pi is a ratio of what to what?
Pi is the ratio of a circle's circumference to its diameter.
Formula to find a circle's circumference from its diameter?
C = (pi)d
Formula to find a circle's circumference from its radius?
C = 2(pi)r
What is an arc of a circle?
An arc is a portion of a circumference of a circle.
What is a minor arc?
The shortest arc between points A and B on a circle's diameter.
What is a major arc?
The longest arc between points A and B on a circle's diameter.
Formula to calculate arc length?
Arc length = (n/360) x pi(2r) where n is the number of degrees.
Formula for the area of a circle?
A = pi(r^2)
Formula for the area of a sector of a circle?
Sector area = (n/360) X (pi)r^2
What is the "solution" for a system of linear equations?
The point of intersection of the systems.
What is the "solution" for a set of inequalities.
The overlapping sections.
What is it called when a point is reflected to the quadrant opposite it (i.e. I to III or II to IV)?
A reflection about the origin.
What is the graph of f(x) shifted upward c units or spaces?
f(x) + c
What is the graph of f(x) shifted downward c units or spaces?
f(x) - c
What is the graph of f(x) shifted left c units or spaces?
f(x + c)
What is the graph of f(x) shifted right c units or spaces?
f(x-c)
What are complementary angles?
Two angles whose sum is 90.
What are congruent triangles?
Triangles with same measure and same side lengths.
Legs: 3, 4. Hypotenuse?
5
Legs 6, 8. Hypotenuse?
10
Legs 5, 12. Hypotenuse?
13
Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
2 & 3/7
8.84 / 5.2
1.7
Evaluate 4/11 + 11/12
1 & 37/132
Evaluate 3& 2/7 / 1/3
9 & 6/7
200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
3
What number between 70 & 75, inclusive, has the greatest number of factors?
72
What are the smallest three prime numbers greater than 65?
67, 71, 73
Which is greater? 64^5 or 16^8
16^8
64^5 = (4^3)^5 = 4^15
16^8=(4^2)^8 = 4^16
Evaluate (4^3)^2
4096
Write 10,843 X 10^7 in scientific notation
1.0843 X 10^11
True or false? 4.809 X 10^7 = .0004809 X 10^11
True
If a=-1 and b=3, what is the value of (4(a^3)(b^2) - 12(a^2)(b^5)) / (16(a^3)(b^2))?
20.5
T or F? Given d,e &f =/ 0, [(d^3)e(f^5)] / 2d(e^3) / [3(d^2)(e^3)(f^7)] / [6(e^5)(f^2)]?
True
Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
2sqrt6
Simplify 9^(1/2) X 4^3 X 2^(-6)?
3
5 bakeries sell an average of 300 muffins per bakery per day. If 2 stop making muffins but the total muffins sold stays the same, what is the average of muffins per bakery sold among the remaining?
500
Reduce: 4.8 : 0.8 : 1.6
6 : 1 : 2
Ratio of ages of Anna and Emma is 3:5 and of Emma and Nicolas is 3:5. What is the ratio of Anna to Nicholas' ages?
9 : 25
What percent of 40 is 22?
55%
Convert 0.7% to a fraction.
7 / 1000
Hector invested $6000. Part was invested in account with 9% simple annual interest, and the rest in account with 7% simple annual interest. If he earned $490 in the first year of these investments, how much did he invest in each account?
$3,500 in the 9% and $2,500 in the 7%.
Employee X is paid 19.50 per hour no matter how many a week. Employee Y earns 18 for the first 40 and 1.5 the hourly wage for every hour after that. If both earned the same amount and worked the same in one week, how many did each work?
48
The perimeter of a square is 48 inches. The length of its diagonal is:
12sqrt2
If Madagascar's exports totaled 1.3 billion in 2009, and 4% came from China, what was the value in millions of the country's exports to China?
52
Whats the difference between factors and multiples?
Factors are few, multiples are many.
How many multiples does a given number have?
Infinite.
P and r are factors of 100. What is greater, pr or 100?
Indeterminable.
If r, t, s & u are distinct, consecutive prime numbers, less than 31, which of the following could be an average of them (4, 4.25, 6, 9, 24, 22, 24)
4.25, 6, 22
Is 0 even or odd?
Even
How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
0
What are the roots of the quadrinomial x^2 + 2x + 1?
The two xes after factoring.
Factor x^2 - xy + x.
x(x - y + 1)
Simplify the expression [(b^2 - c^2) / (b - c)]
(b + c)
Simplify (a^2 + b)^2 - (a^2 - b)^2
4a^2(b)
What is the common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd?
cd
Simplify the expression (p^2 - q^2)/ -5(q - p)
(p + q)/5
What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
2
(a^-1)/a^5
1/a^6
x^2 = 9. What is the value of x?
3, -3
6w^2 - w - 15 = 0
-3/2 , 5/3
5x^2 - 35x -55 = 0
[(7+ sqrt93) /2], [(7 - sqrt93) / 2]
If 10800 is invested at a simple interest rate of 4%, what is the value of the investment after 18 months?
$11,448
If 4500 is invested at a simple interest rate of 6%, what is the value of the investment after 10 months?
4725
What is the maximum value for the function g(x) = (-2x^2) -1?
-1
For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
-8
What transformation occurs if point C is reflected over the x-axis and then the y-axis?
A reflection about the axis.
The four angles around a point measure y, 2y, 35 and 55 respectively. What is the value of y?
90
For similar triangles, the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
What is the ratio of the sides of an isosceles right triangle?
1:1:sqrt2
1:1:sqrt2 is the ratio of the sides of what kind of triangle?
An isosceles right triangle.
What is the ratio of the sides of a 30-60-90 triangle?
1:sqrt3:2
1:sqrt3:2 is the ratio of the sides of what kind of triangle?
A 30-60-90 triangle.
What is the side length of an equilateral triangle with altitude 6?
4sqrt3. The triangle can be divided into two equal 30-60-90 triangles with side 6 as the side in which 6 = xsqrt3. So x =2sqrt3...
In a triangle where the two legs are 4 and 3, what is the value of a line directly intersecting the middle coming from the meeting point of the two legs?
2.4. We calculate the area (6) and then turn the triangle on its side and use x as the height to calculate again. (5x)/2=6
Describe the relationship between 3x^2 and 3(x - 1)^2
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
Describe the relationship between the graphs of x^2 and (1/2)x^2
The second graph is less steep.
Suppose that the graph of f(x) is the result of stretching y=x + 5 away from the x-axis by a factor of 2. What is the new equation for the graph f(x)?
y = (x + 5)/2
Suppose that the graph of f(x) is the result of sliding the graph of y=2x^2 down 3 units of spaces. What is the new equation?
y = 2x^2 - 3
How many sides does a hexagon have?
6
What is an exterior angle?
An angle which is supplementary to an interior angle.
What is the measure of an exterior angle of a regular pentagon?
72
The ratio of the areas of two similar polygons is ...
... the square of the ratios of the corresponding sides.
In similar hexagons, the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
4:5
What is the area of a regular hexagon with side 6?
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
13pi / 2
A cylinder has a surface area of 22pi. If the cylinder has a height of 10, what is the radius?
1
What is the third quartile of the following data set: 44, 58, 63, 63, 68, 70, 82
70
If the 80th percentile of the measurements is 72degrees, about how many measurments are between 69 degrees and 72 degrees? Round your answer to the nearest tenth
18
The objects in a set are called two names:
members or elements
What are the members or elements of a set?
The objects within a set.
What is a finite set?
A set with a number of elements which can be counted.
What is the name of set with a number of elements which cannot be counted?
An infinite set.
What is a subset?
a grouping of the members within a set based on a shared characteristic.
What is the name for a grouping of the members within a set based on a shared characteristic?
A subset.
What is the empty set?
A set with no members, denoted by a circle with a diagonal through it.
What is a set with no members called?
the empty set, denoted by a circle with a diagonal through it.
What is the "union" of A and B?
The set of elements which can be found in either A or B.
What is the set of elements which can be found in either A or B?
The union of A and B.
What is the intersection of A and B?
The set of elements found in both A and B.
What is the set of elements found in both A and B?
The interesection of A and B.
If you have a set of n objects, but you only want to order k of them, what formula do you use to determine the number of permutations?
n! / (n-k)!
Suppose you have a set of n objects, and you want to select k of them, but the order doesn't matter. What formula do you use to determine the number of combinations of n objects taken k at a time?
n! / (k!)(n-k)!
How many 3-digit positive integers are even and do not contain the digit 4?
288 (8 9 4)
From a box of 12 candles, you are to remove 5. How many different sets of 5 candles could you remove?
12! / 5!7! = 792
There are 10 finalists for the school spelling bee. A first, second, and third place trophy will be awarded. In how many ways can the judges award the 3 prizes?
10! / (10-3)! = 720
There are 10 finalists for the school spelling bee. A first, second, and third place trophy will be awarded. How many different people can get the three prizes?
10! / 3!(10-3)! = 120
A company places a 6-symbol code on each product. The code consists of the letter T, followed by 3 numerical digits, and then 2 consonants (Y is a conson). How many codes are possible?
441000 = 1 * 10 * 10 10 10 = 1 * 10 * 10 * 10 * 21 * 21
Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
2^9 / 2 = 256
Find the surface area of a cylinder with radius 3 and height 12.
90pi
What is the surface area of a cylinder with radius 5 and height 8?
130pi
A cylinder has surface area 22pi. If the cylinder has a height of 10, what is its radius?
1
What is the ratio of the surface area of a cube with an edge of 10 to the surface area of a rectangular solid with dimensions 2, 4, and 6?
75:11
A brick with dimensions 10. 15 and 25 weighs 1.5 kg. A second brick (same density) has dimensions 12, 18, and 30. What is the weight of the second brick?
2.592 kg
If 8 schools are in a conference, how many games are played if each team plays each other exactly once?
28. n = 8, k = 2. n! / k!(n-k)!
Which is greater? 27^(-4) or 9^(-8)
27^(-4)
Which is greater? 200x^295 or 10x^294?
Relationship cannot be determined (what if x is negative?)
abate
to decrease; reduce
abdicate
to give up a position, right, or power
aberrant
deviating from what is normal
abeyance
temporary suppression or suspension
abject
miserable; pitiful
abjure
to reject; abandon formally
abscission
the act of cutting; the natural separation of a leaf or other part of a plant
abscond
to depart secretly
abstemious
moderate in appetite
abstinence
the giving up of certain pleasures
abysmal
very bad
accretion
growth in size or increase in amount
accrue
to accumulate; grow by additions
adamant
uncompromising; unyielding
adjunct
something added, attached, or joined
admonish
to caution or reprimand
adulterate
to corrupt or make impure
aesthetic
relating to beauty or the arts
affected
pretentious; phony
affinity
fondness; liking; similarity
aggrandize
to make larger or greater
aggregate
amounting to a whole; total
alacrity
cheerful willingness; eagerness; speed
alchemy
medieval chemical philosophy based on changing metal into gold; a seemingly magical power or process of transmutation
allay
to lessen; ease; soothe
alleviate
to relieve; improve partially
alloy
a combination; a mixture of two or more metals
allure
the power to entice by charm
amalgamate
to combine into a unified whole
ambiguous
unclear or doubtful in meaning
ambivalence
the state of having conflicting emotional attitudes
ambrosia
something delicious; the food of the gods
ameliorate
to improve
amenable
agreeable; cooperative; suited
amenity
something that increases comfort
amulet
ornament worn as a charm against evil spirits
anachronism
something out of the proper time
analgesic
medication that reduces or eliminates pain
analogous
comparable
anarchy
absence of government; state of disorder
anodyne
something that calms or soothes pain
anomalous
irregular; deviating from the norm
antecedent
something that comes before
antediluvian
prehistoric
antipathy
dislike; hostility
apathy
indifference
apex
the highest point
apogee
the point in an orbit most distant from the body being orbited; the highest point
apothegm
a terse, witty saying
appease
to calm, pacify, placate
appellation
name
apposite
strikingly appropriate and relevant
apprise
to inform
approbation
praise, approval
appropriate
to take possession of for one's own use; confiscate
apropos
relevant
arabesque
ornate design featuring intertwined curves; a ballet position in which one leg is extended in back while the other supports the weight of the body
archeology
the study of material evidence of past human life
ardor
great emotion or passion
arduous
extremely difficult; laborious
argot
a specialized vocabulary used by a group
arrest
to stop; to seize
artifact
item made by human craft
artless
guileless; natural
ascetic
one who practices self-denial
asperity
severity; harshness; irritability
aspersion
slander; false rumor
assiduous
diligent; hard-working
assuage
to make less severe
astringent
harsh; severe
asylum
place of refuge or shelter
atavism
in biology, the reappearance of a characteristic in an organism after several generations of absence; individual or a part that exhibits atavism; return of a trait after a period of absence
attenuate
to weaken
audacious
bold; daring
austere
stern; unadorned; simple
autonomous
self-governing; independent
avarice
greed
aver
to affirm; declare to be true
avocation
secondary occupation
avuncular
like an uncle, benevolent and tolerant
axiomatic
taken for granted; self-evident truth
bacchanalian
pertaining to riotous or drunken festivity; pertaining to revelry
banal
commonplace; trite
banter
playful conversation
bard
poet
bawdy
obscene
beatify
to sanctify; to bless; to ascribe a virtue to
bedizen
to dress in a vulgar, showy manner
behemoth
huge creature; anything very large and powerful
belie
to contradict; misrepresent; give a false impression
beneficent
kindly; doing good
bifurcate
to divide into two parts
blandishment
flattery
blase
bored because of frequent indulgence; unconcerned
bolster
to give a boost to; prop up; support
bombastic
pompous; using inflated language
boorish
rude; insensitive
bovine
cowlike
brazen
bold; shameless
broach
to mention for the first time
bucolic
characteristic of the countryside; rustic; pastoral
burgeon
to grow and flourish
burnish
to polish
buttress
to reinforce; support
cacaphonous
unpleasant or harsh-sounding
cadge
to beg; sponge
callous
thick-skinned; insensitive
calumny
false and malicious accusation; slander
canard
false; deliberately misleading story
canon
an established set of principles; a basis or standard for judgment; a group of literary works
cant
insincere talk; language of a particular group
cantankerous
irritable; ill-humored
capricous
fickle
captious
faultfinding; intended to entrap, as in an argument
cardinal
of foremost importance
carnal
of the flesh or body; related to physical appetities
carping
to find fault; complain
cartography
science of making maps
caste
any of the hereditary social classes in Hindu society; social stratification
castigation
punishment; chastisement; criticism
cataclysm
a violent upheaval that causes great destruction and change
catalyst
something that causes change
categorical
absolute; without exception
caucus
smaller group within an organization
causal
involving a cause
caustic
burning; stinging; causing corrosion
celestial
concerned with sky or heavens; sublime
centrifugal
moving away from a center
centripetal
moving or directed toward a center
champion
to defend or support
chasten
to correct by punishment or reproof; to restrain or subdue
chicanery
trickery; fraud
chivalry
the qualities idealized by knighthood such as bravery and gallantry toward women
churlish
rude; boorish
circuitous
roundabout
clamor
noisy outcry
clique
a small, exclusive group
cloister
to confine; seclude
coagulate
thicken; congeal
coalesce
to cause to become one
coda
concluding part of a literary or musical composition; something that summarizes or concludes
codify
to systematize
cognizant
informed; conscious; aware
collage
artistic composition of materials pasted over a surface; an assemblage of diverse elements
commensurate
proportional
compendium
brief, comprehensive summary
complacent
self-satisfied
complaisant
overly polite; willingness to comply with the wishes of others
complement
something that completes or makes up a whole
compliant
yielding
compunction
uneasiness caused by guilt
concave
curving inward
conciliatory
overcoming distrust or hostility
concoct
to invent
concomitant
existing concurrently
condone
to overlook voluntarily; forgive
confound
to baffle; perplex; mix up
congenial
similar in tastes and habits; friendly; suited to
conjugal
pertaining to marriage agreement
connoisseur
expert in matters of taste; expert knowledge or training
conscript
a person compulsorily enrolled for military service
consecrate
to declare sacred
contend
to assert
contentious
quarrelsome; causing quarrels
contiguous
touching; neighboring; connecting without a break
continence
self-control; abstention from sexual activity
contrite
very sorrowful for a wrong; seeking forgiveness
contumacious
disobedient; rebellious
conundrum
riddle; puzzle with no solution
convention
practice widely observed in a group; custom; accepted technique or device
converge
to approach; come together; tend to meet
convex
curved outward
convivial
sociable
convoluted
twisted; complicated
copious
abundant; plentiful
coquette
woman who flirts
cornucopia
horn overflowing with fruit and grain; state of abundance
cosmology
study of the universe as a totality; theory of the origin and structure of the universe
covert
hidden; secret
covetous
desiring something owned by another
cozen
to mislead by trick or fraud; decieve
craven
cowardly
credence
acceptance of something as true
credo
statement of belief or principle; creed
daunt
to discourage; intimidate; dishearten
dearth
scarcity
debauchery
corruption
decorum
proper behavior
defame
to malign; harm someone's reputation
default
to fail to act
deference
respect; regard for another's wish
defunct
no longer existing
delineate
to represent or depict
demographic
related to population balance
demotic
pertaining to people
demur
to express doubt; question or oppose
denigrate
to slur someone's reputation
denizen
an inhabitant; a regular visitor
denouement
outcome; unraveling of the plot of a play or work of literature
clairvoyant
one who can predict the future; psychic
deride
to mock
derivative
something derived; unoriginal
desiccate
to dry completely
desuetude
state of disuse
desultory
random; disconnected; rambling
deterrent
something that discourages or hinders
detraction
the act of taking away
diaphanous
transparent; vague; insubstancial
diatribe
bitter verbal attack
dichotomy
division into two usually contradictory parts
diffidence
shyness; lack of confidence
diffuse
to spread out
digression
act of straying from the main point
dirge
funeral hymn
disabuse
free from a misconception
discerning
perceptive; exhibiting keen insight and good judgement
discomfit
to make uneasy; disconcert
discordant
not in tune
discredit
to dishonor; disgrace
discrepancy
difference between
discrete
constituing a separate thing; distinct
discretion
quality of showing self-restraint in speech or actions
disingenuous
not candid, crafty
disinterested
unpredujiced; objective
disjointed
lacking order or coherence; dislocated
dismiss
put away from consideration; reject
disparage
to belittle
disparate
dissimilar
dissemble
to pretend; disguise one's motives
disseminate
to spread; scatter; disperse
dissolution
disintegration;debauchery
dissonance
discord; lack of harmony
distend
to expand; swell out
distill
extract the essential elements
distrait
inattentive; preoccupied
diverge
to vary; go in different directions from the same point
divest
to strip; deprive; rid
divulge
to make known something that is secret
document
to provide with written evidence to support
doggerel
poor verse
dogmatic
stating opinions without proof
dormant
inactive
dross
waste; worthless matter
dupe
to deceive; trick
ebullient
exhilarated; overly enthusiastic
eclectic
selecting from various sources
effervescence
state of high spirits or liveliness; process of bubling as gas escapes
effete
depleted of vitality; overrefined; decadent
dissident
person who disagrees about beliefs
doctrinaire
dogmatic; unyielding
efficacy
effectiveness; efficiency
effrontery
shameless boldness; presumptuousness
egoism
the tendency to see things in relation to oneself; self-centeredness
egotistical
excessively self-centered; conceited
elegy
poem or song expressing lamentation
elicit
to provoke; draw out
elixir
a sustance believed to have the power to cure ills
Elysian
delightful; blissful
emaciated
thin and wasted
embellish
to adorn; enhance
emollient
soothing; mollifying
empirical
derived from observation or experiment
emulate
to imitate; copy
encomium
a formal expression of praise
endemic
inherent; belonging to an area
enervate
to weaken
engender
to cause; produce
enhance
to increase; improve
entomology
the scientific study of insects
enunciate
to pronounce clearly
ephemeral
short-lived; fleeting
epistemology
branch of philosophy tha texamines the nature of knowledge
equable
steady; unvarying; serene
equanimity
composure; calmness
equivocate
intentionally use vague language
errant
mistaken; straying from the proper course
erudite
learned; scholarly
esoteric
hard to understand; known only to a few
essay
to make an attempt; subject to a test
estimable
admirable; possible to estimate
ethnocentric
based on the attitude tha one's group is superior
etiology
causes or origins
etymology
origin an history of a word
eugenics
study of factors that influence the hereditary qualities of the human race and ways to improve those qualities
eulogy
high praise to a death person
euphemism
use of agreeable or inoffensive language in place of offensive language
euphoria
feeling of extreme happiness
euthanasia
mercy killing
evince
to show plainly; be an indication of
evocative
tending to call to mind or produce a reaction
exacerbate
to aggravate; make worse
exact
to force the payment of; demand and obtain by authority
exculpate
to clear of blame; vindicate
execrable
detertable; abhorrent
exhort
to urge by strong appeals
exigency
crisis; urgent requirements
existential
having to do with existence
exorcise
to expel evil spirits; free from bad influences
expatiate
to speak or write at length
expatriate
to send into exile
expiate
to atone for
explicate
to explain;interpret;clarify
expository
explanatory
extant
in existence; not lost
extemporaneous
unrehearsed
extirpate
to root up; to destroy
extraneous
not essencial
extrapolation
the act of estimation by projecting known information
extrinsic
not inherent of essential
facetious
homorous
facilitate
to make less difficult
factotum
a person who does all sorts of work; a handyman
fallacious
based on a false idea or fact; misleading
fallow
plowed but not sowed; uncultivated
fatuous
foolishly self-satisfied
fauna
animals of a period o region
fawning
seeking flavor by flattering
felicitous
suitable expressed; wee-chose; appropiate
feral
existing in a wild or untamed state
fervor
warmth and intensity of emotion
fetid
having a bad smell
fetter
to bind; confine
fiat
arbitray order; authorization
fidelity
loyalty; exact correspondence
filibuster
use of obstructive tactics in a legislature to block passage of a law
finesse
to handle with a deceptive or evasive strategy; refined in performance
fissure
crevice
flag
to droop; grow weak
fledging
beginner; novice
flora
plants of a region or era
flourish
en embellishment or ornamentation
flout
to treat scornfully
flux
flowing; a continuous moving
foment
to incite; arouse
forbearance
patience
forestall
to prevent; delay
formidable
menacing; threatening
forswear
renounce; repudiate
founder
to sink; fail; colapse
fracas
a loud quarrel; brawl
fractious
quarrelsome; unruly; rebellious
fresco
a painting done on plaster
frieze
ornamental band on a wall
froward
stubbornly contrary; obstinately disobedient
frugality
thrift
fulminate
to attack loudly; denounce
fulsome
so excessive as to be disgusting
fusion
union; synthesis
futile
ineffective; useless; fruitless
florid
ruddy; reddish; flowery
gainsay
to deny; dispute; oppose
gambol
to frolic; leap playfully
garrulous
very talkative; wordy
gauche
coarse and uncouth; clumsy
geniality
cheerfulness; kindliness; sociability
gerrymander
to divide an area into voting districts in a way that favors a political party
glib
fluent in an insincere way; offhand
goad
to prod; urge on
gossamer
sheer; light and delicate; like cobwebs
gouge
to tear out; scoop out; overcharge
grandiloquent
pompous; bombastic
gregarious
outgoing; sociable
grouse
to complain
guileless
free of cunning or deceit; artless
guise
outward appearance; false appearance
gullible
easily deceived
gustatory
affecting the sense of taste
halcyon
calm and peaceful; happy; golden; prosperous
hallowed
holy; sacred
harangue
long, pompous speech; tirade
harrowing
extremely distressing; terrifying
herbivorous
an animal that feeds mainly on plants
hermetic
tighly sealed; magical
heterodox
not widely accepted
hieroglyphics
a system of writing in which pictorial symbols represent meanings or sounds; wirting or symbols that are difficult to decipher
hirsute
covered with hair
histrionic
relating to exaggerated emotional behavior calculated for effect; theatrical acts or performances
homeostasis
automatic maintenance by an organism in balance with itself
homily
sermon; tedious moralizing lecture
homogeneous
composed of identical parts; uniform in composition
hyperbole
purposeful exaggeration for effect
iconoclastic
attacking cherished traditions
idolatry
idol worship; blind or excessive devotion
igneous
produced by fire; volcanic
imbroglio
complicated situation; an entanglement
immutable
inchangeable
impair
to damage; injure
impassive
showing no emotion
impecunious
poor; having no money
impede
to hinder; block
impermeable
impossible to permeate
imperturbable
not easily disturbed
impervious
incapable of being affected; impossible to penetrate
impinge
to strike; encroach
implacable
inflexible; incable of being pleased or calmed down
implausible
unlikely; unbelievable
implicit
implied; understood but not stated
implode
collapse inward violently
imprecation
curse; damnation
impute
to attribute the fault to; relate to a particular cause or source
inadvertenly
carelessly; unintentionally
incarnate
having bodily form
inchoate
imperfectely formed or formulated
incongruity
state of not fitting
inconsequencial
insgnificant; unimportant
incorporate
introduce something into another thing already in existence
incursion
sudden invasion
indeterminate
uncertain; indefinite
indigence
poverty
indolent
habitually lazy; idle
ineluctable
not to be avoided or escaped; inevitable
inert
unable to move; sluggish
ingenous
naive and trusting; lacking sophistication
inherent
firmly established by nature or habit
innocuous
harmless
insensible
unconscious; unresponsive
insinuate
to suggest; say indirectly; imply
insipid
lacking in flavor; dull
insouciant
indifferent; lacking concern or care
insularity
narrow-mindedness; isolation
insuperable
insurmountable; unconquerable
intangible
not material
interdict
to forbid; prohibit
internecine
deadly to both sides
interpolate
to insert; change by adding new words or material
interregnum
interval between reigns; gap in continuity
intimate
marked by close acquaintance
intractable
not easily managed
intransigence
stubbornness; refusal to compromise
introspective
contemplating one's own thoughts and feelings
inundate
to cover with water, overwhelm
inured
hardened; accustomed; used to
invective
verbal abuse
inveigh
to disapprove; protest vehemently
inveigle
to win over by flattering or coaxing
inveterate
confirmed; long standing
invidious
likely to provoke ill will
irascible
easily angered
irresolute
unsure of how to act; weak
itinerant
wandering from place to place; unsettled
itinerary
route of a traveler's journey
jaundiced
havind a yellowish discoloration of the skin; affected by envy
jibe
to be in agreement
jocose
fond of joking; jocular
juggernaut
huge froce destrying everything in its path
junta
group of people united in political intrigue
juxtapose
place side by side
kudos
fame; glory; honor
labile
likely to change
laconic
using few words
lambaste
to trash verbally or physically
lascivious
lustful
lassitude
lethargy; sluggishness
latent
dormant; potential not apparent
laud
praise
lethargic
inactive
levee
en embankment that prevents a river from overflowing
levity
light manner or attitude
liberal
tolerant; broad-minded
libertine
one without moral restraint
libido
sexual desire
lilliputian
extremely small
limn
to draw, describe
limpid
clear; transparent
linguistic
pertaining to language
litany
lengthy recitation; repetitive chant
literati
scholarly of learned persons
litigation
legal proceedings
log
record of a voyage; record of daily activities
loquacious
talkative
lucid
bright; clear; intelligible
lucre
money or profits
luminous
bright; brilliant; glowing
lustrous
shining
machiavellian
crafty; double-dealing
machinations
plots or schemes
maelstrom
whirpool; turmoil
magnaminity
generosity; nobility
malign
to speak evil of
malinger
to feign illness to escape duty
malleable
capable of being shaped by pounding; impressionate
maverick
dissenter
megalomania
delusions of power or importance
menagerie
a variety of animals kept together
mendacious
dishonest
mendicant
beggar
meretricious
gaudy; specious; flasely attractive
mesmerize
to hypnotize
metamorphosis
change; transformation
metaphysics
a branch of philosophy tha tinvestigates the ultimate nature of reality
metereological
concerned with the weather
meticulous
very careful; picky; fastidious
mettle
courage; endurance
mettlesome
full of courage and fortitude
microcosm
a small system having analogies to a larger system
militate
to work against
minatory
threatening; menacing
minuscule
very small
minutia
petty details
misanthrope
one who hates humanity; one who dislikes others
miscellany
mixture of writtings on various subjects
miscreant
villain; criminal
misogynist
one who hates women
mitigate
alleviate; to become less severe
mnemonic
realated to memory; assisting memory
modicum
limited quantity
mollify
to soothe
monolithic
solid and uniform; constituing a single, unified whole
morose
ill-humored; sullen
motley
many colored; made up of many parts
multifarious
diverse
mundane
worldy as opposed to spiritual; concerned with the ordinary
necromancy
black magic
negate
to cancel out; nullify
neologism
new word or expression
neophyte
novice; beginner
nexus
a means of connection; a center
nonplussed
bewildered
nostalgia
sentimental longing for a past time
nostrum
medicine or remedy of doubtful effectiveness
nugatory
trifling; invalid
obdurate
stubborn
obsequious
overly submissive
obsequy
funeral ceremony
obviate
to make unnecessary; to anticipate and prevent
occlude
to shut; block
occult
relating to practices connected with supernatural phenomena
odyssey
a long, adventurous voyage; a quest
officious
too helful; meddlesome
olfactory
concerning the sense of smell
oligarchy
form of government in which power belongs to only a few leaders
onerous
burdensome
onomatopeia
formation or use of words that imitate sounds of the actions they refer to
opprobium
public disgrace; contempt
ornithologist
scientist who studies birds
oscillate
to move back and forth
ostentatious
showy; pretentious
overweening
presumptuous; arrogant
paean
song of joy or triumph; a fervent expression of joy
paleonthology
study of past geological eras through fossil remains
pallid
lacking color or liveliness
panegyric
elaborate praise; formal hymn of praise
paragon
model of perfection or excellence
partisan
one-sided; committed to a party, group or cause
pathological
departing from normal condition
patois
jargon; a regional dialect
paucity
scarcity
pedantic
showing off learning
pellucid
transparent; easily understood
penchant
inclination
penury
extreme poverty
peregrination
wandering from place to place
peremptory
imperative; leaving no choice
perennial
present throughout the years; persistent
perfidious
faithless; disloyal; untrustworthy
perfunctory
superficial; performed really as a duty
perigee
point in an orbit that is closest to the earth
permeable
penetrable
perturb
to disturb greatly; make uneasy or anxious
pervasive
spread throughout every part
petulant
rude; peevish
phlegmatic
unemotional; calm in temperament
phoenix
anything that is restored after suffering great destruction
physiognomy
facial features
piety
devoutness
piquant
pleasantly pungent; attractive
pique
fleeting feeling or hurt pride
placate
soothe; pacify
placid
calm
plaintive
melancholy; mournful
plasticity
pliability; condition of being able to be shaped or formed
platitude
stale; overused expression
platonic
spiritual; theoretical
plethora
excess; overabundance
plumb
to examine deeply; determine the depth
plummet
to fall; plunge
plutocracy
society ruled by the wealthy
porous
full of holes; permeable to liquids
poseur
poerson who affects an attitude to impress others
pragmatic
practical
prate
to talk idly; chatter
prattle
meaningless, foolish talk
preamble
preliminary statement
precarious
uncertain
precept
principle; law
precipitate
to cause to happen; throw down from a height
precipitate
rash; hasty; sudden; done without deliberation
precursor
forerunner; predecessor
preempt
to supersede; appropiate for oneself
prehensile
capable of grasping
premonition
forewarning; presentiment
presage
to foretell; indicate in advance
presumptuous
rude; improperly bold
preternatural
supernatural; beyond the normal use of nature
prevaricate
to quibble; evade the truth
primordial
original; existing from the beginning
pristine
untouched; uncorrupted
probity
honesty; high-mindness
problematic
posing a problem; doubtful
prodigal
wasteful; extravagant; lavish
profound
deep, not superficial
prohibitive
so high as to prevent the purchase or use of, forbidding
proliferate
to increase rapidly
propensity
inclination, tendency
propitiate
to win over, appease
propriety
correct conduct, fitness
proscribe
to condemn, forbid, outlaw
provident
providing for future need, frugal
puissant
powerful
punctilious
careful in observing rules fo behavior
pungent
penetrating, caustic, to the point
pusillanimous
cowerdly
purport
to profess, suppose, claim
quagmire
marsh, difficult situation
quail
to cower, lose heart
qualified
limited, restricted
qualm
sudden feeling of faintness or nausea
query
question
quibble
to argue over insignificant and irrelevant details
quiescent
inactive, still
quorum
number of memeber necessary to conduct a meeting
raconteur
witty, skillful storyteller
rail
to scold with bitter or abusive language
raiment
clothing
ramification
implication, consequence
rarefied
refined
rationale
fundamental reason
rebu
puzzle in whic pictures or symbols represent words
recalcitrant
resisting authority or control
recant
retract a statement of opinion
recluse
person who lives in seclusion and often in solitude
recondite
abstruse, profound
redoubtable
formidable, arousing fear
refractory
stubborn, resisting ordinary methods of treatment
refulgent
brightly shining, resplendent
refute
to contradict, disprove
regale
to entertain
relegate
to consign to an inferior position
remonstrate
to object or protest
renege
to go back on one's word
reparation
amends, compensation
repine
fret, complain
reprise
repetition, especially of a piece of music
reproach
to find fault with, blame
reprobate
morally unprincipled person
repudiate
to reject as having no authority
rescind
to cancel
resolution
determination, resolve
resolve
determination, firmness of purpose
reticent
nor speaking freely, reserved, reluctant
reverent
expressing deep respect, worshipful
riposte
retaliatory action or retort
rococo
excessively ornate
rubric
protocol, title or heading
rue
regret
ruse
trick, crafty stratagem
sage
wise
salacious
lascivious, lustful
salubrious
healthful
salutary
expecting an improvement, favorable to health
sanction
to approve, ratify, permit
sardonic
cynical, scornfully mocking
sartorial
pertaining to tailors
satiate
to satisfy
saturate
imbue througout, soak thoroughly
saturnine
gloomy
satyr
a creature that is half-man, half beast, with the horns and legs of a goat
savor
to enjoy, have a distinctive flavor or smell
schematic
relating to or in the form of an outline or diagram
secrete
produce and release substance into organism
sedition
behaviour prompting rebellion
sedulous
diligent, assiduous
seismic
relating to earthquakes
sensual
relating to the senses, gratifying the physical (sexual) senses
sensuous
relating to the senses
sentient
aware, concious, able to preceive
servile
submissive, obedient
sextant
navigation tool that determines latitude and longitude
shard
a piece of broken glass or pottery
sidereal
relating to the stars
simian
apelike, relating to apes
simile
comparison of one thing with another using "like" or "as"
sinecure
well-paying job that requieres little or no work
singular
unique, extraordinary, odd
sinuous
intricate, complex
skeptic
one who doubts
sobriety
seriousness
sodden
thoroughly soaked, saturated
solicitous
concerned, attentive, eager
soliloquy
literary or dramatic speech by one character, not adressed to others
solvent
able to meet financial obligations
somatic
relating to or affecting the body, corporeal
soporific
sleep producing
sordid
filthy, contemptible and corrupt
specious
seeming to be logical and sound, but not really so
spectrum
band of color, broad range of related ideas or objects
spendthrift
person who spends money recklessly
sporadic
irregular
squalor
filthy, wretched condition
staccato
marked by abrupt, clear-cut sounds
stanch
to stop or check the flow of
stentorian
extremely loud
stigma
mark of disgrace or inferiority
stint
to be sparing
stipulate
to specify as an essential condition
stolid
having or showing little emotion
stratified
arranged in layers
striated
marked with thin, narrow grooves or channels
stricture
something that restrains, negative criticism
strident
loud, harsh, unpleasantly noisy
strut
to swagger, display to impress others
stultify
to impair or reduce to uselessness
stupefy
to dull the senses of, stun, atonish
stygian
dark and gloomy, hellish
subpoena
notice ordering someone to appear in court
subside
to settle down, grow quiet
substantiate
to support with proof or evidence
substantive
essential
subsume
to include, incorporate
subversive
intended to undermine or underthrow, especially an established government
succor
relief, help in time of distress or want
suffrage
the right to vote
sundry
various
supersede
to relace, especially to displace as inferior or antiquated
supine
lying in the back, marked by lethargy
supplant
to replace, substitute
suppliant
beseeching
supplicant
one who asks humbly and earnestly
supposition
the act of assuming to be true or real
syllogism
a form of deductive reasoning with a major premise, a minor premise, and a conclusion
sylvan
related to the woods or forest
tacit
silently understood, implied
talisman
charm to bring good luck and avert misfortune
tangential
peripheral, irrelevant, digressing
tautology
unnecessary repetition
taxonomy
science of classification
tenet
belief, doctrine
tenuous
weak, insubstantial
terrestrial
earthly, commonplace
theocracy
government by priests representing a god
thespian
an actor or actress
timbre
voice tone color
tirade
long, violent speech, verbal assault
toady
flatterer, yes-man
tome
book, usually large and academic
torpor
lethargy, dormancy, sluggishness
torque
a turning or twisting force
tortuous
having many twists and turns, highly complex
tout
to promote or praise energetically
tractable
obedient, yielding
transgression
act of trespassing or violating a law or rule
transient
temporary, fleeting
translucent
partially transparent
travail
work, especially arduous work
travesty
parody, exaggerated imitation, caricature
treatise
article treating a subject systematically and thoroughly
tremulous
trembling, frugal, timid
trepidation
fear and anxiety
truculence
aggressiveness, ferocity
tryst
agreement between lovest to meet, rendez-vous
tumid
swollen, distended
turbid
muddy, opaque, in a state of great confusion
turgid
swollen, pompous
tutelary
serving as a guardian or protector
uncanny
myterious, strange
undulating
moving in waves
unfeigned
not false, genuine
untenable
indefensible
untoward
not favorable, troublesome, unruly
usury
a practice of lending money at exorbitant rates
vacillate
to waver, oscillate
vacuous
empty, void, lacking intelligence
valedictory
pertaining to a farewell
vapid
tasteless, dull
variegated
varied, marked with different colors
vaunt
to boast, drag
venal
mercenary, corruptible
vendetta
prolonged feud marked by bitter hostility
venerate
to adore, honor, respect
veracious
truthful, accurate
verbose
wordy
vertigo
dizziness
vexation
irritation, annoyance
viable
practicable, capable of developing
vindictive
vengeful, unforgiving
virtuoso
someone with master skills, expert musician
visage
appearance, aspect
viscous
thick, syrupy
vitiate
to impair the quality of, corrupt morally
vituperative
using or containing harsh, abusive censure
vivisection
dissection, surgery, or painful experiments performed on a living animal for the purpose of scientific research
vogue
prevailing fashion or practice
volatile
tending to vary frequently, fickle
vortex
whirpool, center of turbulence
warranted
justified
wary
careful, cautious
welter
wallow or roll, toss about, be in turmoil
whimsical
fanciful, unpredictable
wistful
vaguely longing, sadly thoughtful
zealot
one who is fanatically devoted to a cause