Complete GRE Math Flashcards
GRE Math Flashcards - Most Studied - #7,9,10,12 I deleted ones that didn't make sense ... Titles and Authors: Formulas for GRE Quantitative Section by amholt11 GRE Math by Maulleigh GRE math errors by cewind GRE Math by hsingh24 (562 cards)
0
Q
The Perimeter of a rectangle
A
P=2(l+w)
1
Q
formula for distance problems
A
distance=rate×time or d=rt
2
Q
The Perimeter of a Square
A
P=4s (s=side)
3
Q
Area of a Parallelogram:
A
A=(base)(height)
4
Q
(x-y)(x+y)
A
x²-y²
5
Q
(x-y)²
A
x²-2xy+y²
6
Q
(x+y)²
A
x²+2xy+y²
7
Q
An Angle that’s 180°
A
Straight Angle
8
Q
The sum of all angles around a point
A
360°
9
Q
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
A
180
Acute Angle an angle that is less than 90°
Obtuse Angle:angle that is greater than 90° but less than 180°
10
Q
Distance
A
(rate)(time) d=rt
11
Q
Rate
A
d/t (distance)/(time)
12
Q
Time
A
(distance)/(rate) d/r
13
Q
How do you solve proportions?
a/b=c/d
A
Cross multiplication
a/b=c/d
4/6=10/15
4(15)=6(10) 60=60
14
Q
If a lamp increases from $80 to $100, what is the percent increase?
A
= 25%.
= (actual increase/original amount) x 100%
= 20/80 x 100% = 1/4 x 100% = 25%
15
Q
The percent decrease of a quantity
A
= (actual decrease/Original amount) x 100%
16
Q
If a lamp decreases to $80, from $100, what is the decrease in price?
A
= (actual decrease/Original amount) x100%
= 20/100x100% = 20%
17
Q
To increase a number by x%
A
multiply by 1+x%
i.e. 100 x (1+50%)=100x1.5=150
18
Q
To decrease a number by x%
A
multiply by 1-x%
i.e. 100 x (1-50%)=100x.5=50
19
Q
THE DENOMINATOR CAN NEVER
A
BE ZERO! 1/∅=null
20
Q
If a>b then
A
-a<-b
21
Q
The reciprocal of any non-zero number is
A
1/x
22
Q
Probability of an Event
A
P(E) = number of favorable outcomes/total number of possible outcomes
23
Q
If Event is impossible
A
P(E) = ø
24
If E is certain
P(E) = 1/1 = 1
25
Probability of Event all cases
∅≤P(E)≤1
26
Probability of E not occurring:
1 - P(E)
27
Circumference of a circle
pi(diameter)
28
Circumference of a circle
2(pi)r
29
Area of a circle
(pi)r²
30
Volume of a rectangular solid
(length)(width)(height)
31
Volume of a cube
edge³
32
Vertical lines
Do not have slopes!
33
Any Horizontal line slope
zero
34
Slope of any line that goes up from left to right
Positive
35
Slope of any line that goes down as you move from left to right is
Negative
36
Slope
y₂-y₁/x₂-x₁
37
For any number x
Can be negative, zero, or positive
38
X is the opposite of
-X
39
3 is the opposite of
-3
40
The only number that is equal to its opposite
∅ ∅=∅
41
Product of any number and ∅ is
∅
42
If a product of two numbers is ∅, one number must be
∅
43
7 divided by ∅
Null
44
∅ divided by 7
∅
45
The product of odd number of negative numbers
Negative
46
The reciprocal of any non-zero #x is
1/x
47
The product of any number x and its reciprocal
1
48
Dividing by a number is the same as multiplying it by its
Reciprocal
49
∅ Is neither
Positive or Negative
50
Consecutive integers
x, x+1, x+2
51
One is (a prime or not?)
NOT A PRIME
52
Positive integers that have exactly 2 positive divisors are
Prime numbers (2, 3, 5, 7, 11, 13, 17, 19, 23)
53
∅ Is
EVEN
54
∅ is a multiple of
Two (∅×2=∅)
55
∅ is a multiple of
Every number
56
2 is the only
Even prime number
57
b¹
1
58
bⁿ
b∧b∧b (where b is used as a factor n times)
59
2⁵+2³
2⁸
60
2⁵/2³
2²
61
(2²)³
2⁶
62
2³×7³
(2x7)³
63
∅²
∅
64
If a is positive, aⁿ is
Positive
65
If a is negative and n is even then aⁿ is (positive or negative?)
aⁿ is positive
66
-3²
9
67
-3³
-27
68
a(b+c)
ab+ac
69
a(b-c)
ab-ac
70
a>b then a - b is positive or negative?
a-b is positive
71
a
a-b is negative
72
If a
a+c
73
∅ is
Even
74
∅ is
A multiple of every integer
75
a/∅
Null
76
1ⁿ
1
77
1 is a divisor of
every number
78
1 is the
smallest positive integer
79
1 is an
ODD number
80
30 60 90
x, x(SR3), 2x
81
30 60 90
3, 4, 5
82
30 60 90
5, 12, 13
83
30 60 90
3x, 4x, 5x
84
25^(1/2) or sqrt. 25 =
5 OR -5
85
Number of degrees in a triangle
180
86
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)
87
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)
88
What are the irrational numbers?
All real numbers which can't be expressed as a ratio of two integers, positive and negative (pi, -sqrt3)
89
What are the integers?
All numbers multiples of 1.
90
1/2 divided by 3/7 is the same as
1/2 times 7/3
91
A number is divisible by 3 if ...
the sum of its digits is divisible by 3.
92
A number is divisible by 4 is...
its last two digits are divisible by 4.
93
A number is divisible by 6 if...
its divisible by 2 and by 3.
94
A number is divisible by 9 if...
the sum of digits is divisible by 9.
95
10
11, 13, 17, 19
96
20
23, 29
97
30< all primes<40
31, 37
98
40 < all primes<50
41, 43, 47
99
50 < all primes< 60
53, 59
100
60 < all primes <70
61, 67
101
70 < all primes< 80
71, 73, 79
102
1/8 in percent?
12.5%
103
1/6 in percent?
16.6666%
104
3/8 in percent?
37.5%
105
5/8 in percent?
62.5%
106
7/8 in percent?
87.5%
107
5/6 in percent?
83.333%
108
x^4 + x^7 =
x^(4+7) = x^11
109
x^6 / x^3
x^(6-3) = x^3
110
(x^2)^4
x^(2(4)) =x^8 = (x^4)^2
111
a^0 =
1
112
0^0
undefined
113
Can you add sqrt 3 and sqrt 5?
No, only like radicals can be added.
114
Can you subtract 3sqrt4 from sqrt4?
Yes, like radicals can be added/subtracted.
115
(6sqrt3) x (2sqrt5) =
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
116
(12sqrt15) / (2sqrt5) =
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
117
Can you simplify sqrt72?
Yes, because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
118
10^6 has how many zeroes?
6
119
To multiply a number by 10^x
move the decimal point to the right x places
120
What does scientific notation mean?
Expressing a number as the product of a decimal between 1 and 10, and a power of 10.
121
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)
122
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)
123
Define a "monomial"
An expression with just one term (-6x, 2a^2)
124
a^2 - b^2 =
(a - b)(a + b)
125
a^2 + 2ab + b^2
(a + b)^2
126
Solve the quadratic equation ax^2 + bx + c= 0
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
127
If an inequality is multiplied or divided by a negative number....
the direction of the inequality is reversed.
128
What is the "domain" of a function?
The set of input values for a function.
129
What is the "range" of a function?
The set of output values for a function.
130
What is the order of operations?
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
131
What is the sum of the angles of a triangle?
180 degrees
132
Factor a^2 + 2ab + b^2
(a + b)^2
133
a^2 - 2ab + b^2
(a - b)^2
134
a^2 - b^2
(a - b)(a + b)
135
What is the "range" of a series of numbers?
The greatest value minus the smallest.
136
How to determine percent decrease?
(amount of decrease/original price) x 100%
137
Area of a triangle?
(base*height) / 2
138
What is an isoceles triangle?
Two equal sides and two equal angles.
139
Circumference of a circle?
Diameter(Pi)
140
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).
141
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.
142
The larger the absolute value of the slope...
the steeper the slope.
143
What is the slope of a horizontal line?
0
144
What is the slope of a vertical line?
Undefined, because we can't divide by 0.
145
Which quadrant is the upper right hand?
I
146
Which quandrant is the lower right hand?
IV
147
Which quadrant is the upper left hand?
II
148
Which quadrant is the lower left hand?
III
149
What are "supplementary angles?"
Two angles whose sum is 180.
150
If the two sides of a triangle are unequal then the longer side.................
lies opposite the greater angle
151
What is a chord of a circle?
A chord is a line segment joining two points on a circle.
152
What is a central angle?
A central angle is an angle formed by 2 radii.
153
What is a tangent?
A tangent is a line that only touches one point on the circumference of a circle.
154
Pi is a ratio of what to what?
Pi is the ratio of a circle's circumference to its diameter.
155
Formula to find a circle's circumference from its diameter?
C = (pi)d
156
Formula to find a circle's circumference from its radius?
C = 2(pi)r
157
What is an arc of a circle?
An arc is a portion of a circumference of a circle.
158
What is a minor arc?
The shortest arc between points A and B on a circle's diameter.
159
What is a major arc?
The longest arc between points A and B on a circle's diameter.
160
Formula to calculate arc length?
Arc length = (n/360) x pi(2r) where n is the number of degrees.
161
Formula for the area of a circle?
A = pi(r^2)
162
Formula for the area of a sector of a circle?
Sector area = (n/360) X (pi)r^2
163
What is the "solution" for a system of linear equations?
The point of intersection of the systems.
164
What is the "solution" for a set of inequalities.
The overlapping sections.
165
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.
166
What is the graph of f(x) shifted upward c units or spaces?
f(x) + c
167
What is the graph of f(x) shifted downward c units or spaces?
f(x) - c
168
What is the graph of f(x) shifted left c units or spaces?
f(x + c)
169
What is the graph of f(x) shifted right c units or spaces?
f(x-c)
170
What are complementary angles?
Two angles whose sum is 90.
171
What are congruent triangles?
Triangles with same measure and same side lengths.
172
Legs: 3, 4. Hypotenuse?
5
173
Legs 6, 8. Hypotenuse?
10
174
Legs 5, 12. Hypotenuse?
13
175
Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
2 & 3/7
176
8.84 / 5.2
1.7
177
Evaluate 4/11 + 11/12
1 & 37/132
178
Evaluate 3& 2/7 / 1/3
9 & 6/7
179
200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
3
180
What number between 70 & 75, inclusive, has the greatest number of factors?
72
181
What are the smallest three prime numbers greater than 65?
67, 71, 73
182
Which is greater? 64^5 or 16^8
16^8
64^5 = (4^3)^5 = 4^15
16^8=(4^2)^8 = 4^16
183
Evaluate (4^3)^2
4096
184
Write 10,843 X 10^7 in scientific notation
1.0843 X 10^11
185
True or false? 4.809 X 10^7 = .0004809 X 10^11
True
186
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
187
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
188
Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
2sqrt6
189
Simplify 9^(1/2) X 4^3 X 2^(-6)?
3
190
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
191
Reduce: 4.8 : 0.8 : 1.6
6 : 1 : 2
192
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
193
What percent of 40 is 22?
55%
194
Convert 0.7% to a fraction.
7 / 1000
195
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%.
196
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
197
The perimeter of a square is 48 inches. The length of its diagonal is:
12sqrt2
198
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
199
Whats the difference between factors and multiples?
Factors are few, multiples are many.
200
How many multiples does a given number have?
Infinite.
201
P and r are factors of 100. What is greater, pr or 100?
Indeterminable.
202
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
203
Is 0 even or odd?
Even
204
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
205
What are the roots of the quadrinomial x^2 + 2x + 1?
The two xes after factoring.
206
Factor x^2 - xy + x.
x(x - y + 1)
207
Simplify the expression [(b^2 - c^2) / (b - c)]
(b + c)
208
Simplify (a^2 + b)^2 - (a^2 - b)^2
4a^2(b)
209
What is the common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd?
cd
210
Simplify the expression (p^2 - q^2)/ -5(q - p)
(p + q)/5
211
What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
2
212
(a^-1)/a^5
1/a^6
213
x^2 = 9. What is the value of x?
3, -3
214
6w^2 - w - 15 = 0
-3/2 , 5/3
215
5x^2 - 35x -55 = 0
[(7+ sqrt93) /2], [(7 - sqrt93) / 2]
216
If 10800 is invested at a simple interest rate of 4%, what is the value of the investment after 18 months?
$11,448
217
If 4500 is invested at a simple interest rate of 6%, what is the value of the investment after 10 months?
4725
218
What is the maximum value for the function g(x) = (-2x^2) -1?
-1
219
For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
-8
220
What transformation occurs if point C is reflected over the x-axis and then the y-axis?
A reflection about the axis.
221
The four angles around a point measure y, 2y, 35 and 55 respectively. What is the value of y?
90
222
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.
223
What is the ratio of the sides of an isosceles right triangle?
1:1:sqrt2
224
What is the set of elements found in both A and B?
The interesection of A and B.
225
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
226
Perfect Squares 1-15
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225
227
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.)
228
Area of a rectangle
A = length x width
229
How to recognize a # as a multiple of 9
The sum of the digits is a multiple of 9.
230
Slope given 2 points
m= (Y1-Y2)/(X1-X2)
231
Circumference of a Circle
c=2 x pi x r
232
OR pi x D
...
233
Area of a circle
A=pi*(r^2)
234
Perimeter of a rectangle
P= 2L + 2w
235
How to recognize a multiple of 6
Sum of digits is a multiple of 3 and the last digit is even.
236
Volume of a rectangular box
V=L*w*h
237
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.)
238
How to recognize a # as a multiple of 3
The sum of the digits is a multiple of 3
239
(i.e. 45 ... 4 + 5 = 9 so the whole thing is a multiple of 3)
...
240
Area of a triangle
A= (1/2) b*h
241
When dividing exponential #s with the same base, you do this to the exponents...
Subtract them.
242
i.e (5^7)/(5^3)= 5^4
...
243
When multiplying exponential #s with the same base, you do this to the exponents...
Add them.
244
i.e. (5^7) * (5^3) = 5^10
...
245
First 10 prime #s
2, 3, 5, 7, 11, 13, 17, 19, 23, 29
246
A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself
...
247
Find distance when given time and rate
d=rt so r= d/t and t=d/r
248
binomial product of (x+y)(x-y)
x²-y²
249
factored binomial product of (x+y)²
x²+2xy+y²
250
factored binomial product of (x-y)²
x²-2xy+y²
251
binomial product of (x+y)²
(x+y)(x+y)
252
binomial product of (x-y)²
(x+y)(x-y)
253
the measure of a straight angle
180°
254
the slope of a line in y=mx+b
m
255
Pythagorean theorem
a²+b²=c²
256
If a is inversely porportional to b, what does it equal?
ab=k
257
(k is a constant)
...
258
#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.
259
#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.
260
#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.
261
If y is directly proportional to x, what does it equal?
y/x is a constant
262
What is a percent?
A percent is a fraction whose denominator is 100.
263
#1 What is an important property of a 30-60-90 triangle?
• The triangle is a right triangle. http://o.quizlet.com/LfZfJjj3Y2h-Z1nnE21GTQ.png
264
#2 What is an important property of a 30-60-90 triangle?
• The hypotenuse is twice the length of the shorter leg. http://o.quizlet.com/LfZfJjj3Y2h-Z1nnE21GTQ.png
265
#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 http://o.quizlet.com/LfZfJjj3Y2h-Z1nnE21GTQ.png
266
The negative exponent x⁻ⁿ is equivalent to what?
1/xⁿ
267
i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
...
268
formula for area of a triangle
A=½bh
269
formula for volume of a rectangular solid
V=l×w×h
270
formula for the volume of a cube
V=side³
271
#1 What are the important properties of a 45-45-90 triangle?
• The triangle is a right triangle. http://o.quizlet.com/ZRUKVmbufm8JVNHyj6A33Q.png
272
#2 What are the important properties of a 45-45-90 triangle?
• The triangle is isosceles (AC=BC). http://o.quizlet.com/ZRUKVmbufm8JVNHyj6A33Q.png
273
#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. http://o.quizlet.com/ZRUKVmbufm8JVNHyj6A33Q.png
274
formula for distance problems
distance=rate×time or d=rt
275
The sum of the angles in a quadrilateral is
360° http://o.quizlet.com/PhRTJH.MtlGqIDeopsop4A.png
276
The sum of the measures of the n angles in a polygon with n sides
(n-2) x 180 http://o.quizlet.com/ej9Ol2cXbA1a5bjESJ8-Zw.jpg
277
In any polygon, all external angles equal up to
360° http://o.quizlet.com/ej9Ol2cXbA1a5bjESJ8-Zw.jpg
278
In a Regular Polygon, the measure of each exterior angle
360/n http://o.quizlet.com/ej9Ol2cXbA1a5bjESJ8-Zw.jpg
279
The consecutive angles in a parallelogram equal
180° http://o.quizlet.com/aCX960zpf1s9wKu8z.u0tw.jpg
280
A quadrilateral where two diagonals bisect each other
Parallelogram http://o.quizlet.com/aCX960zpf1s9wKu8z.u0tw.jpg
281
In a rectangle, all angles are
Right
282
In a Rectangle, each angles measures
90°
283
The Perimeter of a rectangle
P=2(l+w)
284
The Perimeter of a Square
P=4s (s=side)
285
Area of a Parallelogram:
A=(base)(height) http://o.quizlet.com/aCX960zpf1s9wKu8z.u0tw.jpg
286
(x-y)(x+y)
x²-y²
287
(x-y)²
x²-2xy+y²
288
(x+y)²
x²+2xy+y²
289
An Angle that's 180°
Straight Angle
290
The sum of all angles around a point
360°
291
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
292
Acute Angle an angle that is less than 90°
...
293
Obtuse Angle:angle that is greater than 90° but less than 180°
...
294
Distance
(rate)(time) d=rt
295
Rate
d/t (distance)/(time)
296
Time
(distance)/(rate) d/r
297
How do you solve proportions?
...
298
a/b=c/d
Cross multiplication
299
a/b=c/d
...
300
4/6=10/15
...
301
4(15)=6(10) 60=60
...
302
If a lamp increases from $80 to $100, what is the percent increase?
= 25%.
303
= (actual increase/original amount) x 100%
...
304
= 20/80 x 100% = 1/4 x 100% = 25%
...
305
The percent decrease of a quantity
= (actual decrease/Original amount) x 100%
306
If a lamp decreases to $80, from $100, what is the decrease in price?
= (actual decrease/Original amount) x100%
307
= 20/100x100% = 20%
...
308
To increase a number by x%
multiply by 1+x%
309
i.e. 100 x (1+50%)=100x1.5=150
...
310
To decrease a number by x%
multiply by 1-x%
311
i.e. 100 x (1-50%)=100x.5=50
...
312
THE DENOMINATOR CAN NEVER
BE ZERO! 1/∅=null
313
If a>b then
-a<-b
314
The reciprocal of any non-zero number is
1/x
315
Probability of an Event
P(E) = number of favorable outcomes/total number of possible outcomes
316
If Event is impossible
P(E) = ø
317
If E is certain
P(E) = 1/1 = 1
318
Probability of Event all cases
∅≤P(E)≤1
319
Probability of E not occurring:
1 - P(E)
320
Circumference of a circle
pi(diameter)
321
Circumference of a circle
2(pi)r
322
Area of a circle
(pi)r²
323
Volume of a rectangular solid
(length)(width)(height)
324
Volume of a cube
edge³
325
Vertical lines
Do not have slopes!
326
Any Horizontal line slope
zero
327
Slope of any line that goes up from left to right
Positive
328
Slope of any line that goes down as you move from left to right is
Negative
329
Slope
y₂-y₁/x₂-x₁
330
For any number x
Can be negative, zero, or positive
331
X is the opposite of
-X
332
3 is the opposite of
-3
333
The only number that is equal to its opposite
∅ ∅=∅
334
Product of any number and ∅ is
∅
335
If a product of two numbers is ∅, one number must be
∅
336
7 divided by ∅
Null
337
∅ divided by 7
∅
338
The product of odd number of negative numbers
Negative
339
The reciprocal of any non-zero #x is
1/x
340
The product of any number x and its reciprocal
1
341
Dividing by a number is the same as multiplying it by its
Reciprocal
342
∅ Is neither
Positive or Negative
343
Consecutive integers
x, x+1, x+2
344
One is (a prime or not?)
NOT A PRIME
345
Positive integers that have exactly 2 positive divisors are
Prime numbers (2, 3, 5, 7, 11, 13, 17, 19, 23)
346
∅ Is
EVEN
347
∅ is a multiple of
Two (∅×2=∅)
348
∅ is a multiple of
Every number
349
2 is the only
Even prime number
350
b¹
1
351
bⁿ
b∧b∧b (where b is used as a factor n times)
352
2⁵+2³
2⁸
353
2⁵/2³
2²
354
(2²)³
2⁶
355
2³×7³
(2x7)³
356
∅²
∅
357
If a is positive, aⁿ is
Positive
358
If a is negative and n is even then aⁿ is (positive or negative?)
aⁿ is positive
359
-3²
9
360
-3³
-27
361
a(b+c)
ab+ac
362
a(b-c)
ab-ac
363
a>b then a - b is positive or negative?
a-b is positive
364
a
a-b is negative
365
If a
a+c
366
∅ is
Even
367
∅ is
A multiple of every integer
368
a/∅
Null
369
1ⁿ
1
370
1 is a divisor of
every number
371
1 is the
smallest positive integer
372
1 is an
ODD number
373
30 60 90
x, x(SR3), 2x
374
30 60 90
3, 4, 5
375
30 60 90
5, 12, 13
376
30 60 90
3x, 4x, 5x
377
25^(1/2) or sqrt. 25 =
5 OR -5
378
Number of degrees in a triangle
180
379
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)
380
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)
381
What are the irrational numbers?
All real numbers which can't be expressed as a ratio of two integers, positive and negative (pi, -sqrt3)
382
What are the integers?
All numbers multiples of 1.
383
1/2 divided by 3/7 is the same as
1/2 times 7/3
384
A number is divisible by 3 if ...
the sum of its digits is divisible by 3.
385
A number is divisible by 4 is...
its last two digits are divisible by 4.
386
A number is divisible by 6 if...
its divisible by 2 and by 3.
387
A number is divisible by 9 if...
the sum of digits is divisible by 9.
388
10
11, 13, 17, 19
389
20
23, 29
390
30< all primes<40
31, 37
391
40 < all primes<50
41, 43, 47
392
50 < all primes< 60
53, 59
393
60 < all primes <70
61, 67
394
70 < all primes< 80
71, 73, 79
395
1/8 in percent?
12.5%
396
1/6 in percent?
16.6666%
397
3/8 in percent?
37.5%
398
5/8 in percent?
62.5%
399
7/8 in percent?
87.5%
400
5/6 in percent?
83.333%
401
x^4 + x^7 =
x^(4+7) = x^11
402
x^6 / x^3
x^(6-3) = x^3
403
(x^2)^4
x^(2(4)) =x^8 = (x^4)^2
404
a^0 =
1
405
0^0
undefined
406
Can you add sqrt 3 and sqrt 5?
No, only like radicals can be added.
407
Can you subtract 3sqrt4 from sqrt4?
Yes, like radicals can be added/subtracted.
408
(6sqrt3) x (2sqrt5) =
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
409
(12sqrt15) / (2sqrt5) =
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
410
Can you simplify sqrt72?
Yes, because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
411
10^6 has how many zeroes?
6
412
To multiply a number by 10^x
move the decimal point to the right x places
413
What does scientific notation mean?
Expressing a number as the product of a decimal between 1 and 10, and a power of 10.
414
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)
415
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)
416
Define a "monomial"
An expression with just one term (-6x, 2a^2)
417
a^2 - b^2 =
(a - b)(a + b)
418
a^2 + 2ab + b^2
(a + b)^2
419
Solve the quadratic equation ax^2 + bx + c= 0
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
420
If an inequality is multiplied or divided by a negative number....
the direction of the inequality is reversed.
421
What is the "domain" of a function?
The set of input values for a function.
422
What is the "range" of a function?
The set of output values for a function.
423
What is the order of operations?
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
424
What is the sum of the angles of a triangle?
180 degrees
425
Factor a^2 + 2ab + b^2
(a + b)^2
426
a^2 - 2ab + b^2
(a - b)^2
427
a^2 - b^2
(a - b)(a + b)
428
What is the "range" of a series of numbers?
The greatest value minus the smallest.
429
How to determine percent decrease?
(amount of decrease/original price) x 100%
430
Area of a triangle?
(base*height) / 2
431
What is an isoceles triangle?
Two equal sides and two equal angles.
432
Circumference of a circle?
Diameter(Pi)
433
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).
434
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.
435
The larger the absolute value of the slope...
the steeper the slope.
436
What is the slope of a horizontal line?
0
437
What is the slope of a vertical line?
Undefined, because we can't divide by 0.
438
What are "supplementary angles?"
Two angles whose sum is 180.
439
If the two sides of a triangle are unequal then the longer side.................
lies opposite the greater angle
440
What is a chord of a circle?
A chord is a line segment joining two points on a circle.
441
What is a central angle?
A central angle is an angle formed by 2 radii.
442
What is a tangent?
A tangent is a line that only touches one point on the circumference of a circle.
443
Pi is a ratio of what to what?
Pi is the ratio of a circle's circumference to its diameter.
444
Formula to find a circle's circumference from its diameter?
C = (pi)d
445
Formula to find a circle's circumference from its radius?
C = 2(pi)r
446
What is an arc of a circle?
An arc is a portion of a circumference of a circle.
447
What is a minor arc?
The shortest arc between points A and B on a circle's diameter.
448
What is a major arc?
The longest arc between points A and B on a circle's diameter.
449
Formula to calculate arc length?
Arc length = (n/360) x pi(2r) where n is the number of degrees.
450
Formula for the area of a circle?
A = pi(r^2)
451
Formula for the area of a sector of a circle?
Sector area = (n/360) X (pi)r^2
452
What is the "solution" for a system of linear equations?
The point of intersection of the systems.
453
What is the "solution" for a set of inequalities.
The overlapping sections.
454
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.
455
What is the graph of f(x) shifted upward c units or spaces?
f(x) + c
456
What is the graph of f(x) shifted downward c units or spaces?
f(x) - c
457
What is the graph of f(x) shifted left c units or spaces?
f(x + c)
458
What is the graph of f(x) shifted right c units or spaces?
f(x-c)
459
What are complementary angles?
Two angles whose sum is 90.
460
What are congruent triangles?
Triangles with same measure and same side lengths.
461
Legs: 3, 4. Hypotenuse?
5
462
Legs 6, 8. Hypotenuse?
10
463
Legs 5, 12. Hypotenuse?
13
464
Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
2 & 3/7
465
8.84 / 5.2
1.7
466
Evaluate 4/11 + 11/12
1 & 37/132
467
Evaluate 3& 2/7 / 1/3
9 & 6/7
468
200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
3
469
What number between 70 & 75, inclusive, has the greatest number of factors?
72
470
What are the smallest three prime numbers greater than 65?
67, 71, 73
471
Which is greater? 64^5 or 16^8
16^8
472
64^5 = (4^3)^5 = 4^15
...
473
16^8=(4^2)^8 = 4^16
...
474
Evaluate (4^3)^2
4096
475
Write 10,843 X 10^7 in scientific notation
1.0843 X 10^11
476
True or false? 4.809 X 10^7 = .0004809 X 10^11
True
477
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
478
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
479
Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
2sqrt6
480
Simplify 9^(1/2) X 4^3 X 2^(-6)?
3
481
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
482
Reduce: 4.8 : 0.8 : 1.6
6 : 1 : 2
483
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
484
What percent of 40 is 22?
55%
485
Convert 0.7% to a fraction.
7 / 1000
486
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%.
487
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
488
The perimeter of a square is 48 inches. The length of its diagonal is:
12sqrt2
489
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
490
Whats the difference between factors and multiples?
Factors are few, multiples are many.
491
How many multiples does a given number have?
Infinite.
492
P and r are factors of 100. What is greater, pr or 100?
Indeterminable.
493
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
494
Is 0 even or odd?
Even
495
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
496
What are the roots of the quadrinomial x^2 + 2x + 1?
The two xes after factoring.
497
Factor x^2 - xy + x.
x(x - y + 1)
498
Simplify the expression [(b^2 - c^2) / (b - c)]
(b + c)
499
Simplify (a^2 + b)^2 - (a^2 - b)^2
4a^2(b)
500
What is the common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd?
cd
501
Simplify the expression (p^2 - q^2)/ -5(q - p)
(p + q)/5
502
What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
2
503
(a^-1)/a^5
1/a^6
504
x^2 = 9. What is the value of x?
3, -3
505
6w^2 - w - 15 = 0
-3/2 , 5/3
506
5x^2 - 35x -55 = 0
[(7+ sqrt93) /2], [(7 - sqrt93) / 2]
507
If 10800 is invested at a simple interest rate of 4%, what is the value of the investment after 18 months?
$11,448
508
If 4500 is invested at a simple interest rate of 6%, what is the value of the investment after 10 months?
4725
509
What is the maximum value for the function g(x) = (-2x^2) -1?
-1
510
For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
-8
511
What transformation occurs if point C is reflected over the x-axis and then the y-axis?
A reflection about the axis.
512
The four angles around a point measure y, 2y, 35 and 55 respectively. What is the value of y?
90
513
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.
514
What is the ratio of the sides of an isosceles right triangle?
1:1:sqrt2
515
1:1:sqrt2 is the ratio of the sides of what kind of triangle?
An isosceles right triangle.
516
What is the ratio of the sides of a 30-60-90 triangle?
1:sqrt3:2
517
1:sqrt3:2 is the ratio of the sides of what kind of triangle?
A 30-60-90 triangle.
518
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...
519
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
520
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.
521
Describe the relationship between the graphs of x^2 and (1/2)x^2
The second graph is less steep.
522
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
523
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
524
How many sides does a hexagon have?
6
525
What is an exterior angle?
An angle which is supplementary to an interior angle.
526
What is the measure of an exterior angle of a regular pentagon?
72
527
The ratio of the areas of two similar polygons is ...
... the square of the ratios of the corresponding sides.
528
In similar hexagons, the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
4:5
529
What is the area of a regular hexagon with side 6?
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
530
A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
13pi / 2
531
A cylinder has a surface area of 22pi. If the cylinder has a height of 10, what is the radius?
1
532
What is the third quartile of the following data set: 44, 58, 63, 63, 68, 70, 82
70
533
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
534
The objects in a set are called two names:
members or elements
535
What are the members or elements of a set?
The objects within a set.
536
What is a finite set?
A set with a number of elements which can be counted.
537
What is the name of set with a number of elements which cannot be counted?
An infinite set.
538
What is a subset?
a grouping of the members within a set based on a shared characteristic.
539
What is the name for a grouping of the members within a set based on a shared characteristic?
A subset.
540
What is the empty set?
A set with no members, denoted by a circle with a diagonal through it.
541
What is a set with no members called?
the empty set, denoted by a circle with a diagonal through it.
542
What is the "union" of A and B?
The set of elements which can be found in either A or B.
543
What is the set of elements which can be found in either A or B?
The union of A and B.
544
What is the intersection of A and B?
The set of elements found in both A and B.
545
What is the set of elements found in both A and B?
The interesection of A and B.
546
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)!
547
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)!
548
How many 3-digit positive integers are even and do not contain the digit 4?
288 (8 * 9 * 4)
549
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
550
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
551
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
552
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 * 21 * 21
553
Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
2^9 / 2 = 256
554
Find the surface area of a cylinder with radius 3 and height 12.
90pi
555
What is the surface area of a cylinder with radius 5 and height 8?
130pi
556
A cylinder has surface area 22pi. If the cylinder has a height of 10, what is its radius?
1
557
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
558
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
559
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)!
560
Which is greater? 27^(-4) or 9^(-8)
27^(-4)
561
Which is greater? 200x^295 or 10x^294?
Relationship cannot be determined (what if x is negative?)
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