Section 1
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The reciprocal of any non-zero number is
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Cards (377)
Section 1
(50 cards)
The reciprocal of any non-zero number is
1/x
To decrease a number by x%
multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
Area of a Parallelogram:
A=(base)(height)
Probability of Event all cases
∅≤P(E)≤1
The percent decrease of a quantity
= (actual decrease/Original amount) x 100%
The Perimeter of a Square
P=4s (s=side)
The product of odd number of negative numbers
Negative
If E is certain
P(E) = 1/1 = 1
X is the opposite of
-X
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%
An Angle that's 180°
Straight Angle
Distance
(rate)(time) d=rt
The sum of all angles around a point
360°
Circumference of a circle
2(pi)r
If Event is impossible
P(E) = ø
Rate
d/t (distance)/(time)
The product of any number x and its reciprocal
1
Dividing by a number is the same as multiplying it by its
Reciprocal
To increase a number by x%
multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
Probability of an Event
P(E) = number of favorable outcomes/total number of possible outcomes
The only number that is equal to its opposite
∅ ∅=∅
3 is the opposite of
-3
If a product of two numbers is ∅, one number must be
∅
Any Horizontal line slope
zero
Circumference of a circle
pi(diameter)
(x+y)²
x²+2xy+y²
∅ Is neither
Positive or Negative
If a lamp decreases to $80, from $100, what is the decrease in price?
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
THE DENOMINATOR CAN NEVER
BE ZERO! 1/∅=null
Probability of E not occurring:
1 - P(E)
The Perimeter of a rectangle
P=2(l+w)
Vertical lines
Do not have slopes!
formula for distance problems
distance=rate×time or d=rt
Volume of a rectangular solid
(length)(width)(height)
If a>b then
-a<-b
For any number x
Can be negative, zero, or positive
Area of a circle
(pi)r²
Slope of any line that goes down as you move from left to right is
Negative
Slope of any line that goes up from left to right
Positive
(x-y)(x+y)
x²-y²
∅ divided by 7
∅
7 divided by ∅
Null
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°
Slope
y₂-y₁/x₂-x₁
Time
(distance)/(rate) d/r
(x-y)²
x²-2xy+y²
Product of any number and ∅ is
∅
The reciprocal of any non-zero #x is
1/x
Volume of a cube
edge³
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
Section 2
(50 cards)
1/2 divided by 3/7 is the same as
1/2 times 7/3
If a<b, then
a+c<b+c
a(b+c)
ab+ac
30 60 90
3, 4, 5
A number is divisible by 6 if...
its divisible by 2 and by 3.
A number is divisible by 3 if ...
the sum of its digits is divisible by 3.
1 is a divisor of
every number
20<all primes<30
23, 29
∅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.
Positive integers that have exactly 2 positive divisors are
Prime numbers (2, 3, 5, 7, 11, 13, 17, 19, 23)
∅ is a multiple of
Two (∅×2=∅)
1 is the
smallest positive integer
a/∅
Null
30< all primes<40
31, 37
b¹
1
1ⁿ
1
∅ Is
EVEN
∅ is a multiple of
Every number
If a is positive, aⁿ is
Positive
bⁿ
b∧b∧b (where b is used as a factor n times)
A number is divisible by 9 if...
the sum of digits is divisible by 9.
-3³
-27
a>b then a - b is positive or negative?
a-b is positive
30 60 90
x, x(SR3), 2x
Number of degrees in a triangle
180
50 < all primes< 60
53, 59
Consecutive integers
x, x+1, x+2
(2²)³
2⁶
2⁵/2³
2²
-3²
9
30 60 90
3x, 4x, 5x
2⁵+2³
2⁸
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)
a<b then a - b is positive or negative?
a-b is negative
∅ is
Even
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)
One is (a prime or not?)
NOT A PRIME
40 < all primes<50
41, 43, 47
a(b-c)
ab-ac
2³×7³
(2x7)³
10<all primes<20
11, 13, 17, 19
30 60 90
5, 12, 13
∅ is
A multiple of every integer
1 is an
ODD number
If a is negative and n is even then aⁿ is (positive or negative?)
aⁿ is positive
A number is divisible by 4 is...
its last two digits are divisible by 4.
25^(1/2) or sqrt. 25 =
5 OR -5
2 is the only
Even prime number
Section 3
(50 cards)
What are "supplementary angles?"
Two angles whose sum is 180.
What is the slope of a horizontal line?
0
0^0
undefined
1/6 in percent?
16.6666%
To multiply a number by 10^x
move the decimal point to the right x places
If an inequality is multiplied or divided by a negative number....
the direction of the inequality is reversed.
a^0 =
1
Which quadrant is the upper left hand?
II
7/8 in percent?
87.5%
x^4 + x^7 =
x^(4+7) = x^11
What is the "range" of a function?
The set of output values for a function.
x^6 / x^3
x^(6-3) = x^3
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)
Can you simplify sqrt72?
Yes, because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
What is the order of operations?
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
What is the "domain" of a function?
The set of input values for a function.
70 < all primes< 80
71, 73, 79
a^2 - b^2 =
(a - b)(a + b)
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.
What does scientific notation mean?
Expressing a number as the product of a decimal between 1 and 10, and a power of 10.
Solve the quadratic equation ax^2 + bx + c= 0
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
a^2 - b^2
(a - b)(a + b)
(12sqrt15) / (2sqrt5) =
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
What is the sum of the angles of a triangle?
180 degrees
The larger the absolute value of the slope...
the steeper the slope.
(x^2)^4
x^(2(4)) =x^8 = (x^4)^2
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 a "monomial"
An expression with just one term (-6x, 2a^2)
Area of a triangle?
(base*height) / 2
3/8 in percent?
37.5%
10^6 has how many zeroes?
6
Factor a^2 + 2ab + b^2
(a + b)^2
60 < all primes <70
61, 67
a^2 + 2ab + b^2
(a + b)^2
(6sqrt3) x (2sqrt5) =
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
5/8 in percent?
62.5%
What is the slope of a vertical line?
Undefined, because we can't divide by 0.
Can you add sqrt 3 and sqrt 5?
No, only like radicals can be added.
a^2 - 2ab + b^2
(a - b)^2
What is an isoceles triangle?
Two equal sides and two equal angles.
How to determine percent decrease?
(amount of decrease/original price) x 100%
Which quandrant is the lower right hand?
IV
Which quadrant is the upper right hand?
I
Circumference of a circle?
Diameter(Pi)
5/6 in percent?
83.333%
Which quadrant is the lower left hand?
III
What is the "range" of a series of numbers?
The greatest value minus the smallest.
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).
1/8 in percent?
12.5%
Can you subtract 3sqrt4 from sqrt4?
Yes, like radicals can be added/subtracted.
Section 4
(50 cards)
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.
Simplify 9^(1/2) X 4^3 X 2^(-6)?
3
What is the graph of f(x) shifted downward c units or spaces?
f(x) - c
What is the graph of f(x) shifted upward c units or spaces?
f(x) + c
What is a tangent?
A tangent is a line that only touches one point on the circumference of a circle.
Whats the difference between factors and multiples?
Factors are few, multiples are many.
What is the graph of f(x) shifted right c units or spaces?
f(x-c)
Formula for the area of a sector of a circle?
Sector area = (n/360) X (pi)r^2
True or false? 4.809 X 10^7 = .0004809 X 10^11
True
What are the smallest three prime numbers greater than 65?
67, 71, 73
Formula for the area of a circle?
A = pi(r^2)
What are congruent triangles?
Triangles with same measure and same side lengths.
If the two sides of a triangle are unequal then the longer side.................
lies opposite the greater angle
Formula to find a circle's circumference from its radius?
C = 2(pi)r
Evaluate 4/11 + 11/12
1 & 37/132
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%.
What is a chord of a circle?
A chord is a line segment joining two points on a circle.
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
Legs: 3, 4. Hypotenuse?
5
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
What is a minor arc?
The shortest arc between points A and B on a circle's diameter.
Evaluate (4^3)^2
4096
Evaluate 3& 2/7 / 1/3
9 & 6/7
Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
2sqrt6
What are complementary angles?
Two angles whose sum is 90.
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 is the graph of f(x) shifted left c units or spaces?
f(x + c)
Formula to calculate arc length?
Arc length = (n/360) x pi(2r) where n is the number of degrees.
The perimeter of a square is 48 inches. The length of its diagonal is:
12sqrt2
Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
2 & 3/7
What is the "solution" for a system of linear equations?
The point of intersection of the systems.
8.84 / 5.2
1.7
200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
3
Legs 5, 12. Hypotenuse?
13
What percent of 40 is 22?
55%
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
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
What is a major arc?
The longest arc between points A and B on a circle's diameter.
Pi is a ratio of what to what?
Pi is the ratio of a circle's circumference to its diameter.
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
Convert 0.7% to a fraction.
7 / 1000
What number between 70 & 75, inclusive, has the greatest number of factors?
72
Reduce: 4.8 : 0.8 : 1.6
6 : 1 : 2
What is an arc of a circle?
An arc is a portion of a circumference of a circle.
Formula to find a circle's circumference from its diameter?
C = (pi)d
What is the "solution" for a set of inequalities.
The overlapping sections.
Write 10,843 X 10^7 in scientific notation
1.0843 X 10^11
Which is greater? 64^5 or 16^8
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
What is a central angle?
A central angle is an angle formed by 2 radii.
Legs 6, 8. Hypotenuse?
10
Section 5
(50 cards)
What is the ratio of the sides of an isosceles right triangle?
1:1:sqrt2
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.)
5x^2 - 35x -55 = 0
[(7+ sqrt93) /2], [(7 - sqrt93) / 2]
How to recognize a # as a multiple of 3
The sum of the digits is a multiple of 3
Circumference of a Circle
c=2 x pi x r
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
factored binomial product of (x+y)²
x²+2xy+y²
What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
2
Slope given 2 points
m= (Y1-Y2)/(X1-X2)
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.)
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
For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
-8
Area of a rectangle
A = length x width
If 10800 is invested at a simple interest rate of 4%, what is the value of the investment after 18 months?
$11,448
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
Simplify (a^2 + b)^2 - (a^2 - b)^2
4a^2(b)
Factor x^2 - xy + x.
x(x - y + 1)
What are the roots of the quadrinomial x^2 + 2x + 1?
The two xes after factoring.
Perfect Squares 1-15
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225
Find distance when given time and rate
d=rt so r= d/t and t=d/r
P and r are factors of 100. What is greater, pr or 100?
Indeterminable.
Area of a triangle
A= (1/2) b*h
(a^-1)/a^5
1/a^6
What is the set of elements found in both A and B?
The interesection of A and B.
x^2 = 9. What is the value of x?
3, -3
(i.e. 45 ... 4 + 5 = 9 so the whole thing is a multiple of 3)
...
What transformation occurs if point C is reflected over the x-axis and then the y-axis?
A reflection about the axis.
First 10 prime #s
2, 3, 5, 7, 11, 13, 17, 19, 23, 29
Volume of a rectangular box
V=Lwh
What is the maximum value for the function g(x) = (-2x^2) -1?
-1
Is 0 even or odd?
Even
When multiplying exponential #s with the same base, you do this to the exponents...
Add them.
How to recognize a multiple of 6
Sum of digits is a multiple of 3 and the last digit is even.
6w^2 - w - 15 = 0
-3/2 , 5/3
How to recognize a # as a multiple of 9
The sum of the digits is a multiple of 9.
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 common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd?
cd
i.e (5^7)/(5^3)= 5^4
...
binomial product of (x+y)(x-y)
x²-y²
i.e. (5^7) * (5^3) = 5^10
...
Perimeter of a rectangle
P= 2L + 2w
Simplify the expression (p^2 - q^2)/ -5(q - p)
(p + q)/5
The four angles around a point measure y, 2y, 35 and 55 respectively. What is the value of y?
90
How many multiples does a given number have?
Infinite.
When dividing exponential #s with the same base, you do this to the exponents...
Subtract them.
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.
Simplify the expression [(b^2 - c^2) / (b - c)]
(b + c)
A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself
...
OR pi x D
...
Area of a circle
A=pi*(r^2)
Section 6
(50 cards)
#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
formula for volume of a rectangular solid
V=l×w×h
The Perimeter of a Square
P=4s (s=side)
the measure of a straight angle
180°
#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.
i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
...
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
#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
A quadrilateral where two diagonals bisect each other
Parallelogram http://o.quizlet.com/aCX960zpf1s9wKu8z.u0tw.jpg
Rate
d/t (distance)/(time)
formula for area of a triangle
A=½bh
a/b=c/d
...
The sum of all angles around a point
360°
(x-y)²
x²-2xy+y²
#1 What are the important properties of a 45-45-90 triangle?
• The triangle is a right triangle. http://o.quizlet.com/ZRUKVmbufm8JVNHyj6A33Q.png
The Perimeter of a rectangle
P=2(l+w)
#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
(k is a constant)
...
Area of a Parallelogram:
A=(base)(height) http://o.quizlet.com/aCX960zpf1s9wKu8z.u0tw.jpg
(x-y)(x+y)
x²-y²
binomial product of (x-y)²
(x+y)(x-y)
#2 What are the important properties of a 45-45-90 triangle?
• The triangle is isosceles (AC=BC). http://o.quizlet.com/ZRUKVmbufm8JVNHyj6A33Q.png
Pythagorean theorem
a²+b²=c²
An Angle that's 180°
Straight Angle
Acute Angle an angle that is less than 90°
...
The consecutive angles in a parallelogram equal
180° http://o.quizlet.com/aCX960zpf1s9wKu8z.u0tw.jpg
How do you solve proportions?
...
In a rectangle, all angles are
Right
formula for distance problems
distance=rate×time or d=rt
Distance
(rate)(time) d=rt
What is a percent?
A percent is a fraction whose denominator is 100.
Time
(distance)/(rate) d/r
If a is inversely porportional to b, what does it equal?
ab=k
factored binomial product of (x-y)²
x²-2xy+y²
In a Rectangle, each angles measures
90°
If y is directly proportional to x, what does it equal?
y/x is a constant
(x+y)²
x²+2xy+y²
#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.
In a Regular Polygon, the measure of each exterior angle
360/n http://o.quizlet.com/ej9Ol2cXbA1a5bjESJ8-Zw.jpg
Obtuse Angle:angle that is greater than 90° but less than 180°
...
The negative exponent x⁻ⁿ is equivalent to what?
1/xⁿ
In any polygon, all external angles equal up to
360° http://o.quizlet.com/ej9Ol2cXbA1a5bjESJ8-Zw.jpg
binomial product of (x+y)²
(x+y)(x+y)
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
the slope of a line in y=mx+b
m
a/b=c/d
Cross multiplication
#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.
formula for the volume of a cube
V=side³
The sum of the angles in a quadrilateral is
360° http://o.quizlet.com/PhRTJH.MtlGqIDeopsop4A.png
#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
Section 7
(50 cards)
2 is the only
Even prime number
The product of odd number of negative numbers
Negative
Probability of an Event
P(E) = number of favorable outcomes/total number of possible outcomes
∅ divided by 7
∅
4/6=10/15
...
Circumference of a circle
pi(diameter)
i.e. 100 x (1-50%)=100x.5=50
...
If a>b then
-a<-b
The reciprocal of any non-zero number is
1/x
Probability of E not occurring:
1 - P(E)
THE DENOMINATOR CAN NEVER
BE ZERO! 1/∅=null
= 20/100x100% = 20%
...
The product of any number x and its reciprocal
1
If Event is impossible
P(E) = ø
Dividing by a number is the same as multiplying it by its
Reciprocal
= 20/80 x 100% = 1/4 x 100% = 25%
...
The percent decrease of a quantity
= (actual decrease/Original amount) x 100%
Slope of any line that goes down as you move from left to right is
Negative
If a lamp decreases to $80, from $100, what is the decrease in price?
= (actual decrease/Original amount) x100%
Any Horizontal line slope
zero
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)
Circumference of a circle
2(pi)r
Slope
y₂-y₁/x₂-x₁
To increase a number by x%
multiply by 1+x%
i.e. 100 x (1+50%)=100x1.5=150
...
∅ Is
EVEN
∅ Is neither
Positive or Negative
If E is certain
P(E) = 1/1 = 1
Volume of a rectangular solid
(length)(width)(height)
For any number x
Can be negative, zero, or positive
∅ is a multiple of
Every number
Area of a circle
(pi)r²
The only number that is equal to its opposite
∅ ∅=∅
7 divided by ∅
Null
The reciprocal of any non-zero #x is
1/x
∅ is a multiple of
Two (∅×2=∅)
X is the opposite of
-X
Volume of a cube
edge³
If a product of two numbers is ∅, one number must be
∅
= (actual increase/original amount) x 100%
...
If a lamp increases from $80 to $100, what is the percent increase?
= 25%.
To decrease a number by x%
multiply by 1-x%
3 is the opposite of
-3
Slope of any line that goes up from left to right
Positive
Vertical lines
Do not have slopes!
Probability of Event all cases
∅≤P(E)≤1
4(15)=6(10) 60=60
...
Consecutive integers
x, x+1, x+2
Product of any number and ∅ is
∅
Section 8
(50 cards)
a/∅
Null
1/8 in percent?
12.5%
What are the integers?
All numbers multiples of 1.
1/6 in percent?
16.6666%
40 < all primes<50
41, 43, 47
If a is positive, aⁿ is
Positive
30 60 90
3x, 4x, 5x
20<all primes<30
23, 29
-3³
-27
2³×7³
(2x7)³
10<all primes<20
11, 13, 17, 19
(2²)³
2⁶
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.
25^(1/2) or sqrt. 25 =
5 OR -5
70 < all primes< 80
71, 73, 79
∅ is
A multiple of every integer
∅²
∅
b¹
1
30 60 90
3, 4, 5
-3²
9
30 60 90
5, 12, 13
1 is the
smallest positive integer
30 60 90
x, x(SR3), 2x
1 is a divisor of
every number
A number is divisible by 9 if...
the sum of digits is divisible by 9.
∅ is
Even
60 < all primes <70
61, 67
A number is divisible by 6 if...
its divisible by 2 and by 3.
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)
A number is divisible by 4 is...
its last two digits are divisible by 4.
What are the irrational numbers?
All real numbers which can't be expressed as a ratio of two integers, positive and negative (pi, -sqrt3)
Number of degrees in a triangle
180
If a<b, then
a+c<b+c
a(b-c)
ab-ac
5/8 in percent?
62.5%
1 is an
ODD number
2⁵/2³
2²
If a is negative and n is even then aⁿ is (positive or negative?)
aⁿ is positive
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)
2⁵+2³
2⁸
a<b then a - b is positive or negative?
a-b is negative
1ⁿ
1
a(b+c)
ab+ac
7/8 in percent?
87.5%
3/8 in percent?
37.5%
bⁿ
b∧b∧b (where b is used as a factor n times)
30< all primes<40
31, 37
a>b then a - b is positive or negative?
a-b is positive
50 < all primes< 60
53, 59
Section 9
(50 cards)
5/6 in percent?
83.333%
What is the slope of a horizontal line?
0
What are "supplementary angles?"
Two angles whose sum is 180.
a^2 - 2ab + b^2
(a - b)^2
10^6 has how many zeroes?
6
Define a "monomial"
An expression with just one term (-6x, 2a^2)
a^2 - b^2 =
(a - b)(a + b)
Can you add sqrt 3 and sqrt 5?
No, only like radicals can be added.
What is the "domain" of a function?
The set of input values for a function.
Factor a^2 + 2ab + b^2
(a + b)^2
What is an isoceles triangle?
Two equal sides and two equal angles.
Area of a triangle?
(base*height) / 2
What is a major arc?
The longest arc between points A and B on a circle's diameter.
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)
Circumference of a circle?
Diameter(Pi)
a^2 + 2ab + b^2
(a + b)^2
Can you simplify sqrt72?
Yes, because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
What is an arc of a circle?
An arc is a portion of a circumference of a circle.
Formula to find a circle's circumference from its diameter?
C = (pi)d
If the two sides of a triangle are unequal then the longer side.................
lies opposite the greater angle
What is the slope of a vertical line?
Undefined, because we can't divide by 0.
What is the sum of the angles of a triangle?
180 degrees
a^0 =
1
What is the "range" of a function?
The set of output values for a function.
(6sqrt3) x (2sqrt5) =
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
x^4 + x^7 =
x^(4+7) = x^11
The larger the absolute value of the slope...
the steeper the slope.
(x^2)^4
x^(2(4)) =x^8 = (x^4)^2
What is a tangent?
A tangent is a line that only touches one point on the circumference of a circle.
Formula to calculate arc length?
Arc length = (n/360) x pi(2r) where n is the number of degrees.
To multiply a number by 10^x
move the decimal point to the right x places
x^6 / x^3
x^(6-3) = x^3
Pi is a ratio of what to what?
Pi is the ratio of a circle's circumference to its diameter.
0^0
undefined
Formula to find a circle's circumference from its radius?
C = 2(pi)r
(12sqrt15) / (2sqrt5) =
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
What is a minor arc?
The shortest arc between points A and B on a circle's diameter.
How to determine percent decrease?
(amount of decrease/original price) x 100%
What is a chord of a circle?
A chord is a line segment joining two points on a circle.
Solve the quadratic equation ax^2 + bx + c= 0
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
Can you subtract 3sqrt4 from sqrt4?
Yes, like radicals can be added/subtracted.
What does scientific notation mean?
Expressing a number as the product of a decimal between 1 and 10, and a power of 10.
What is the "range" of a series of numbers?
The greatest value minus the smallest.
a^2 - b^2
(a - b)(a + b)
If an inequality is multiplied or divided by a negative number....
the direction of the inequality is reversed.
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.
What is a central angle?
A central angle is an angle formed by 2 radii.
What is the order of operations?
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
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).
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)
Section 10
(50 cards)
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%.
Simplify (a^2 + b)^2 - (a^2 - b)^2
4a^2(b)
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 are complementary angles?
Two angles whose sum is 90.
What percent of 40 is 22?
55%
What are the smallest three prime numbers greater than 65?
67, 71, 73
Evaluate 4/11 + 11/12
1 & 37/132
Whats the difference between factors and multiples?
Factors are few, multiples are many.
Is 0 even or odd?
Even
Which is greater? 64^5 or 16^8
16^8
Factor x^2 - xy + x.
x(x - y + 1)
200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
3
Simplify the expression [(b^2 - c^2) / (b - c)]
(b + c)
What is the "solution" for a set of inequalities.
The overlapping sections.
Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
2sqrt6
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
What is the graph of f(x) shifted downward c units or spaces?
f(x) - c
Reduce: 4.8 : 0.8 : 1.6
6 : 1 : 2
What is the graph of f(x) shifted left c units or spaces?
f(x + c)
How many multiples does a given number have?
Infinite.
Legs: 3, 4. Hypotenuse?
5
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
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
What number between 70 & 75, inclusive, has the greatest number of factors?
72
Evaluate 3& 2/7 / 1/3
9 & 6/7
What are the roots of the quadrinomial x^2 + 2x + 1?
The two xes after factoring.
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
Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
2 & 3/7
What are congruent triangles?
Triangles with same measure and same side lengths.
What is the graph of f(x) shifted upward c units or spaces?
f(x) + c
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
Formula for the area of a sector of a circle?
Sector area = (n/360) X (pi)r^2
True or false? 4.809 X 10^7 = .0004809 X 10^11
True
What is the "solution" for a system of linear equations?
The point of intersection of the systems.
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
Evaluate (4^3)^2
4096
16^8=(4^2)^8 = 4^16
...
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
Convert 0.7% to a fraction.
7 / 1000
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
64^5 = (4^3)^5 = 4^15
...
Legs 6, 8. Hypotenuse?
10
Legs 5, 12. Hypotenuse?
13
Simplify 9^(1/2) X 4^3 X 2^(-6)?
3
Formula for the area of a circle?
A = pi(r^2)
Write 10,843 X 10^7 in scientific notation
1.0843 X 10^11
P and r are factors of 100. What is greater, pr or 100?
Indeterminable.
8.84 / 5.2
1.7
The perimeter of a square is 48 inches. The length of its diagonal is:
12sqrt2
What is the graph of f(x) shifted right c units or spaces?
f(x-c)
Section 11
(50 cards)
1:1:sqrt2 is the ratio of the sides of what kind of triangle?
An isosceles right triangle.
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
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
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
Simplify the expression (p^2 - q^2)/ -5(q - p)
(p + q)/5
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)!
The ratio of the areas of two similar polygons is ...
... the square of the ratios of the corresponding sides.
What is the common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd?
cd
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
What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
2
The objects in a set are called two names:
members or elements
What is the ratio of the sides of an isosceles right triangle?
1:1:sqrt2
What is the third quartile of the following data set: 44, 58, 63, 63, 68, 70, 82
70
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 sliding the graph of y=2x^2 down 3 units of spaces. What is the new equation?
y = 2x^2 - 3
What is the "union" of A and B?
The set of elements which can be found in either A or B.
What is the measure of an exterior angle of a regular pentagon?
72
What is the maximum value for the function g(x) = (-2x^2) -1?
-1
What are the members or elements of a set?
The objects within a set.
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.
1:sqrt3:2 is the ratio of the sides of what kind of triangle?
A 30-60-90 triangle.
What is a set with no members called?
the empty set, denoted by a circle with a diagonal through it.
How many 3-digit positive integers are even and do not contain the digit 4?
288 (8 9 4)
What is the set of elements which can be found in either A or B?
The union of A and B.
A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
13pi / 2
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 transformation occurs if point C is reflected over the x-axis and then the y-axis?
A reflection about the axis.
If 4500 is invested at a simple interest rate of 6%, what is the value of the investment after 10 months?
4725
For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
-8
What is the intersection of A and B?
The set of elements found in both A and B.
6w^2 - w - 15 = 0
-3/2 , 5/3
5x^2 - 35x -55 = 0
[(7+ sqrt93) /2], [(7 - sqrt93) / 2]
x^2 = 9. What is the value of x?
3, -3
What is the area of a regular hexagon with side 6?
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
In similar hexagons, the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
4:5
What is the name of set with a number of elements which cannot be counted?
An infinite set.
A cylinder has a surface area of 22pi. If the cylinder has a height of 10, what is the radius?
1
What is an exterior angle?
An angle which is supplementary to an interior angle.
What is a subset?
a grouping of the members within a set based on a shared characteristic.
How many sides does a hexagon have?
6
What is the set of elements found in both A and B?
The interesection of A and B.
If 10800 is invested at a simple interest rate of 4%, what is the value of the investment after 18 months?
$11,448
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.
(a^-1)/a^5
1/a^6
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)!
The four angles around a point measure y, 2y, 35 and 55 respectively. What is the value of y?
90
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...
What is the ratio of the sides of a 30-60-90 triangle?
1:sqrt3:2
What is a finite set?
A set with a number of elements which can be counted.
Section 12
(12 cards)