Section 1
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What is a percent?
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Cards (316)
Section 1
(50 cards)
What is a percent?
A percent is a fraction whose denominator is 100.
The sum of the measures of the n angles in a polygon with n sides
(n-2) x 180
the measure of a straight angle
180°
Perimeter of a rectangle
P= 2L + 2w
Area of a triangle
A= (1/2) b*h
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
binomial product of (x-y)²
(x+y)(x-y)
The negative exponent x⁻ⁿ is equivalent to what?
1/xⁿ i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
#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.
The consecutive angles in a parallelogram equal
180°
#1 What are the important properties of a 45-45-90 triangle?
• The triangle is a right triangle.
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.)
factored binomial product of (x+y)²
x²+2xy+y²
#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
#2 What is an important property of a 30-60-90 triangle?
• The hypotenuse is twice the length of the shorter leg.
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.)
Circumference of a Circle
c=2 x pi x r OR pi x D
Slope given 2 points
m= (Y1-Y2)/(X1-X2)
binomial product of (x+y)(x-y)
x²-y²
factored binomial product of (x-y)²
x²-2xy+y²
Perfect Squares 1-15
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225
In any polygon, all external angles equal up to
360°
#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.
When dividing exponential #s with the same base, you do this to the exponents...
Subtract them. i.e (5^7)/(5^3)= 5^4
binomial product of (x+y)²
(x+y)(x+y)
the slope of a line in y=mx+b
m
When multiplying exponential #s with the same base, you do this to the exponents...
Add them. i.e. (5^7) * (5^3) = 5^10
Pythagorean theorem
a²+b²=c²
If a is inversely porportional to b, what does it equal?
ab=k (k is a constant)
Find distance when given time and rate
d=rt so r= d/t and t=d/r
A quadrilateral where two diagonals bisect each other
Parallelogram
In a rectangle, all angles are
Right
formula for distance problems
distance=rate×time or d=rt
formula for the volume of a cube
V=side³
Area of a circle
A=pi*(r^2)
#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 volume of a rectangular solid
V=l×w×h
How to recognize a # as a multiple of 9
The sum of the digits is a multiple of 9.
In a Rectangle, each angles measures
90°
In a Regular Polygon, the measure of each exterior angle
360/n
Volume of a rectangular box
V=Lwh
#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.
The sum of the angles in a quadrilateral is
360°
formula for area of a triangle
A=½bh
How to recognize a multiple of 6
Sum of digits is a multiple of 3 and the last digit is even.
If y is directly proportional to x, what does it equal?
y/x is a constant
#2 What are the important properties of a 45-45-90 triangle?
• The triangle is isosceles (AC=BC).
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 rectangle
A = length x width
#1 What is an important property of a 30-60-90 triangle?
• The triangle is a right triangle.
Section 2
(50 cards)
Area of a Parallelogram:
A=(base)(height)
Vertical lines
Do not have slopes!
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 of any line that goes down as you move from left to right is
Negative
If a product of two numbers is ∅, one number must be
∅
To increase a number by x%
multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
Area of a circle
(pi)r²
If a lamp decreases to $80, from $100, what is the decrease in price?
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
Circumference of a circle
pi(diameter)
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%
∅ Is neither
Positive or Negative
Slope of any line that goes up from left to right
Positive
Slope
y₂-y₁/x₂-x₁
∅ divided by 7
∅
Dividing by a number is the same as multiplying it by its
Reciprocal
The reciprocal of any non-zero #x is
1/x
(x-y)(x+y)
x²-y²
For any number x
Can be negative, zero, or positive
The product of any number x and its reciprocal
1
To decrease a number by x%
multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
If E is certain
P(E) = 1/1 = 1
(x+y)²
x²+2xy+y²
Probability of E not occurring:
1 - P(E)
Rate
d/t (distance)/(time)
Probability of Event all cases
∅≤P(E)≤1
Time
(distance)/(rate) d/r
The product of odd number of negative numbers
Negative
THE DENOMINATOR CAN NEVER
BE ZERO! 1/∅=null
X is the opposite of
-X
The Perimeter of a Square
P=4s (s=side)
Product of any number and ∅ is
∅
Distance
(rate)(time) d=rt
Circumference of a circle
2(pi)r
If a>b then
-a<-b
The only number that is equal to its opposite
∅ ∅=∅
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
Any Horizontal line slope
zero
The sum of all angles around a point
360°
An Angle that's 180°
Straight Angle
The Perimeter of a rectangle
P=2(l+w)
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
The percent decrease of a quantity
= (actual decrease/Original amount) x 100%
Volume of a cube
edge³
Consecutive integers
x, x+1, x+2
Volume of a rectangular solid
(length)(width)(height)
(x-y)²
x²-2xy+y²
If Event is impossible
P(E) = ø
7 divided by ∅
Null
3 is the opposite of
-3
Section 3
(50 cards)
2⁵/2³
2²
A number is divisible by 3 if ...
the sum of its digits is divisible by 3.
1 is a divisor of
every number
∅²
∅
2³×7³
(2x7)³
One is (a prime or not?)
NOT A PRIME
2 is the only
Even prime number
2⁵+2³
2⁸
bⁿ
b∧b∧b (where b is used as a factor n times)
1/2 divided by 3/7 is the same as
1/2 times 7/3
If a is positive, aⁿ is
Positive
1 is an
ODD number
50 < all primes< 60
53, 59
40 < all primes<50
41, 43, 47
A number is divisible by 6 if...
its divisible by 2 and by 3.
∅ Is
EVEN
a(b-c)
ab-ac
∅ is a multiple of
Two (∅×2=∅)
10<all primes<20
11, 13, 17, 19
30 60 90
5, 12, 13
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)
1 is the
smallest positive integer
If a is negative and n is even then aⁿ is (positive or negative?)
aⁿ is positive
a/∅
Null
20<all primes<30
23, 29
∅ is
Even
30 60 90
x, x(SR3), 2x
a(b+c)
ab+ac
30 60 90
3x, 4x, 5x
What are the integers?
All numbers multiples of 1.
If a<b, then
a+c<b+c
b¹
1
60 < all primes <70
61, 67
a>b then a - b is positive or negative?
a-b is positive
25^(1/2) or sqrt. 25 =
5 OR -5
-3²
9
(2²)³
2⁶
30 60 90
3, 4, 5
a<b then a - b is positive or negative?
a-b is negative
30< all primes<40
31, 37
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)
-3³
-27
∅ is
A multiple of every integer
∅ is a multiple of
Every number
A number is divisible by 9 if...
the sum of digits is divisible by 9.
What are the irrational numbers?
All real numbers which can't be expressed as a ratio of two integers, positive and negative (pi, -sqrt3)
A number is divisible by 4 is...
its last two digits are divisible by 4.
Number of degrees in a triangle
180
1ⁿ
1
Positive integers that have exactly 2 positive divisors are
Prime numbers (2, 3, 5, 7, 11, 13, 17, 19, 23)
Section 4
(50 cards)
What are "supplementary angles?"
Two angles whose sum is 180.
(x^2)^4
x^(2(4)) =x^8 = (x^4)^2
70 < all primes< 80
71, 73, 79
Can you simplify sqrt72?
Yes, because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
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.
(6sqrt3) x (2sqrt5) =
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
What is the order of operations?
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
a^0 =
1
If an inequality is multiplied or divided by a negative number....
the direction of the inequality is reversed.
What is the sum of the angles of a triangle?
180 degrees
5/6 in percent?
83.333%
Solve the quadratic equation ax^2 + bx + c= 0
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
What does scientific notation mean?
Expressing a number as the product of a decimal between 1 and 10, and a power of 10.
a^2 - b^2
(a - b)(a + b)
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)
What is the "range" of a function?
The set of output values for a function.
1/6 in percent?
16.6666%
What is the slope of a horizontal line?
0
How to determine percent decrease?
(amount of decrease/original price) x 100%
a^2 + 2ab + b^2
(a + b)^2
What is the "range" of a series of numbers?
The greatest value minus the smallest.
Area of a triangle?
(base*height) / 2
To multiply a number by 10^x
move the decimal point to the right x places
What is a tangent?
A tangent is a line that only touches one point on the circumference of a circle.
(12sqrt15) / (2sqrt5) =
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
The larger the absolute value of the slope...
the steeper the slope.
If the two sides of a triangle are unequal then the longer side.................
lies opposite the greater angle
Can you add sqrt 3 and sqrt 5?
No, only like radicals can be added.
3/8 in percent?
37.5%
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).
x^4 + x^7 =
x^(4+7) = x^11
Can you subtract 3sqrt4 from sqrt4?
Yes, like radicals can be added/subtracted.
a^2 - b^2 =
(a - b)(a + b)
Circumference of a circle?
Diameter(Pi)
Define a "monomial"
An expression with just one term (-6x, 2a^2)
What is the slope of a vertical line?
Undefined, because we can't divide by 0.
7/8 in percent?
87.5%
What is a central angle?
A central angle is an angle formed by 2 radii.
Factor a^2 + 2ab + b^2
(a + b)^2
What is a chord of a circle?
A chord is a line segment joining two points on a circle.
What is an isoceles triangle?
Two equal sides and two equal angles.
a^2 - 2ab + b^2
(a - b)^2
0^0
undefined
What is the "domain" of a function?
The set of input values for a function.
x^6 / x^3
x^(6-3) = x^3
10^6 has how many zeroes?
6
1/8 in percent?
12.5%
Pi is a ratio of what to what?
Pi is the ratio of a circle's circumference to its diameter.
5/8 in percent?
62.5%
Section 5
(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.
Is 0 even or odd?
Even
P and r are factors of 100. What is greater, pr or 100?
Indeterminable.
Formula for the area of a circle?
A = pi(r^2)
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
Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
2sqrt6
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
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
Write 10,843 X 10^7 in scientific notation
1.0843 X 10^11
Formula for the area of a sector of a circle?
Sector area = (n/360) X (pi)r^2
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
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
Formula to calculate arc length?
Arc length = (n/360) x pi(2r) where n is the number of degrees.
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%.
Evaluate 4/11 + 11/12
1 & 37/132
Legs 5, 12. Hypotenuse?
13
Legs: 3, 4. Hypotenuse?
5
Whats the difference between factors and multiples?
Factors are few, multiples are many.
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 the graph of f(x) shifted left c units or spaces?
f(x + c)
What percent of 40 is 22?
55%
Convert 0.7% to a fraction.
7 / 1000
8.84 / 5.2
1.7
What is a major arc?
The longest arc between points A and B on a circle's diameter.
Simplify 9^(1/2) X 4^3 X 2^(-6)?
3
Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
2 & 3/7
What is the graph of f(x) shifted upward c units or spaces?
f(x) + c
What is an arc of a circle?
An arc is a portion of a circumference of a circle.
The perimeter of a square is 48 inches. The length of its diagonal is:
12sqrt2
Formula to find a circle's circumference from its radius?
C = 2(pi)r
How many multiples does a given number have?
Infinite.
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
What are congruent triangles?
Triangles with same measure and same side lengths.
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 number between 70 & 75, inclusive, has the greatest number of factors?
72
Reduce: 4.8 : 0.8 : 1.6
6 : 1 : 2
What is a minor arc?
The shortest arc between points A and B on a circle's 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
What is the graph of f(x) shifted downward c units or spaces?
f(x) - c
What is the graph of f(x) shifted right c units or spaces?
f(x-c)
Evaluate (4^3)^2
4096
What is the "solution" for a system of linear equations?
The point of intersection of the systems.
200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
3
Legs 6, 8. Hypotenuse?
10
True or false? 4.809 X 10^7 = .0004809 X 10^11
True
What is the "solution" for a set of inequalities.
The overlapping sections.
What are the smallest three prime numbers greater than 65?
67, 71, 73
Evaluate 3& 2/7 / 1/3
9 & 6/7
What are complementary angles?
Two angles whose sum is 90.
Formula to find a circle's circumference from its diameter?
C = (pi)d
Section 6
(50 cards)
1:sqrt3:2 is the ratio of the sides of what kind of triangle?
A 30-60-90 triangle.
What are the roots of the quadrinomial x^2 + 2x + 1?
The two xes after factoring.
What is the ratio of the sides of a 30-60-90 triangle?
1:sqrt3:2
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
In similar hexagons, the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
4:5
Simplify the expression (p^2 - q^2)/ -5(q - p)
(p + q)/5
What is the area of a regular hexagon with side 6?
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
-8
What is a finite set?
A set with a number of elements which can be counted.
1:1:sqrt2 is the ratio of the sides of what kind of triangle?
An isosceles right triangle.
What is the maximum value for the function g(x) = (-2x^2) -1?
-1
(a^-1)/a^5
1/a^6
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.
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
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 a set with no members called?
the empty set, denoted by a circle with a diagonal through it.
What is the name of set with a number of elements which cannot be counted?
An infinite set.
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
What is the "union" of A and B?
The set of elements which can be found in either A or B.
What is the common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd?
cd
If 4500 is invested at a simple interest rate of 6%, what is the value of the investment after 10 months?
4725
The objects in a set are called two names:
members or elements
The ratio of the areas of two similar polygons is ...
... the square of the ratios of the corresponding sides.
Describe the relationship between the graphs of x^2 and (1/2)x^2
The second graph is less steep.
What are the members or elements of a set?
The objects within a set.
What is the measure of an exterior angle of a regular pentagon?
72
6w^2 - w - 15 = 0
-3/2 , 5/3
Simplify the expression [(b^2 - c^2) / (b - c)]
(b + c)
What is the name for a grouping of the members within a set based on a shared characteristic?
A subset.
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.
What is a subset?
a grouping of the members within a set based on a shared characteristic.
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...
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
Factor x^2 - xy + x.
x(x - y + 1)
What is the intersection of A and B?
The set of elements found in both A and B.
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
Simplify (a^2 + b)^2 - (a^2 - b)^2
4a^2(b)
What is the ratio of the sides of an isosceles right triangle?
1:1:sqrt2
The four angles around a point measure y, 2y, 35 and 55 respectively. What is the value of y?
90
What is an exterior angle?
An angle which is supplementary to an interior angle.
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
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 set of elements found in both A and B?
The interesection of A and B.
What is the empty set?
A set with no members, denoted by a circle with a diagonal through it.
What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
2
Section 7
(16 cards)