Section 1
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formula for the volume of a cube
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Cards (316)
Section 1
(50 cards)
formula for the volume of a cube
V=side³
#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.
factored binomial product of (x-y)²
x²-2xy+y²
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.)
The consecutive angles in a parallelogram equal
180°
#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.
If a is inversely porportional to b, what does it equal?
ab=k (k is a constant)
#1 What are the important properties of a 45-45-90 triangle?
• The triangle is a right triangle.
the measure of a straight angle
180°
A quadrilateral where two diagonals bisect each other
Parallelogram
Slope given 2 points
m= (Y1-Y2)/(X1-X2)
Perfect Squares 1-15
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225
#2 What is an important property of a 30-60-90 triangle?
• The hypotenuse is twice the length of the shorter leg.
When dividing exponential #s with the same base, you do this to the exponents...
Subtract them. i.e (5^7)/(5^3)= 5^4
If y is directly proportional to x, what does it equal?
y/x is a constant
In a Regular Polygon, the measure of each exterior angle
360/n
factored binomial product of (x+y)²
x²+2xy+y²
#2 What are the important properties of a 45-45-90 triangle?
• The triangle is isosceles (AC=BC).
In a rectangle, all angles are
Right
When multiplying exponential #s with the same base, you do this to the exponents...
Add them. i.e. (5^7) * (5^3) = 5^10
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.)
In a Rectangle, each angles measures
90°
Perimeter of a rectangle
P= 2L + 2w
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
The sum of the measures of the n angles in a polygon with n sides
(n-2) x 180
binomial product of (x-y)²
(x+y)(x-y)
Area of a triangle
A= (1/2) b*h
formula for area of a triangle
A=½bh
In any polygon, all external angles equal up to
360°
How to recognize a # as a multiple of 9
The sum of the digits is a multiple of 9.
#1 What is an important property of a 30-60-90 triangle?
• The triangle is a right triangle.
the slope of a line in y=mx+b
m
Find distance when given time and rate
d=rt so r= d/t and t=d/r
binomial product of (x+y)(x-y)
x²-y²
Area of a circle
A=pi*(r^2)
Area of a rectangle
A = length x width
#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.
Circumference of a Circle
c=2 x pi x r OR pi x D
Volume of a rectangular box
V=Lwh
#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
Pythagorean theorem
a²+b²=c²
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)
#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.
formula for volume of a rectangular solid
V=l×w×h
formula for distance problems
distance=rate×time or d=rt
The negative exponent x⁻ⁿ is equivalent to what?
1/xⁿ i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
binomial product of (x+y)²
(x+y)(x+y)
The sum of the angles in a quadrilateral is
360°
What is a percent?
A percent is a fraction whose denominator is 100.
How to recognize a multiple of 6
Sum of digits is a multiple of 3 and the last digit is even.
Section 2
(50 cards)
Product of any number and ∅ is
∅
For any number x
Can be negative, zero, or positive
Volume of a rectangular solid
(length)(width)(height)
If a>b then
-a<-b
Area of a Parallelogram:
A=(base)(height)
∅ Is neither
Positive or Negative
Time
(distance)/(rate) d/r
Circumference of a circle
2(pi)r
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%
Probability of an Event
P(E) = number of favorable outcomes/total number of possible outcomes
Rate
d/t (distance)/(time)
(x+y)²
x²+2xy+y²
The percent decrease of a quantity
= (actual decrease/Original amount) x 100%
Area of a circle
(pi)r²
If E is certain
P(E) = 1/1 = 1
Volume of a cube
edge³
Dividing by a number is the same as multiplying it by its
Reciprocal
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°
The product of any number x and its reciprocal
1
Probability of E not occurring:
1 - P(E)
Distance
(rate)(time) d=rt
The only number that is equal to its opposite
∅ ∅=∅
3 is the opposite of
-3
∅ divided by 7
∅
The reciprocal of any non-zero number is
1/x
7 divided by ∅
Null
If Event is impossible
P(E) = ø
Circumference of a circle
pi(diameter)
Consecutive integers
x, x+1, x+2
The sum of all angles around a point
360°
If a product of two numbers is ∅, one number must be
∅
Slope of any line that goes up from left to right
Positive
X is the opposite of
-X
The Perimeter of a rectangle
P=2(l+w)
Slope
y₂-y₁/x₂-x₁
(x-y)(x+y)
x²-y²
An Angle that's 180°
Straight Angle
(x-y)²
x²-2xy+y²
Slope of any line that goes down as you move from left to right is
Negative
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
Vertical lines
Do not have slopes!
The Perimeter of a Square
P=4s (s=side)
If a lamp decreases to $80, from $100, what is the decrease in price?
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
To increase a number by x%
multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
Any Horizontal line slope
zero
Probability of Event all cases
∅≤P(E)≤1
THE DENOMINATOR CAN NEVER
BE ZERO! 1/∅=null
The product of odd number of negative numbers
Negative
The reciprocal of any non-zero #x is
1/x
To decrease a number by x%
multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
Section 3
(50 cards)
b¹
1
A number is divisible by 4 is...
its last two digits are divisible by 4.
If a is positive, aⁿ is
Positive
∅ is a multiple of
Every number
One is (a prime or not?)
NOT A PRIME
30 60 90
3, 4, 5
1 is a divisor of
every number
2⁵+2³
2⁸
-3²
9
What are the integers?
All numbers multiples of 1.
25^(1/2) or sqrt. 25 =
5 OR -5
∅²
∅
30< all primes<40
31, 37
2³×7³
(2x7)³
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>b then a - b is positive or negative?
a-b is positive
Number of degrees in a triangle
180
a(b+c)
ab+ac
1/2 divided by 3/7 is the same as
1/2 times 7/3
∅ is
Even
(2²)³
2⁶
1 is the
smallest positive integer
20<all primes<30
23, 29
60 < all primes <70
61, 67
30 60 90
3x, 4x, 5x
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)
∅ is
A multiple of every integer
A number is divisible by 9 if...
the sum of digits is divisible by 9.
1 is an
ODD number
40 < all primes<50
41, 43, 47
30 60 90
5, 12, 13
If a<b, then
a+c<b+c
2 is the only
Even prime number
50 < all primes< 60
53, 59
-3³
-27
10<all primes<20
11, 13, 17, 19
If a is negative and n is even then aⁿ is (positive or negative?)
aⁿ is positive
1ⁿ
1
∅ is a multiple of
Two (∅×2=∅)
A number is divisible by 3 if ...
the sum of its digits is divisible by 3.
a(b-c)
ab-ac
30 60 90
x, x(SR3), 2x
2⁵/2³
2²
A number is divisible by 6 if...
its divisible by 2 and by 3.
a/∅
Null
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)
Positive integers that have exactly 2 positive divisors are
Prime numbers (2, 3, 5, 7, 11, 13, 17, 19, 23)
∅ Is
EVEN
a<b then a - b is positive or negative?
a-b is negative
bⁿ
b∧b∧b (where b is used as a factor n times)
Section 4
(50 cards)
Pi is a ratio of what to what?
Pi is the ratio of a circle's circumference to its diameter.
Solve the quadratic equation ax^2 + bx + c= 0
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
(12sqrt15) / (2sqrt5) =
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
What is a central angle?
A central angle is an angle formed by 2 radii.
Can you simplify sqrt72?
Yes, because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
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)
If an inequality is multiplied or divided by a negative number....
the direction of the inequality is reversed.
How to determine percent decrease?
(amount of decrease/original price) x 100%
x^4 + x^7 =
x^(4+7) = x^11
5/8 in percent?
62.5%
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)
a^2 - 2ab + b^2
(a - b)^2
a^2 - b^2 =
(a - b)(a + b)
Can you subtract 3sqrt4 from sqrt4?
Yes, like radicals can be added/subtracted.
What is the "range" of a series of numbers?
The greatest value minus the smallest.
Area of a triangle?
(base*height) / 2
7/8 in percent?
87.5%
a^2 + 2ab + b^2
(a + b)^2
1/6 in percent?
16.6666%
What is an isoceles triangle?
Two equal sides and two equal angles.
a^0 =
1
What is the "range" of a function?
The set of output values for a function.
Define a "monomial"
An expression with just one term (-6x, 2a^2)
To multiply a number by 10^x
move the decimal point to the right x places
70 < all primes< 80
71, 73, 79
What is a tangent?
A tangent is a line that only touches one point on the circumference of a circle.
Can you add sqrt 3 and sqrt 5?
No, only like radicals can be added.
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.
1/8 in percent?
12.5%
What is the slope of a vertical line?
Undefined, because we can't divide by 0.
If the two sides of a triangle are unequal then the longer side.................
lies opposite the greater angle
10^6 has how many zeroes?
6
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).
What is the sum of the angles of a triangle?
180 degrees
What is the slope of a horizontal line?
0
a^2 - b^2
(a - b)(a + b)
What are "supplementary angles?"
Two angles whose sum is 180.
What is the order of operations?
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
5/6 in percent?
83.333%
What is the "domain" of a function?
The set of input values for a function.
Circumference of a circle?
Diameter(Pi)
x^6 / x^3
x^(6-3) = x^3
The larger the absolute value of the slope...
the steeper the slope.
0^0
undefined
(x^2)^4
x^(2(4)) =x^8 = (x^4)^2
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 a chord of a circle?
A chord is a line segment joining two points on a circle.
Factor a^2 + 2ab + b^2
(a + b)^2
(6sqrt3) x (2sqrt5) =
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
Section 5
(50 cards)
Legs 6, 8. Hypotenuse?
10
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%.
8.84 / 5.2
1.7
Legs 5, 12. Hypotenuse?
13
Formula for the area of a circle?
A = pi(r^2)
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.
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
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
Is 0 even or odd?
Even
Reduce: 4.8 : 0.8 : 1.6
6 : 1 : 2
What is the graph of f(x) shifted upward c units or spaces?
f(x) + c
What are the smallest three prime numbers greater than 65?
67, 71, 73
Legs: 3, 4. Hypotenuse?
5
Convert 0.7% to a fraction.
7 / 1000
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 find a circle's circumference from its radius?
C = 2(pi)r
Formula to find a circle's circumference from its diameter?
C = (pi)d
Simplify 9^(1/2) X 4^3 X 2^(-6)?
3
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
What is a major arc?
The longest arc between points A and B on a circle's diameter.
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
What is the graph of f(x) shifted left c units or spaces?
f(x + c)
Whats the difference between factors and multiples?
Factors are few, multiples are many.
P and r are factors of 100. What is greater, pr or 100?
Indeterminable.
What is the "solution" for a set of inequalities.
The overlapping sections.
What percent of 40 is 22?
55%
What is a minor arc?
The shortest arc between points A and B on a circle's diameter.
What is an arc of a circle?
An arc is a portion of a circumference of a circle.
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 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.
Evaluate 4/11 + 11/12
1 & 37/132
What is the "solution" for a system of linear equations?
The point of intersection of the systems.
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
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
Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
2sqrt6
What is the graph of f(x) shifted right c units or spaces?
f(x-c)
Write 10,843 X 10^7 in scientific notation
1.0843 X 10^11
200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
3
The perimeter of a square is 48 inches. The length of its diagonal is:
12sqrt2
True or false? 4.809 X 10^7 = .0004809 X 10^11
True
What are complementary angles?
Two angles whose sum is 90.
Evaluate (4^3)^2
4096
What is the graph of f(x) shifted downward c units or spaces?
f(x) - c
Evaluate 3& 2/7 / 1/3
9 & 6/7
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
Formula to calculate arc length?
Arc length = (n/360) x pi(2r) where n is the number of degrees.
How many multiples does a given number have?
Infinite.
Section 6
(50 cards)
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 transformation occurs if point C is reflected over the x-axis and then the y-axis?
A reflection about the axis.
A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
13pi / 2
What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
2
What is the area of a regular hexagon with side 6?
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
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 common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd?
cd
What is the ratio of the sides of a 30-60-90 triangle?
1:sqrt3:2
The objects in a set are called two names:
members or elements
What are the members or elements of a set?
The objects within a set.
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
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 the intersection of A and B?
The set of elements found in both A and B.
What is a set with no members called?
the empty set, denoted by a circle with a diagonal through it.
What is the name for a grouping of the members within a set based on a shared characteristic?
A subset.
6w^2 - w - 15 = 0
-3/2 , 5/3
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...
(a^-1)/a^5
1/a^6
The four angles around a point measure y, 2y, 35 and 55 respectively. What is the value of y?
90
What is the measure of an exterior angle of a regular pentagon?
72
If 4500 is invested at a simple interest rate of 6%, what is the value of the investment after 10 months?
4725
What are the roots of the quadrinomial x^2 + 2x + 1?
The two xes after factoring.
What is the ratio of the sides of an isosceles right triangle?
1:1:sqrt2
Describe the relationship between the graphs of x^2 and (1/2)x^2
The second graph is less steep.
Simplify the expression (p^2 - q^2)/ -5(q - p)
(p + q)/5
1:1:sqrt2 is the ratio of the sides of what kind of triangle?
An isosceles right triangle.
What is a subset?
a grouping of the members within a set based on a shared characteristic.
A cylinder has a surface area of 22pi. If the cylinder has a height of 10, what is the radius?
1
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
For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
-8
For similar triangles, the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
What is the 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.
Factor x^2 - xy + x.
x(x - y + 1)
Simplify (a^2 + b)^2 - (a^2 - b)^2
4a^2(b)
What is the maximum value for the function g(x) = (-2x^2) -1?
-1
What is a finite set?
A set with a number of elements which can be counted.
What is the "union" of A and B?
The set of elements which can be found in either A or B.
The ratio of the areas of two similar polygons is ...
... the square of the ratios of the corresponding sides.
What is the set of elements found in both A and B?
The interesection of A and B.
What is the name of set with a number of elements which cannot be counted?
An infinite set.
What is the set of elements which can be found in either A or B?
The union of A and B.
What is an exterior angle?
An angle which is supplementary to an interior angle.
5x^2 - 35x -55 = 0
[(7+ sqrt93) /2], [(7 - sqrt93) / 2]
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 third quartile of the following data set: 44, 58, 63, 63, 68, 70, 82
70
x^2 = 9. What is the value of x?
3, -3
If 10800 is invested at a simple interest rate of 4%, what is the value of the investment after 18 months?
$11,448
Simplify the expression [(b^2 - c^2) / (b - c)]
(b + c)
Section 7
(16 cards)