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Cards (562)
Section 1
(50 cards)
For any number x
Can be negative, zero, or positive
Dividing by a number is the same as multiplying it by its
Reciprocal
Volume of a cube
edge³
The reciprocal of any non-zero #x is
1/x
∅ divided by 7
∅
The sum of all angles around a point
360°
Probability of E not occurring:
1 - P(E)
Slope of any line that goes up from left to right
Positive
∅ Is neither
Positive or Negative
THE DENOMINATOR CAN NEVER
BE ZERO! 1/∅=null
If a lamp decreases to $80, from $100, what is the decrease in price?
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
If E is certain
P(E) = 1/1 = 1
The Perimeter of a rectangle
P=2(l+w)
Slope
y₂-y₁/x₂-x₁
Area of a Parallelogram:
A=(base)(height)
The reciprocal of any non-zero number is
1/x
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
X is the opposite of
-X
Probability of Event all cases
∅≤P(E)≤1
(x-y)(x+y)
x²-y²
Volume of a rectangular solid
(length)(width)(height)
formula for distance problems
distance=rate×time or d=rt
Rate
d/t (distance)/(time)
Any Horizontal line slope
zero
7 divided by ∅
Null
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%
Slope of any line that goes down as you move from left to right is
Negative
If Event is impossible
P(E) = ø
Area of a circle
(pi)r²
An Angle that's 180°
Straight Angle
The Perimeter of a Square
P=4s (s=side)
Time
(distance)/(rate) d/r
The product of odd number of negative numbers
Negative
If a product of two numbers is ∅, one number must be
∅
(x+y)²
x²+2xy+y²
Distance
(rate)(time) d=rt
Vertical lines
Do not have slopes!
The only number that is equal to its opposite
∅ ∅=∅
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°
Circumference of a circle
pi(diameter)
Probability of an Event
P(E) = number of favorable outcomes/total number of possible outcomes
3 is the opposite of
-3
To decrease a number by x%
multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
Product of any number and ∅ is
∅
If a>b then
-a<-b
To increase a number by x%
multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
Circumference of a circle
2(pi)r
(x-y)²
x²-2xy+y²
The percent decrease of a quantity
= (actual decrease/Original amount) x 100%
The product of any number x and its reciprocal
1
Section 2
(50 cards)
1ⁿ
1
∅ is
Even
30 60 90
5, 12, 13
-3³
-27
2 is the only
Even prime number
20<all primes<30
23, 29
(2²)³
2⁶
If a is positive, aⁿ is
Positive
1 is an
ODD number
∅ is a multiple of
Every number
2⁵/2³
2²
1 is a divisor of
every number
∅²
∅
One is (a prime or not?)
NOT A PRIME
30 60 90
3x, 4x, 5x
a(b-c)
ab-ac
b¹
1
Consecutive integers
x, x+1, x+2
2³×7³
(2x7)³
Positive integers that have exactly 2 positive divisors are
Prime numbers (2, 3, 5, 7, 11, 13, 17, 19, 23)
1 is the
smallest positive integer
A number is divisible by 6 if...
its divisible by 2 and by 3.
If a is negative and n is even then aⁿ is (positive or negative?)
aⁿ is positive
a/∅
Null
25^(1/2) or sqrt. 25 =
5 OR -5
∅ is a multiple of
Two (∅×2=∅)
30 60 90
x, x(SR3), 2x
Number of degrees in a triangle
180
30 60 90
3, 4, 5
∅ is
A multiple of every integer
∅ Is
EVEN
40 < all primes<50
41, 43, 47
-3²
9
50 < all primes< 60
53, 59
10<all primes<20
11, 13, 17, 19
a>b then a - b is positive or negative?
a-b is positive
a<b then a - b is positive or negative?
a-b is negative
If a<b, then
a+c<b+c
A number is divisible by 9 if...
the sum of digits is divisible by 9.
a(b+c)
ab+ac
2⁵+2³
2⁸
1/2 divided by 3/7 is the same as
1/2 times 7/3
bⁿ
b∧b∧b (where b is used as a factor n times)
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.
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 3 if ...
the sum of its digits is divisible by 3.
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)
What are the integers?
All numbers multiples of 1.
Section 3
(50 cards)
Factor a^2 + 2ab + b^2
(a + b)^2
a^2 - 2ab + b^2
(a - b)^2
5/8 in percent?
62.5%
What is the order of operations?
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
What is an isoceles triangle?
Two equal sides and two equal angles.
5/6 in percent?
83.333%
a^2 - b^2 =
(a - b)(a + b)
Circumference of a circle?
Diameter(Pi)
Which quadrant is the lower left hand?
III
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)
(x^2)^4
x^(2(4)) =x^8 = (x^4)^2
Area of a triangle?
(base*height) / 2
Define a "monomial"
An expression with just one term (-6x, 2a^2)
If an inequality is multiplied or divided by a negative number....
the direction of the inequality is reversed.
The larger the absolute value of the slope...
the steeper the slope.
What are "supplementary angles?"
Two angles whose sum is 180.
What is the "domain" of a function?
The set of input values for a function.
0^0
undefined
1/8 in percent?
12.5%
Which quadrant is the upper left hand?
II
Can you simplify sqrt72?
Yes, because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
Solve the quadratic equation ax^2 + bx + c= 0
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
How to find the circumference of a circle which circumscribes a square?
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
When does a function automatically have a restricted domain (2)?
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
10^6 has how many zeroes?
6
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)
Can you add sqrt 3 and sqrt 5?
No, only like radicals can be added.
What does scientific notation mean?
Expressing a number as the product of a decimal between 1 and 10, and a power of 10.
60 < all primes <70
61, 67
1/6 in percent?
16.6666%
a^2 - b^2
(a - b)(a + b)
What is the sum of the angles of a triangle?
180 degrees
(6sqrt3) x (2sqrt5) =
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
7/8 in percent?
87.5%
70 < all primes< 80
71, 73, 79
To multiply a number by 10^x
move the decimal point to the right x places
What is the "range" of a function?
The set of output values for a function.
Can you subtract 3sqrt4 from sqrt4?
Yes, like radicals can be added/subtracted.
Which quandrant is the lower right hand?
IV
a^2 + 2ab + b^2
(a + b)^2
How to determine percent decrease?
(amount of decrease/original price) x 100%
x^6 / x^3
x^(6-3) = x^3
What is the slope of a horizontal line?
0
What is the "range" of a series of numbers?
The greatest value minus the smallest.
What is the slope of a vertical line?
Undefined, because we can't divide by 0.
(12sqrt15) / (2sqrt5) =
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
3/8 in percent?
37.5%
a^0 =
1
x^4 + x^7 =
x^(4+7) = x^11
Which quadrant is the upper right hand?
I
Section 4
(50 cards)
What is the graph of f(x) shifted upward c units or spaces?
f(x) + c
True or false? 4.809 X 10^7 = .0004809 X 10^11
True
Evaluate (4^3)^2
4096
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.
Write 10,843 X 10^7 in scientific notation
1.0843 X 10^11
Evaluate 3& 2/7 / 1/3
9 & 6/7
Employee X is paid 19.50 per hour no matter how many a week. Employee Y earns 18 for the first 40 and 1.5 the hourly wage for every hour after that. If both earned the same amount and worked the same in one week, how many did each work?
48
What is an arc of a circle?
An arc is a portion of a circumference of a circle.
Formula for the area of a sector of a circle?
Sector area = (n/360) X (pi)r^2
Convert 0.7% to a fraction.
7 / 1000
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
Reduce: 4.8 : 0.8 : 1.6
6 : 1 : 2
Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
2 & 3/7
If the two sides of a triangle are unequal then the longer side.................
lies opposite the greater angle
What is the graph of f(x) shifted left c units or spaces?
f(x + c)
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
Formula for the area of a circle?
A = pi(r^2)
Formula to find a circle's circumference from its radius?
C = 2(pi)r
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
8.84 / 5.2
1.7
What is the graph of f(x) shifted downward c units or spaces?
f(x) - c
200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
3
Formula to find a circle's circumference from its diameter?
C = (pi)d
What are congruent triangles?
Triangles with same measure and same side lengths.
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
The perimeter of a square is 48 inches. The length of its diagonal is:
12sqrt2
Whats the difference between factors and multiples?
Factors are few, multiples are many.
What are complementary angles?
Two angles whose sum is 90.
What is the "solution" for a set of inequalities.
The overlapping sections.
Evaluate 4/11 + 11/12
1 & 37/132
What is a chord of a circle?
A chord is a line segment joining two points on a circle.
What is the "solution" for a system of linear equations?
The point of intersection of the systems.
What is the graph of f(x) shifted right c units or spaces?
f(x-c)
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 9^(1/2) X 4^3 X 2^(-6)?
3
Legs 6, 8. Hypotenuse?
10
Formula to calculate arc length?
Arc length = (n/360) x pi(2r) where n is the number of degrees.
What percent of 40 is 22?
55%
What is a major arc?
The longest arc between points A and B on a circle's diameter.
What is a minor arc?
The shortest arc between points A and B on a circle's diameter.
Legs 5, 12. Hypotenuse?
13
What is a central angle?
A central angle is an angle formed by 2 radii.
Pi is a ratio of what to what?
Pi is the ratio of a circle's circumference to its diameter.
Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
2sqrt6
What is a tangent?
A tangent is a line that only touches one point on the circumference of a circle.
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%.
Legs: 3, 4. Hypotenuse?
5
What are the smallest three prime numbers greater than 65?
67, 71, 73
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
Section 5
(50 cards)
For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
-8
i.e (5^7)/(5^3)= 5^4
...
When dividing exponential #s with the same base, you do this to the exponents...
Subtract them.
How to recognize a # as a multiple of 9
The sum of the digits is a multiple of 9.
Slope given 2 points
m= (Y1-Y2)/(X1-X2)
OR pi x D
...
Find distance when given time and rate
d=rt so r= d/t and t=d/r
Simplify the expression [(b^2 - c^2) / (b - c)]
(b + c)
What is the set of elements found in both A and B?
The interesection of A and B.
If 4500 is invested at a simple interest rate of 6%, what is the value of the investment after 10 months?
4725
i.e. (5^7) * (5^3) = 5^10
...
When multiplying exponential #s with the same base, you do this to the exponents...
Add them.
Area of a triangle
A= (1/2) b*h
factored binomial product of (x+y)²
x²+2xy+y²
(a^-1)/a^5
1/a^6
Perfect Squares 1-15
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225
For similar triangles, the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
What is the ratio of the 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
If 10800 is invested at a simple interest rate of 4%, what is the value of the investment after 18 months?
$11,448
What are the roots of the quadrinomial x^2 + 2x + 1?
The two xes after factoring.
binomial product of (x+y)(x-y)
x²-y²
What is the common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd?
cd
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 maximum value for the function g(x) = (-2x^2) -1?
-1
5x^2 - 35x -55 = 0
[(7+ sqrt93) /2], [(7 - sqrt93) / 2]
P and r are factors of 100. What is greater, pr or 100?
Indeterminable.
x^2 = 9. What is the value of x?
3, -3
How to recognize a # as a multiple of 3
The sum of the digits is a multiple of 3
How many multiples does a given number have?
Infinite.
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.)
6w^2 - w - 15 = 0
-3/2 , 5/3
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
(i.e. 45 ... 4 + 5 = 9 so the whole thing is a multiple of 3)
...
How to recognize a multiple of 6
Sum of digits is a multiple of 3 and the last digit is even.
Area of a circle
A=pi*(r^2)
Simplify the expression (p^2 - q^2)/ -5(q - p)
(p + q)/5
What transformation occurs if point C is reflected over the x-axis and then the y-axis?
A reflection about the axis.
Simplify (a^2 + b)^2 - (a^2 - b)^2
4a^2(b)
Is 0 even or odd?
Even
First 10 prime #s
2, 3, 5, 7, 11, 13, 17, 19, 23, 29
Area of a rectangle
A = length x width
The four angles around a point measure y, 2y, 35 and 55 respectively. What is the value of y?
90
Factor x^2 - xy + x.
x(x - y + 1)
What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
2
What is the ratio of the sides of an isosceles right triangle?
1:1:sqrt2
Perimeter of a rectangle
P= 2L + 2w
A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself
...
Volume of a rectangular box
V=Lwh
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.)
Section 6
(50 cards)
In a rectangle, all angles are
Right
#2 What is the relationship between lengths of the sides of a triangle and the measure of the angles of the triangle?
• The shortest side is opposite the smallest angle.
#3 What is 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
#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.
Distance
(rate)(time) d=rt
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
(x+y)²
x²+2xy+y²
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
The Perimeter of a rectangle
P=2(l+w)
Rate
d/t (distance)/(time)
The Perimeter of a Square
P=4s (s=side)
If y is directly proportional to x, what does it equal?
y/x is a constant
the slope of a line in y=mx+b
m
(x-y)²
x²-2xy+y²
The negative exponent x⁻ⁿ is equivalent to what?
1/xⁿ
How do you solve proportions?
...
#1 What are the important properties of a 45-45-90 triangle?
• The triangle is a right triangle. http://o.quizlet.com/ZRUKVmbufm8JVNHyj6A33Q.png
Obtuse Angle:angle that is greater than 90° but less than 180°
...
a/b=c/d
...
What is a percent?
A percent is a fraction whose denominator is 100.
In a Regular Polygon, the measure of each exterior angle
360/n http://o.quizlet.com/ej9Ol2cXbA1a5bjESJ8-Zw.jpg
The sum of all angles around a point
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.
formula for distance problems
distance=rate×time or d=rt
formula for the volume of a cube
V=side³
factored binomial product of (x-y)²
x²-2xy+y²
Acute Angle an angle that is less than 90°
...
Time
(distance)/(rate) d/r
In a Rectangle, each angles measures
90°
Area of a Parallelogram:
A=(base)(height) http://o.quizlet.com/aCX960zpf1s9wKu8z.u0tw.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
binomial product of (x-y)²
(x+y)(x-y)
A quadrilateral where two diagonals bisect each other
Parallelogram http://o.quizlet.com/aCX960zpf1s9wKu8z.u0tw.jpg
the measure of a straight angle
180°
(x-y)(x+y)
x²-y²
i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
...
The sum of the angles in a quadrilateral is
360° http://o.quizlet.com/PhRTJH.MtlGqIDeopsop4A.png
(k is a constant)
...
#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
In any polygon, all external angles equal up to
360° http://o.quizlet.com/ej9Ol2cXbA1a5bjESJ8-Zw.jpg
The consecutive angles in a parallelogram equal
180° http://o.quizlet.com/aCX960zpf1s9wKu8z.u0tw.jpg
binomial product of (x+y)²
(x+y)(x+y)
Pythagorean theorem
a²+b²=c²
An Angle that's 180°
Straight Angle
If a is inversely porportional to b, what does it equal?
ab=k
formula for volume of a rectangular solid
V=l×w×h
#2 What are the important properties of a 45-45-90 triangle?
• The triangle is isosceles (AC=BC). http://o.quizlet.com/ZRUKVmbufm8JVNHyj6A33Q.png
#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 area of a triangle
A=½bh
a/b=c/d
Cross multiplication
Section 7
(50 cards)
∅ is a multiple of
Two (∅×2=∅)
If E is certain
P(E) = 1/1 = 1
4/6=10/15
...
X is the opposite of
-X
Product of any number and ∅ is
∅
The only number that is equal to its opposite
∅ ∅=∅
Slope of any line that goes up from left to right
Positive
If a product of two numbers is ∅, one number must be
∅
The product of odd number of negative numbers
Negative
= (actual increase/original amount) x 100%
...
One is (a prime or not?)
NOT A PRIME
If a lamp decreases to $80, from $100, what is the decrease in price?
= (actual decrease/Original amount) x100%
4(15)=6(10) 60=60
...
Dividing by a number is the same as multiplying it by its
Reciprocal
Probability of E not occurring:
1 - P(E)
Circumference of a circle
pi(diameter)
= 20/100x100% = 20%
...
Slope
y₂-y₁/x₂-x₁
If Event is impossible
P(E) = ø
Probability of an Event
P(E) = number of favorable outcomes/total number of possible outcomes
2 is the only
Even prime number
∅ Is neither
Positive or Negative
∅ is a multiple of
Every number
∅ divided by 7
∅
3 is the opposite of
-3
The reciprocal of any non-zero #x is
1/x
The percent decrease of a quantity
= (actual decrease/Original amount) x 100%
If a>b then
-a<-b
i.e. 100 x (1-50%)=100x.5=50
...
For any number x
Can be negative, zero, or positive
If a lamp increases from $80 to $100, what is the percent increase?
= 25%.
Vertical lines
Do not have slopes!
To decrease a number by x%
multiply by 1-x%
Circumference of a circle
2(pi)r
The reciprocal of any non-zero number is
1/x
Volume of a cube
edge³
The product of any number x and its reciprocal
1
THE DENOMINATOR CAN NEVER
BE ZERO! 1/∅=null
7 divided by ∅
Null
i.e. 100 x (1+50%)=100x1.5=150
...
Probability of Event all cases
∅≤P(E)≤1
Consecutive integers
x, x+1, x+2
Any Horizontal line slope
zero
Slope of any line that goes down as you move from left to right is
Negative
= 20/80 x 100% = 1/4 x 100% = 25%
...
∅ Is
EVEN
To increase a number by x%
multiply by 1+x%
Area of a circle
(pi)r²
Positive integers that have exactly 2 positive divisors are
Prime numbers (2, 3, 5, 7, 11, 13, 17, 19, 23)
Volume of a rectangular solid
(length)(width)(height)
Section 8
(50 cards)
7/8 in percent?
87.5%
b¹
1
3/8 in percent?
37.5%
50 < all primes< 60
53, 59
A number is divisible by 4 is...
its last two digits are divisible by 4.
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
a(b-c)
ab-ac
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)
1ⁿ
1
20<all primes<30
23, 29
30< all primes<40
31, 37
-3³
-27
2⁵+2³
2⁸
If a is positive, aⁿ is
Positive
a<b then a - b is positive or negative?
a-b is negative
30 60 90
3x, 4x, 5x
70 < all primes< 80
71, 73, 79
Number of degrees in a triangle
180
2³×7³
(2x7)³
∅ is
Even
What are the irrational numbers?
All real numbers which can't be expressed as a ratio of two integers, positive and negative (pi, -sqrt3)
30 60 90
x, x(SR3), 2x
a>b then a - b is positive or negative?
a-b is positive
If a is negative and n is even then aⁿ is (positive or negative?)
aⁿ is positive
1/8 in percent?
12.5%
1/6 in percent?
16.6666%
a/∅
Null
1 is a divisor of
every number
40 < all primes<50
41, 43, 47
1 is the
smallest positive integer
A number is divisible by 9 if...
the sum of digits is divisible by 9.
If a<b, then
a+c<b+c
30 60 90
5, 12, 13
30 60 90
3, 4, 5
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)
A number is divisible by 6 if...
its divisible by 2 and by 3.
-3²
9
∅ is
A multiple of every integer
What are the integers?
All numbers multiples of 1.
2⁵/2³
2²
(2²)³
2⁶
a(b+c)
ab+ac
10<all primes<20
11, 13, 17, 19
bⁿ
b∧b∧b (where b is used as a factor n times)
∅²
∅
60 < all primes <70
61, 67
1 is an
ODD number
5/8 in percent?
62.5%
Section 9
(50 cards)
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).
Area of a triangle?
(base*height) / 2
What is an isoceles triangle?
Two equal sides and two equal angles.
What is the "range" of a function?
The set of output values for a function.
Can you simplify sqrt72?
Yes, because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
(x^2)^4
x^(2(4)) =x^8 = (x^4)^2
What is the slope of a vertical line?
Undefined, because we can't divide by 0.
Pi is a ratio of what to what?
Pi is the ratio of a circle's circumference to its diameter.
What are "supplementary angles?"
Two angles whose sum is 180.
a^2 + 2ab + b^2
(a + b)^2
Define a "monomial"
An expression with just one term (-6x, 2a^2)
(6sqrt3) x (2sqrt5) =
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
Can you add sqrt 3 and sqrt 5?
No, only like radicals can be added.
Circumference of a circle?
Diameter(Pi)
Can you subtract 3sqrt4 from sqrt4?
Yes, like radicals can be added/subtracted.
What is a chord of a circle?
A chord is a line segment joining two points on a circle.
What is the slope of a horizontal line?
0
What is a central angle?
A central angle is an angle formed by 2 radii.
How to determine percent decrease?
(amount of decrease/original price) x 100%
10^6 has how many zeroes?
6
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 sum of the angles of a triangle?
180 degrees
5/6 in percent?
83.333%
What is a major arc?
The longest arc between points A and B on a circle's diameter.
When does a function automatically have a restricted domain (2)?
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
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^0 =
1
What is an arc of a circle?
An arc is a portion of a circumference of a circle.
a^2 - b^2
(a - b)(a + b)
What is a tangent?
A tangent is a line that only touches one point on the circumference of a circle.
a^2 - 2ab + b^2
(a - b)^2
If an inequality is multiplied or divided by a negative number....
the direction of the inequality is reversed.
Formula to find a circle's circumference from its diameter?
C = (pi)d
What is the "domain" of a function?
The set of input values for a function.
The larger the absolute value of the slope...
the steeper the slope.
Formula to find a circle's circumference from its radius?
C = 2(pi)r
0^0
undefined
x^6 / x^3
x^(6-3) = x^3
If the two sides of a triangle are unequal then the longer side.................
lies opposite the greater angle
What is a minor arc?
The shortest arc between points A and B on a circle's diameter.
What is the "range" of a series of numbers?
The greatest value minus the smallest.
Formula to calculate arc length?
Arc length = (n/360) x pi(2r) where n is the number of degrees.
Factor a^2 + 2ab + b^2
(a + b)^2
(12sqrt15) / (2sqrt5) =
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
To multiply a number by 10^x
move the decimal point to the right x places
What is the order of operations?
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
x^4 + x^7 =
x^(4+7) = x^11
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)
Solve the quadratic equation ax^2 + bx + c= 0
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
Section 10
(50 cards)
64^5 = (4^3)^5 = 4^15
...
Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
2 & 3/7
Legs 6, 8. Hypotenuse?
10
Formula for the area of a sector of a circle?
Sector area = (n/360) X (pi)r^2
Evaluate 3& 2/7 / 1/3
9 & 6/7
Legs: 3, 4. Hypotenuse?
5
Is 0 even or odd?
Even
How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
0
True or false? 4.809 X 10^7 = .0004809 X 10^11
True
What is the graph of f(x) shifted upward c units or spaces?
f(x) + c
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%.
Convert 0.7% to a fraction.
7 / 1000
What are the roots of the quadrinomial x^2 + 2x + 1?
The two xes after factoring.
What is the graph of f(x) shifted downward c units or spaces?
f(x) - c
T or F? Given d,e &f =/ 0, [(d^3)e(f^5)] / 2d(e^3) / [3(d^2)(e^3)(f^7)] / [6(e^5)(f^2)]?
True
Simplify (a^2 + b)^2 - (a^2 - b)^2
4a^2(b)
Evaluate 4/11 + 11/12
1 & 37/132
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 the "solution" for a system of linear equations?
The point of intersection of the systems.
Legs 5, 12. Hypotenuse?
13
Formula for the area of a circle?
A = pi(r^2)
16^8=(4^2)^8 = 4^16
...
What is the "solution" for a set of inequalities.
The overlapping sections.
What is the graph of f(x) shifted left c units or spaces?
f(x + c)
What percent of 40 is 22?
55%
Whats the difference between factors and multiples?
Factors are few, multiples are many.
The perimeter of a square is 48 inches. The length of its diagonal is:
12sqrt2
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.
8.84 / 5.2
1.7
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
What number between 70 & 75, inclusive, has the greatest number of factors?
72
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
P and r are factors of 100. What is greater, pr or 100?
Indeterminable.
Factor x^2 - xy + x.
x(x - y + 1)
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
Evaluate (4^3)^2
4096
How many multiples does a given number have?
Infinite.
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
Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
2sqrt6
Simplify 9^(1/2) X 4^3 X 2^(-6)?
3
What are the smallest three prime numbers greater than 65?
67, 71, 73
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 are complementary angles?
Two angles whose sum is 90.
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 the expression [(b^2 - c^2) / (b - c)]
(b + c)
Reduce: 4.8 : 0.8 : 1.6
6 : 1 : 2
What is the graph of f(x) shifted right c units or spaces?
f(x-c)
What are congruent triangles?
Triangles with same measure and same side lengths.
Which is greater? 64^5 or 16^8
16^8
Section 11
(50 cards)
Describe the relationship between the graphs of x^2 and (1/2)x^2
The second graph is less steep.
A cylinder has a surface area of 22pi. If the cylinder has a height of 10, what is the radius?
1
If 4500 is invested at a simple interest rate of 6%, what is the value of the investment after 10 months?
4725
What is a subset?
a grouping of the members within a set based on a shared characteristic.
What is the third quartile of the following data set: 44, 58, 63, 63, 68, 70, 82
70
What is the empty set?
A set with no members, 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.
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 area of a regular hexagon with side 6?
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
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)!
What is an exterior angle?
An angle which is supplementary to an interior angle.
What is the maximum value for the function g(x) = (-2x^2) -1?
-1
6w^2 - w - 15 = 0
-3/2 , 5/3
5x^2 - 35x -55 = 0
[(7+ sqrt93) /2], [(7 - sqrt93) / 2]
What is a set with no members called?
the empty set, denoted by a circle with a diagonal through it.
What is the measure of an exterior angle of a regular pentagon?
72
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
1:1:sqrt2 is the ratio of the sides of what kind of triangle?
An isosceles right triangle.
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
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
For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
-8
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 the "union" of A and B?
The set of elements which can be found in either A or B.
In similar hexagons, the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
4:5
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 a finite set?
A set with a number of elements which can be counted.
What is the ratio of the sides of a 30-60-90 triangle?
1:sqrt3:2
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)!
What is the common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd?
cd
Simplify the expression (p^2 - q^2)/ -5(q - p)
(p + q)/5
What is the intersection of A and B?
The set of elements found in both A and B.
What is the ratio of the sides of an isosceles right triangle?
1:1:sqrt2
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 transformation occurs if point C is reflected over the x-axis and then the y-axis?
A reflection about the axis.
(a^-1)/a^5
1/a^6
The ratio of the areas of two similar polygons is ...
... the square of the ratios of the corresponding sides.
The objects in a set are called two names:
members or elements
What is the set of elements found in both A and B?
The interesection of A and B.
What are the members or elements of a set?
The objects within a set.
How many 3-digit positive integers are even and do not contain the digit 4?
288 (8 9 4)
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 coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
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
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
1:sqrt3:2 is the ratio of the sides of what kind of triangle?
A 30-60-90 triangle.
A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
13pi / 2
x^2 = 9. What is the value of x?
3, -3
How many sides does a hexagon have?
6
Section 12
(12 cards)