Quantitative Reasoning DAT
Convert 2 and 3/7 to a fraction
17/7 pg 737
What is 1/8 converted to percent?
12.5%
What is the volue of a 4-by-5-by-6 box?
120
Change 0.564 to a fraction
141/250 pg 741
HOw many degrees are in 5π/6 radians?
150 pg 830
In the right triangle on pg 828, if the sine of angle theta is 0.5, what is the value of x?
16
What is the volume of a pyramid with height 3 and B=16?
16
What is the area of a circle of radius 4?
16π
What is the surface area of a sphere if the radius is 2?
16π
In the figure below, the perimeter of isosceles trapezoid ABCD is 50. If BC=9 and AD=21, what is the length of the diagonal AC? pg 803
17
What do consecutive angles in a parallelogram add up to?
180
What is the sum of the interior angles of all triangles?
180 degrees
how many degrees does 1 radian correspond to?
180/π or 57.3
What are the side ratios of a 45°-45°-90° triangle?
1:1:√2
What are the side ratios of a 30-60-90 degree triangle?
1:√3:2
What is the mode of the set {1, 2, 2, 2, 3, 4, 4, 5, 6}?
2
Which is the only even prime number?
2
what is log(100)
2
What equation can be used to determine the perimeter of a rectangle?
2 (length + width)
What are the first 4 prime numbers?
2, 3, 5, 7
A square and a regular hexagon have the same perimeter. If the area of the square is 2.25, what is the area of the hexagon?
2.598
Find the average of 12,15,23,40,40
26
What is the equation for surface area of a rectangular solid?
2lw + 2wh + 2 lh
Factor the following polynomial: 8xy + 18y²
2x(4x+9y)
For the function f(x) = sinx, sin(x+2π) = sinx for all x, then what is the period of the function?
2π
How many radians are there in the circumference of any circle?
2π
What is the period for the function f(x)=sinx?
2π
If two angles of a triangle are 100 and 50, what is the third angle?
30
What is the name of the integer of the logarithmic number when working with logarithms to the base 10?
characteristic
What does it mean to make combinations in probability?
choosing small groups from a larger group
How do you add or subtract polynomials?
combine like terms pg 758
What is the decimal fraction called when working with logs in the base 10?
mantissa
How do you multiply powers with the same exponent?
multiply the bases and keep the exponent
How do you determine the tangent of the angle theta in a right triangle?
the length of the opposite side over the length of the adjacent side
Why is the value of arctan x defined to be in the interval -90<y<90?
Because there are infinitely many values of y such that tany=x and a function must associate exactly one number with each number in the domain
Why don't piecewise functions have a general form?
Because they can be continuous or discontinuous
Which of the following lines has no point of intersection with the line y=4x+5? pg 822
C
What is the solution set of |2x-3|<7 pg 767
C.
If (3ⁿ^2)(9ⁿ)(3)=27 and x>0, what is the value of x? A. 0.27 B. 0.41 C. 0.73 D. 1.41. E. 1.92
C. 0.73 pg 774
The average of 3,15,18, and 8 is A. 5 B. 9 C. 11 D. 15 E. 18
C. 11
2/7 + 1/4 = A. 1/11 B. 3/28 C. 15/28 D. 7/8 E. 13/11
C. 15/28
If 19 19 then x= ---- = --- 5x+17 31 A. 0.4 B. 1.4 C. 2.8 D. 3.4 E. 4.8
C. 2.8 They have the same numerator, so they will have the same denominator. Thus 5x+17 = 31
A code is to be made by arranging 7 letters. Three of the letters used will be the letter A, two of the letters used wll be the letter B, one of the letters used will be the letter C, and one of the letters used will be the letter D. If there is only one way to present each letter, how many different codes are possible? A. 42 B. 210 C. 420 D. 5040 E. 6025
C. 420 pg 796
Caol spends 1/4 of her savings on a stereo, and then she spends 1/3 less than she spent on the sterio for a television. What fraction of her savings did she spend on the sterio and television together? A. 1/4 B. 2/7 C. 5/12 D. 7/12 E. 3/4
C. 5/12
If θ is an acute angle for which tan² θ = 6 tan θ - 9, what is the approximate measure of θ? A. 30° B. 45° C. 75° D. 90° E. 105°
C. 75
Pg 771 #3
D
If 8ⁿ=16ⁿ⁻¹, then what is x? A. 1/8 B. 1/2 C. 2 D. 4 E. 8
D. 4 pg 764
Amanda goes to the toy store to buy 1 ball and 3 different board games. If the toy store is stocked with 3 types of balls and 6 types of board games, how many different selections of the 4 items can amanda make? A. 20 B. 23 C. 40 D. 60 E. 80
D. 60 page 795
Ron begins reading a book at 4:30 pm and reads at a steady pace of 30 pages per hour. Michelle begins reading a copy of the same book at 6:00 pm. If Michelle started 5 pages behind the page that Ron started on and reads at an average pace of 50 pages per hour, at what time would Ron and Michelle be reading the same page? A. 7 pm B. 7:30 pm C. 8 pm D. 8:30 pm E. 9 pm
D. 8:30 pm pg 721
How many integers are in the solution set of |4x+3|<8? A. none B. two C. three D. four E. five
D. four page 776
Which of the following shaded regions shows the graph of the inequality y ≤ |x + 2|? Pg 825
E.
If a pencil costs 0.26, what is the cost of 96 pencils? A. 2.49 B. 12.00 C. 24.00 D. 22.96 E. 24.96
E. 24.96
Convert the following word problem into an equation: Guiseppa's weight s 75 pounds more than twice Jovanna's weight
G=2J+75
What does the pythagorean theorem state and what equation corresponds with it?
In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs
How does the degree of "lean" of a rhombus affect its area and how?
It dereases the area, because the more leaned over it is, it would have a smaller height
If x is a point of the domain, then what is f(x)?
It is the number associated with x by the function f
How do you find the probability that one or another of two mutually exclusive events will occur?
Just add the probabilities of the two events
Graph y - √(2x-5)
Pg 769
Graph y = 3x + 2
Pg 769
Graph y = |x + 1|
Pg 769
If f(x)=f(x+R), what is R in this situation?
R is the smallest positive number for which the function is ture
Convert the following word problem into an equation: The sum of Richard's age and Cindy's age in years is 17 more than the amount by which Tim's age is greater than Kathy's age
R+C=(T-K) + 17
What does the inverse tangent of x represent conceptually?
The angle y such that -90<y<90 and tan y=x.
What is the range of a set?
The difference between the largest term in the set and the smallest ter
What is a product?
The result of multiplication
What is a difference?
The result of subtraction
What is a reciprocal?
The result of switching the numerator and denominator of a fraction
What is true of the standard deviation of sets {1, 2, 3} and {101, 102, 103}?
They have the sae standard deviations
What is a square?
a four sided figure with four riht angles and four equal sides
What is a rhombus?
a four-sided figure with four equal sides
What is a rectangle?
a four-sided figure with four right angles in which opposite sides are equal and diagonals are equal
What is a trapezoid?
a four-sided figure with one pair of parallel sides and one pair of nonparallel sides
What is an improper fraction?
a fraction whose numerator is greater than the denominator
What is a prime number?
a natural number which is divisible by exactly 2 natural numbers, itself and 1
What is a mixed number?
a number consisting of an integer and a fraction
What is an irrational number?
a number which never terminates and never repeats
What is an arc of a circle?
a piece of the circumference of the circle
What is a piece of the area of a circle called?
a sector
What is an isosceles triangle?
a triangle that has two equal sides
What is a cylinder?
a uniform solid whose base is a cricle
What is the equation for cotangent?
adjacent/opposite
What 3 types of numbers are rational?
all integers, all numbers with finite decimals, or any numbers with repeating decimals
What is a real number?
all numbers on the number line
What is an elementary event in terms of probability?
an event that is a set consisting of only one outcome
What is a cone?
an object formed from a round base connected to a point called a vertex
What is the equation for area of a rhombus?
base x height
Why can the inverse sine function not be defined for x values below negative 1 or above 1?
because inverse sine finds the angle y such that sin y =x and that angle y is between -90° and 90°. Since the sine of -90 is -1 and the sine of 90 is 1, that becomes the new domain of the inverse sine
Why are the y values of -90 and 90 not possible values of the inverse tangent function?
because tan 90 and tan -90 are both underfined
How do you determine the x or y intercept when graphing a function?
by setting x or y as zero
What is the name for the reciprocal of tangent?
cotangent
What method do you use to solve a proportion?
cross-multiplu
What is 2/3 in decimal and percent?
decimal: 0.66 percent: 66 2/3 %
What is 3/4 in decimal and percent?
decimal: 0.75 percent: 75%
How often does the graph of y=tan x repeat itself?
every 180 degrees
How often does the trigonometric function f(x)=sin(x) repeat itself?
every 360 degrees
What two methods can you use to compare fractions?
express them with a common denominator or convert to decimals
How do you divide fractions?
flip the numerator and denominator of the fraction you're dividing by, then multiply
When is the graph of y=tan x undefined?
for every odd multiple of 90 degrees
What is the sign of the answer if you multiply or divide two numbers with the same sign?
gives a positive result
Is 2 a prime number, why or why not?
it is because it is divisible by only 2 natural numbers (1 and 2)
How do you determine the number of permutations, or arrangements, of n items?
it is n! or n factorial
Is 51 a prime number, why or why not?
it is not because it is divisible by 1, 3, 17, and 51. So it is divisible by more than two natural numbers
Is 0.3333333... rational or irrational/
it is rational because it can be represented as a ratio of two integers: 1/3
How do you determine the sine of angle theta in a right triangle?
it is the lenght of the side opposite the angle divided by the lenght of the hypotenuse
How do you determine the cosine of a right angle?
it is the length of the side adjacent to angle theta divided by the length of the hypotenuse
How do you determine the value of n factorial?
it is the product of n and every positive integer smaller than n
What is an empty set in terms of probability and how is it represented?
it is the unique set having no elements, which is represented by ∅
If the length of one side of a triangle is 3 and another is 7, what will be the length of the third side according to the triangle inequality theorem?
it must be greater than 4 but less than 10
How can you differentiate between a combination and permutation question?
it the selectron is unordered, its a combination. If it's ordered, it's a permutation
How do you multiply powers with the same base?
keep the base and add the exponents
How do you raise a power to an exponent?
keep the base and multiply the exponents
How do you divide powers with the same base?
keep the base and subtract the exponents
How can you convert a mixed number to an improper fraction?
keep the denominator of the fraction and multiply the integer portion by the number in the denominator, then add this to the original numerator of the mixed fraction
How do you combine like terms?
keep the variable part unchanged while ading or subtracting the coefficients pg 758
What are the two sides of a right triangle called which form a right angle?
legs
What is the equation for area of a rectangle?
length x width
What is the equation for the volume of a rectangular solid?
length x width x height
What is log(s/t) equivalent to?
log (s) - log (t)
What is log (s*t) equivalent to?
log(s)+log (t)
How do you multiply polynomials?
multiple each term in the first polynomial by each term in the second pg 758
What magnitude does the total change by in an increase of one logarithmic unit in base 10?
multiply it by 10
How do you multiply mononomials?
multiply te coefficients and the variables separately pg 758
What i the basic formular for probability?
number of desired outcomes/number of possible outcomes
What does it mean if two events are independent?
one of these events has absolutely no effect on the probability of the other
What is the order of operations?
parentheses exponents multiplication division addition subtraction
If the order of selection matters, do you use a combination or a permutation?
permutation
For al xyz..... pg 757
pg 757
If a=...... pg 765
pg 765
A bag contains 20 identical plastic tiles. Eleven of the tiles are marked with the numbers 1 through 11 inclusive. The remaining 9 tiles are marked with the letters A through I inclusive. If a single tile is drawn at random from the bag, what is the probability that it bears either an even number or a vowel?
pg 781 2/5
What is the equation for determining standard deviation?
pg 785
In the figure above (pg 797), then length of the segment PS is 2x+12, and the lenght of segment PQ is 6x-10. If R is the midpoint of segment QS, what is the length of segment PR?
pg 798
What is the difference between a line with a negative vs positive slope?
positive: line that goes uphill from left to right negative: line that goes downhill
How do you add fractions?
put the fractions in a form so that they have the same denominators, then add the numerators together
How do you dubstract fractions?
put the fractions in a form so that they have the same denominators, then subtract the numerators from one another
How do you solve an equation when the unknown is an exponent?
re-express both sides of the equation so that the two sides have the same base
When estimating the solution to a subtraction problem, how do you round the numbers?
round both numbers in the same direction
When estimating the solution to a division problem, how do you round the numbers?
round both numbers in the same directiong
When estimating the solution to a multiplication problem, how do you round the numbers?
round one number up and the other number down
What is the name for the reciprocal of cosine?
secant
What does tan²x + 1 =?
sec²x
What is the equation for area of a square?
side²
What is the median of a group containing an even number of terms?
the average of the two middle numbers
What is true of corresponding angles and sides in similar triangles?
the correspondng angles are equal and correspondng sides are proportional
What is the standard deviation of a set?
the dispersion of a set of numbers around the ean
Between the sets {1, 3, 5} and {0, 3, 6}, which has a smaller standard deviation? Calculate the standard deviation for each
the first one 1. √8/3 2. √6 Pg 786
What is the median of a group containing an odd number of terms?
the middle value when they are arranged in numerical order
What is the mode of a set?
the number that appears most frequently
If one leg of a right triangle is 36 and the hypotenuse is 39, what is the lenght of the other leg? how can you determine this?
the other leg is 15, because it is a 5-12-13 triangle
What is the height of a triangle?
the perpindicular distance between the side that's chosen as the base and the opposite vertex
How do you find the probability of two events, A and B, occuring if they are independent?
the probability of event A occurring multiplied the probability of event B occurring
What is a sum?
the result of addition
What is the hypotenuse of a right triangle?
the side opposite the right angle
What is the measure of the exterior angle of a traingle equal to?
the sum of the measures of the remote interior angles
What is true of the length, width, and height of a cube, a type of rectangular solid?
they are all equal
What is true of the presence of irrational numbers?
they are not all that uncommon, and there is atleast one irrational number between any 2 rational ones
What is a natural number
they are the counting numbers starting from 1
What is true of the slopes of lines that are perpindicular to each other?
they have negative reciprocal slopes
What is true of the slopes of lines that are parallel to each other?
they have the same slope
What are similar triangles?
triangles which have the same shape
What is the slope of a line parallel to the y-axis?
undefined
What is the shape and equation for a quadratic function?
y = ax² + bx + c and is a parabola
What is the equation and shape of a linear function?
y = mx + b, which is a straight line
Order the following from least to greatest: 4/9, 3/4, 4/5, 11/12, 13/15
yellow notebook under heading QR video 9 4/9, 3/4, 4/5, 13/15, 11/12
How and when can you factor difference of squares?
you can factor two identifiable squares with a minus sign between them a²-b²=(a-b)(a+b)
When solving an inequality, how do you know when to reverse the inequality sign?
you reverse it when you multiply or divide both sides by a negative number
What are three common irrational numbers in math?
π e √2
In the figure below, rectangle ABCD is inscribed in a circle. If the radius of the circle is 1 and AB=1, what is the area of the shaded region? pg 810
π/3 - √3/4
What is the equation for area of the base of a cylinder?
πr²
What is the formula for the area of a circle?
πr²
Waht is the equation for volume of a cylinder?
πr²h
What is i equivalent to?
√-1
If one leg of a right triangle is 2 and the other is 3, what is the hypotenuse?
√13
In the figure below, ∆ABC is equilateral and ∆ADC is isosceles. If AC=1, what is the distance from B to D? pg 802
√3 - 1 ------- 2
Convert this to an addition problem and solve: (-4) -1
(-4) + (-1)=-5
What is the volume of a sphere if the radius is 2?
(32π)/3
Convert the following word problem into an equation: In 5 years, Sandy will be four years younger than twice Tina's age
(S+5)=2(T+5)-4
What is the equation to measure the length of an arc of a circle?
(n/360) (2πr)
What is log(0.1)?
-1
When 2x³ + 3x -4x + k is divided by x+2, the remainder is 3. What is the value of k?
-1 pg 759
What is sin 210°?
-1/2 pg 832
Solve x² +4x+2=0 pg 765
-2±√2
What is the sum of -7 and +4?
-3
What is the arctan(-1) and why?
-45, because tan(-45)=1
Convert this to an addition problem and solve: (-5) -(-2)
-5 + 2=-3
What is log(1)
0
What is the slope of a line that is parallel to the x-axis?
0
what is log(10)
1
What is i⁴, i⁵, i⁶?
1 i -1
What is i⁰, i¹, i², i³
1 i -1 -i
If 2x-9y=11 and x+12y=-8, what is the value of x+y?
1 pg 766
how many radians are in a central angle if it intercepts an arc with length equal to the radius
1 radian
What are the five steps for determining the standard deviation of a set?
1. Find the arithmetic mean of the set 2. Subtract the mean of the set from each term in that set 3. Square each result 4. Take the mean of those squares 5. Calculate the positive square root of that average
How can you find the area of a right triangle?
1/2(leg1)(leg2)
What equation is used to give the volume of a cone?
1/3πr²h
There are 4 blue disks and 12 green disks in a container. Two disks are to be removed from the container, one after the other. What is the probability that the first disk selected is blue and the second disk selected is green?
1/5
What is the median value of 2,7,8,12,16, and 37?
10
Solve 30 - 5 x 4 + (7-3)² ÷8
12
What is 25% of 48?
12
How any edges and vertices are there in a rectangular solid?
12 edges and 8 vertices
How many ways ae there to arrange the letters in the word ASSETS?
120 pg 790
If log5(x)=3, then x=?
125
A company is selecting 4 members of its board of directors to it on an ethics subcommittee. If the board has 9 members, any of whom may serve on the subcommittee, how many differen selectrions of members could the company make?
126 pg 787
If the probability of finding a pearl in a given oyster is 1/3 and the probability of any given pearl being black is 2/5, what's the probability that if you crack open a randomly chosen oyster, you'll find a black pearl?
2/15
What is the volume of a cylinder with r=2 and h=5?
20π
What is the area of a 7-by-3 rectangle?
21
What is the range of the set {2, 4, 10, 20, 26}?
24
What is the area of a square with side lenght 5?
25
If the value of a certain piece of property now is 350% of its original value when Kim purchased it, by what percent has the value of the property increased since Kim purchased it?
250%
What is log(1,000)
3
If the hypotenuse of a 30-60-90 degree triangle is 6, then what are the two legs?
3 and 3√3
What is the simplest pythagorean triplet?
3,4,5
Solve (6.2E5)/(2.0E-7)
3.1E12
solve (6.0x10⁴)²
3.6E9 pg 743
solve 3.7E4 +1.5E3
3.9E4 pg 744
How many degrees correspond to 2π radians
360
If the radius of a circle is 6 and the measure of a sectors special angle is 30°, then what is the area of the sector?
3π
How many radians are there in 270 degrees?
3π/2
If both legs of a 45-45-90 triangle is 3, what is the hypotenuse?
3√2
What is log10(10000)?
4
Convert 23/4 to a mixed number
5 and 3/4
How many feet are there in a mile?
5,280
solve (1.1E6)(5.0E17)
5.5E23
What is the reciprocal of 3/5?
5/3
What is 1/2 converted to percent?
50%
If the average of 10 numbers is 50, what is the sum of all of the numbers?
500
Convert 5 and 8/9 to a fraction
53/9
If logb(36)=2 then b=?
6
Solve 66 x (3-2) ÷ 11?
6
What is true of the angles in an equilateral triangle?
60 degrees each
convert 3/5 to a percent
60% pg 744
What is the volume of a cube whose side is length 2?
8
What is the addition problem that corresponds to this subtraction problem? 8-5
8 + (-5)
In the rectangular solid in the figure below (pg 816), what is the distance from vertex A to vertex B?
9
Pg 771 #2
A
What is a parallelogram?
A four-sided figure with two pairs of parallel sides with opposite sides and angles equal to one another
What defines a right triangle?
A triangle with one right angle
If sin θ = 1/2 cos θ, and 0 < θ < π/2, the value of 1/2 sin θ is A. 0.22 B. 0.25 C. 0.45 D. 0.50 E. 0.75
A. 0.22 Pg 838
Pg 837 # 2 A. 1 B. 2 C. cos θ + sinθ D. cos θ - sinθ E. cos²θ + sin² θ
A. 1
In the list 3, 4, 5, 5, 5,5, 7, 11, 21, what fraction of the data is less than the mode? A. 2/9 B. 1/3 C. 2/3 D. 7/9 E. 8/9
A. 2/9
What is the general formula for the area of a triangle?
A=1/2 (base)(height)
What is an integer?
All numbers with no fractional or decimal parts, including negative whole numbers and zero
Pg 751 #4
B
When 3x³-7x+7 is divided by x+2, the remainder is: A. -5 B. -3 C. 1 D. 3 E. 5
B. -3 pg 773
Which of the following numbers is smallest? A. 0.1 B. 0.01 C. 0.0407 D. 0.03995 E. 0.043999
B. 0.01
A certain circular stopwatch has exactly 60 second marks and a single hand. If the hand of the watch is randomly set to one of the marks and allowed to count exactly 10 seconds, what is the probability that the hand will stop less than 10 marks on either side of the 53-second mark? A. 1/6 B. 19/60 C. 1/3 D. 29/60 E. 41/60
B. 19/60
If a bicyclist in motion increases his speed by 30 percent and then increases this speed by 10 percent, what percent of the original speed is the total increase in speed? A. 40% B. 43% C. 64% D. 140% E. 180%
B. 43%
Subtract 8 from 2
-6
What are the 5 major steps when graphing equations?
-determine which type of function is presented -identify the y-intercepts and the x-intercepts -identify the zeros of the functions -find the domain -determine the range
What are the 6 main types of functions?
-linear -absolute value -quadratic -polynomial -radical -piecewiseq
In a right triangle, what does sin²θ + cos²θ equal?
1
A bag contains ten identically shaped plastic tiles.Six of the tiles are red, three are blue, and one is black. If two tiles are drawn at random from the bag, without replacement, what is the probability that the first tile drawn is red and the second tile drawn is black?
1/15
What is log25(5)?
1/2
What is the reciprocal of 2?
1/2
Solve this equation using the distributive law: 3+5 ----- 2
1/2(3) + 1/2 (5) 3/2+5/2=8/2 4
Solve for x: x/5 = 3/4
15/4 or 3.75 pg 738
If a cone has radius of 3 and a height of 6, what is the volume?
18π (pg 818)
If log10(100)=c, then c=?
2
What is log4(16)?
2
What is the ratio of 20 oranges to 12 apples?
20/12 or 5/3
If the distance between the city of New York and the city of London is approximately 3,500 miles, how many inches apart are these cities?
222,000,000 Pg 748
What are the answers to the following: (-4) * (-7) (-50)/(-5)
28 10
If the radius of a circle is 5 and the central angle is 72°, what is the length of the arc?
2π
What is an operation?
A process that is performed on one or more numbers. The four basic arithmetic operations are addition, substraction, multiplication, and division
What is the value of 2,886/37 A. 78 B. 708 C. 780 D. 7008 E. 7800
A. 78
If 4x+ky=15 and x-ky=-25, which of the following could be the values of x and y? A. x=-3 and y=-5 B. x=-2 and y=3 C. x=0 and y=-2 D. x=2 and y=3 E. x=3 and y=2
B. x=-2 and y=3
What is the value of 5 (1/4) /7 A. 7/20 B. 5/7 C. 3/4 D. 6/7 E. 3
C. 3/4
What is the cost of a blouse that is priced at 50.00 with a tax of 7%? A. 35.00 B. 50.35 C. 53.50 D. 62.75 E. 85.00
C. 53.50
16+0.267+36.78 A. 5.347 B. 8.26 C. 50.036 D. 52.047 E. 53.047
E. 53.047
A machine is made up of two components, A and B. Each component either works or fails. The failure or nonfailure of one component is independent of the failure or nonfailure of the other component. The machine works if at least one of the components works. If the probability that each component works is 2/3, what is the probability that the machine works? A. 1/9 B. 4/9 C. 1/2 D. 2/3 E. 8/9
E. 8/9 page 795
What does 1 + cot²x =?
csc²x
If p,q, and r are positive integers such that q is a factor of r and r is a multiple of p, which of the following must be an integer? pg 724
c
What is 123 in scientific notation?
1.23 x 10²
Pg 723 # 4
B pg 726
What five traits do all triangles share?
-sum of the interior angles is 180 -measure of exterior angle is equal to the sum of the measures of the remote interior angles -the measures of the three exterior angles are 360 -they all have the same area formula -triangle inequality theorem
What are four signals that icking numbers will be a possible approach to a problem?
-variables in the answer choices -percents in the answer choices -answers that are fractions of an unknown value -number property questions
A fari six-sided die with sides numbered 1, 2, 3, 4, 5 and 6 is thrown What is the probability it lands with an even number facing up?
1/2
What is sin 30° equal to?
1/2
What is sin 390° equal to?
1/2
What is the equation for lateral area of a cone?
1/2(c)(l) where c is the circumference of the base and l is the slant height
Out of the 1,000 employees of a company, 5 employees have the job title of accountant. If one of these employees is selected at random, what is the probability this employee has the job title of accountant?
1/200
What is the equation for volume of a pyramid?
1/3 Bh
A bag contains 10 identical balls numbered 1 through 10 inclusive. If a ball is drawn from the bag at random, what is the probability (as percent) that it bears a number less than four?
30%
If the new price of an item is 130% of its previous price, then what is the percent increase of the price?
30%
What is the arcsin(1/2) equal to and why?
30° because sin 30=1/2 and 30 is in the interval -90<y<90
County X holds an annual math competition to which each county high school sends a team of 4 students. If school A has 6 boys and 7 girls whose math grades qualify them to be on their school's team, and competition rules stipulate that the team must consist of 2 boys and 2 girls, how many different teams might school A send to the competition?
315 pg 788
A restaurat is hanging 7 large tiles on its wall in a single row. How many arrangements of tiles are possible if there are 3 white tiles and 4 blue tiles?
35 pg 790
What is the mode of the set {35, 42, 35, 57, 57, 19}
35 and 57
What is the sum of the three exterior angles of a triangle?
360
What must be the sum of the exterior angles of all polygons?
360
What is 0.042 in scientific notation?
4.2 x 10⁻²
What is the equation for the volume of a sphere?
4/3 πr³
If one leg of a right triangle is 30 and the hypotenuse is 50, what is the other leg?
40
If a number increases from 50 to 70, what is the percent increase?
40%
If an item goes on sale at 60% of its previous price, then what is the percent decrease?
40%
What is the equation for the surface area of a sphere?
4πr²
What is the median of 4,5,100,1, and 6?
5
Suppose a fair sided die with sides numbered 1 through 6 is tossed. What is the probability that a 4 is not rolled?
5/6
A certain pet store has 13 mice in a single tank. five of the mice are white, and 8 of the mice are brown. If the store clerk reaches int teh mice's tank to select a mouse at random, what is the probability that the mouse is white?
5/`13
Suppose a fair coin is tossed and a fair die with sides numbered 1,2,3,4,5, and 6 is rolled. Ket A be the event that the oin toss results in a head. Let B be the event that the roll of the die results in a 5. What is the probability that at least one of the events A or B ocurs?
7/12 pg 783
In the figure below (pg 814), the bases of the right uniform solid...
72
There are 6 children at a family reunion, 3 boys and 3 girls. They will be lined up single-file for a photo, alternating genders. How many arrangements of the children are possible for this photo?
72 pg 789
How many ways are there to arrange the letters in the word ascent?
720 pg 788
A car rental companty charges for mileage as follows: x dollars per mile for the first n miles and x+1 dollars per mile for each mile over n miles. How much will the mileage charge be, in doullars, for a journey of d miles where d>n? A. d(x+1)-n B. xn+d C. xn +d(x+1) D. x(n+d) -d E. xd+n
A pg 718
Pg 771 #5
B pg 773
If x=3-y² and y=-2, what is the value of x? A. -2 B. -1 C. 1 D. 2 E. 3
B. -1
What is the y-coordinate of the point at which the graph of y = 2 sin x - cos 2x intersects the y-axis? A. -2 B. -1 C. 0 D. 1 E. 2
B. -1
In the figure below, what is the value of cos θ? Pg 837 A. 0.25 B. 0.66 C. 0.75 D. 0.80 E. 1.25
B. 0.66
If 2 is the remainder when m is divided by 5, what is the remainder when 3m is divided by 5? A. 0 B. 1 C. 2 D. 3 E. 4
B. 1
Which of the following fractions is largest? A. 1/5 B. 1/2 C. 2/7 D. 2/10 E. 3/9
B. 1/2
A certain machine produces toy cars in a repeating cycle of blue, red, green, yellow, and black. If a string of six consecutively produced cars is selected at random from all the possible strings of six consecutively produced cars, what is the probability that, in the string selected, two of the cars are red? A. 1/6 B. 1/5 C. 1/3 D. 2/5 E. 1/2
B. 1/5
A certain school has 50 students assigned to five distinct classes so that the numbers of students in the classes are consecutive and each student is assigned to only one class. What is the probability that a student selected at random from the 50 students is in one of the two largest classes? A. 38% B. 42% C. 46% D. 48% E. 56%
C. 46%
A crate of apples contains 1 bruised apple for every 30 apples in the crate. Three out of every four bruised apples are considered not fit to sell, and every apple that is not fit to sell is bruised. If there are 12 apples not fit to sell in the crate, then how many total apples are there in the crate? A. 270 B. 360 C. 480 D. 600 E. 720
C. 480
Each writer for the local newspaper is paid as follows, a dollars for each of the first n stories each month and a+b dollars for each story thereafter, where a > b. How many more dollars will a writer who submits n+a stories in a month earn than a writer who submits n+b stories? A. (a-b)(a+b+n) B. a-b C. a²-b² D. n(a-b) E. n(a+b)
C. a²-b² pg 725
Company Z spent 1/4 of its revenues last year on marketing and 1/7 of the remainder on maintenance of its facilities. What fraction of last year's original revenues did ompany Z have left after its marketing and maintenance expenditures? A. 5/14 B. 1/2 C. 17/28 D. 9/14 E. 41/56
D. 9/14 pg 726
Pg 835
E
What is different between the median of a list of even vs odd aount of nubers in ascending or descending order?
The median of a list of odd numbers is the middle number whereas the median of a list of even numbers is the average of the two middle numbers
What is a pythagorean triplet?
a set of integers that fits the pythagorean theorem
What is a sphere?
a three-dimensional circle that makes a perfectly round ball
What is an isosceles trapezoid?
a trapezoid with two equal nonparallel sides
What is an equilateral triangle?
a triangle that has three equal sides
What is a rectangular solid?
a uniform solid whose base is a rectangle and whose height is perpindicular to its base
What is a degree?
a unit of measure for describing angles
What is true of the angles in an isosceles triangle?
angles opposite from the equal sides are equal
What is a rational number?
any number tha can be represented as a ratio of two integers
What are two ways to denote inverse tangent?
arctan tan⁻¹
What two ways is the inverse sine function of x represented?
arctan x or sin⁻¹ x
What is the equation for the volume of a uniform solid?
area of the base x height
What is the equation for finding the area of a parallelogram?
base x height
Why is the value of sin⁻¹ defined to be on the interval -90<y<90?
because there are infinitely many y such that siny=x, and a function must associate exactly one number with each number in the domain
What two measures can be used to describe angles?
degrees and radians
How can you find the area of an equilateral triangle?
divide it into two 30-60-90 triangles or use the formula s²√3 ----- 4
How do you divide powers with the same exponent?
divide the bases and keep the exponent
How do you convert a fraction into a decimal?
divide the numerator by the denominator
How can you convert an improper fraction to a mixed number?
divide the numerator by the denominator and put the remainder at the numerator of the fraction
How do you convert a percent to a fraction or decimal?
divide the percent by 100%
How can you find trigonometric functions of an angle greater than 90 degrees?
draw the angle on a unit circle and rotate the appropriate # of degrees counterclockwise to create a right triangle, then switch opposite and adjacent in the functions pg 831
What are mutually exclusive events?
events for which the occurence of one event eliminates the possibility of the occurrence of the other event
How often does the graph of y=sin x repeat itself?
every interval of length 360 degrees or 2pi radians
What is the formula for volume of a cube?
e³ where e is the length of an edge of a cube
What must be true in order for a function to be periodic with period R?
f(x)=f(x+R) where R is the smallest positive number for which this is true
What ist he difference between f and f(x)?
f: the entire process of using the instructions to associate numbers with other numbers f(x): the exact number that the function f associates with the number x
How do you find the probability of event A or eent B occuring when they are mutually exclusive?
find the probability of A and the probability of B and add these two probabilities
How do you find the probability that at least one of event A or event B occurs?
find the probability of event A and the porbability of event B, add them and then subtract from this sum the probability that both events A and B will occur P(A or B)=P(A)+P(B)-P(A and B)
For which x values is arctan x defined?
for all real x values
A right circular cone and a sphere have equal volumes. If the radius of the base of the cone is 2x and the radius of the sphere is 3x, what is the height of the cone in terms of x?
h=27x pg 819
What is the name of the side opposite the right angle in a right triangle?
hypotenuse
What is the equation for secent?
hypotenuse/adjacent
What is the equation for cosecant?
hypotenuse/opposite
What is the imaginary unit for imaginary units?
i
For which x values is the inverse sine of x defined?
if it is between -1 and 1
How can you determine if a triangle is a 3-4-5 triangle?
if the leg to leg ratio is 3:4 or if the leg to hypotenuse ratio is 3:5 or 4:5
For which values of x does the graph y=sin x increase vs decrease?
increas: 0≤x≤90, 270≤x≤360 decrease: 90≤x≤180, 180≤x≤270
What are the equations for percent increase and decreas?
increas: amount of increase divided by original whole multiplied by 100 decrease: amount of decrease divided by original whole multiplied by 100
How can you solve an equation for one variable in terms of another?
isolate the one variable on one side of the equation, leaving an expression containing the other variable on the other side of the equation
If you shift the decimal point to the right or left in a number, what effect does that have on the characteristic of the logarithm of that number?
it increases or decreases it
Is 3.75 a rational or irrational number?
it is a rational number because it can be represented as a ratio of two integers: 375/1000
Is 1 a prime number, why or why not?
it is not, because it is divisible only by 1 natural number (1)
Is the product of an irrational and rational number rational or irrational?
it will be irrational
Is the sum of an irrational and rational number irrational or rational/
it will be irrational
What is the definition of i?
i²=-1
How do you multiply fractions?
multiply the numerators by each other and the denominators by each other
What does the property of -1 state?
multiplying or dividing a nonzero number by -1 changes the sign of the number
What is log (sⁿ) equivalent to?
n * log (s)
Change 415/3220 into a decimal via long division
pg 740 0.13
For log(7,435) what is the characteristic and mantissa?
pg 750 characteristic: 3 mantissa: 0.87128
Draw the graph of y=sinx
pg 832
Draw the graph of y=cos x
pg 833
What does the graph of y=tan x look like?
pg 834
Wat are the two types of closed figures?
polygons and circles
Using the triangle on pg 827, determine the sin, cos, and tan of theta
sin: .6 cos: .8 tan: .75
What is the name for the reciprocal of cosecant?
sine
How many faces are there on a rectangular solid?
six
How can you determine the probability that an event will not occur?
subtract the probability that the event will occur by 1
What is the formula for determining average?
sum of terms / number of terms
What does the commutative property state?
switching the order of any two numbers being added or multiplied together does not affect the result
What does the associative property state?
terms can be regrouped without changing the result
What does the property of 1 state?
that multiplying or dividing a number by 1 does not change teh number
What does the triangle inequality theorem state?
that the length of any one side of a triangle must be greater than the positive difference and less than the sum of the lengths of the other two sides
What is a central angle as it relates to a circle?
the angle formed by two radii of the circle
When you take the inverse sine of x, what are you conceptually finding?
the angle y such that sin y =x and -90°<y<90°
What are the bases of a uniform solid?
the top and bottom faces of the shape
In scientific notation, how can you convert 10ⁿ to an integer?
the value of n will be the number of zeros following the 1 in the integer
In scientific notation, how can you convert 10⁻ⁿ to an integer?
the value of x will be the number of places behind the decimal point
What is the definition of a solid?
three dimensional objects with lenght, width, and height
What are the rules for determining how many roots there are when using the quadratic formula and whether they are real or complex?
two different real roots if b²-4ac >0 one double real root if b²-4ac =0 two complex conjugate roots if b²-4ac <0
How do you multiply binomials?
use FOIL pg 758
Convert the following word problem into an equation: w is less than y
w=y-x
What is canceling in terms of fractions?
when the number in the numerator of one fraction matches the number in the denominator of the other, you can cancel them both out
What allows a uniform solid to be formed?
when you take a plane and move it through space without tilting it
Solve the equation 3x-10y=-5x+6y for x in terms of y
x=2y pg 765
Solve x² -7x +12=0
x=3,4
How do you multiply two numbers in scientific notation together?
you multiply twogether the two integers and add together the two powers on the ten
The moon revolves around the Earth at a speed of approximately 1.02 kilometers per second. How many kilometers per hour is this approximate speed?
3672 pg 748
Simplify 5 sin²x + 5cos²x
5 pg 829
What is the circumference of a circle with radius 3?
6π
What are the answers to the following: (-2) * (+3) 8/(-4)
-6 -2
What is the sum of -6 and -3?
-9
What do you get when you multiply a number by its reciprocal?
1
If the ratio of males to feales is 1 to 2, then what is the males-to-people ratio? What is the ratio of females-to-people?
1/3 2/3
Solve this using the distributive property: 4(3+7)
12+28=40
What two equations can be used to find the circumference of a circle?
2πr πd
The ratio of dogs to cats in an apartment building is 3 to 2. If there are a total of 50 animals in the apartment building and all of the animals in the building are dogs or cats, how many dogs are in the building?
30 pg 739
What is the addition problem that corresponds to this subtraction problem? 9 - (-10)
9+10
The manufacturer of Sleep-EZ mattresses is offering a 10% discount on the price of its king-size mattress. Some retailers are offering additional discounts. If a retailer offers an additional 20% discount, then what is the total discount available at that retailer? A. 10% B. 25% C. 28% D. 30% E. 32%
C. 28% Pg 718
A certain board game is played by rolling a pair of fair six-sided dice then moving one's piece forward the number of spaces indicated by the sum showing on the dice. A player is "frozen" if her opponent's piece comes to rest in the space already occupied by her piece. If player A is about to roll and is currently six spaces behind player B, what is the probability that player B will be frozen after player A rolls?
B. 5/36 page 795
What is a number line?
a straight line extending infinitely in either direction on which real numbers are represented as points
What equation corresponds to the distributive law?
a(b+c) = ab +ac
What is the range of a function?
all the values that y can have for the function
What is the domain of a function?
all values that x can have for the function
Why can the distributive property be used for division as well as multiplication?
dividing by a number is the same as multiplying by the reciprocal
How can you convert any addition problem into a subtraction problem?
changing the operation sign from a minus to plus and then switch the sign on the second number
On the number line, is zero even or odd?
even
How can you identify the zeros of functions while graphing?
find the x-intercepts of the graph of the equation y=f(x)
What is the sign of the answer if you multiply or divide two numbers with different signs?
it gives a negative result
On the number line, is zero positive or negative?
neither
Use the pythagorean theorem to derive the three trig identities
pg 829
When estimating the solution to an addition problem, how do you round the numbers?
round one number up and the other number down
What is the circumference of a circle measuring?
the total distance around the circle
What is an x-intercept?
the x-coordinate of a point where the graph crossesx the x-axis
What is a y-intercept?
the y-coordinate of a point where the graph crosses the y-axis
What is the answer if you divide a number by zero
undefined
In which case of division does the distributive property not work?
when the sum or difference is in the denominator
What is the shape and equation for a polynomial function?
y = p(x) where p is a polynomial. It takes a squiggly-line shape
What is the shape and equation for an absolute value function?
y = | ax + b | where a and b are constants. It is a V-shape
What are the two general forms of linear equations?
y=mx+b x= a constant
