CAO- Algebra IA
A survey asked 30 people what their favorite genre of television broadcasting was, and the results were tabulated above. Find the probability that a person chosen at random was female, given that they like comedy. Round the answer to the nearest hundredth.
0.55
Combine like terms.
A
Graph the line, given the equation. y = 3x - 5
A
equation
A mathematical statement that uses an equals sign to equate two algebraic expressions.
solution of a one variable equation
A value of the variable in an equation that makes the equation true.
Combine like terms.
B
For which equation is x = 4 not a solution?
C
Verify the equation below with each of the values listed for x to find a solution. 5 = 3x + 4
C
Compute a value for t that satisfies the equation below.
D
In the sentence below, which word refers to a mathematical operation? Jane has 3 dollars per dollar Mark has.
c) per
Diane needs 165 pieces of candy to hand out to guests at a party she is hosting. Each bag of candy contains 20 pieces. She has 25 pieces left over from a previous party. She calculates she needs to purchase 7 additional bags of candy to meet the 165 piece of candy requirement. Which of the equations below verifies that she needs 7 additional bags of candy?
A
To test that the solution to the equation below is x = 4, which of the following calculations should be performed?
A
To test that the solution to the equation below is x = 5, which of the following calculations should be performed?
A
mathematical model
An equation or graph that represents a data set.
Draw a box-and-whisker plot for the set of data. 27, 35, 44, 51, 52, 54, 56, 69, 69, 79, 80, 100, 100
B
This list shows the age at which 38 U.S. Presidents died. Before you can make a frequency table, you need to decide how to set up the age intervals. What is the BEST way to group these ages into six intervals?
B
Maria solved the equation below and got x = -4. Which of the following choices verifies that her solution is correct? 5x + 22 = x + 6
D. 5(-4) + 22 = (-4) + 6 -20 + 22 = 2 2 = 2
Which of the following can be determined about events A and C from the table above?
P(A|C)=0.16;P(A), the events are independent
additive inverse
The element of a set such that, when added to another given element, the resulting sum is the additive identity of the set. The opposite of a real number.
multiplicative inverse
The element of a set that, when multiplied by another given element, has a resulting product of the multiplicative identity of the set. The reciprocal of a real number.
addition property of equality
The property stating that adding the same quantity to (or subtracting the same quantity from) both sides of an equation does not change the solution set.
multiplication property of equality
The property stating that multiplying or dividing both sides of an equation by the same value does not change the solution set.
A student attempts to solve for x in the equation below. Which statement best applies to the work shown below?
The student combined like terms incorrectly to get to line 1.
isolate a variable
To get a variable all by itself on one side of an equation.
A position-time graph can tell how much an object's position has changed over a given amount of time.
True
Two-way tables are used to organize certain types of data. What is another type of graphic organizer that can be used to represent the same type of data? Describe what these two organizers have in common.
Venn diagram
Select the algebraic equation that correctly represents the given sentence. Dale currently has $599 in his savings account. Prior to getting paid, he had $230 in his savings account. How much was Dale's paycheck?
a) $230 + x = $599 x = $369
Sue bought a pair of jeans and a shirt for $55.75. If the jeans cost $25.25, how much did she pay for the shirt?
a) $30.50
At her job, Mary works 4 hours on Monday, 3 hours on Wednesday, and 6 hours on Saturday. Her boss adds a $10 bonus to her paycheck, which then totals $120.50. What is Mary's hourly pay?
a) $8.50
Solve. 14y + 20 = 4y
a) -2
Solve. 2(x − 4) - 4x = 0
a) -4
Solve the equation for t. 3t - 6t + 8 - 7t = - 2
a) 1
Two is thirty-one, divided by the sum of a number and four. Find the number.
a) 11.5
The length of a rectangle, l, is six meters more than its width, w. If the perimeter of the rectangle is 36 meters, what is the length of the rectangle, in meters?
a) 12
To test that the solution to the equation below is z = -2, which of the following calculations should be performed? 12 = 2z + 16
a) 12 = 2(-2)+16
When 5 is added to 2 times a number, the result is 45. Find the number.
a) 20
Which inequality represents "35 is less than 3 times 4 more than a number"?
a) 35 < 3(x + 4)
Combine like terms. 3a + b + a
a) 4a + b
A student takes ten exams during a semester and receives the following grades: 90, 85, 97, 76, 89, 58, 82, 102, 70, and 67. Find the five-number summary used in a boxplot.
a) 58, 70, 83.5, 90, 102
Meg opened a savings account with $44.50. She puts in $22.25 in the account each week when she gets paid. She is saving to purchase a blu-ray player that costs $178.00. How many weeks will it take her to save enough money?
a) 6 weeks
A poll taken before an election asks a sample of people which candidate they plan to vote for. What is the probability that a person in the population chosen at random is a female and voting for a Republican?
a) 9/51
Which of the following describes the best method of solving two-step equations?
a) Apply the multiplication property of equality first, and then apply the addition property of equality to isolate the variable.
A student is attempting to write the statement below as an equation. Which of the following statements best applies to the sample mathematical work? Statement: If 3 times a number is added to itself, the result is 30. Work: (1) Let x be the unknown quantity. (2) The phrase "3 times a number" results in x + 3. (3) The phrase "is added to itself" results in + x. (4) Add these values from step 2 and step 3 togther and set that equal to 30.
a) The interpretation in step 2 is incorrect or invalid.
A student attempts to solve for c in the equation below. Which statement best applies to the work shown below?
a) The student followed all rules correctly and solved for c.
A student attempts to solve for a in the equation below. Which statement best applies to the work shown below?
a) The student incorrectly applied the multiplication property of equality before the addition property of equality.
Which of the following BEST describes how to use the addition property of equality to isolate the variable y below?
a) add 2/3 to both sides of the equation
Which of the following BEST describes how to use the addition property of equality to isolate the variable m below? -6 = -3 + m
a) add 3 to both sides of the equation
Name the property for the given statement. 2 + 4 = 2 + 4
a) addition property of equality
Which property would be used to isolate the variable h in this equation? h + 12 = 26
a) addition property of equality
In the sentence below, which word or phrase refers to a mathematical operation? While driving on the freeway, Jennifer was operating her vehicle at 10 miles per hour more than Amy.
a) more than
Which of the following BEST describes how to use the multiplication property of equality to isolate the variable x below?
a) multiply both sides of the equation by 1/3
Which equation represents two less than a number is equal to 10?
a) n - 2 = 10
Which of the following is an example of a valid use of the addition property of equality?
a) to isolate the g in the equation g - 4 = 0, add 4 to both sides of the equation
Solve. -5(1 - 5x) + 5(-8x - 2) = -4x - 8x
a) x = -5
Determine the solution to the given equation. 4 + 3y = 6y - 5
a) y=3
Select the algebraic equation that correctly represents the given sentence. Jane currently has $3,360 in her savings account. Prior to getting paid, she had $1,230 in her savings account. How much was Jane's paycheck?
b) $1,230 + x = $3,360 x = $2,130
Select the algebraic equation that correctly represents the given sentence. Tina had $640 in her bank account. When she took out d dollars, her balance was $460.
b) $640 - d = $460
At his job, Rob works 6 hours on Monday, 7 hours on Tuesday, and 2 hours on Friday. He receives a $15 bonus, which causes his weekly paycheck to total $153.75. What is Rob's hourly pay?
b) $9.25
Solve for x. 5x + 8 + 3x = 3 - 2x - 5
b) -1
Solve. 8x - 4(-5x - 2) = 12x
b) -1/2
Solve for y in the equation 4y + 15 = -5y + 9.
b) -2/3
Determine which equation below has a solution of x = 2.
b) -4x + 3 = 8x - 21
Determine which equation below has a solution of b = 3.
b) -8 = 3 + 4b - 8 - 5b
Solve the equation for a. 55a - 44a = 11
b) 1
Let event A be defined as a randomly chosen vehicle being silver or black. Let event B be defined as a randomly chosen vehicle being a car or a truck. Find P(~B|~A).
b) 1/4
Solve the equation for a. 88a - 3 = 19
b) 1/4
Consider this equation: 4x - 5 + 6x = 6
b) 10x - 5 = 6
One dimension of a rectangular map is 8 inches and the perimeter is 40 inches. What is the other dimension of the map?
b) 12 inches
Manufacturers are testing a new cologne before it's released. A machine uses sensors to determine if the cologne is working (maintaining a scent for 1 hour) 60% of the time. Another machine tests if the cologne works all the time (maintains a scent for over 5 hours). Find the probability that the cologne works all the time, given that it works 60% of the time.
b) 15/37
Suppose a new data pair with an x-coordinate of 30 was entered into the data set below. If the new data pair followed the same trend that currently exists in the data set, which of the following would be an appropriate y-coordinate? {(45, 18), (62, 13), (72, 11), (55, 15), (38, 21), (26, 31), (93, 9), (64, 13), (29, 28), (33, 25), (49, 17)}
b) 25
Select the algebraic equation that correctly represents the given sentence, and solve the equation. If 3 is subtracted from twice a number, the result is 8 less than the number.
b) 2x - 3 = x - 8 x = -5
Lisa needs 125 pieces of candy for her guests at a party she is hosting. The candies come in packages of 35. She already has 20 pieces of candy left over from a previous party. How many packages of candy will Lisa have to buy to have 125 pieces of candy exactly? Create a two-step equation that models this problem and select which of the values below satisfies that equation.
b) 3
A poll taken before an election asks a sample of people which candidate they plan to vote for. What is the probability that a person randomly chosen from the population is voting for a Democrat?
b) 33/56
Determine which equation below has a solution of x = 1/2
b) 3x - 1 - 4x= -2x + 7x - 4
For a large cooking project, Arthur needs to put 18 cups of water into a large pot. He can transport a maximum of 4 cups from the sink in a single trip. The pot already contains 5 cups of water. How many trips are required for Arthur to fill the pot to 18 cups?
b) 4
Solve. 3(4x − 2x) = 8
b) 4/3
Find the value of x that makes the statement true.
b) 5
Evaluate the function for f(-2)
b) 7
Find the value of x that makes the statement true.
b) 7
Which of the following can be determined from the table above?
b) A=23, B=38, C=19, D=57, E=81
A doctor's office records the age at which 200 patients were treated for chicken pox. 60% of the patients were treated before age 15. 40% of the patients who were under 15 were female. 20 of the patients were 30 or older. Half of the people who were treated after their 30th birthday were female. 95 men were involved in the study.
b) A=48, B=10, C=120, D=13
Cindy is a first-year math teacher who has just collected a chapter test from her 4th period students. As Cindy reviews the test scores, she notices that while she has several students who have earned an A, most of the test scores are in the C to B range. She also notices that two of the scores are much lower than the rest, each earning an F. This makes sense to her, as those two students were absent for much of the chapter. However, she must now report to her principal on the performance of her class on this test. Which measure of central tendency should Cindy use in her report to the principal, if she wants to portray her students in the most favorable manner?
b) Cindy should use the median of the test scores to produce the most positive report.
Give the slope and y-intercept of the line, given the equation. y = 14x + 5
b) Slope = 14 y-intercept = 5
A student attempts to solve for x in the equation below. Which statement best applies to the work shown below?
b) The student did not properly apply the addition property of equality to isolate x.
A student is asked to solve the equation below and to justify his/her steps. Identify what, if anything, is incorrect in the math or justification. j - 8 = -13
b) The student improperly applied the addition property of equality in the second step.
Name the property for the given statement. 2(10 + 15) = 2(10) + 2(15)
b) distributive property
Name the property for the given statement. (4 - 6)(3) = (4)(3) - (6)(3)
b) distributive property
Which of the following expressions is used when referring to the outcomes of two variables?
b) joint probabilities
Which of the following BEST describes how to use the multiplication property of equality to isolate the variable n below?
b) multiply both sides of the equation by 13/12
Which of the following BEST describes how use of the multiplication property of equality to isolate the variable x below? -3x = 12
b) multiply by -1/3 on both sides of the equation
Which of the following BEST summarizes how to solve for the variable x in the equation below, and which rule was used to do so?
b) multiply by 3/2 on both sides of the equation by the multiplication property of equality
When modeling word problems as mathematical equations, which of the following is not a synonym for the addition operation?
b) product
Following the recommended steps for solving equations, what should be your first step in solving the given equation? 2x - 3 - 4x − 2x = -6
b) subtract 4x from 2x
Which property of equality would be used to isolate the variable a in this equation? a - 4 = 12
b) subtraction property of equality
Which of the following is an example of a valid use of the addition property of equality?
b) to isolate the z in the equation z + 8 = 14, add -8 to both sides of the equation
Which equation represents "a number increased by 8 is equal to sixteen"?
b) y + 8 = 16
Ted bought a sweatshirt and a T-shirt for $45.60. If the sweatshirt cost $24.50, how much did he pay for the T-shirt?
c) $21.10
Jan spent $53 for boots. This was $15 less than twice what she spent for a blouse. How much did she spend on the blouse?
c) $34
Lisa has $15 in her piggy bank. How much additional money does she need to buy a game that costs $75?
c) $60
Determine which equation below has a solution of a = 2.
c) -2 = 2 + 5a - 2 - 6a
Determine which equation below has a solution of x = 2.
c) -4x - 6 + x = -2x + x - 10
Solve the equation for x. -10 + 3x + 6x = -10
c) 0
At a dance competition, contestants were allowed to choose between four different dance moves: the Double Jim Jim, the B Bounce, the Abe Lincoln, and the Conky. Some of the contestants perform the moves well, and others do not. Given that a contestant is doing a good job, find the probability that the contestant is doing the Double Jim Jim.
c) 1/6
Solve the equation.
c) 11/29
If 75 equals a number plus four times the number, find the number.
c) 15
A sample of students were surveyed during lunch and asked whether or not they played a sport. A student randomly chosen from the sample plays a sport. Find the probability that the student is a junior or a senior.
c) 15/44
A large pizza pie with 15 slices is shared among 6 students. How many full slices of pizza can each student have?
c) 2
If the distance from your house to the basketball game is 110 miles and you travel 50 miles per hour, how many hours would it take you to get there? Use the formula d = rt (distance equals rate times time).
c) 2.2 hours
At a dance competition, contestants were allowed to choose between four different dance moves: the Double Jim Jim, the B Bounce, the Abe Lincoln, and the Conky. Some of the contestants perform the moves well, and others do not. Given that a contestant is doing a good job, find the probability that contestant is doing the Conky.
c) 2/3
375 students went to Six Flags over Georgia. Fifteen buses were filled, and 15 students rode with their parents. How many students were on each bus?
c) 24
The speed, s, of an ant (in centimeters per second) is related to the temperature, t (in degrees Celsius), by the formula If an ant is moving at 4 centimeters per second, what is the temperature? Round your answer to the nearest degree.
c) 28
A vine 6 cm tall is planted in a garden. It grows 4 centimeters a day. How many days will it take to reach 122 cm in height?
c) 29
Which of the following is not an example of like terms?
c) 2b and 2
Pinky, of Pinky's New and Used Auto, took an inventory of her vehicle lot and recorded it in the table above. Find the probability that a truck chosen at random is used.
c) 4/7
A group of men and women were asked what their favorite pet was, and the results of the survey were tabulated above. Let event A be defined as randomly choosing someone who picked cats or "other" as their favorite pet. Let event B be defined as randomly selecting a person who is female. Find P(B|~A)
c) 7/15
Find the value of x that makes the statement true. 43 = 16 + 3x
c) 9
Solve for the variables in the table.
c) A=32, B=17, C=3, D=8, E=54
Justify the first step that David took in verifying that x = 5 is a solution for the equation 8x - 13 = 2x + 17.
c) David replaced x with 5.
Which of the following can be determined from the table above?
c) Events B and C are independent.
Which of the following can be determined about events B and D from the table above?
c) P(B|D)=0.25, P(B)=0.25; the events are independent
Give the slope and y-intercept of the line, given the equation. y = - 8
c) Slope = 0 y-intercept = -8
A student attempts to solve for x in the equation below. Which statement best applies to the work shown below?
c) The student did not properly apply the multiplication property of equality to isolate x.
When doing homework, a student uses the multiplication property of equality to solve for c below. Which statement BEST applies to the sample? 5c = 10
c) The use of the multiplication property of equality is sound, and the answer is correct.
A student solved the equation -5x + 2x + 2 = 20 - 6x and got x = 6. His work shown below is his check for this problem. Which statement best applies to the work shown?
c) The work in his check is all correct, thus x = 6.
When attempting to do his homework, Mark incorrectly uses the addition property of equality below. Which statement would correct Mark's error? 1) 8 + x = 2 2) 8 - 8 + x = 2 3) x = 2
c) To balance the equation, Mark should also subtract 8 from the right side of the equation in step 2.
Which of the following is not a true statement about solving two-step equations?
c) Two-step equations require all numbers to be whole numbers in order to solve.
Which of the following BEST describes how to use the addition property of equality to isolate the variable y below? y - 12 = 14
c) add 12 to both sides of the equation
Which of the following best describes how to use of the addition property of equality to isolate the variable x below? 5 = x - 2
c) add 2 to both sides of the equation
Name the property for the given statement.
c) multiplication property of equality
Which property of equality would be used to isolate the variable b in this equation?
c) multiplication property of equality
Which property would be used to isolate the variable j in this equation? 7*j=49
c) multiplication property of equality
Solve. -2(6 - 20n) = 20(2n - 3)
c) no solution
Solve. -3(5 - 15n) = 15(3n - 2)
c) no solution
Verify the equation below with each of the values listed for s to find a solution.
c) s = 1
Compute a value for s that satisfies the equation below.
c) s=0
Compute a value for s that satisfies the equation below.
c) s=22/15
In solving an equation for x, 3 is subtracted from one side of the equation. What needs to be done to the other side of the equation?
c) subtract 3
Which of the following is an example of a valid use of the multiplication property of equality?
c) to isolate t in the equation 8t = -4, multiply both sides of the equation by 1/8
Solve. 4x + 2(3x - 9) = x
c) x = 2
Forty people were randomly sampled and surveyed as to the number of pets in their household. The results are listed below. What is the mean, median, and mode of the household pet data?
d) 1.4, 1, 0
For which equation is 2003-05-02-00-00_files/i0070000.jpg a solution?
d) 10x - 3 = -8
Solve for y in the equation -11y = -143.
d) 13
Let event A be defined as a randomly selected vehicle being silver or black. Let event B be defined as a randomly selected vehicle being a car or a truck. Find P(~B|A)
d) 13/36
Franky, of Franky's New and Used Auto, took an inventory of his vehicle lot and recorded it in the table above. Find the probability that a vehicle chosen at random is new.
d) 20/29
A sample of students were surveyed during lunch and asked whether or not they played a sport. A student randomly chosen from the sample plays a sport. Find the probability that the student is a freshman or a senior.
d) 23/44
Solve the equation for x. 50 = -6x + 4x - 8
d) 29
Select the algebraic equation that correctly represents the given sentence, and solve the equation. If 4 is subtracted from twice a number, the result is 12 less than the number.
d) 2x - 4 = x - 12 x = -8
A group of men and women were asked what their favorite pet was, and the results of the survey were tabulated. Let event A be defined as randomly choosing someone who picked cats or dogs as their favorite pet. Let event B be defined as a randomly chosen person being male. Find P(B|~A).
d) 3/4
An online survey asked a sample of high school students their favorite type of music, and the results were tabulated above. Find the probability that a person chosen at random is not a senior, given that the student's favorite music is country or pop.
d) 47/60
For which equation is x = 9 a solution?
d) 4x + 5 = 41
Solve for x.
d) 75
An online survey asked a sample of high school students their favorite type of music, and the results were tabulated above. Find the probability that a person chosen at random did not choose pop music, given that the student is a sophomore or a junior.
d) 87/203
Combine like terms. 4(2a + b) + b
d) 8a + 5b
100 people were asked if they like playing the puzzle game sudoku, solving two-way tables, or both. 4% of the people only liked sudoku. 50% of the people who only liked sudoku were female. 90% of the people liked both. 60% of the people who liked both were female. 40 men were involved in the study.
d) A=2, B=54, C=4, D=2
Which of the following can be determined from the table above?
d) Events E and B are independent.
A student solved the equation 6s - 10 = 2 + 3s + s and got s = -4. His work shown below is his check for this problem. Which statement best applies to the work shown?
d) His check does not work, thus
Give the slope and y-intercept of each line, given the equation.
d) Slope = 1; y-intercept = -2
A student attempts to solve for c in the equation below. Which statement best applies to the work shown below?
d) The student correctly solved the two-step equation.
A student is asked to solve the equation below and to justify her/his steps. Identify what, if anything, is incorrect in her/his math or justification. x + 4 = -8
d) There is no error. The student's justification is correct.
A student is asked to solve the equation below and to justify her/his steps. Identify what, if anything, is incorrect in her/his math or justification. z - 3 = 11
d) There is no error. The student's justification is correct.
A student is asked to solve the equation below and to justify his/her steps. Identify what, if anything, is incorrect in his/her math or justification. (3)k = 18
d) There is no error. The student's justification is correct.
A plane is on its approach to land on the runway. The jet's height above the ground is given in feet as a function of the time in seconds. The following table tracks the plane as it lands:
d) Yes, this function is linear; the slope is -100 feet/second.
Solve. 20 - 5r = 20 - 5r
d) all real numbers
Solve. 45 - 4r = 45 - 4r
d) all real numbers
In solving an equation for x, you distribute a -4 on one side of the equation. What needs to be done to the other side of the equation?
d) nothing
Verify the equation below with each of the values listed for t to find a solution. 4 = 3t - 2
d) t = 2
Compute a value for t that satisfies the equation below.
d) t = 3
Which of the following is an example of a valid use of the multiplication property of equality?
d) to isolate s in the equation -4s = -12, multiply both sides of the equation by -1/4
Compute a value for x that satisfies the equation below. -x + 5 = 1
d) x = 4
Verify the equation below with each of the values listed for x to find a solution. 2 = 3x + 4
d) x= -2/3
Verify the equation below with each of the values listed for s to find a solution.
s=29/6