Algebra Questions

Part 1 of 2 Use synthetic division and the factor theorem to determine whether x 4 is a factor of f x f x 3x3 15x2 16x 16 Complete the first row of the synthetic division table

5 2 Graph the solution to the system y 7 y2 3 Show Your Work

For the given polynomial P x and the given c use the remainder theorem to find P c P x 3x 5x 7x 3 5 P c Simplify your answer www

A 3 Each point on the graph represents a polar bear Explain the answer to each question below Heights and Masses of 8 Polar Bears E 4 2 Height m 14 0 a Which bear has the greatest mass What is this mass b Which bear is the shortest What is its height c Which two bears have the same mass What is this mass 10 d Which two bears have the same height What is this height 8 A B 4 This graph shows the height of the tide in a harbour as a function of time in one day Explain the answer to each question below Height of the Tide in a Harbour 6 B 4 0 00 00 H 200 400 600 800 Mass kg 06 00 12 00 18 00 24 00 Time 24 h clock a What is the greatest height At what times does it occur b What is the least height At what times does it occur c How high is the tide at 04 00 d When is the tide 4 m high 5 To raise a flag Sepideh pulls the rope steadily with both hands for a short time then moves both hands up the rope and pulls again She does this until the flag has been raised Which graph best represents the height of the flag Give reasons for your choice Graph A Graph B Time s Graph C Distance from home km Time s 2 0 6 Gill runs for exercise This graph shows her distance from home during one of her runs Describe Gill s run for each segment of the graph Gill s Run 1 0 O A B Time s Graph D D 20 30 10 Time min Time s 5 3 Interpreting and Sketching Graphs 281

9 9 y Zx 2 V Ia ia y x 2

8 y x 4 2 13 y x 6 6 A B 6 D 17 y AV V x X N

6 x 6y 42 7x 3y 24 A B D 8 8 14 8 4 V V x X X X

Graph linear Inequalities Sketch the solution to each system of inequalities 2 1 y x 3 y 3x 1 A B 6 D y V y X X X

4 12 y x 1 3 V 3 432 2

10 y 2x 2 y2 x 3 4 3 2 1 ZO

4 2x y 3 4x y 3 A B D 4 AV H A V x X x N

11 11 y x 3 x 3 4 3 2 1

3 x 3y 9 x 3y 3 A B O D T 2 A R N y y y V A2 y X x X

5 x y 3 y 1 A B D y y 4 X X

7 y x 3 7 y x 3 2 A B O D

Graph linear Inequalities Sketch the solution to each system of inequalities 1 y x 3 y 3x 1 A B D 4 14 V X x 2 3 2 y x 1 2 y2 2 A B D x 1 y y y X X X x

Find the standard deviation for the group of data items 5 1 5 1 5 1 5 1 The standard deviation is Round to two decimal places as needed

Use the display of data to find the mean median mode and midrange The mean of the data is Round to the nearest tenth as needed Frequency 79944 HTT P N9TY 6

Find a the mean b the deviation from the mean for each data item and c the sum of the deviations in part b for the following group of data items 56 66 61 56 71 a The mean is Simplify your answer

Use the display of data to find the mean median mode and midrange The mean of the data is Frequency 10 8 420 2 Score 10 20 30 40 50 Round to the nearest tenth as needed

Find the median for the data items in the given frequency distribution Score x 3 Frequency f 3 1 3 2 3 The median is Type an integer or a decimal 4 3 10 5 7 6 5 7 7 8 5 9 3 10 5

work 12 2 Find the mean for the data items in the given frequency distribution Score x Frequency f The mean is 1 2 2 3 32 2 4 6 5 5 Round to 3 decimal places as needed 65 5 7 8 8 6 9 3 10 3

Find the mode for the data items in Score x Frequency f 1 2 2 2 3 1 gr 4 4 5 8 6 7 7 5 8 4 9 5 Use a comma to separate answers as needed 10 2 1 Select the correct choice below and if necessary fill in the answer box to complete your choice OA The mode s is are OB There is no mode

Determine whether the following statement makes sense or does not make sense and explain your reasoning Improperly worded questions can steer respondents towards answers that are not their own Choose the correct answer below GILB OA The statement does not make sense because the wording of a question does not affect how a respondent will answer OB The statement makes sense because if a question is worded improperly respondents might not know what is actually being asked C The statement does not make sense because questions cannot be worded improperly OD The statement makes sense because improperly worded questions cannot be answered correctly

Click the icon to view the bar graph Choose the correct answer below OA The bars are not scaled proportionately in terms of the data they represent OB The wrong impression has been created about how the data are changing because equally spaced intervals are not used on the horizontal axis OC The scale of the vertical axis makes the differences in bar height look larger than they really are OD The images in front of or behind each bar make it look as though the bars are taller than they really are Sports Riches Weekly Pay Thousands of Dollars 275 250 225 200 175 150 125 A 100 0 of data F C Barcelona Spain Soccer Oklahoma City Thunder U S A Average Weekly Pay on Selected Sports Teams Toronto Raptors Canada Miami Heat USA Manchester United U K San Francisco Giants U S A New York Yankees U S A S

Determine whether the statement makes sense or does not make sense and explain your reasoning The graph shown below indicates that for the period from 2016 to 2019 the percentage of Americans whose educational attainment was high school graduate or more has rapidly increased of HS Graduates or More Educational Attainment in the United States 90 2 90 0 89 8 89 6 89 4 89 2 89 0 88 8 2015 2016 2017 Year 2018 2019 OU C of I Sa Choose the correct answer below OA No it does not make sense the time interval on the horizontal axis creates an overall impression of the percentage of Americans with a high school educatio or better increasing rapidly OB Yes the statement makes sense OC No it does not make sense the percentage of Americans with a high school education or better increased more rapidly during the period from 2015 2016 OD No it does not make sense the scale on the vertical axis is stretched to create an overall impression of the percentage of Americans with a high school education or better increasing rapidly

A professor had students keep track of their social interactions for a week The number of social interactions over the week is shown in the grouped frequency distribution to the right Among the classes with the greatest frequency which class has the least number of social interactions Choose the correct answer below A 65 69 OC 60 64 OE 70 74 G 50 54 OL 55 59 BO B 75 79 OD 45 49 OF 85 89 H 90 94 J 80 84 Number of Social Interactions 45 49 50 54 55 59 60 64 65 69 70 74 75 79 80 84 85 89 90 94 Frequency 12 18 18 18 9 8 7 7 0 3

The histogram shows the starting salaries rounded to the nearest thousand dollars for college graduates based on a random sample of recent graduates Determine whether the following statement is true or false according to the graph The percentage of starting salaries falling above those shown by any rectangular bar is equal to the percentage of starting salaries falling below the bar Choose the correct answer below BOCCO of Graduates Frequency 400 300 200 100 0 A False because this is not true for any rectangular bar OB True because this is true when there is odd number of bars OC False because this is only true if there is an even number of bars D True because the percentage of starting salaries falling below and above each bar must sum to 100 Starting Salaries of Recent College Graduates 41 45 46 50 51 55 56 60 61 65 66 70 71 75 Salary thousands of dollars Q Q

Describe what is misleading in the visual display of data below Marijuana Use Among College Students in the Last 30 Days Never Used 29 3 Not in Last 30 Days 10 Used 1 9 Days 5 5 Used 10 29 Days 3 5 Used All 30 Days 1 7 Choose the correct answer below A The chart is too small B The percentages do not add up to 100 C The title does not explain what is being displayed D Colors on the chart are too light and distort the data

12 1 The histogram shows the starting salaries rounded to the nearest thousand dollars for college graduates based on a random sample of recent graduates Determine whether the following statement is true or false according to the graph More college graduates had starting salaries in the 61 000 65 000 range than in the 46 000 50 000 range Choose the correct answer below of Graduates Frequency 400 300 200 100 Question 8 12 1 23 Starting Salaries of Recent College Graduates 41 45 46 50 51 55 56 60 61 65 66 70 71 75 Salary thousands of dollars Q IEEEIN Points A False because the bar for 61 65 has the same height as the bar for 46 50 B False because the bar for 61 65 is shorter than the bar for 46 50 OC True because the bar for 61 65 is taller than the bar for 46 50 D True because the sum of the heights of the first two bars in the graph is greater than the sum of the heights of the last two bars

A professor had students keep track of their social interactions for a week The number of social interactions over the week is shown in the following grouped frequency distribution What is the class width The class width is Type a whole number Points 0 of 1 Number of Social Interactions 20 26 27 33 34 40 41 47 48 54 55 61 62 68 69 75 76 82 83 89 Frequencies 15 HARSHST 4 14 17 13 5 7 1 19 11 14

A professor had students keep track of their social interactions for a week The number of social interactions over the week is shown in the following grouped frequency distribution How many students had at least 45 social interactions for the week The number of students was Type a whole number Points 0 of 1 Number of Social Interactions 15 19 20 24 25 29 30 34 35 39 40 44 45 49 50 54 55 59 60 64 Frequency a 12 11 18 20 19 504 9 7

was given to students in an introductory statistics class during the first week of the course One question asked How stressed have you been in the last 2 weeks on a sca 10 with 0 being not at all stressed and 10 being as stressed as possible The students responses are shown in the frequency distribution How many students were involved in the study Click the icon to view the frequency distribution students Type a whole number Frequency Distribution Stress Rating 0 1 2 3 4 5 6 7 8 9 10 CHCELED Frequency 4 3 2 12 16 13 11 33 24 12 12 m

Consider the graph of the exponential function below 10 5 10 5 0 5 10 0 6 5 1 powered by desmos

a Find the domain Use interval notation E b Find the range Use interval notation y E x c Find the y intercept Enter your answer as an ordered pair O Decreasing 100 d Is f x an increasing growing or decreasing decaying function O Increasing equation e Find the equation of the horizontal asymptote Enter your answer as an equatic f Graph the function by dragging the y intercept to the correct position and the

a Graph the function by dragging each of the following to the correct position the horizontal asymptote the y intercept a second point 20 10 10 0 1 10 2 2 10 1

Define an exponential function f x which passes through the points 0 25 and 2 1 Enter your answer in the form a b where b 0

a 9 1 2 b 16 1 5 G 161 5

a 16 b 92 c 162

a 5 2 b 4 3 c 2 1

a 2 b 2 c 45 d 4

Evaluate without a calculator a 5 b 23

Find all rational zeros of the following polynomial funct P x x 43 x 55 x X 7 7 x 13

2 Find the equation of a power function passing through 2 2 and 1 8

Determine whether or not the graph shown is the graph of a polynomial function 10 8 6 8 6 16 40 3 5 O not a polynomial funct O polynomial function

The width of a rectangle is x OA 3x 12x 27 ft OB 3x 12x 27 ft O C 3x 12x 27 ft O D 3x 10x 59 3 x 3 ft feet and its area is 3x 11x 23x 9 square feet Write a polynomial that represents the length of the rectangle m

Rewrite the quadratic function in standard form f x 2x 6x f x Give the vertex x y

Simplify each of the following Enter the exact answers Enclose numerators and denominators in parentheses For example a b 1 a 729

You decide to purchase a car for 22 750 Assuming the sales tax is 5 5 of the purchase price find each of the following a What is the total cost including sales tax b If you make a down payment of 18 of the total cost find the down payment c Assuming you finance the remaining cost at an annual interest rate of 7 05 for 10 years find the monthly payment

4 10 points Use the Remainder Theorem and Synthetic Division to evaluate P c for P x 2x 21x 9x 200 at c 9 antanirions sie