Answers KISD SS-3391B-Algebra II Honors B Exam OnlyCumulative Exam

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Julia is offered a job selling advertising for two different companies. Company A offers a base salary of $30,000 per year plus a year-end bonus equal to 3% of her total sales. Company B offers a base salary of $25,000 per year plus a year-end bonus equal to 5% of her total sales. Which statement best describes the two offers?

Company A pays better when total sales are less than $37,500, but company B pays better when total sales exceed $37,500.

Company A pays better when total sales are less than $250,000, but company B pays better when total sales exceed $250,000.

Company B pays better when total sales are less than $37,500, but company A pays better when total sales exceed $37,500.

Company B pays better when total sales are less than $250,000, but company A pays better when total sales exceed $250,000.

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Arthur drops a ball from a height of 81 feet above the ground. Its height, h, is given by the equation h = –16t2 + 81, where t is the time in seconds. For which interval of time is the height of the ball less than 17 feet?

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Myra uses an inverse variation function to model the data for the ordered pairs below.(2, 30), (3, 20), (4, 15), (5, 12), (6, 10)Which statement best explains whether an inverse variation function is the best model for the data?

An inverse function is the best model because as x increases, y decreases.

An inverse function is the best model because the products of corresponding x- and y-values are equal.

An inverse variation function is not the best model because data points approximate a straight line.

An inverse variation function is not the best model because the data points show an exponential decay.

What is the solution of ?

x = –2500

x = –50

x = –2.5

no solution

The graph below shows the function .Which statement is true?

There is a hole at x = 3 and an asymptote at x = –1.

There is an asymptote at x = –1 and no hole.

There is a hole at x = 3 and no asymptote.

There is an asymptote at x = 3 and a hole at x = –1.

Phan fills the tank of her car with gasoline before starting her road trip. The table below shows the amount of gas left in her tank as she drives.Number of Hours vs. Amount Left in TankNumber of Hours Spent Driving (h)3579Amount of Gas Left in Tank, in gallons (g)12840Which equation models the amount of gas left in the car as Phan drives, and how many gallons of gasoline does it take to fill her tank?

g = 18 – 2h; 18 gallons

g = 18 – 2h; 16 gallons

g = 3h + 3; 30 gallons

g = 3h + 3; 12 gallons

Aaliyah, Julio, Dan, and Miriam are each studying sets of data. Aaliyah is working with 14 data pairs with a correlation coefficient of 0.9. Julio is working with 13 data pairs with a correlation coefficient of –0.8. Dan is working with 10 data pairs with a correlation coefficient of 0.1. Miriam is working with 15 data pairs with a correlation coefficient of –0.2. For which two data sets is a linear regression model reasonable?

Aaliyah’s and Julio’s data sets

Julio’s and Miriam’s data sets

Dan’s and Miriam’s data sets

Miriam’s and Aaliyah’s data sets

Which system is equivalent to ?

StartLayout Enlarged left-brace 1st Row 5 x squared + 6 y squared = 50 2nd row negative 21 x squared minus 6 y squared = 10 EndLayout

StartLayout Enlarged left-brace 1st Row 5 x squared + 6 y squared = 50 2nd row negative 21 x squared minus 6 y squared = 30 EndLayout

StartLayout Enlarged left-brace 1st Row 35 x squared + 42 y squared = 250 2nd row negative 35 x squared minus 10 y squared = negative 50 EndLayout

StartLayout Enlarged left-brace 1st Row 35 x squared + 42 y squared = 350 2nd row negative 35 x squared minus 10 y squared = negative 50 EndLayout

Which graph shows the solution to the equation below?

On a coordinate plane, 2 curves intersect at (1, 1). One curve curves up and to the right from quadrant 3 into quadrant 1. The other curve curves down from quadrant 1 into quadrant 4.

On a coordinate plane, 2 identical curves are shown. One curve starts at y = negative 3, and the other curve starts at y = 1.

On a coordinate plane, a curve and a line are shown.

On a coordinate plane, a curve and a cubic function are shown.

Determine if the given function has any points of discontinuity. Explain your reasoning.

There is a point of discontinuity at x = b because the denominator has the factor x – b.

There are points of discontinuity at both x = – b and x = b because the numerator has factors of x + b and x – b.

There is a point of discontinuity at x = -b only because the factor of x – b is common to both the numerator and denominator.

There is a point of discontinuity at x = b only because the factor of x – b is common to both the numerator and denominator and factors out.

What is the value of ?

–4.00

–0.25

1.51

2.41

The scatterplot shows the ages and finishing times of seven men who ran a charity 5K run. Use the labeled points to create a linear model that predicts the race time (y) of a man of any age (x). Which equation represents this linear model?

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The parent function f(x) = x3 is translated to form g(x), as shown on the graph. The translated function can be written in the form g(x) = (x – h)3 + k.

h = 4 k = –2

h = –4 k = –2

h = 4 k = 2

h = –4 k = 2

Which expressions are equivalent to ? Select three correct answers.(4)x(2)x

128 Superscript StartFraction x Over 3 EndFraction

128 Superscript StartFraction 3 Over x EndFraction

(4)x

(4 (2 Superscript one-third Baseline) ) Superscript x

(2)x

Which statement is true about the solution of ?

x = –2 is an extraneous solution, and x = 6 is a true solution.

x = 6 is an extraneous solution, and x = –2 is a true solution.

Both x = –2 and x = 6 are extraneous solutions.

Both x = –2 and x = 6 are true solutions.

Which equation shows a valid step in solving ?

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The amount of simple interest accrued on a sum of money varies jointly with the amount of money, the interest rate, and the time the money is invested. A sum of money is invested at a simple interest rate of 4% for 3 years and accrues $168 in interest. The same sum of money is invested in a second account at a simple interest rate of 6% for 4 years. Which statement is true?

The amount of interest accrued on the second account is less than double the amount of interest accrued on the first account.

The amount of interest accrued on the second account is double the amount of interest accrued on the first account.

The amount of interest accrued on the second account is more than double but less than triple the interest accrued on the first account.

The amount of interest accrued on the second account is more than triple the interest accrued on the first account.

Which equation is represented by the graph below?

y = one-eighth e Superscript x

y = one-half e Superscript x

y = 2 e Superscript x

y = 8 e Superscript x

What are the domain and range of f(x) = 2(3x)?

domain: ; range:

What is written as a single logarithm?

log Subscript 2 Baseline left-bracket StartFraction x cubed Over (StartFraction 3 Over x + 4 EndFraction) EndFraction Right-bracket

log Subscript 2 Baseline (StartFraction 3 x cubed Over x + 4 EndFraction)

log Subscript 2 Baseline left-bracket (StartStartFraction x cubed Over 3 EndFraction) Over x + 4 EndEndFraction Right-bracket

log Subscript 2 Baseline (StartFraction x cubed Over 3 + (x + 4) EndFraction)

Which graph shows the correct solution to the linear-quadratic system of inequalities below?

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Which of the following is the inverse of ?

y = log Subscript one-twelfth Baseline x

y = log Subscript 12 Baseline StartFraction 1 Over x EndFraction

y = log Subscript x Baseline 12

y = log Subscript 12 Baseline x

Based on the type of equations in the system, what is the greatest possible number of solutions?

Alice’s backyard is a rectangular piece of property that is twice as long as it is wide. The total area of her yard is 1,000 m2. What is the approximate width of her backyard?A = lw

11.2 m

15.8 m

22.4 m

44.8 m

Which graph represents the function ?

On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens up and to the left in quadrant 2.

On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrants 1 and 4, and the other curve opens up and to the left in quadrants 2 and 3.

On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrants 1 and 2, and the other curve opens up and to the left in quadrant 3.

On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrants 3 and 4.

What are the domain and range of the function f(x) = 4?

{x| x is a real number}; {y| y > 0}

{x| x > 4}; {y| y > 0}

{x| x is a real number}; {y| y > 4}

{x| x > 4}; {y| y > 4}

Which equation is the inverse of y = x2 + 16?

y = x2 – 16

y = plus-or-minus StartRoot x EndRoot minus 16

y = plus-or-minus StartRoot x minus 16 EndRoot

y = x2 – 4

What is the solution of ?

x = 5

x = 13

x = 20

x = 328

What is the solution of ?

–8

–6

The amount of a sample remaining after t days is given by the equation , where A is the initial amount of the sample and h is the half-life, in days, of the substance. A sample contains 18% of its original amount of Radon-222. The half-life of Radon-222 is about 3.8 days. Which is the best estimate for the age of the sample?

1.5 days

2.5 days

9.4 days

21.1 days

What is the solution of ?

c = 0 and c = 3

all real numbers

all real numbers, except c ¹ 0 and c ¹ 3

no solution

Which graph can be used to find the solution(s) to 8 – 4x = 2x – 4?

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Which of the following is true regarding the solution to the logarithmic equation below?

is not a true solution because

is a true solution because

Which expression is equivalent to the following complex fraction?

StartFraction (y + 1) (y minus 1) Over y squared EndFraction

StartFraction y + 1 Over y minus 1 EndFraction

StartFraction y minus 1 Over y + 1 EndFraction

StartFraction y squared Over (y + 1) (y minus 1) EndFraction

For what value of x does ?

no solution

Which equation describes a rational function with x-intercepts at –4 and 2, a vertical asymptote at x = 1 and x = –1, and a horizontal asymptote at y = –3?

f(x) =

Graph the function f(x) = x3 – 3x – 2. Based on the graph, which value for x is a double root of this function?

–2

–1

A toy rocket is launched straight up into the air with an initial velocity of 60 ft/s from a table 3 ft above the ground. If acceleration due to gravity is –16 ft/s2, approximately how many seconds after the launch will the toy rocket reach the ground?h(t) = at2 + vt + h0

0.05 s

2.03 s

3.80 s

3.70 s

Look at this image.Choose the function that represents the triangular numbers.

y = 0.5x + 0.5

y = 0.5x + 0.5x

y =

y = 0.5x2 + 0.5x

An object falls from a window. The distance the object has traveled, d, varies jointly with the acceleration due to gravity and the square of the time elapsed. The object has fallen 5.929 meters in 1.1 seconds, and the acceleration due to gravity is 9.8 meters per second squared. Assuming the object continues to fall and the acceleration due to gravity remains the same, what is the total distance the object travels in 2 seconds?

10.8 m

19.6 m

21.6 m

39.2 m

The graph of a logarithmic function is shown below.What is the domain of the function?

x < 0

x > 0

x < 1

all real numbers

If , what are the first three terms of the sequence defined by the recursive formula below?

8, 26, 80

2, 8, 26

8, 2, 0

5, 8, 26

How does the graph of g(x) = 3x – 2 compare to the graph of f(x) = 3x?

The graph of g(x) is a translation of f(x) 2 units left.

The graph of g(x) is a translation of f(x) 2 units right.

The graph of g(x) is a translation of f(x) 2 units up.

The graph of g(x) is a translation of f(x) 2 units down.

The function y = – 3 is graphed only over the domain of {x | –8 < x < 8}. What is the range of the graph?

{y | –5 < y < 5}

{y | –5 < y < –1}

{y | 1 < y < 5}

{y | 1 < y < –1}

What is the value of ?

Which graph can be used to find the real solution(s) to 3 – 4x = –3 – x2 – 4x?

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Which of the following shows the true solution to the logarithmic equation

x = negative 1

x = 1

and

, , and

What is the solution set of the quadratic inequality

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The function that represents the average cost per person, including transportation, to a museum is . Which statement is true about the graph of the function?

The horizontal asymptote y = 0 means the cost approaches zero as the number of people increases.

The horizontal asymptote y = 8 means the average cost approaches $8 as the number of people increases.

The vertical asymptote x = 0 means the cost approaches zero as the number of people increases.

The vertical asymptote x = 8 means the cost approaches zero as the number of people increases.

What is the solution to the equation ?

x = –3

x = –3 and x = 0

x = 0 and x = 3

x = 3

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