# Kalfree Only

LESSON 2
##### Question 1 of 20
0.0/ 5.0 Points
Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists.

3x – 2y + 2z – w = 2
4x + y + z + 6w = 8
-3x + 2y – 2z + w = 5
5x + 3z – 2w = 1

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A. {(2, 0, – , )}
B. {(1, – , , 6)}
C. ∅
D. {( , 0, – , )}

##### Question 2 of 20
0.0/ 5.0 Points
Solve the system of equations using matrices. Use Gauss-Jordan elimination.

3x – 7 – 7z = 7
6x + 4y – 3z = 67
-6x – 3y + z = -62

A. {( 7, 1, 7)}
B. {( 14, 7, -7)}
C. {( -7, 7, 14)}
D. {( 7, 7, 1)}

##### Question 3 of 20
0.0/ 5.0 Points
Find the product AB, if possible.

A = , B =

A.
B.
C.
D.

##### Question 4 of 20
0.0/ 5.0 Points
Use Cramer’s rule to solve the system. 2x + 4y – z = 32 x – 2y + 2z = -5 5x + y + z = 20

A. {( 1, -9, -6)}
B. {( 2, 7, 6)}
C. {( 9, 6, 9)}
D. {( 1, 9, 6)}

##### Question 5 of 20
0.0/ 5.0 Points
Find the products AB and BA to determine whether B is the multiplicative inverse of A.
A = , B =

A. B = A-1
B. B ≠ A-1

##### Question 6 of 20
5.0/ 5.0 Points
Let A = and B = . Find A – 3B.

A.
B.
C.
D.

##### Question 7 of 20
5.0/ 5.0 Points
Find the inverse of the matrix, if possible.

A =

A.
B.
C.
D.

##### Question 8 of 20
0.0/ 5.0 Points
Let B = [-1 3 6 -3]. Find -4B.

A. [-4 12 24 -12]
B. [-3 1 4 -5]
C. [4 -12 -24 12]
D. [4 3 6 -3]

##### Question 9 of 20
0.0/ 5.0 Points
Evaluate the determinant.

A.
B.
C.
D.

##### Question 10 of 20
0.0/ 5.0 Points
Give the order of the matrix, and identify the given element of the matrix.

; a12

A. 4 × 2; -11
B. 4 × 2; 14
C. 2 × 4; 14
D. 2 × 4; -11

##### Question 11 of 20
0.0/ 5.0 Points
Find the product AB, if possible.
A = , B =

A.
B. AB is not defined.
C.
D.

##### Question 12 of 20
5.0/ 5.0 Points
Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists.

x + y + z = 9
2x – 3y + 4z = 7
x – 4y + 3z = -2

A. {(-+ , + , z)}
B. {( + , , z)}
C. {(- + , , z)}
D. {( + , + , z)}

##### Question 13 of 20
5.0/ 5.0 Points
Find the products AB and BA to determine whether B is the multiplicative inverse of A.

A = , B =

A. B = A-1
B. B ≠ A-1

##### Question 14 of 20
0.0/ 5.0 Points
Solve the matrix equation for X.

Let A = and B = ; 4X + A = B

A. X =
B. X =
C. X =
D. X =

##### Question 15 of 20
0.0/ 5.0 Points
Find the product AB, if possible.

A = , B =

A.
B.
C.
D. AB is not defined.

##### Question 16 of 20
5.0/ 5.0 Points
Use Cramer’s rule to determine if the system is inconsistent system or contains dependent equations.

2x + 7 = 8
6x + 3y = 24

A. system is inconsistent
B. system contains dependent equations

##### Question 17 of 20
5.0/ 5.0 Points
Find the product AB, if possible.

A = , B =

A.
B.
C.
D. AB is not defined.

##### Question 18 of 20
0.0/ 5.0 Points
Evaluate the determinant.

A. 60
B. -30
C. -60
D. 30

##### Question 19 of 20
5.0/ 5.0 Points
Determinants are used to show that three points lie on the same line (are collinear). If
= 0,
then the points ( x1, y1), ( x2, y2), and ( x3, y3) are collinear. If the determinant does not equal 0, then the points are not collinear. Are the points (-2, -1), (0, 9), (-6, -21) and collinear?

A. Yes
B. No

##### Question 20 of 20
0.0/ 5.0 Points
Solve the system of equations using matrices. Use Gaussian elimination with back-substitution.

3x + 5y – 2w = -13
2x + 7z – w = -1
4y + 3z + 3w = 1
-x + 2y + 4z = -5

A. {(-1, – , 0, )}
B. {(1, -2, 0, 3)}
C. {( , -2, 0, )}
D. {( , – , 0, )}

LESSON 3
##### Question 1 of 20
0.0/ 5.0 Points
Halley’s comet has an elliptical orbit with the sun at one focus. Its orbit shown below is given approximately by In the formula, r is measured in astronomical units. (One astronomical unit is the average distance from Earth to the sun, approximately 93 million miles.) Find the distance from Halley’s comet to the sun at its greatest distance from the sun. Round to the nearest hundredth of an astronomical unit and the nearest million miles.

A. 12.13 astronomical units; 1128 million miles
B. 91.54 astronomical units; 8513 million miles
C. 5.69 astronomical units; 529 million miles
D. 6.06 astronomical units; 564 million miles

##### Question 2 of 20
0.0/ 5.0 Points
Use the center, vertices, and asymptotes to graph the hyperbola.

(x – 1)2 – 9(y – 2)2= 9

A.
B.
C.
D.

##### Question 3 of 20
0.0/ 5.0 Points
Find the standard form of the equation of the ellipse and give the location of its foci.

A. + = 1
foci at (- , 0) and ( , 0)

B. = 1
foci at (- , 0) and ( , 0)

C. + = 1
foci at (- , 0) and ( , 0)

D. + = 1
foci at (-7, 0) and ( 7, 0)

##### Question 4 of 20
0.0/ 5.0 Points
Rewrite the equation in a rotated x’y’-system without an x’y’ term. Express the equation involving x’ and y’ in the standard form of a conic section.

31x2 + 10xy + 21y2-144 = 0

A. x‘2 = -4 y’
B. y‘2 = -4x’
C. + = 1
D. + = 1

##### Question 5 of 20
0.0/ 5.0 Points
Find the standard form of the equation of the ellipse satisfying the given conditions. Foci: (0, -2), (0, 2); y-intercepts: -5 and 5

A. + = 1
B. + = 1
C. + = 1
D. + = 1

##### Question 6 of 20
0.0/ 5.0 Points
Find the vertices and locate the foci for the hyperbola whose equation is given.

49x2 – 100y2= 4900

A. vertices: ( -10, 0), ( 10, 0)
foci: (- , 0), ( , 0)

B. vertices: ( -10, 0), ( 10, 0)
foci: (- , 0), ( , 0)

C. vertices: ( -7, 0), ( 7, 0)
foci: (- , 0), ( , 0)

D. vertices: (0, -10), (0, 10)
foci: (0, – ), (0, )

##### Question 7 of 20
5.0/ 5.0 Points
Write the equation in terms of a rotated x’y’-system using θ, the angle of rotation. Write the equation involving x’ and y’ in standard form. xy +16 = 0; θ = 45°

A. +  = 1
B. y‘2 = -32x’
C. + = 1
D. = 1

##### Question 8 of 20
0.0/ 5.0 Points
Write the appropriate rotation formulas so that in a rotated system the equation has no x’y’-term.

10x2 – 4xy + 6y2– 8x + 8y = 0

A. x = -y’; y = x’
B. x = x’ – y’; y = x’ + y’
C. x = (x’ – y’); y = (x’ + y’)
D. x = x’ – y’; y = x’ + y’

##### Question 9 of 20
0.0/ 5.0 Points
Find the location of the center, vertices, and foci for the hyperbola described by the equation.

= 1

A. Center: ( -4, 1); Vertices: ( -10, 1) and ( 2, 1); Foci: and
(

B. Center: ( -4, 1); Vertices: ( -9, 1) and ( 3, 1); Foci: ( -3 + , 2) and ( 2 + , 2)
C. Center: ( -4, 1); Vertices: ( -10, -1) and ( 2, -1); Foci: ( -4 – , -1) and ( -4 + , -1)
D. Center: ( 4, -1); Vertices: ( -2, -1) and ( 10, -1); Foci: and

##### Question 10 of 20
0.0/ 5.0 Points
Sketch the plane curve represented by the given parametric equations. Then use interval notation to give the relation’s domain and range.

x = 2t, y = t2+ t + 3

A. Domain: (-∞, ∞); Range: -1x, ∞)

B. Domain: (-∞, ∞); Range: [ 2.75, ∞)

C. Domain: (-∞, ∞); Range: [ 3, ∞)

D. Domain: (-∞, ∞); Range: [ 2.75, ∞)

##### Question 11 of 20
0.0/ 5.0 Points
Use vertices and asymptotes to graph the hyperbola. Find the equations of the asymptotes.

y = ±

A. Asymptotes: y = ± x

B. Asymptotes: y = ± x

C. Asymptotes: y = ± x

D. Asymptotes: y = ± x

##### Question 12 of 20
0.0/ 5.0 Points
Graph the ellipse.

16(x – 1)2 + 9(y + 2)2= 144

A.
B.
C.
D.

##### Question 13 of 20
0.0/ 5.0 Points
Is the relation a function?

y = x2+ 12x + 31

A. Yes
B. No

##### Question 14 of 20
5.0/ 5.0 Points
Determine the direction in which the parabola opens, and the vertex.

y2= + 6x + 14

A. Opens upward; ( -3, 5)
B. Opens upward; ( 3, 5)
C. Opens to the right; ( 5, 3)
D. Opens to the right; ( 5, -3)

##### Question 15 of 20
0.0/ 5.0 Points
Match the equation to the graph.

x2= 7y

A.
B.
C.
D.

0.0/ 5.0 Points
y2= -2x

A.
B.
C.
D.

##### Question 17 of 20
0.0/ 5.0 Points
Convert the equation to the standard form for a hyperbola by completing the square on x and y.

x2 – y2+ 6x – 4y + 4 = 0

A. (x + 3)2 + (y + 2)2 = 1
B. = 1
C. (x + 3)2 – (y + 2)2 = 1
D. (y + 3)2– (x + 2)2 = 1

##### Question 18 of 20
0.0/ 5.0 Points
Eliminate the parameter t. Find a rectangular equation for the plane curve defined by the parametric equations.

x = 6 cos t, y = 6 sin t; 0 ≤ t ≤ 2π

A. x2 – y2 = 6; -6 ≤ x ≤ 6
B. x2 – y2 = 36; -6 ≤ x ≤ 6
C. x2 + y2 = 6; -6 ≤ x ≤ 6
D. x2 + y2 = 36; -6 ≤ x ≤ 6

##### Question 19 of 20
5.0/ 5.0 Points
Convert the equation to the standard form for a parabola by completing the square on x or y as appropriate.

y2+ 2y – 2x – 3 = 0

A. (y + 1)2 = 2(x + 2)
B. (y – 1)2 = -2(x + 2)
C. (y + 1)2 = 2(x – 2)
D. (y – 1)2 = 2(x + 2)

##### Question 20 of 20
0.0/ 5.0 Points
Convert the equation to the standard form for a hyperbola by completing the square on x and y.

y2 – 25x2+ 4y + 50x – 46 = 0

A. – (x – 2)2 = 1
B. – (y – 1)2 = 1
C. (x – 1)2= 1
D. – (x – 1)2 = 1

LESSON 4
##### Question 1 of 20
0.0/ 5.0 Points
The finite sequence whose general term is an = 0.17n2 – 1.02n + 6.67 where n = 1, 2, 3, …, 9 models the total operating costs, in millions of dollars, for a company from 1991 through 1999.

Find

A. \$21.58 million
B. \$27.4 million
C. \$23.28 million
D. \$29.1 million

##### Question 2 of 20
5.0/ 5.0 Points
Use the formula for the sum of the first n terms of a geometric sequence to solve. Find the sum of the first 8 terms of the geometric sequence: -8, -16, -32, -64, -128, . . . .

A. -2003
B. -2040
C. -2060
D. -2038

##### Question 3 of 20
5.0/ 5.0 Points
Find the probability. What is the probability that a card drawn from a deck of 52 cards is not a 10?

A. 12/13
B. 9/10
C. 1/13
D. 1/10

##### Question 4 of 20
0.0/ 5.0 Points
Find the common difference for the arithmetic sequence. 6, 11, 16, 21, . . .

A. -15
B. -5
C. 5
D. 15

##### Question 5 of 20
0.0/ 5.0 Points
Find the indicated sum.

A. 28
B. 16
C. 70
D. 54

##### Question 6 of 20
0.0/ 5.0 Points
Evaluate the expression.

1 –

A.
B.
C.
D.

##### Question 7 of 20
0.0/ 5.0 Points
Find the sum of the infinite geometric series, if it exists. 4 – 1 ++ . . .

A. – 1
B. 3
C.
D. does not exist

##### Question 8 of 20
0.0/ 5.0 Points
Find the probability. One digit from the number 3,151,221 is written on each of seven cards. What is the probability of drawing a card that shows 3, 1, or 5?

A. 5/7
B. 2/7
C. 4/7
D. 3/7

##### Question 9 of 20
0.0/ 5.0 Points
A game spinner has regions that are numbered 1 through 9. If the spinner is used twice, what is the probability that the first number is a 3 and the second is a 6?

A. 1/18
B. 1/81
C. 1/9
D. 2/3

##### Question 10 of 20
5.0/ 5.0 Points
Use the formula for the sum of the first n terms of a geometric sequence to solve. Find the sum of the first four terms of the geometric sequence: 2, 10, 50, . . . .

A. 312
B. 62
C. 156
D. 19

##### Question 11 of 20
0.0/ 5.0 Points
Write a formula for the general term (the nth term) of the geometric sequence.

, – , , –, . . .

A. an = n – 1
B. an =   (n – 1)
C. an = n – 1

D. an = n – 1

##### Question 12 of 20
5.0/ 5.0 Points
Does the problem involve permutations or combinations? Do not solve. In a student government election, 7 seniors, 2 juniors, and 3 sophomores are running for election. Students elect four at-large senators. In how many ways can this be done?

A. permutations
B. combinations

##### Question 13 of 20
5.0/ 5.0 Points
Solve the problem. Round to the nearest hundredth of a percent if needed. During clinical trials of a new drug intended to reduce the risk of heart attack, the following data indicate the occurrence of adverse reactions among 1100 adult male trial members. What is the probability that an adult male using the drug will experience nausea?

A. 2.02%
B. 1.73%
C. 27.59%
D. 2.18%

##### Question 14 of 20
0.0/ 5.0 Points
The general term of a sequence is given. Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. an= 4n – 2

A. arithmetic, d = -2
B. geometric, r = 4
C. arithmetic, d = 4
D. neither

##### Question 15 of 20
5.0/ 5.0 Points
Evaluate the factorial expression.

A. n + 4!
B. 4!
C. (n + 3)!
D. 1

##### Question 16 of 20
5.0/ 5.0 Points
If the given sequence is a geometric sequence, find the common ratio.

, , , ,

A.
B. 30
C.
D. 4

##### Question 17 of 20
5.0/ 5.0 Points
Solve the problem. Round to the nearest dollar if needed. Looking ahead to retirement, you sign up for automatic savings in a fixed-income 401K plan that pays 5% per year compounded annually. You plan to invest \$3500 at the end of each year for the next 15 years. How much will your account have in it at the end of 15 years?

A. \$77,295
B. \$75,525
C. \$76,823
D. \$73,982

##### Question 18 of 20
0.0/ 5.0 Points
Find the term indicated in the expansion.

(x – 3y)11; 8th term

A. -721,710x7y4
B. -721,710x4y7
C. 240,570x7y4
D. 240,570x4y8

##### Question 19 of 20
0.0/ 5.0 Points
Find the probability. Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice will be greater than 10?

A. 1/12
B. 5/18
C. 3
D. 1/18

##### Question 20 of 20
5.0/ 5.0 Points
Does the problem involve permutations or combinations? Do not solve. A club elects a president, vice-president, and secretary-treasurer. How many sets of officers are possible if there are 15 members and any member can be elected to each position? No person can hold more than one office.

A. permutations
B. combinations

LESSON 5
##### Question 1 of 20
0.0/ 5.0 Points
Find the slope of the tangent line to the graph of f at the given point.

f(x) = at ( 36, 6)

A.
B. 12
C. 3
D.

##### Question 2 of 20
5.0/ 5.0 Points
Use properties of limits to find the indicated limit. It may be necessary to rewrite an expression before limit properties can be applied.

A. 16
B. does not exist
C. -16
D. 0

##### Question 3 of 20
0.0/ 5.0 Points
Use properties of limits to find the indicated limit. It may be necessary to rewrite an expression before limit properties can be applied.

(2x2 + 2x + 3)2

A. -9
B. 9
C. does not exist
D. 1

##### Question 4 of 20
0.0/ 5.0 Points
Complete the table for the function and find the indicated limit.

A. -0.0300, -0.0200, -0.0100, 0.0100, 0.0200, 0.0300 limit = -1
B. -0.0300, -0.0200, -0.0100, 0.0100, 0.0200, 0.0300 limit = 0
C. -0.0300, -0.0200, -0.0100, 0.0100, 0.0200, 0.0300 limit = 0.1
D. -0.0300, -0.0200, -0.0100, 0.0100, 0.0200, 0.0300 limit = 1

##### Question 5 of 20
0.0/ 5.0 Points
Use the definition of continuity to determine whether f is continuous at a.

f(x) = 5x4 – 9x3+ x – 7a = 7

A. Not continuous
B. Continuous

##### Question 6 of 20
0.0/ 5.0 Points
Find the slope of the tangent line to the graph of f at the given point.

f(x) = x2+ 5x at (4, 36)

A. 13
B. 21
C. 9
D. 3

##### Question 7 of 20
0.0/ 5.0 Points
Use the definition of continuity to determine whether f is continuous at a.

f(x) = a = 4

A. Not continuous
B. Continuous

##### Question 8 of 20
0.0/ 5.0 Points
Graph the function. Then use your graph to find the indicated limit. f(x) = 7exf(x)

A. 0
B. 7
C. 1
D. -7

##### Question 9 of 20
0.0/ 5.0 Points
The graph of a function is given. Use the graph to find the indicated limit and function value, or state that the limit or function value does not exist.

a. f(x)
b. f(1)

A. a.  f(x) = 1
b. f(1) = 0

B. a. f(x) does not exist
b. f(1) = 2

C. a. f(x) = 2
b. f(1) = 2

D. a. f(x) = 2
b. f(1) = 1

##### Question 10 of 20
0.0/ 5.0 Points
Choose the table which contains the best values of x for finding the requested limit of the given function.

A.
B.
C.
D.

##### Question 11 of 20
5.0/ 5.0 Points
Choose the table which contains the best values of x for finding the requested limit of the given function.

(x2+ 8x – 2)

A.
B.
C.
D.

##### Question 12 of 20
0.0/ 5.0 Points
Determine for what numbers, if any, the given function is discontinuous.

f(x) =

A. 5
B. None
C. 0
D. -5, 5

##### Question 13 of 20
0.0/ 5.0 Points
Complete the table for the function and find the indicated limit.

A. -1.22843; -1.20298; -1.20030; -1.19970; -1.19699; -1.16858 limit = -1.20
B. -2.18529; -2.10895; -2.10090; -2.09910; -2.09096; -2.00574 limit = -2.10
C. -4.09476; -4.00995; -4.00100; -3.99900; -3.98995; -3.89526 limit = -4.0
D. 4.09476; 4.00995; 4.00100; 3.99900; 3.98995; 3.89526 limit = 4.0

##### Question 14 of 20
0.0/ 5.0 Points
The function f(x) = x3describes the volume of a cube, f(x), in cubic inches, whose length, width, and height each measure x inches. If x is changing, find the average rate of change of the volume with respect to x as x changes from 1 inches to 1.1 inches.

A. 2.33 cubic inches per inch
B. -3.31 cubic inches per inch
C. 23.31 cubic inches per inch
D. 3.31 cubic inches per inch

##### Question 15 of 20
0.0/ 5.0 Points
The graph of a function is given. Use the graph to find the indicated limit and function value, or state that the limit or function value does not exist.

a. f(x)
b. f(3)

A. a. f(x) = 3
b. f(3) = 5

B. a. f(x) = 5
b. f(3) = 5

C. a. f(x) = 4
b. f(3) does not exist

D. a. f(x) does not exist
b. f(3) = 5

##### Question 16 of 20
0.0/ 5.0 Points
Use the definition of continuity to determine whether f is continuous at a.

f(x) =
a = -5

A. Not continuous
B. Continuous

##### Question 17 of 20
0.0/ 5.0 Points
Use the graph and the viewing rectangle shown below the graph to find the indicated limit.

( x2 – 2)

[-6, 6, 1] by [-6, 6, 1]

A. (x2 – 2) = -6
B. (x2 – 2) = 2
C. (x2 – 2) = -2
D. (x2 – 2) = 6

##### Question 18 of 20
5.0/ 5.0 Points
Use properties of limits to find the indicated limit. It may be necessary to rewrite an expression before limit properties can be applied.

5

A. -5
B. 0
C. 5
D. 2

##### Question 19 of 20
0.0/ 5.0 Points
Find the derivative of f at x. That is, find f ‘(x). f(x) = 7x + 8; x = 5

A. 40
B. 8
C. 35
D. 7

##### Question 20 of 20
0.0/ 5.0 Points
Graph the function. Then use your graph to find the indicated limit.

f(x) = , f(x)

A. 6
B. -2
C. -6
D. 2

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