AnswersDSD-CR-Secondary Math III-Term 2Unit Test

Unit Test — Unit test Answers

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1
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If f(–2) = 0, what are all the factors of the function ? Use the Remainder Theorem.

Question illustration
A
(x + 2)(x + 60)
B
(x – 2)(x – 60)
C
(x – 10)(x + 2)(x + 6)
D
(x + 10)(x – 2)(x – 6)
2
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According to the Rational Root Theorem, what are all the potential rational roots of f(x) = 5x3 – 7x + 11?

A
, , , 5
Option A
B
, 1, , 11
Option B
C
, , , , , 5, 11
Option C
D
0, , , , , , 5, 11
Option D
3

What are the solutions of the equation (2x + 3)2 + 8(2x + 3) + 11 = 0? Use u substitution and the quadratic formula to solve.

A
x = StartFraction negative 4 plus-or-minus StartRoot 5 EndRoot Over 2 EndFraction
Option A
B
x = StartFraction negative 7 plus-or-minus StartRoot 5 EndRoot Over 2 EndFraction
Option B
C
x = –7 and x = –2
D
x = –1 and x = 4
4

A cube has side length x. One side of the cube is increased by 4 inches, and another side is doubled. The volume of the new rectangular prism is 450 cubic inches. The equation can be used to find x. What was the side length of the original cube? Use a graphing calculator and a system of equations to find the answer.

Question illustration
A
4 inches
B
5 inches
C
9 inches
D
10 inches
5

The price that a company charged for a basketball hoop is given by the equation where x is the number of hoops that are produced, in millions. It costs the company $30 to make each basketball hoop. The company recently reduced its production to 1 million hoops but maintained its profit of 15 million dollars. Approximately how many basketball hoops did the company previously produce to make the same profit?

Question illustration
A
1.3 million hoops
B
1.4 million hoops
C
15 million hoops
D
30 million hoops
6

Which polynomial function has a leading coefficient of 1, roots –2 and 7 with multiplicity 1, and root 5 with multiplicity 2?

A
f(x) = 2(x + 7)(x + 5)(x – 2)
B
f(x) = 2(x – 7)(x – 5)(x + 2)
C
f(x) = (x + 7)(x + 5)(x + 5)(x – 2)
D
f(x) = (x – 7)(x – 5)(x – 5)(x + 2)
7

Which statement describes the graph of this polynomial function?

Question illustration
A
The graph crosses the x-axis at x = 0 and touches the x-axis at x = 3.
B
The graph touches the x-axis at x = 0 and crosses the x-axis at x = 3.
C
The graph crosses the x-axis at x = 0 and touches the x-axis at x = –3.
D
The graph touches the x-axis at x = 0 and crosses the x-axis at x = –3.
8

A polynomial function has a root of –3 with multiplicity 2, a root of 0 with multiplicity 1, a root of 1 with multiplicity 1, and a root of 3 with multiplicity 2. If the function has a positive leading coefficient and is of even degree, which could be the graph of the function?

A
mc015-1.jpg
Option A
B
mc015-2.jpg
Option B
C
mc015-3.jpg
Option C
D
mc015-4.jpg
Option D
9

Which of the following describes the roots of the polynomial function ?

Question illustration
A
–2 with multiplicity 2, 4 with multiplicity 1, and –1 with multiplicity 3
B
–2 with multiplicity 3, 4 with multiplicity 2, and –1 with multiplicity 4
C
2 with multiplicity 2, –4 with multiplicity 1, and 1 with multiplicity 3
D
2 with multiplicity 3, –4 with multiplicity 2, and 1 with multiplicity 4
10

What is the polynomial function of lowest degree with lead coefficient 1 and roots 1 and 1 + i?

A
f(x) = x2 – 2x + 2
B
f(x) = x3 – x2 + 4x – 2
C
f(x) = x3 – 3x2 + 4x – 2
D
f(x) = x2 – x + 2
11

The graphs of two polynomial equations do not intersect. Kelly concludes that the system has no solution. Which statement best explains why Kelly’s reasoning is correct or incorrect?

A
She is incorrect because systems may have only complex solutions which are not visible on a graph.
B
She is incorrect because the solutions may have multiplicity greater than 1.
C
She is correct because all solutions are intersection points of the graphs.
D
She is correct because the solutions are irrational.
12

Let a, b, and c be real numbers where a b c 0. Which of the following functions could represent the graph below?

Question illustration
A
f(x) = x2(x – a)2(x – b)4(x – c)
B
f(x) = x3(x – a)3(x – b)(x – c)2
C
f(x) = x4(x – a)(x – b)3(x – c)3
D
f(x) = (x – a)2(x – b)(x – c)6
13

What is the sum of the first seven terms of the geometric series?3 + 12 + 48 + 192 + ...

A
4,372
B
12,288
C
16,383
D
65,535
14

Which geometric series converges?

A
StartFraction 1 Over 81 EndFraction + StartFraction 1 Over 27 EndFraction + one-ninth + one-third + ellipsis
Option A
B
1 + one-half + one-fourth + one-eighth + ellipsis
Option B
C
Sigma-Summation Underscript n = 1 Overscript infinity EndScripts 7 (negative 4) Superscript n minus 1
Option C
D
Sigma-Summation Underscript n = 1 Overscript infinity EndScripts one-fifth (2) Superscript n minus 1
Option D
15

Which statement best describes the equation (x + 5)2 + 4(x + 5) + 12 = 0?

A
The equation is quadratic in form because it can be rewritten as a quadratic equation with u substitution u = (x + 5).
B
The equation is quadratic in form because when it is expanded, it is a fourth-degree polynomial.
C
The equation is not quadratic in form because it cannot be solved by using the quadratic formula.
D
The equation is not quadratic in form because there is no real solution.
16

Which expression is equivalent to ?

Question illustration
A
mc023-2.jpg
Option A
B
mc023-3.jpg
Option B
C
–18z – 5
D
–18z + 10
17

According to the Rational Root Theorem, which is a factor of the polynomial f(x) = 3x3 – 5x2 – 12x + 20?

A
2x + 1
B
2x – 1
C
3x + 5
D
3x – 5
18

Which expression is equivalent to 3 + 4y – y(9 – 2y) + 5?

A
8 – 7y
B
mc008-1.jpg
Option B
C
mc008-2.jpg
Option C
D
mc008-3.jpg
Option D
19

The polynomial function is graphed below.Which is a potential rational root of f(x) at point P?

Question illustration
A
The root at point P may be .
Option A
B
The root at point P may be .
Option B
C
The root at point P may be .
Option C
D
The root at point P may be .
Option D
20

A painter is painting a wall with an area of 150 ft2. He decides to paint half of the wall and then take a break. After his break, he paints half of the remaining unpainted portion and then takes another break. If he continues to paint half of the remaining unpainted portion between breaks, approximately what portion of the original wall will be painted when he takes his fifth break?

A
112.50 ft2
B
145.31 ft2
C
147.66 ft2
D
290.63 ft2

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