AnswersDSD-CR-Secondary Math III-Term 2Cumulative Exam

Cumulative Exam — Cumulative exam Answers

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21
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Which expression is equivalent to ? Assume .

Question illustration
A
a Superscript 9 Baseline b Superscript 6
Option A
B
a Superscript 9 Baseline b Superscript 12
Option B
C
StartFraction 1 Over a cubed b squared EndFraction
Option C
D
StartFraction a Superscript 29 Baseline b Superscript 6 Baseline EndFraction
Option D
22
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One root of is x = –10. What are all the roots of the function? Use the Remainder Theorem.

Question illustration
A
x = –25 or x = 10
B
x = –25, x = 1, or x = 10
C
x = –10 or x = 5
D
x = –10, x = –5, or x = 5
23

According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function?f(x) = (x3 – 3x + 1)2

A
2 roots
B
3 roots
C
6 roots
D
9 roots
24

The first figure of the Sierpinski triangle has one shaded triangle. The second figure of the Sierpinski triangle has three shaded triangles. The third figure of the Sierpinski triangle has nine shaded triangles. Which summation represents the total number of shaded triangles in the first 15 figures?

A
Sigma-Summation Underscript n = 1 Overscript 15 EndScripts 1 (3) Superscript n minus 1
Option A
B
Sigma-Summation Underscript n = 1 Overscript 15 EndScripts 3 (1) Superscript n minus 1
Option B
C
Sigma-Summation Underscript n = 1 Overscript 15 EndScripts 1 (one-third) Superscript n minus 1
Option C
D
Sigma-Summation Underscript n = 1 Overscript 15 EndScripts one-third (1) Superscript n minus 1
Option D
25

What are the solutions of the equation x4 + 95x2 – 500 = 0? Use factoring to solve.

A
and x = ±10
Option A
B
and x = ±10i
Option B
C
and x = ±10i
Option C
D
and x = ±10
Option D
26

Which expression is equivalent to the following complex fraction?

Question illustration
A
StartFraction 3 y + 5 x Over 2 (y minus 2 x) EndFraction
Option A
B
StartFraction 2 (y minus 2 x) Over 3 y minus 5 x EndFraction
Option B
C
StartFraction 2 (y minus 2 x) (3 y minus 5 x) Over x squared y squared EndFraction
Option C
D
StartFraction x squared y squared Over 2 (y minus 2 x) (3 y minus 5 x) EndFraction
Option D
27

Patricia is studying a polynomial function f(x). Three given roots of f(x) are , 3 + 4i, and 10. Patricia concludes that f(x) must be a polynomial with degree 4. Which statement is true?

Question illustration
A
Patricia is correct because must be a root.
Option A
B
Patricia is correct because 3 – 4i must be a root.
C
Patricia is not correct because both 3 – 4i and must be roots.
Option C
D
Patricia is not correct because both 3 – 4i and must be roots.
Option D
28

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

Question illustration
A
–3 with multiplicity 2 and 6 with multiplicity 4
B
–3 with multiplicity 4 and 6 with multiplicity 2
C
3 with multiplicity 2 and –6 with multiplicity 4
D
3 with multiplicity 4 and –6 with multiplicity 2
29

Which equation is quadratic in form?

A
4(x – 2)2 + 3x – 2 + 1 = 0
B
8x5 + 4x3 + 1 = 0
C
10x8 + 7x4 + 1 = 0
D
9x16 + 6x4 + 1 = 0
30

Simplify the expression . Assume .

Question illustration
A
Negative StartFraction 1 Over 16 a squared b squared EndFraction
Option A
B
StartFraction a squared b squared Over 4 EndFraction
Option B
C
Negative 16 a squared b squared
Option C
D
16 a squared b squared
Option D
31

According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function?f(x) = 8x7 – x5 + x3 + 6

A
3 roots
B
4 roots
C
7 roots
D
8 roots
32

Brayden is simplifying the expression 4n – (n – 3)2. He begins by distributing the negative to the terms inside the parentheses. What should he have done instead?

A
combine like terms
B
square the binomial
C
cube the binomial
D
rewrite the expression as a fraction
33

What is the product?

Question illustration
A
StartFraction 5 Over 4 k squared EndFraction
Option A
B
StartFraction 5 k squared Over 4 EndFraction
Option B
C
StartFraction 5 k Superscript 4 Baseline Over 4 EndFraction
Option C
D
StartFraction 5 Over 4 k Superscript 4 Baseline EndFraction
Option D
34

The polynomial equation has complex roots . What is the other root? Use a graphing calculator and a system of equations.

Question illustration
A
–3
B
–1
C
3
D
10
35

Use synthetic division to solve . What is the quotient?

Question illustration
A
3 x cubed + 12 x squared + 26 x + 61 + StartFraction 132 Over x + 2 EndFraction
Option A
B
3 x cubed + 2 x + 5
Option B
C
3 x cubed + 12 x squared + 26 x + 61 + StartFraction 132 Over x minus 2 EndFraction
Option C
D
3 x Superscript 4 Baseline + 2 x squared + 5 x
Option D
36

At which root does the graph of f(x) = (x + 4)6(x + 7)5 cross the x-axis?

A
–7
B
–4
C
4
D
7
37

Which statement describes the graph of f(x) = –x4 + 3x3 + 10x2?

A
The graph crosses the x-axis at x = 0 and touches the x-axis at x = 5 and x = –2.
B
The graph touches the x-axis at x = 0 and crosses the x-axis at x = 5 and x = –2.
C
The graph crosses the x-axis at x = 0 and touches the x-axis at x = –5 and x = 2.
D
The graph touches the x-axis at x = 0 and crosses the x-axis at x = –5 and x = 2.
38

What must be a factor of the polynomial function f(x) graphed on the coordinate plane below?

Question illustration
A
x – 3
B
x – 1
C
x + 1
D
x + 3
39

What are all the rational roots of the polynomial f(x) = 20x4 + x3 + 8x2 + x – 12?

A
and
Option A
B
and
Option B
C
–1, , , and 1
Option C
D
–1, , , and 1
Option D
40

Which expression is equivalent to ? Assume .

Question illustration
A
StartFraction a Over b Superscript 5 Baseline
Option A
B
StartFraction 1 Over a b Superscript 5 Baseline Endfraction
Option B
C
StartFraction a cubed b Over 1 EndFraction
Option C
D
StartFraction b Over a EndFraction
Option D

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