Answers DSD-CR-Secondary Math III-Term 2Cumulative Exam

Cumulative Exam Answers

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Which expression is equivalent to ?

StartFraction 2 (a + 1) squared Over a cubed EndFraction

StartFraction 6 a squared Over a + 1 EndFraction

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The polynomial function f(x) is a fourth degree polynomial. Which of the following could be the complete list of the roots of f(x)?

3, 4, 5, 6

3, 4, 5, 6i

3, 4, ,

3, 4, 5 + i, –5 + i

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

–9

–1

What is the quotient?

(t + 3) squared

(t + 4) squared

StartFraction 1 Over (t + 4) squared EndFraction

StartFraction 1 Over (t + 3) squared EndFraction

Which of the following graphs could be the graph of the function f(x) = x3 + 8?

mc019-1.jpg

mc019-2.jpg

mc019-3.jpg

mc019-4.jpg

Which expression is equivalent to ? Assume .

–50x8y18

–2x8y18

–2x12y72

5x8y18

Which expression is equivalent to ?

mc019-2.jpg

mc019-3.jpg

mc019-4.jpg

mc019-5.jpg

Which expression is equivalent to ?

–4b – 2

4b + 2

mc011-2.jpg

mc011-3.jpg

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

x – 4

x – 2

x + 2

x + 4

Use synthetic division to solve . What is the quotient?

x squared + 4 x + 3

x squared minus 6 x + 13 minus StartFraction 80 Over x minus 5 EndFraction

x cubed + 4 x squared + 3 x

x squared minus 6 x + 13 minus StartFraction 80 Over x + 5 EndFraction

What are the solutions of the equation 9x4 – 2x2 – 7 = 0? Use u substitution to solve.

and x = ±1

and x = ±i

and x = ±1

and x = ±i

According to the Rational Root Theorem, is a potential rational root of which function?

f(x) = 4x4 – 7x2 + x + 25

f(x) = 9x4 – 7x2 + x + 10

f(x) = 10x4 – 7x2 + x + 9

f(x) = 25x4 – 7x2 + x + 4

What is the difference?

StartFraction x squared + 4 x minus 1 Over x (x + 2) EndFraction

StartFraction x squared + 4 x + 1 Over x (x + 2) EndFraction

StartFraction 4 Over negative 1 (x squared + x minus 2) EndFraction

StartFraction x squared + 6 x + 1 Over x (x + 2) EndFraction

Which equation could be used to calculate the sum of the geometric series?

S 5 = StartFraction one-third (1 minus (two-thirds) Superscript 5 Baseline) Over (1 minus two-thirds) EndFraction

S 5 = StartFraction two-thirds (1 minus (one-third) Superscript 5 Baseline) Over (1 minus one-third) EndFraction

S = StartFraction one-third Over (1 minus two-thirds) EndFraction

S = StartFraction two-thirds Over (1 minus one-third) EndFraction

If a polynomial function f(x) has roots and –6, what must be a factor of f(x)?

(x + ( )

(x – ())

(x + ())

(x – ())

The graph of f(x) = 4x3 – 13x2 + 9x + 2 is shown below. How many roots of f(x) are rational numbers?

Which of the following describes the zeroes of the graph of f(x) = –x5 + 9x4 – 18x3?

0 with multiplicity 3, –3 with multiplicity 2, and –2 with multiplicity 1

0 with multiplicity 3, 3 with multiplicity 1, and 6 with multiplicity 1

0 with multiplicity 3, 3 with multiplicity 2, and 2 with multiplicity 1

0 with multiplicity 3, –3 with multiplicity 1, and –6 with multiplicity 1

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

What substitution should be used to rewrite x8 – 3x4 + 2 = 0 as a quadratic equation?

u = x2

u = x4

u = x8

u = x16

Sandra graphed the system of equations that can be used to solve . What are the roots of the polynomial equation?

–12, 12

–4, 3

–3, 4

–1, 1

Which expression is equivalent to ? Assume .

a Superscript 9 Baseline b Superscript 6

a Superscript 9 Baseline b Superscript 12

StartFraction 1 Over a cubed b squared EndFraction

StartFraction a Superscript 29 Baseline b Superscript 6 Baseline EndFraction

One root of is x = –10. What are all the roots of the function? Use the Remainder Theorem.

x = –25 or x = 10

x = –25, x = 1, or x = 10

x = –10 or x = 5

x = –10, x = –5, or x = 5

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

2 roots

3 roots

6 roots

9 roots

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?

Sigma-Summation Underscript n = 1 Overscript 15 EndScripts 1 (3) Superscript n minus 1

Sigma-Summation Underscript n = 1 Overscript 15 EndScripts 3 (1) Superscript n minus 1

Sigma-Summation Underscript n = 1 Overscript 15 EndScripts 1 (one-third) Superscript n minus 1

Sigma-Summation Underscript n = 1 Overscript 15 EndScripts one-third (1) Superscript n minus 1

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

and x = ±10

and x = ±10i

and x = ±10

Which expression is equivalent to the following complex fraction?

StartFraction 3 y + 5 x Over 2 (y minus 2 x) EndFraction

StartFraction 2 (y minus 2 x) Over 3 y minus 5 x EndFraction

StartFraction 2 (y minus 2 x) (3 y minus 5 x) Over x squared y squared EndFraction

StartFraction x squared y squared Over 2 (y minus 2 x) (3 y minus 5 x) EndFraction

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?

Patricia is correct because must be a root.

Patricia is correct because 3 – 4i must be a root.

Patricia is not correct because both 3 – 4i and must be roots.

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

–3 with multiplicity 2 and 6 with multiplicity 4

–3 with multiplicity 4 and 6 with multiplicity 2

3 with multiplicity 2 and –6 with multiplicity 4

3 with multiplicity 4 and –6 with multiplicity 2

Which equation is quadratic in form?

4(x – 2)2 + 3x – 2 + 1 = 0

8x5 + 4x3 + 1 = 0

10x8 + 7x4 + 1 = 0

9x16 + 6x4 + 1 = 0

Simplify the expression . Assume .

Negative StartFraction 1 Over 16 a squared b squared EndFraction

StartFraction a squared b squared Over 4 EndFraction

Negative 16 a squared b squared

16 a squared b squared

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

3 roots

4 roots

7 roots

8 roots

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?

combine like terms

square the binomial

cube the binomial

rewrite the expression as a fraction

What is the product?

StartFraction 5 Over 4 k squared EndFraction

StartFraction 5 k squared Over 4 EndFraction

StartFraction 5 k Superscript 4 Baseline Over 4 EndFraction

StartFraction 5 Over 4 k Superscript 4 Baseline EndFraction

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

–3

–1

Use synthetic division to solve . What is the quotient?

3 x cubed + 12 x squared + 26 x + 61 + StartFraction 132 Over x + 2 EndFraction

3 x cubed + 2 x + 5

3 x cubed + 12 x squared + 26 x + 61 + StartFraction 132 Over x minus 2 EndFraction

3 x Superscript 4 Baseline + 2 x squared + 5 x

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

–7

–4

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

The graph crosses the x-axis at x = 0 and touches the x-axis at x = 5 and x = –2.

The graph touches the x-axis at x = 0 and crosses the x-axis at x = 5 and x = –2.

The graph crosses the x-axis at x = 0 and touches the x-axis at x = –5 and x = 2.

The graph touches the x-axis at x = 0 and crosses the x-axis at x = –5 and x = 2.

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

x – 3

x – 1

x + 1

x + 3

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

and

–1, , , and 1

Which expression is equivalent to ? Assume .

StartFraction a Over b Superscript 5 Baseline

StartFraction 1 Over a b Superscript 5 Baseline Endfraction

StartFraction a cubed b Over 1 EndFraction

StartFraction b Over a EndFraction

If –3 + i is a root of the polynomial function f(x), which of the following must also be a root of f(x)?

–3 – i

–3i

3 – i

According to the Rational Root Theorem, the following are potential roots of f(x) = 60x2 – 57x – 18., , 3, 6Which is an actual root of f(x)?

Negative six-fifths

Negative one-fourths

A high-interest savings account pays 5.5% interest compounded annually. If $300 is deposited initially and again at the first of each year, which summation represents the money in the account 10 years after the initial deposit?

Sigma-Summation Underscript n = 1 Overscript 10 EndScripts 300 (0.055) Superscript n minus 1