AnswersAlgebra II - MA3111 CRCumulative Exam

Cumulative Exam — Cumulative exam Answers

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1
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Use synthetic division to solve . What is the quotient?

Question illustration
A
x squared + 4 x + 3
Option A
B
x squared minus 6 x + 13 minus StartFraction 80 Over x minus 5 EndFraction
Option B
C
x cubed + 4 x squared + 3 x
Option C
D
x squared minus 6 x + 13 minus StartFraction 80 Over x + 5 EndFraction
Option D
2
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Which graph represents the same relation as the rule y = 2x, for all real numbers x?

A
A coordinate plane has 5 points. The points are (negative 2, negative 4), (negative 1, negative 2), (0, 0), (1, 2), (2, 4).
Option A
B
On a coordinate plane, a horizontal line intercepts the y-axis at (0, 2).
Option B
C
On a coordinate plane, a straight line with positive slope intercepts the axis at (0, 0). The line goes through points (negative 2, negative 4) and (2, 4).
Option C
D
On a coordinate plane, 11 points form a vertical line that crosses the x-intercept at (2, 0).
Option D
3

Which expression is equivalent to (4 + 7i)(3 + 4i)?

A
–16 + 37i
B
12 – 28i
C
16 – 37i
D
37 + 16i
4

What is the completely factored form of 8x2 – 50?

A
2(x + 5)(x – 5)
B
2(2x – 5)(2x – 5)
C
2(2x + 5)(2x + 5)
D
2(2x + 5)(2x – 5)
5

Which expression is equivalent to –8?

A
–2–3
B
(Negative one-half) Superscript negative 3
Option B
C
(one-half) Superscript negative 3
Option C
D
2–3
6

Which expression is equivalent to ?

Question illustration
A
StartFraction 2 (a + 1) squared Over a cubed EndFraction
Option A
B
6a
C
2a
D
StartFraction 6 a squared Over a + 1 EndFraction
Option D
7

For which interval is the average rate of change of f(x) negative?

Question illustration
A
from x = –3.5 to x = –1
B
from x = –3 to x = 3
C
from x = 0 to x = 2.5
D
from x = 3 to x = 4.5
8

What is the product of ?

Question illustration
A
StartFraction 7 Over m Superscript 5 EndFraction
Option A
B
7m6
C
StartFraction 10 Over m Superscript 5 EndFraction
Option C
D
10m6
9

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

Question illustration
A
f(x) = 4x4 – 7x2 + x + 25
B
f(x) = 9x4 – 7x2 + x + 10
C
f(x) = 10x4 – 7x2 + x + 9
D
f(x) = 25x4 – 7x2 + x + 4
10

The graph below shows the number of houses sold over x days. What is the average rate of change from day 2 to day 10?

Question illustration
A
Negative four-thirds
Option A
B
Negative three-fourths
Option B
C
6
D
8
11

What is the solution to the equation ?

Question illustration
A
x = –3
B
x = –3 and x = 0
C
x = 0 and x = 3
D
x = 3
12

The quotient of (x4 – 3x2 + 4x – 3) and (x2 + x – 3) is a polynomial. What is the quotient?

A
x4 – 2x2 + 5x – 6
B
x2 – x + 1
C
x6 + x5 – 6x4 + x3 + 10x2 – 15x + 9
D
x4 – 4x2 + 3x
13

Which value must be added to the expression x2 – 3x to make it a perfect-square trinomial?

A
Three-halves
Option A
B
Nine-fourths
Option B
C
6
D
9
14

Subtract from .

Question illustration
A
mc011-3.jpg
Option A
B
mc011-4.jpg
Option B
C
mc011-5.jpg
Option C
D
mc011-6.jpg
Option D
15

What is the binomial expansion of (x + 2y)7?

A
2x7 + 14x6y + 42x5y2 + 70x4y3 + 70x3y4 + 42x2y5 + 14xy6 + 2y7
B
x7 + 14x6y + 42x5y2 + 70x4y3 + 70x3y4 + 42x2y5 + 14xy6 + y7
C
x7 + 7x6y + 21x5y2 + 35x4y3 + 35x3y4 + 21x2y5 + 7xy6 + y7
D
x7 + 14x6y + 84x5y2 + 280x4y3 + 560x3y4 + 672x2y5 + 448xy6 + 128y7
16

Which expression is equivalent to the following complex fraction?

Question illustration
A
StartFraction (y + 1) (y minus 1) Over y squared EndFraction
Option A
B
StartFraction y + 1 Over y minus 1 EndFraction
Option B
C
StartFraction y minus 1 Over y + 1 EndFraction
Option C
D
StartFraction y squared Over (y + 1) (y minus 1) EndFraction
Option D
17

If f(x) = –x2 + 3x + 5 and g(x) = x2 + 2x, which graph shows the graph of (f + g)(x)?

A
On a coordinate plane, a straight line with a negative slope crosses the y-axis at (0, 5) and crosses the x-axis at (1, 0).
Option A
B
On a coordinate plane, a parabola opens down. It goes through (negative 2, negative 4), has a vertex at (0, 5), and goes through (2, negative 2)
Option B
C
On a coordinate plane, a parabola opens up. It goes through (negative 3, 7), has a vertex at (negative 1, 2), and goes through (0, 5).
Option C
D
On a coordinate plane, a straight line with a positive slope crosses the x-axis at (negative 1, 0) and crosses the y-axis at (0, 5)
Option D
18

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)?

A
3, 4, 5, 6
B
3, 4, 5, 6i
C
3, 4, ,
Option C
D
3, 4, 5 + i, –5 + i
19

What is the remainder when (x3 + 1) is divided by (x2 – x + 1)?

A
x + 1
B
x
C
2
D
0
20

Which of the following graphs represents a function?

A
On a coordinate plane, a graph shows an image of a curved line connected to a straight line. The curved line is upward facing and goes through the y-axis at (0, 0.75). The curved line connects with the straight line at (1, 0.75). The straight line has a negative slope and goes through the x-axis at (2, 0).
Option A
B
On a coordinate plane, a circle intercepts the x-axis at points (negative 2, 0) and (2, 0) and intercepts the y-axis between points 3 and 4 and also between points negative 3 and negative 4.
Option B
C
On a coordinate plane, a parabola opens right and has a vertex at (negative 3, 3).
Option C
D
A coordinate plane has 7 points. The points are (negative 4, 3), (negative 2, negative 5), (negative 1, negative 3), (1, 3), (2, negative 2), (4, negative 2), (4, 2).
Option D

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