Name: ______________________
Class: _________________
Date: _________
ID: A
Algebra 2 Mini-MAFS 3 (To be given after Chapter 3)
MAFS.912.A-APR.1.1, MAFS.912.A-APR.2.2, MAFS.912.A-APR.2.3
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1
A cooler, complete with lid, is in the shape of a rectangular prism and its outer dimensions have a length 4
times the width and height 3 times the width. The inside of the cooler (with the lid on) has a uniform
coating of insulation foam that is one inch thick. Let x represent the width of the cooler. What is the
volume of the inside of the cooler?
3
2
3
A. 12x + 5x + 8x − 1
3
2
B. 12x − 19x + 8x − 1
2
2
C. 12x − 19x − 6x − 1
3
2
D. 12x − 38x + 32x − 8
4
2
The sides of a pentagon are x − 2x, x ,
1 3 2
1 2
x , x + 4, and x + x − 1. Which polynomial represents the
2
4
perimeter of the pentagon?
1 3 9 2
x + x −x+3
2
4
4
11 2
B. x +
x −x+3
4
4
A. x +
3
1 3 5 2
x + x −x+3
2
4
4
1 3 9 2
D. x + x + x − x − 1
2
4
4
C. x +
The rectangle shown is enlarged so that the horizontal length is multiplied by 2x and the vertical width is
1
multiplied by x. What is the difference in the perimeters of the two rectangles?
2
2
x − 4x + 2
2
x + 6x − 4
5 3
2
x − 7x + 2
2
3 2
B. − x − 25x + 6
2
A.
4
3
2
3
2
C. 5x − 14x + 4
D. 5x − 10x + 4x
A circular fountain is surrounded by a circular walkway. The radius of the fountain is x + 2 feet and the width
the walkway is 4 feet. Which expression represents the area of the walkway?
2
A. 4 πx + 16 πx + 16 π square feet
B. 16 πx + 40 π square feet
C. 8 πx square feet
D. 8 πx + 32 π square feet
1
Name: ______________________
5
If the polynomials P(x) and Q(x) are related by the equation P(x) = Q(x)(x − 4) + P(4), which statement
must be true?
A.
B.
C.
D.
6
P(4) must equal –4 if 4 is a zero of P(x).
P(4) must equal P(x) divided by (x – 4).
P(4) must equal 0 if 4 is a zero of P(x).
P(4) must equal 4 if 4 is a zero of P(x).
4
B. 2
2
C. 0
3
D. 6
2
Given the polynomial P(x) = x − x − 8x + 12, what is the value of R(x) in the equation
P(x) = Q(x)(x + 3) + R(x)?
A. –36
8
3
Consider the polynomial function P(x) = x + ax − 5x + 4x + 12, where a is an unknown real number. If
x − 2 is a factor of the polynomial, what is the value of a?
A. −2
7
ID: A
B. 0
C. 6
D. 28
3
2
Gloria attempted to find the remainder when P(x) = x − x − 30x + 72 is divided by ( x − 3 ) . Her work is
shown below. What error did she make, and how should she correct it?
3
2
P(x) = x − x − 30x + 72
3
2
P(−3) = (−3) − (−3) − 30(−3) + 72
= −27 − 9 + 90 + 72
= 126
A. Gloria should have found P(3) using the Remainder Theorem. The remainder should
be 0.
B. Gloria should have written the third step as −27 + 9 + 90 + 72. The remainder should
be 144.
C. Gloria should have found P(8) using the Remainder Theorem. The remainder should
be 280.
3
2
D. Gloria should have written the second step as P(−3) = (−3) − (−3) − 30(3) + 72. The
remainder should be –54.
9
ÊÁ 1
ˆ˜
For the polynomial P(x) = −(x − 3) ÁÁÁÁ x − 8 ˜˜˜˜ ( x − 1 ) , which statement is NOT true?
ÁË 2
˜¯
A.
B.
C.
D.
The
The
The
The
graph of
graph of
function
graph of
P(x)
P(x)
P(x)
P(x)
has 1 y-intercept.
has 4 x-intercepts.
has 3 zeros.
has an x-intercept of 3.
2
Name: ______________________
ID: A
10 The graph of a cubic polynomial function is shown. Which function fits the graph?
A. f(x) = (x + 2)(x + 3)(x + 1)
B. f(x) = (x − 2)(x − 1)(x − 3)
C. f(x) = (x − 2)(x + 1)(x − 3)
D. f(x) = (x − 1)(x + 2)(x + 3)
11 The graph of a 4th degree polynomial function is shown below. What are the zeros of the graph of the
function, and what is the multiplicity of each?
A. A zero at (1,0) with a multiplicity 2 and a zero
B. A zero at (1,0) with a multiplicity 1 and a zero
C. A zero at (–1,0) with a multiplicity 2, a zero at
at (3,0) with a multiplicity 1
D. A zero at (–1,0) with a multiplicity 1, a zero at
zero at (1,0) with a multiplicity 2
3
at (3,0) with a multiplicity 1
at (–1,0) with a multiplicity 2
(1,0) with a multiplicity 1, and a zero
(–3,0) with a multiplicity 1, and a
Name: ______________________
ID: A
12 A 4th degree polynomial function f has a zero at -1, a zero at 1, and a zero at -2. The zero at -2 has a
multiplicity of two. When x → ∞, f(x) → −∞. Which of the following could be the graph of function f.
A.
C.
B.
D.
4
ID: A
Algebra 2 Mini-MAFS 3 (To be given after Chapter 3)
MAFS.912.A-APR.1.1, MAFS.912.A-APR.2.2, MAFS.912.A-APR.2.3
Answer Section
MULTIPLE CHOICE
1
ANS:
MSC:
2 ANS:
MSC:
3 ANS:
MSC:
4 ANS:
MSC:
5 ANS:
MSC:
6 ANS:
MSC:
7 ANS:
MSC:
8 ANS:
MSC:
9 ANS:
MSC:
10 ANS:
MSC:
11 ANS:
MSC:
12 ANS:
MSC:
D
DOK
A
DOK
C
DOK
D
DOK
C
DOK
A
DOK
B
DOK
A
DOK
B
DOK
C
DOK
C
DOK
D
DOK
PTS: 1
STA: MAFS.912.A-APR.1.1
PTS: 1
STA: MAFS.912.A-APR.1.1
PTS: 1
STA: MAFS.912.A-APR.1.1
PTS: 1
STA: MAFS.912.A-APR.1.1
PTS: 1
STA: MAFS.912.A–APR.2.2
PTS: 1
STA: MAFS.912.A–APR.2.2
PTS: 1
STA: MAFS.912.A–APR.2.2
PTS: 1
STA: MAFS.912.A–APR.2.2
PTS: 1
STA: MAFS.912.A-APR.2.3
PTS: 1
STA: MAFS.912.A-APR.2.3
PTS: 1
STA: MAFS.912.A-APR.2.3
PTS: 1
STA: MAFS.912.A-APR.2.3
2
1
2
2
2
2
2
3
1
2
2
2
1