Name: ______________________
Class: _________________
Date: _________
ID: A
Algebra 2 Hon MINIMAFS 1 (To be used after Chapter 1)
MAFS.912.A-SSE.2.3, MAFS.912.F-IF.3.8, MAFS.912.N-CN.3.7, MAFS.912.N-CN.1.2
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
____
1. Manuel wants to determine the zeros of the quadratic function f(x) = 2x2 + 5x – 12. Which would be the
best form for him to use?
a.
f(x) = (2x – 2)(x + 6)
c.
f(x) = (2x + 3)(x – 4)
b.
f(x) = (2x – 3)(x + 4)
d.
f(x) = (2x + 6)(x – 2)
2
2. Mark wants to complete the square for the function f(x) = 12x − 72x so that he can find its minimum
value. His work is shown below. Which choice gives the function’s actual minimum value, best explains
the error Mark made in his steps, and provides a suggestion for fixing his mistake?
2
f(x) = 12x − 72x
Ê 2
ˆ
= 12 ÁÁÁÁ x − 6x ˜˜˜˜
Ë
¯
Ê 2
ˆ
= 12 ÁÁÁÁ x − 6x + 9 ˜˜˜˜ + 12(9)
Ë
¯
= 12 ( x − 3 ) ( x − 3 ) + 108
2
= 12 ( x − 3 ) + 108
Step 1
Step 2
Step 3
Step 4
a.
He should have subtracted 12(9) in step 2 instead of adding 12(9). To fix it, he
should change the last term to “– 108.” thus giving him –108 as the actual
minimum value.
b.
He factored incorrectly in Step 3 and should change ( x − 3 ) ( x − 3 ) to " ( x − 2 ) ( x − 3 ) . "
The value of 108 is the actual minimum.
c.
He should have added 9 in Step 2 instead of 12(9)=108. To fix it, he should change
the last term to “+ 9.” in Step 2 thus giving him 9 as the actual minimum value.
d.
Ê 2
ˆ
He factored incorrectly in the first step and should change 12 ÁÁÁÁ x − 6x ˜˜˜˜ to
Ë
¯
Ê 2
ˆ
Á
˜
6 ÁÁÁ 2x − 12x ˜˜˜ . The minimum value is 0.
Ë
¯
1
Name: ______________________
____
ID: A
3. Jennifer observed a rocket fired from the ground with an initial vertical velocity of 96 ft/s. She knows
that she can model the height h (in feet) of the rocket at time t (in seconds) using the function
2
h(t) = −16t + 96t. In her journal, she had re-written the function for the model as h(t) = −16t(t − 6).
What would be the best reason for Jennifer to change the function into this form?
____
____
a.
To find the maximum height of the rocket.
b.
To find the number of seconds it takes for the rocket to reach its maximum height.
c.
To find the number of seconds it takes for the rocket to hit the ground.
d.
To find the average speed of the rocket.
4. Which of the following equations are NOT expressed by the graph below?
a.
y = (x + 3)(x − 1)
b.
y = x − 2x − 3
2
2
c.
y = (x − 1) − 4
d.
y = (x − 3)(x + 1)
2
5. What is the axis of symmetry for the graph of the function f(x) = 9x + 12x + 4?
a.
x=−
2
3
b.
x=
2
3
c.
2
x=−
4
3
d.
x=
4
3
Name: ______________________
____
____
____
ID: A
2
6. The graphs of f and g are shown below on the coordinate plane. If f(x) = x , which of the following
could be the equation of g(x)?
2
c.
g(x) =
1
2
(x + 4) − 5
10
2
d.
g(x) =
1
2
(x − 4) − 5
10
a.
g(x) = 10(x − 4) − 5
b.
g(x) = 10(x + 4) − 5
2
7. For which values of b does the equation 2x + bx + 18 = 0 have exactly one real solution?
a.
b = −15 or b = 15
c.
b = −9 or b = 9
b.
b = −6 or b = 6
d.
b = −12 or b = 12
2
8. Solve the equation 2x − 4x + 9 = 0 and select its solutions from the choices below.
a.
b.
2−
22
2
1−
i
or
2+
22
2
22
i 22
or 1 +
2
2
c.
d.
3
2−
14
2
1−
i
or
2+
14
2
14
i 14
or 1 +
2
2
Name: ______________________
____
ID: A
2
9. Nikita claimed that the equation x + 16 = 0 could be solved by using its factored form of
( x − 16i) ( x + 16i) = 0. She would have selected choice D below. Verify that she is correct or incorrect
2
by selecting the correct solutions to the equation x + 16 = 0 from the choices below.
a.
x = 2i
b.
x=i
2 or x = −2i
2 or x = −i
2
2
c.
x = 4i or x = −4i
d.
x = 16i or x = −16i
____ 10. Which of the following is equivalent to (−25 − 3i) + ( 7 − 5i) ?
a.
−32 − 2i
b.
−18 − 8i
c.
−26i
d.
26
d.
26 − 2i
Ê
2ˆ
____ 11. What is the product 2i ÁÁÁÁ 6 − 8i − 5i ˜˜˜˜ when written in a + bi form?
Ë
¯
a.
16 + 22i
b.
16 + 2i
c.
26 + 12i
____ 12. Jeremy is trying to determine what factor when multiplied by a + bi (where a and b are real numbers) will
always result in a real product. What is the factor, and which statement best justifies why this is true?
2
a.
The factor is i, because i ( a − bi) = a − bi which is always a real number.
b.
The factor is i, because i ( a − bi) = ai − bi which is always a real number.
c.
The factor is a − bi, because ( a − bi) ( a + bi) = a − 2abi − ( bi) which is always a real
number.
2
2
The factor is a − bi, because ( a − bi) ( a + bi) = a − ( bi) which is always a real
number.
d.
2
2
4
2
ID: A
Algebra 2 Hon MINIMAFS 1 (To be used after Chapter 1)
MAFS.912.A-SSE.2.3, MAFS.912.F-IF.3.8, MAFS.912.N-CN.3.7, MAFS.912.N-CN.1.2
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:
B
DOK
A
DOK
C
DOK
A
DOK
A
DOK
B
DOK
D
DOK
D
DOK
C
DOK
B
DOK
A
DOK
D
DOK
PTS: 1
STA: MAFS.912.A-SSE.2.3
PTS: 1
STA: MAFS.912.A–SSE.2.3
PTS: 1
STA: MAFS.912.A-SSE.2.3
PTS: 1
STA: MAFS.912.F-IF.3.8
PTS: 1
STA: MAFS.912.F-IF.3.8
PTS: 1
STA: MAFS.912.F-IF.3.8
PTS: 1
STA: MAFS.912.N-CN.3.7
PTS: 1
STA: MAFS.912.N-CN.3.7
PTS: 1
STA: MAFS.912.N-CN.3.7
PTS: 1
STA: MAFS.912.N-CN.1.2
PTS: 1
STA: MAFS.912.N-CN.1.2
PTS: 1
STA: MAFS.912.N-CN.1.2
1
2
2
2
1
2
2
1
2
1
2
2
1