February Break Extra Credit 2015-16
Assessment ID:
ib.577576
Directions: Answer the following question(s).
1
Select the statement that is true for the
graphs of all functions g(x).
3
A. The graph of g(x + 1) is the graph of g(x) shifted
up 1 unit.
B. The graph of g(x + 1) is the graph of g(x) shifted
right 1 unit.
C. The graph of g(–x) is the graph of g(x) reflected
over the x–axis.
D. The graph of g(–x) is the graph of g(x) reflected
over the y–axis.
A student claims that a negative x–coordinate
will always result in a negative tanθ when θ is
the angle formed by the x–axis and the line
that connects the origin to the point. What
information would disprove the student's
claim? Select two choices.
A. If point A is located at (–4, –4), then tanθ equals
–1.
B. If point A is located at (–3, 5), then tanθ equals
–5/3.
C. If point A is located at (4, 5), then tanθ equals
4/5.
2
A student claims that sin2θ + cos2θ = 1 can
only be written one other way. First, decide if
the student is correct. Next, justify your
decision by either providing examples that
support or disprove the student's claim.
Select two choices.
D. If point A is located at (–4, –7), then tanθ equals
7/4.
E. If point A is located at (4, 8), then tanθ equals 2.
F. If point A is located at (–3, –3), then tanθ equals
1.
A. The student is correct. The identity can only be
rewritten as sin2θ = 1 – cos2θ.
4
B. The student is correct. The identity can only be
rewritten as cos2θ = 1 – sin2θ.
C. The student is correct. The identity can only be
rewritten as cos2θ = 1 – cos2θ.
D. The student is incorrect. The identity can also be
rewritten as sin2θ = 1 – cos2θ and
cos2θ = 1 – sin2θ.
E. The student is incorrect. The identity can also be
rewritten as sin2θ = 1 – cos2θ and
sin2θ = 1 – sin2θ.
F.
The student is incorrect. The identity can also be
rewritten as cos2θ = 1 – sin2θ and
cos2θ = –1 + sin2θ.
A student claims that they can use rules
about the coordinates of point A to tell
whether the cosine of the angle formed by the
x–axis and the line that connects the origin to
point A will equal a positive or a negative
value. What information would support the
student's claim? Select two choices.
A. If the x– and y–coordinates are negative, the
cosine will equal a positive value.
B. If the x– and y–coordinates are negative, the
cosine will equal a negative value.
C. If the x–coordinate is negative, the cosine will
equal a negative value.
D. If the y–coordinate is positive, the cosine will
equal a positive value.
E. If the x–coordinate is in Quadrant I, the cosine
will equal a negative number.
F.
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If the x–coordinate is in Quadrant II, the cosine
will equal a positive number.
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Page 1
February Break Extra Credit 2015-16
Assessment ID:
ib.577576
Directions: Answer the following question(s).
5
On a circle, a line is drawn from the origin to
A(5, 12). The angle θ is between the line and
the x–axis. A student argues that the
Pythagorean Theorem can be used to find
cosθ. Identify the strategy that supports the
student's argument.
A. Use a ruler to determine the length of the
hypotenuse.
B. Use the squares of 5 and 12 to find the length of
the hypotenuse.
6
The length of an arc on a circle is
π inches.
3
Alyssa contends that this means that the
measure of the central angle on the circle will
also be
2
π radians for every circle. Test
3
Alyssa's conjecture by selecting two choices
that are true.
A. A circle with a radius of 1 inch and a central
C. Use a trigonometric formula to determine the
length of the hypotenuse.
2
angle of
2
3
D. Use the arc to calculate the hypotenuse.
of
2
3
π radians forms an arc with a length
π inches.
B. A circle with a radius of 1 inch and a central
angle of
2
3
of
4
3
π radians forms an arc with a length
π inches.
C. A circle with a radius of 2 inches and a central
angle of
2
3
of
2
3
π radians forms an arc with a length
π inches.
D. A circle with a radius of 2 inches and a central
angle of
2
3
of
4
3
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π radians forms an arc with a length
π inches.
Continue: Turn to the next page.
Page 2
Assessment ID:
February Break Extra Credit 2015-16
ib.577576
Directions: Answer the following question(s).
7
Kyle is working in the lab using sound waves
and finding the models to describe the sound
waves. He neglected to find the model of the
sound wave shown below.
ƒ(x) = 3cos
8
( )
2π
x
ƒ(x) = 4sin(πx)
3
Which of the following options correctly
graphs the function of the radio station's
radio signal?
Which graph of the sound wave correctly
matches the equation above?
A.
A student studying radio signals decided to
focus in on a certain radio station to
determine the graph of the radio signals
used. The student determined that the radio
station uses the following function for its
radio signals.
A.
B.
B.
C.
C.
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D.
Generated
On February 11, 2016, 1:32 PM PST
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Page 3
February Break Extra Credit 2015-16
Assessment ID:
ib.577576
Directions: Answer the following question(s).
9
A.
B.
C.
D.
Which of the following values for x are
solutions to the equation x2 – 2x = –10?
Select two that apply.
12
A.
B.
C.
D.
E.
0
1 + 3i
1 – 3i
1 + √ 10i
E. 1 – √ 10i
10
13
The table below shows points that are on the
graph of the function h(x).
x
3
5
Lorelai claims that (x + 3) is a factor of
p(x) = x4 + 5x3 + x2 – 11x + 12. Which of the
following methods could she use to prove her
claim? Select three that apply.
is a polynomial
C. show that p(x) = (x + 3) · q(x) for some
polynomial q(x)
(1, –1)
D. show that the remainder when p(x) is divided by
(2, 0)
(x + 3) is 0
(3, 11)
(4, 10)
14
(5, 1)
Maggie claims that the function g(x) =
x
–4
is the inverse of the function of ƒ(x) = 3x + 4.
Which statement provides a correct analysis
of Maggie's claim?
Maggie's claim is correct because if you add 4 to
g(x) and then multiply it by 3 you get ƒ(x).
B. Maggie's claim is correct because when g(x) is
substituted into every occurrence of x in ƒ(x),
ƒ(g(x)) = x, and when ƒ(x) is substituted into
every occurrence of x in g(x), g(ƒ(x)) = x.
C.
0
x+3
3
A.
–3
show that the quotient of
Select all of the points that are on the graph
of the inverse function h–1(x).
11
–5
A. show that the value of p(3) is 0
B.
p(x)
0 1 2 3 4 5
h(x) 2 5 8 11 14 17
A.
B.
C.
D.
E.
Which of the following values are zeros of
x(x + 5)(x – 3)? Select three that apply.
Maggie's claim is incorrect because when g(x) is
substituted into every occurrence of x in ƒ(x),
ƒ(g(x)) = x – 8; therefore, g(x) is not the inverse
of ƒ(x).
D. Maggie's claim is incorrect because when g(x) is
substituted into every occurrence of x in ƒ(x),
ƒ(g(x)) = x; therefore, g(x) is not the inverse of
ƒ(x).
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A.
B.
C.
D.
E.
F.
15
A.
B.
C.
D.
Tarik claims that the function
ƒ(x) = 5x5 – 15x4 – 45x3+ 85x2 + 90x – 120 has
no zeros for 0 ≤ x ≤ 5. Based on the
factorization of ƒ(x), which values of x could
be used to refute Tarik's claim? Select two
that apply.
0
1
2
3
4
5
Which expression is equal to
(6i – 5) – (2 – 3i)?
–3 + 3i
–7 + 3i
–3 + 9i
–7 + 9i
Continue: Turn to the next page.
Page 4
February Break Extra Credit 2015-16
Assessment ID:
ib.577576
Directions: Answer the following question(s).
16
A student claims that the function
ƒ(x) = 6x4 + 4x2 – 3 is an even function. Is the
student correct?
20
A.
–
A. The student is correct because when ƒ(x) is
changed into ƒ(–x), it results in the same
function, ƒ(x) = 6x4 + 4x2 – 3.
ƒ(x) =
+
4x2
– 3 is an odd function.
B.
17
A.
B.
C.
D.
C.
18
4i2
4 – 4i
4i – 4i
What is the simplified form of –3 √ –8 ?
A. 6i
B. 12i
C. –6i √ 2
D.
What is the product of (2 – 3i) (6 + 4i)?
A.
B. 10i
C. –10i
D. 24 – 10i
24
21
A.
B.
C.
D.
22
A.
B.
C.
D.
23
A.
B.
C.
D.
E.
Illuminate Itembank™
Generated On February 11, 2016, 1:32 PM PST
–6 ± √ 46
4
D. –12i √ 2
19
–6 ± i √ 34
4
Select each quantity that represents an
imaginary number.
4i
–3 ± √ 19
2
D. The student is not correct because
ƒ(x) = 6x4 + 4x2 – 3 is neither an odd nor even
function.
3±i
2
B. The student is correct only when x > 0.
C. The student is not correct because
6x4
What is the value of x in the equation 2x2 + 6x
= –5?
What is the simplified form of (–7 + 8i) – (–5i +
4i2)?
–11 + 3i
–11 + 13i
–3 + 3i
–3 + 13i
Serena claims that (x + 3) is a factor of
p(x) = x4 + 6x3 + 12x2 + 10x + 3. Which
equation must Serena show to be true in
order to prove her claim?
p(0) = 3
p(3) = 0
p(0) = –3
p(–3) = 0
Evan claims that three of the polynomials
below have a remainder of 0 when divided by
x + 4. Select each polynomial that supports
Evan's claim.
p(x) = x3 – 12x + 16
p(x) = x3 – 5x2 + 8x – 4
p(x) = x3 – 7x2 + 14x – 8
p(x) = x3 + 3x2 – 10x – 24
p(x) = x3 + 12x2 + 48x + 64
Continue: Turn to the next page.
Page 5
February Break Extra Credit 2015-16
Assessment ID:
ib.577576
Directions: Answer the following question(s).
24
A.
B.
C.
D.
E.
F.
The graph of a function, ƒ(x), is plotted on the
coordinate plane. Select two of the following
functions that would move the graph of the
function to the right on the coordinate plane.
ƒ(x + 6)
ƒ(x) + 4
ƒ(x – 3) + 1
ƒ(x) – 3
ƒ(x – 5)
27
A.
B.
C.
D.
(a + b)(a2 – ab + b2)
(a – b)(a2 + ab + b2)
(a – b)(a2 – ab + b2)
(a – b)(a2 – ab – b2)
ƒ(x + 2) – 7
28
25
Wyatt is asked to prove the polynomial
identity a3 – b3. Which of the following
expressions is the equivalent form of this
identity?
Which statement is true for all functions f(x)?
A. The graph of –f(x) is the graph of f(x) reflected
over the x–axis.
B. The graph of –f(x) is the graph of f(x) reflected
over the y–axis.
C. The graph of f(kx) is the graph of f(x) shifted left
A.
B.
C.
D.
The polynomial identity (a – b)2 can be
expanded into which of the following
expressions?
a2 – b2
a2 – ab + b2
a2 – 2ab – b2
a2 – 2ab + b2
or right by k units.
D. The graph of f(x) + k is the graph of f(x) shifted
left or right by k units.
26
James is working with the equation
ax2 + bx + c = 0. Which of the following will
James be able to prove is the solution for x?
A.
29
A.
B.
C.
D.
It can be proven that the expression
(a + b)(a2 – ab + b2) is equivalent to which of
the following polynomial identities?
(a + b)3
(a – b)3
a3 + b3
a3 – b3
B.
30
C.
D.
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A.
B.
C.
D.
Factor the polynomial f(x) = x2 – x – 6 to
determine the zeros of the function.
(–1, 0) and (6, 0)
(1, 0) and (–6, 0)
(–3, 0) and (2, 0)
(3, 0) and (–2, 0)
Continue: Turn to the next page.
Page 6
February Break Extra Credit 2015-16
Assessment ID:
ib.577576
Directions: Answer the following question(s).
31
Adam graphed a polynomial with zeros at x = –1, x = 2 and x = 5. Which of the following graphs did
he draw?
A.
C.
B.
D.
32
A.
B.
C.
D.
Find the remainder of (3x4 – 2x3 + x2 – 5x + 8)
÷ (x + 2) by using the Remainder Theorem.
–18
4
34
86
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Page 7
February Break Extra Credit 2015-16
Assessment ID:
ib.577576
Directions: Answer the following question(s).
33
A.
B.
C.
D.
Identify the zeros of the graphed polynomial.
(0, –5)
(0, 5)
35
A.
B.
C.
D.
Which of these polynomial functions is
graphed below?
y = x3 – 8
y = x3 – 2
y = x3 + 2
y = x3 + 8
(–5, 0) and (1, 0)
(5, 0) and (–1, 0)
36
Perform the operation.
(5x4 + 3x2 + 8) ÷ (x2 + 2x – 1)
34
Which of these polynomial functions is
graphed below?
A.
B.
C.
D.
A.
B.
C.
D.
5x2 – 10x + 28 +
5x2 – 7 +
–66x + 36
x2 + 2x – 1
27x – 7
x2
+ 2x – 1
5x2 + 10x + 18 +
5x3 + 5x2 + 8x +
26 – 10
x2
+ 2x – 1
16
x2
+ 2x – 1
y = –x2 + 2x – 1
y = –x2 + 1
y = x2 – 2x + 1
y = x2 – 1
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Page 8
February Break Extra Credit 2015-16
Assessment ID:
ib.577576
Directions: Answer the following question(s).
37
A.
Which statement below can only be true if the
functions, ƒ(x) and g(x), are inverses of each
other?
f–1(x) =
1
f(x)
1
and g–1(x) =
g(x)
B. ƒ(g(x)) = x and g(ƒ(x)) = x
C. ƒ(ƒ(x)) = x and g(g(x)) = x
D. ƒ(g(x)) = g(ƒ(x))
38
Each of the four graphs below represents a function. Which function has an inverse that is also a
function?
A.
C.
B.
D.
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Page 9
February Break Extra Credit 2015-16
Assessment ID:
ib.577576
Directions: Answer the following question(s).
39
If i = √ –1 , which graph below shows –4 + 2i correctly on the plane at Point Z?
A.
C.
B.
D.
40
A.
B.
C.
D.
Use the table below to evaluate i49:
–1
1
-i
i
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Page 10