The unit test blueprint lists topics currently taught in the unit along with both readiness and supporting standards. The
suggested percentage is included to give teachers an idea of how much of the topic should be tested in the unit with
respect to the other topics. The percentage was found by taking into account both the percentage tested on the STAAR
EOC as well as time spent on the topic in this unit. Sample problems are written to meet the rigor of the TEKS.
Unit: Graphing &
Applications of Trig
TEKS
Topics tested
Graphing Sine
and Cosine (with
transformations)
P.2D,
P.2F,
P.2G,
P.2I
P.4A
Subject: Pre-Calculus
Suggested
Percent
30%
Sample Test Questions
f ( x)  cos x so
that the new function has the same symmetry as y  sin x ?
What transformation could be performed on
(P.2D, P.2G, P.2I)
A
B
C
*D

I
phase shift
II
phase shift

III phase shift

2
3
2

2
and a vertical reflection
I only
I and II only
II and III only
I, II and III
The graph of
y  sin x is transformed to meet the following
criteria:




period of 6
amplitude of 2
relative minimum values of -5
phase shift between  and 2
Which graph satisfies the criteria? (P.2F, P.2G)
A
The unit test blueprint lists topics currently taught in the unit along with both readiness and supporting standards. The
suggested percentage is included to give teachers an idea of how much of the topic should be tested in the unit with
respect to the other topics. The percentage was found by taking into account both the percentage tested on the STAAR
EOC as well as time spent on the topic in this unit. Sample problems are written to meet the rigor of the TEKS.
B
C
D
The graph of
f ( x) is below.
The unit test blueprint lists topics currently taught in the unit along with both readiness and supporting standards. The
suggested percentage is included to give teachers an idea of how much of the topic should be tested in the unit with
respect to the other topics. The percentage was found by taking into account both the percentage tested on the STAAR
EOC as well as time spent on the topic in this unit. Sample problems are written to meet the rigor of the TEKS.
Which equation could not represent
f ( x) ? (P.2F)


f ( x)  3sin  x    1
4

3 

B
f ( x)  3cos  x 
 1
4 

5 

*C f ( x)  3cos  x 
 1
4 

7 

D
f ( x)  3sin  x 
 1
4 

A
Which is a correct statement about the graph of


f ( x)  4sin  x    2 ? (P.2I)
3

A The graph is increasing on the interval
5
 

 2n  , where n  .
   2n ,
6
 6

B The graph has a relative maximum value of 2.
C
The range of the graph is
4, 4 .
D The zeros of the function are
where n 
7

 2n and  2n ,
6
2
.
The population of foxes in a certain forest varies sinusoidally
with time and can be represented by the function
 
P(t )  550  250 cos 
 t  2.3  , where t=0 represents
3.1


January 1, 2000.
Approximately when did the first maximum population of
foxes occur after the year 2000? (P.2I)
A
B
C
D
April 2002
February 2003
May 2005
August 2011
The unit test blueprint lists topics currently taught in the unit along with both readiness and supporting standards. The
suggested percentage is included to give teachers an idea of how much of the topic should be tested in the unit with
respect to the other topics. The percentage was found by taking into account both the percentage tested on the STAAR
EOC as well as time spent on the topic in this unit. Sample problems are written to meet the rigor of the TEKS.
Jody graphed the y values of the points marked on the circle
on an axis at the specific angle measures.
What is the equation of the function that goes through the
points he graphed? (P.4A)
y  sin x
*B y  2sin x
y  cos x
C
y  2 cos x
D
A
Sinusoidal
Applications
P.20,
P.4A
P.5N
25%
NOTE: USE THE WATER WHEEL PROBLEM FOR THE NEXT
TWO QUESTIONS.
A waterwheel with a radius of 9 feet rotates at 6 revolutions
per minute. The center is 8 feet above the water. Two
seconds after a stopwatch is started, point P is at its greatest
height, 17 feet above the water.
Which equation represents d, the distance point P is above
the water at time t, the time since the stopwatch was
started? (P.2O)
A
d
17

 17
cos   t  2   
2
5
 2
The unit test blueprint lists topics currently taught in the unit along with both readiness and supporting standards. The
suggested percentage is included to give teachers an idea of how much of the topic should be tested in the unit with
respect to the other topics. The percentage was found by taking into account both the percentage tested on the STAAR
EOC as well as time spent on the topic in this unit. Sample problems are written to meet the rigor of the TEKS.


d  9sin   t  8    8
4



*C d  9 cos   t  2    8
5

B


d  9sin   t  6.5   8
3

D
After how many seconds after the stopwatch is started will point P
reach a maximum height for the third time? (P.4A)
A
2 seconds
B
7 seconds
*C 22 seconds
D
27 seconds
The temperature in an office building was measured at certain times
during one day as indicated in the table below.
Time
Temperature (C)
5 am
9 am
11 am
1 pm
5 pm
9 pm
11 pm
13
16
19
22
25
22
19
At what time is the temperature the same as it is at 2 pm?
(P.5N)
A 12 am
B 8 am
*C 8 pm
D 10 pm
A sinusoidal function




g  x  satisfies the following conditions.
Period of 
Relative minimum values of -1
Relative maximum values of 5
Same phase shift as y  cos(3 x   )  1
The unit test blueprint lists topics currently taught in the unit along with both readiness and supporting standards. The
suggested percentage is included to give teachers an idea of how much of the topic should be tested in the unit with
respect to the other topics. The percentage was found by taking into account both the percentage tested on the STAAR
EOC as well as time spent on the topic in this unit. Sample problems are written to meet the rigor of the TEKS.
What is the value of
A
-1
B

 
g    ? (P.5N)
 6
3 3
2
2
C
0
*D 2
Graphing all Trig
functions
P.2D,
P.2F,
P.2I.
P.4A
P.5N
P.2L
p.2M
20%
Which of the following is not an odd function? (P.2D, P.2I)
A
*B
C
D
y  tan x
y  sec x
y  csc x
y  cot x
The table below represents a tangent function
x


2

2

2
h(x).
h(x)
1
-3
und
-1
The graph of which function is the same as the graph of
(P.4A)
B
x 
f ( x)  2 tan     1
2 2
f ( x)  2 tan  x    1
C
f ( x)  2cot  x    1
*D
x 
f ( x)  2 cot     1
2 2
A
h(x) ?
Which statement incorrectly describes the behavior around an
asymptote of the graph of
1


f ( )  sec     ?
4
4

P.2L)
A
As


5
, f ( )  
4
(P.2I, P.2M,
The unit test blueprint lists topics currently taught in the unit along with both readiness and supporting standards. The
suggested percentage is included to give teachers an idea of how much of the topic should be tested in the unit with
respect to the other topics. The percentage was found by taking into account both the percentage tested on the STAAR
EOC as well as time spent on the topic in this unit. Sample problems are written to meet the rigor of the TEKS.

B
As
3
 
, f ( )  
4
*C As

D
As

4
, f ( )  
 

11
, f ( )  
4
Which graph represents the function
(P.2F)
A
*B
C

1
f ( x)  csc  x    1
6
2
?
The unit test blueprint lists topics currently taught in the unit along with both readiness and supporting standards. The
suggested percentage is included to give teachers an idea of how much of the topic should be tested in the unit with
respect to the other topics. The percentage was found by taking into account both the percentage tested on the STAAR
EOC as well as time spent on the topic in this unit. Sample problems are written to meet the rigor of the TEKS.
D
The graph of g(x) is below.
Which equation has the same zeros as g(x)? (P.2I)
*A
B
C
D


f ( x)   tan  x  
3



f ( x)  2 cot  2 x  
3

1


f ( x)  tan  2 x  
4
3



f ( x)  cot  x  
3

Charlie is swimming toward shore from a point 50 meters from a
buoy as shown below.

d
50 m
Which equation represents d, the distance Charlie is from shore in
terms of the angle,
 ? (P.5N)
The unit test blueprint lists topics currently taught in the unit along with both readiness and supporting standards. The
suggested percentage is included to give teachers an idea of how much of the topic should be tested in the unit with
respect to the other topics. The percentage was found by taking into account both the percentage tested on the STAAR
EOC as well as time spent on the topic in this unit. Sample problems are written to meet the rigor of the TEKS.
d  50cot 
d  50 tan 
d  50sec
d  50csc
A
B
C
D
Inverse Trig
Functions
P.2D,
P.2E,
P.2F,
P.2H,
P.2I
P.2P
25%
The domain of the function
  3 
  4 , 4  .
*A
B
C


f ( x)  sin  x    2
4

Which graph represents
f 1 ( x) ?
is restricted to
(P.2E, P.2H)
The unit test blueprint lists topics currently taught in the unit along with both readiness and supporting standards. The
suggested percentage is included to give teachers an idea of how much of the topic should be tested in the unit with
respect to the other topics. The percentage was found by taking into account both the percentage tested on the STAAR
EOC as well as time spent on the topic in this unit. Sample problems are written to meet the rigor of the TEKS.
D
The graph of which function has the same symmetry as the graph
below. (P.2D, P.2F)
A
f ( x)  arcsin  2 x  

*B
f ( x)  arccos  2 x  

C
D
f ( x)  arcsin( x  1)
f ( x)  arccos( x  1)
The function
2
2
f ( x)  arccos( x)
is transformed to create a function,
g ( x ) , with the values in the table below.
x
-2
-1.5
g(x)
0


3
-1


2
-0.5

2
3
0

Which of the following is not true about the graph of
P.2I)
A
The domain of
B
The range of
2,0 .
is   ,0 .
g ( x)
g ( x)
is
C
The graph has a zero as 2 .
*D The graph is increasing on the interval (-2, 0).
g ( x ) ? (P.2F,
The unit test blueprint lists topics currently taught in the unit along with both readiness and supporting standards. The
suggested percentage is included to give teachers an idea of how much of the topic should be tested in the unit with
respect to the other topics. The percentage was found by taking into account both the percentage tested on the STAAR
EOC as well as time spent on the topic in this unit. Sample problems are written to meet the rigor of the TEKS.
Which of the following is equivalent to
I
A
B
C
D
  7
sin 1  sin 
  3



? (P.2P)

 7  
sin 1  cos 

 3 


 7  
II
cos 1  cos 

 3 

 7  
1 
III cos  sin 

  3 
I only
II only
III only
I and III only
TEKS
P.2D describe symmetry of graphs of even and odd functions
P.2E determine an inverse function, when it exists, for a given function over its domain or a subset of its domain and
represent the inverse using multiple representations
P.2F graph exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise
defined functions, including step functions
P.2G graph functions, including exponential, logarithmic, sine, cosine, rational, polynomial, and power functions and
their transformations, including af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d, in mathematical and realworld problems
P.2H graph arcsin x and arccos x and describe the limitations on the domain
P.2I determine and analyze the key features of exponential, logarithmic, rational, polynomial, power, trigonometric,
inverse trigonometric, and piecewise defined functions, including step functions such as domain, range, symmetry,
relative maximum, relative minimum, zeros, asymptotes, and intervals over which the function is increasing or
decreasing
P.2O develop and use a sinusoidal function that models a situation in mathematical and real-world problems
P.4A determine the relationship between the unit circle and the definition of a periodic function to evaluate
trigonometric functions in mathematical and real-world problems
P.5N generate and solve trigonometric equations in mathematical and real-world problems