Download ADVANCED ALGEBRA AND TRIGONOMETRY EXAM

Accelerated Math 3
Cumulative Assessment
Name ___________________________________
200 points total
Each of the following is worth 2 points (1 – 25).
1. Find the length of the circular arc subtended by the central angle whose radian measure is 2
radians and the diameter of the circle is 10. MA3A2d
A. 5
B. 5
C. 10
D. 10
E. 20
2. Find the exact value of sin t and tan t when the terminal side of and angle of t radians in
standard position passes through the point (3,-2). MA3A2b,c
2 13 2
3 13 2
3 13 3
2 13 2
3 13 2
,
,
,
,
,
A. 
B.
C. 
D. 
E.
13 3
13 3
13 2
13
3
13
3
Answer the following questions about the function h(t) = -4cos(3t 
3. What is its period?

A.
B.2
6
2
3
E.
C. 3
D. -7
E. 7
D. -1
E. 1
6. What is the phase shift?



A.
units left B.
units right C.
units left
18
6
6
MA3A3a,b MA3A6a
7. tan t =
5
4
A. 
B. 
3
5
) - 3. MA3A3c
D. 6
5. What is the maximum value of h(t)?
A. -7
B. -4
C. -3
Use the information that sin t = 
6

2
C.
4. What is its amplitude?
A. -4
B. 4

D.

units right
18
E. 4 units down
3
and sec t 0 to find each of the following:
5
C.
4
5
D. 
3
4
E.
3
4
8. cos t =
5
A. 
3
B. 
4
5
C.
4
5
D. 
3
4
E.
3
4
9. csc t =
5
A. 
3
B. 
4
5
C.
4
5
D. 
3
4
E.
3
4
10. The function h(t) = sin t has
MA3A3a,b
(a) A maximum value at x = 0
(b) A minimum value at x = 0

(c) A maximum value at x =
2

(d) A minimum value at x =
2
(e) (b) A minimum value at x = π.
.
Use this information to answer questions 11 and 12. Given a right triangle with right angle at C
and a = 4 and b = 6, find: MA3A6a,c
11.  A =
A. 561836
12. c =
A. 7.21
B. 58583
C. 414837
D. 334124
E. None of these
C. 10.0
D. 2.0
E. None of these.
B. 4.47
13. Find A in ABC if a=25, b=12, and B=18. MA3A6c
A. 40.07
B.42.27
C. 42.27 or 137.73
D.139.93
E. 40.07or 139.93
14. Find the area of triangle ABC if b = 30, c =25 and A = 63. MA3A7
A.179.83
B. 191.13
C. 287.06
D. 334.13
E. 344.51
15. sec2 x – tan2 x is an identity for which of the following: MA3A5
A. 1
B. sin2x – cos2x
C. cos2x – sin2x
D. 1 - tan2x
E. 1 - cot2x
16. Simplify the given expression sin 43 cos 37 – cos 43 sin 37 MA3A5
A. sin 6
B. cos 6
C. sin 80
D. cos 80
E. None of these
Use this information to answer problems 18 – 19. x lies in the first and y lies in the second
4
8
quadrant. Sin x = , and cos y =  . MA3A5
5
17
17. Find the exact value of cos (x+ y).
13
36
A.
B. 
85
85
18. Find the exact value of sin 2x.
8
24
A.
B.
5
25
C.
36
85
D.
84
85
C.
9
25
D.
3
5
E. 
84
85
E. None of these
19. Which of the following is not a solution to sin 2x + cos x =0 over the interval  0,2 )?
MA3A6a

5
7
3
11
A.
B.
C.
D.
E.
2
6
6
2
6
 3
20. Which of the following is not a solution for sin 3x =
in the interval 0  x  ?
2
MA3A6a
A.210
B.240
C. 660
D.960
E. 1020
21. Find sin
A.
2
3
-1
 2 
  . MA3A8a
 3 

B.
3
C.
3
2
D. 
3
2
E.
1
2
22. Which parametric equations describe a spiral beginning at the origin for t  0 ? MA3A12a
A. x = t cos(t) and y = t sin(t)
B. x = t sin(t) and y = t sin(t)
C. x = 5 cos(t) and y = 5 sin(t)
D. x = cos(t) and y = sin(t)
E. x = t and y = sin(t)
23. Which parametric equations describe a circle with its center at the origin and a radius of 7
for 0  t  2 ? MA3A12a
A. x = 7 cos(t) and y = 7 sin(t)
B. x = 7 sin(t) and y = 7 sin(t)
C. x = cos(7t) and y = sin(7t)
1
1
D. x  cos t and y  sin t
7
7
E. x = 49 cos(t) and y = 49 sin(t)
24. The central limit theorem tells us that as sample size increases the sampling distribution of
the mean becomes MA3D1
a.
more shaped like the population distribution.
b.
less normally distributed but more leptokurtic.
c.
more normally distributed with a smaller range of scores.
d.
more normally distributed with a larger range of scores.
25. The central limit theorem states that the mean of the sampling distribution of the mean is
equal to the population MA3D1
a.
mean divided by the population standard deviation.
b.
mean.
c.
standard deviation divided by the square root of N.
d.
standard deviation.
Each of the following is worth 3 points (26-42).
x+2
x+2
 = continuous. MA3A1a
gx =
26. Choose the function thatgxis
10x-1
10x-1
3
3
3
3
2
2
2
2
1
1
1
-2
2
-2
-1
-2
-2
-2
c.
-3
2
-1
-1
-2
b.
-3
1
-2
2
-1
-2
a.
2
d.
-3
-3
5
4
3
2
1
-4
-2
2
-1
4
27. What appears to be the domain of the function shown?
MA3A1b
a.  4.5  y  4.5
b. 2  y  
c.  2.9  x  2.9
d.  3  x  
-2
-3
-4
6
-5
4
P
2
28. Give the coordinates for the point P shown. MA3A13a
5 
5 
5 


 5 

a.  5,  b.  5,  c.   5,
 d.   5, 
6 
6 
6 

 6 


5
5
2
4
6
29. Which point is not equivalent to the point (6,120º)? MA3A13a
a) 6,480º 
b)  6,300º 
c) 6,480º 
d) 6,240º 
30. What is the magnitude of the vector 6,15 ? MA3A10a
a)
21
b) 261
c) 21
d)
261
31. Give the component form of the vector with head at (3,-8) and the tail at (0,5). MA3A10c
a) 3,8
b) 0,5
c) 3,13
d)  3,13
32. Choose the sequence that is neither arithmetic nor geometric. MA3A9b
a) 2, 4, 6, 8,…
b) 3, 9, 27, 81,…
c) 1, 3, 4, 7…
d) 1, 1, 1, 1,…
33. What type of function is shown in figure 2?
MA3A4a
a. Rational
b. Polynomial
c. Square root
d. Absolute value
6
4
2
5
-2
-4
figure 2
34. Convert -5 + 6i into trigonometric form. MA3A11a _______________________________
35. Give the direction of the vector  8,1 . MA3A10b _______________________________
36. Find the 565th partial sum of the sequence given by
tn  30.1 MA3A9e
a.  3.33
b. =3.33
c. 17,628
d. this sequence does not have a sum
n
37. Find the 3 third roots of unity. MA3A11b
_____________________________
_____________________________
_____________________________
38. 4  7i 
6
MA3A11b
_______________________________________________
39. A ship is pulled by two tugboats. One pulls with a force of 8.6 tons at a heading (direction)
of 30º. The second pulls with a force of only 7 tons. What should his heading be so that the
ship is pulled with a heading of 50º? MA3A10d
__________________________________________________________________________
40. What is the proper  notation for the 16th partial sum of the sequence beginning
4, 8, 16, 32…?
MA3A9f
a)
 (4,8,16,32,...)
16
b)
16
 2 n 1
n 1
15
c)
 2 n 1
16
d)
 2(n  1)
n 1
n0

41. Find 5 (.99) n  3 MA3A9f
_______________________________________________
n 1
42. The graphs of f(x) and g(x) are given in figure 3. Which composition is shown in figure 4?
MA3A4c
a)
b)
c)
d)
f(g(x))
g(f(x))
f(f(x))
g(g(x))
f(x)
4
4
2
2
-5
5
g(x)
-5
5
-2
-2
-4
-4
figure 3
figure 4
43. A message (m) is to be encoded with a mathematical rule (r(m)) that sends each character in
the plaintext to a character in the cipher text. MA3A4c
(3 points)
 Would the recipient of this message, faced with the task of decoding it, need r(m)
to be a relation, function, or one–to–one function? Why?
 In what ways would the decoding be cumbersome/complicated/impossible if r(m)
was not what you claim it needs to be above?
44. Consider the sequence whose nth term Tn is given by Tn  Tn1  Tn2 . MA3A9a,b,c
 Complete the table for this sequence (4 points).
 What name is given to this sequence (1 point)?
 This sequence is neither geometric nor arithmetic. It does have
some things in common with these familiar types of sequences,
T
though. In a geometric sequence n  r . We called r the
Tn 1
common ratio. The sequence above does not have a common
T
ratio but has an interesting property that n does approach a
Tn 1
fixed number as n gets very large. Give a rough approximation
of this number (4 points).
 This particular number is important in mathematics. What is this
number called (1 point)?
n
Tn
1
1
2
1
3
4
5
6
45. Compare and contrast the graphs of y = ex and y = log x. Discuss intercepts, asymptotes, and
symmetries. MA3A4a
(10 points)
(3x  1)
. Is the function discontinuous?
3x 2  10  3
Explain why or why not? Graph the function accurately. Then, graph its inverse on the same
graph and label. MA3A1a,b
(10 points)
46. Consider the following function: f ( x ) 
47. Draw the parent graph and each of the three transformations that would result in the given
graph. Write the equation of each graph (including the one graphed) and describe the
transformation (or movement). MA3A4b
(10 points)
48. Unit Circle – fill in special values. MA3A2a,c,e
(30 points)
Unit Circle
On each radius, mark the radian measure of the value of x and degree measure of the angle made with the positive xaxis and the radius. In the parentheses, write the ordered pair (cos x, sin x), and in the blank write the tangent of the
angle.
( ___ , ___ ) ___
( ___ , ___ ) ___
( ___ , ___ ) ___
( ___ , ___ ) ___
( ___ , ___ ) ___
( ___ , ___ ) ___
( ___ , ___ ) ___
( ___ , ___ ) ___
( ___ , ___ ) ___
( ___ , ___ ) ___
( ___ , ___ ) ___
( ___ , ___ ) ___
( ___ , ___ ) ___
( ___ , ___ ) ___
( ___ , ___ ) ___
( ___ , ___ ) ___
Sketch the graph of the two equations for one complete period. Give at least one value on each
axis as a scale.
MA3A13b
(10 points)
49. r  4 sin 5
50. r 2  25 sin 2
51. 300 high-risk patients received an experimental AIDS vaccine. The patients were followed
for a period of 5 years and ultimately 53 came down with the virus. Assuming all patients
were exposed to the virus, construct a 99% CI for the proportion of individuals protected.
Given: The 99% CI for p is where z = 2.58. What inferences can be said about the given
population?
MA3D2 & MA3D3
(10 points)