Exam

Name_____________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find the length of the arc on a circle of radius r intercepted by a central angle 6. Round answer to two decimal places.

1) r 15.61 inches, e= 1500

A) 41.07 inches B) 40.87 inches C) 40.97 inch

1)

es D) 41.17 inches ------­

Use a vertic

2) y

al shift to graph the function.

cos x - 2 2) ___

3 Y

2

2lt XIt -\

-2

A) B)

3 Y

2

X X -2lt -It It 2lt -2lt -It It 2lt

-I

-2

-3

C) D)

Y3

2

It -\

-2

1

Find the exact value of the expression. Do not use a calculator.

3) If tan e= 9, find the exact value of cot [; - eJ 3) ___

A)8 B) 10 C)9 O).!..9

Find the exact value of the expression, if possible. Do not use a calculator.

4) ___4) sm-1 [sm [67rrJ] A) 6rr B) 3.. C)~ 0)2.

7 7 6rr rr

5) cos (cos-1 0.4) 5) ___

A) 3.5 B) 2.7 C) 0.4 0) 0.9

Find the reference angle for the given angle.

6) 5rr 6) ___ 4

B) 3rr C)3.. O)~4 4 4

Graph the function.

7) ___7) Y=! sm (x + rr)

y 2

x 11

-2

A) B)

y y 2 2

x x

-2 -2

2

C) D) yy

22

xx

-2-2

18) Y = -2 cos-x 8)

2

y

3

x 1t

-3

A) B)

y y

3 3

x x

3

C) D) y

3

xx

Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s.

9) r = 1.8 meters, s == 4.14 meters 9) ___

A) 1.6 radians B) 0.9 radians C) 2.3 radians D) 0.56 radians

Sin t and cos t are given. Use identities to find the indicated value. Where necessary, rationalize denominators. 5 -2~

10) sin t =7' cos t =-7-' Find csc t. 10) ___

A)~ B) -7~ C).:!:::lf D) 2­12 12 5 5

Use a calculator to solve the equation on the interval [0, 271). Round the answer to two decimal places.

11) sin x == -0.29 11) ___

A) 0.29, 5.99 B) 0.29, 3.44 C) 3.44, 5.99 D) 0.29, 1.87

Solve the problem.

12) cos 6x + cos 4x 12) ___

A) 2 cos 5x sin x B) 2 cos 5x cos x C) 2 cos 5x D) 2 sin 5x sin x

Solve the equation on the interval [0, 271).

13) sin2 x + sin x == 0 13) ___

471 571 71 271 71 571 371 A) 0, 71'3'3 B) 0, 71'3'3 C) 0, 71, 3' D) 0,71'2

Complete the identity.

14) sin (a + ~) + sin (a - ~) = ? 14) ___

A) sin a cos ~ B) 2cos a cos ~ C) 2sin a cos ~ D) cos~ cos a

Solve the equation on the interval [0,271).

15) cos x = sin x 15) ___

A) 371 :!..:!:.. B) 2!. 571 C) 2!. 771 D) l!!.. 571 4 ' 2 4' 4 4' 4 4 ' 4

4

---

__ _

Fill in the blank using the word product, sum, quotient, or difference.

16) The fonnula sin a cos ~ = ~ (sin (a + ~) + sin (a - ~)] can be used to change a ___of 16)

a sine and a cosine into the of two sine expressions.

A) quotient, sum B) quotient, difference

C) product, difference D) product, sum

Complete the identity.

17) 2 cot x =? 17) ___ 1 + cot2 x

A) tan2x B) cos2x C) cot2x D) sin2x

Use a balf-angle formula to find the exact value of the expression.

18) ___18) sin ~;

A)~ B)~ C)-~ D)-~2

Solve the problem.

19) Two airplanes leave an airport at the same time, one going northwest (bearing 135 0) at 409 mph 19) ___ and the other going east at 325 mph. How far apart are the planes after 4 hours (to the nearest mile)?

A) 2262 miles B) 679 miles C) 2716 miles D) 2134 miles

20) A force is given by the vector F = 5i + 7j. The force moves an object along a straight line from the 20) ___ point (10, 6) to the point (12, 19). Find the work done if the distance is measured in feet and the force is measured in pounds.

A) -81 foot-pounds B) 101 foot-pounds

C) -101 foot-pounds D) 79 foot-pounds

Use Heron's formula to find the area of the triangle. Round to the nearest square unit.

21) a 12 meters, b =18 meters, c =7 meters 21) ___

A) 50 square meters B) 52 square meters

C) 13 square meters D) 25 square meters

Solve the problem.

22) One number is 4 less than a second number. Twice the second number is 16 less than 5 times the 22) first. Find the two numbers. -- ­

A) 7 and 11 B) 8 and 12 C) -12 and-8 D) 9 and 13

5

Solve the system by the addition method.

23) x2 - y2 4 23) ___

9x2 + 4y2 =36

A) {(O, 3), (0, -3)1 B) {(3,O), (-3, O)} C) {(2, 0), (-2, O)} D) {(O, 2), (0, -2)1

Graph the solution set of the system of inequalities or indicate that the system has no solution.

24) y 2: 1 24) ___

2:!:x:!:6 x - 2y 2:-2 x+y~6

Y'6

4

2

2 4 6 x-.6 ~4 -2

. -2

A) B)

x-2 x

. -2

6

---

C) 0)

xx

Solve the system of equations by the substitution method.

25) x - 2y == -7 25) ___

9x- 3y =-48

A) {(-6, 2)} B) {(5, 2)} C) {(-5, I)} 0)0

Solve the problem using matrices.

26) The final grade for an algebra course is determined by grades on the midterm and final exam. The 26) grades for four students and two possible grading systems are modeled by the following matrices.

Midterm Final

Student 1 [ 73 79]Student 2 44 62 Student 3 85 89 Student 4 98 96

System System 1 2

Midterm [ 0.2 0.5 Final 0.8 0.5 ] Find the final course score for Student 3 for both grading System 1 and System 2.

A) System 1: 88.2; System 2: 87 B) System 1: 61.5; System 2: 112.5

C) System 1: 39.8; System 2: 53 0) System 1: 77.8; System 2: 76

Evaluate the determinant.

27) 27) ___

I~ ~ I A) 14 B) 34 C) 56 0)-14

7

Write the linear system as a matrix equation in the form AX :: H, where A is the coefficient matrix and H is the constant matrix.

28) 2x+ 8z 78 28) 4y + 9z 85

8x + 3y + 3z 54

A) B)

[~ 0 4 3 m~Hm [~m~H~]

C)

[~ 0 4 9 m~Hm

D)

[:8 9 3 m~] [m

Write the augmented matrix for the system of equations.

29) -2x + 5y + 9z 52 29) ___

3x + 9y + 8z 97 8x + 6y + 8z 88

A) B) C) D) -25952] -259] 5295-2] -23852] 39897 398 9789 3 59697

[ [ [ [86888 868 8886 8 98888

Solve the problem.

30) Tides go up and down in a 14-hour period. The average depth of a certain river is 11 m and ranges 30) ___ from 8 to 14 m. The variation can be approximated by a sine curve. Write an equation that gives the approximate variation y, if x is the number of hours after midnight and high tide occurs at 8:00 am.

· (nx 4.5nA)y=3sm T-T B) y= 3 sm ---­. (nx 8n~ 7 7

. nx 8n C) y=l1 Sin(~x -8n D)y=l1sm(T-T1

Use a vertical shift to graph the function.

31) y = -3 sin(2X + ~J- 2 31) ___

6 Y

4

2

x -It It

-2

8

A) B)

6 Y 6 Y

x x

C) D)

6 Y 6 Y

4 4

2 2

x

Graph the function. IT

32)y=2cos(x-4") 32) ___

y

3

x -11 11

9

A) B) yy

33

xx

q 0)

y y

3 3

x x

-3

Find the exact value of the expression.

33) cos (245° - 5°)

A)...[3 B) 49 2 12

1 q-­2

0)_...[3 2

33)

Complete the identity.

34) sin (x + ~) ? 34)

A) -sin x B) sin x q cos x 0) -cos x

Graph the solution set of the system of inequalities or indicate that the system has no solution.

10

35) ___35) -x + 6y <30 x?:2

':t . .. . . , , , . , , , '\6

.......... s

:-10: : : : ~5: : :: ::::?:::: W x

.••••••J """"'"

A) B)

x

C) D)

x

11

---

Find the inverse of the matrix. if possible.

36) 36)

A= [ -5 -1 ] -1 -5

A) B) q No inverse 0)

o 0

1 5

[21 [~ ~]o 0

Use a sketch to find the exact value of the expression.

37) esc [tan-1 fJ

o 0

1 5

21] o 0

37)

A)!di B)~ q..!. 0)23 2

Use the figure to find the exact value of the trigonometric function.

38) ___38)

13 5

e 12

Find cos 28.

A) 119 B) 118 q 120 0) _ 119 169 169 169 169

Solve the problem.

39) Mrs. White wants to crochet hats and afghans for a church fundraising bazaar. She needs 8 hours 39) to make a hat and 3 hours to make an afghan, and she has no more than 51 hours available. She has material for no more than 12 items, and she wants to make at least two afghans. Let x = the number of hats she makes and y ::::: the number of afghans she makes. Write a system of inequalities that describes these constraints.

A) 3x + 8y :s 51 B) 8x + 3y :: 51 q 8x + 3y :s 51 0) 8x+ 3y s51 x + y:s 12 x + y:s 12 x + Y s 12 x + Ys 12 x:s2 y:: 2 x::2 y:: 2

12

---

__ _

Write the system of linear equations represented by the augmented matrix. Use X, y, z, and, if necessary, w for the variables.

40) 40) __

~ ~ : -~ 1[ 8 S 0 2

A) 2x 6y + 4z =-2 B) 2x + 6y + 4z = -2 6x + 3z =-4 6x + 3z = 4 8x + Sy -2 8x + Sz = 2

C) 2x + 6y + 4z =-2 D) 2x + 6y + 4z =-2 6x + Y + 3z = 4 6x + 3z = 4 8x + Sy + z = 2 8x + Sy = 2

Solve the problem.

41) A building 300 feet tall casts a 60 foot long shadow. If a person stands at the end of the shadow 41) and looks up to the top of the building, what is the angle of the person's eyes to the top of the building (to the nearest hundredth of a degree)? (Assume the person's eyes are 4 feet above ground level.)

A) 78.54" B) 11.70" C) 78.31" D) 78.69"

Rewrite the expression in terms of the given function or functions.

42) sin2 x + sin x-I + cos2 x; sin x 42)

A) sin x B) -sin x C) 2sin x D) 2 + sin x

13