Download Math I - Abu Dhabi Polytechnic

ABU DHABI POLYTECHNIC
ACADEMIC SUPPORT
DEPARTMENT
Challenge Exam
Sample version
Mathematics II
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STUDENT NAME
STUDENT
NUMBER
A
CRN
DEPARTMENT
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boxes above.
Answer all questions. Use the 3 blank pages at the end.
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you may lose marks.
Total number
of correct
answers
Score
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There are 40 questions. Each is 2.5 points.
Pass if Total Points ≥70, Fail if Total Points < 70
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to cheat a serious offense that will result in disciplinary
action taken against involved individuals.
RESULT
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Formula Sheet
1. Heros’s formula for the area of a triangle:
1
𝐴 = √𝑠(𝑠 − 𝑎)(𝑠 − 𝑏)(𝑠 − 𝑐), where 𝑠 = 2 (𝑎 + 𝑏 + 𝑐)
2. Area of the parallelogram: 𝐴 = 𝑏 × ℎ
3. Trapezoidal Rule:
4. Simpson’s Rule:
5.
sin() =  sin()
,
cos() =
tan() =  tan()
,
csc() =  csc()
sec() =
,
cot() =  cot()

sec()
Trigonometric functions applications:
s = r

cos()
,
A =
𝟏

r2
𝟐
,
v = r
Vectors:
Ax = A cos 
Ay = A sin 
 Law of sines using the following triangle where the sides are given as a,b,c
and the angles are given as A, B, C.
B
𝒂
𝐬𝐢𝐧 𝑨

=
𝒃
𝐬𝐢𝐧 𝑩
=
𝒄
𝐬𝐢𝐧 𝑪
Law of cosines:
a2 = b2 + c2  2bc cos A
b2 = a2 + c2  2ac cos B
c2 = a2 + b2  2ab cos C
.
C
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the measures of two angles, one positive and one negative, that are coterminal with the given angle.
1) 131.3°
A) 491.3°; -228.7°
B) 491.3°; -48.7°
C) 311.3°, -228.7°
D) 311.3°; -48.7°
1)
Solve the problem.
2) Find the supplement of 12°.
A) 78°
B) 348°
2)
C) 168°
3) Find the complement of 79°.
A) 101°
B) 11°
C) 191°
4) Two angles of a triangle are 37° and 97°. Find the third angle.
A) 226°
B) 44°
C) 134°
D) 258°
D) 281°
D) 46°
Find the area.
5)
3)
4)
5)
34 m
29 m
49.5 m
A) 1400 m 2
B) 490 m 2
C) 420 m 2
D) 720 m 2
Find the missing length in the right triangle.
6) The legs of a right triangle are 93.1 cm and 60.4 cm. Find the length of the hypotenuse.
A) 70.8 cm
B) 111 cm
C) 71 cm
D) 110 cm
6)
Solve the problem.
7) A bike trail is in the shape of a trapezoid. Find the distance around the trail.
15.0 km
7)
3.49 km
A) 39.69 km
5.60 km
15.6 km
B) 87.36 km
C) 19.5 km
1
D) 39.7 km
Determine the indicated arc or angle.
8) FindBC.
66°
8)
56°
A) 56°
B) 114°
C) 112°
Convert to degree measure. Round to two decimal places, if necessary.
9) 2.002 rad
A) 229.12°
B) 115.01°
C) 114.71°
D) 28°
D) 229.42°
9)
For the given angle in standard position, designate the quadrant in which the terminal side lies.
10) -
4
rad
10)
A) IV
B) II
C) I
D) III
Find the requested function value of .
3
11) If sin = , find cos .
8
A)
8
55
B)
11)
3
55
C)
12) If sin = 0.2857, find cos .
A) 0.04444
B) 3.354
55
8
C) 0.9583
D)
55
3
D) 0.1556
Find the requested part of the triangle. Round your answer to two decimal places.
13) Find the measure of the angle A in degrees.
12)
13)
6.2
A) 57.27°
9.18
B) 55.57°
C) 34.03°
D) 55.97°
Solve the problem. Round results to an appropriate number of significant digits.
14) From a boat on the lake, the angle of elevation to the top of a cliff is 17°48'. If the base of the cliff is
2266 ft from the boat, how high is the cliff (to the nearest foot)?
A) 738 ft
B) 731 ft
C) 741 ft
D) 728 ft
2
14)
Sketch the graph of the line with the given equation.
15) y = 4x - 4
15)
A)
B)
C)
D)
Solve by the method of elimination by addition or subtraction.
16) x - 3y = 26
4x - 4y = 48
A) x = -5, y = -6
B) x = 5, y = -7
C) x = 4, y = -6
17) 9x + 62 = 7y
-6x - 2y = 8
A) x = -4, y = 6
16)
D) Inconsistent
17)
B) x = -3, y = 5
C) x = -3, y = 6
3
D) Inconsistent
Evaluate the determinant.
18)
1 2
2 1
A) 5
18)
B) 0
C) -3
Solve the system of equations by determinants.
19) x + 4y = 17
5x + y = 8
5
11
A) x = - , y = 7
3
C) x = -
19)
15
77
,y=
19
19
Determine the quadrant containing the terminal side of
20) csc > 0 and sec > 0
A) Quadrant III
B) Quadrant II
21) cot > 0 and sin < 0
A) Quadrant III
D) 3
B) x =
15
77
,y=
19
19
D) x =
15
77
,y=19
19
under the given conditions.
B) Quadrant IV
C) Quadrant IV
D) Quadrant I
C) Quadrant II
D) Quadrant I
20)
21)
Determine the indicated component or components of the vector. Round to an appropriate number of significant digits.
22) Magnitude = 188.5, = 195.8°
22)
Find the horizontal and vertical components of V.
A) 181.4, 51.3
B) -181.4, 51.3
C) -181.4, -51.3
D) 181.4, -51.3
With the given set of components, find R and .
23) Rx = 8.0, Ry = -5.0
23)
A) R = 13.0, = 328°
C) R = 9.4, = 328°
B) R = 9.4, = -32°
D) R = 13.0, = -32°
Find the missing parts of the triangle.
24) B = 27.8°
C = 107.8°
b = 13.17
A) A = 42.4°, a = 28.89, c = 21.76
C) A = 44.4°, a = 21.76, c = 28.89
24)
B) A = 42.4°, a = 26.89, c = 19.76
D) A = 44.4°, a = 19.76, c = 26.89
25) B = 63°30'
a = 12.20
c = 7.80
A) No triangle satisfies the given conditions.
C) b = 11.17, A = 77°49', C = 38°41'
25)
B) b = 12.17, A = 75°07', C = 41°23'
D) b = 13.17, A = 73°07', C = 37°23'
Find the missing parts of the triangle. (Find angles to the nearest hundredth of a degree.)
26) a = 7.8
b = 13.9
c = 15.5
A) No triangle satisfies the given conditions.
B) A = 30.15°, B = 63.52°, C = 86.33°
C) A = 32.15°, B = 61.52°, C = 86.33°
D) A = 28.15°, B = 63.52°, C = 88.33°
4
26)
Find the amplitude, period or displacement.
1
27) Find the period of y = 5 sin ( x - ).
3
2
A) 5
27)
B) 3
C)
2
D) 6
Use the trapezoidal rule to find the area.
28) A pool was measured every 2.25 yd. The distances across the pool (in yards) are given in the
diagram. Find the area.
28)
3.94 3.85 3.27 3.71 3.42 3.37 3.97 3.55 0.00
A) 57.0 yd2
B) 85.0 yd2
C) 93.6 yd2
D) 61.0 yd2
Use Simpson's Rule to find the area.
29) A pool was measured every 2.50 yd. The distances across the pool (in yards) are given in the
diagram. Find the area.
29)
2.91 2.98 3.59 2.53 2.87 3.41 2.73 3.62 0.00
A) 53.4 yd2
B) 58.0 yd2
C) 59.5 yd2
D) 54.0 yd2
Solve the problem.
30) The perimeter of a rectangular room is 62 ft. The width is 15 ft. Find the length.
A) 47 ft
B) 15 ft
C) 17 ft
D) 16 ft
30)
For the given angle in standard position, designate the quadrant in which the terminal side lies.
31)
4
rad
A) III
31)
B) I
C) II
5
D) IV
Find the requested function value of .
13
, find cot .
32) If csc =
2
A)
2
165
B)
32)
165
2
C)
13
165
D)
165
13
Solve the right triangle. Round results to an appropriate number of significant digits.
33) B = 59.7°, c = 0.697 cm
A) A = 30.3°, b = 1.193 cm, a = 0.352 cm
B) A = 30.3°, b = 1.193 cm, a = 0.602 cm
C) A = 30.3°, b = 0.602 cm, a = 0.352 cm
D) A = 30.3°, b = 0.352 cm, a = 0.602 cm
Find the requested part of the triangle. Round your answer to two decimal places.
34) Find the measure of the angle A in degrees.
33)
34)
7.27
A) 24.79°
6.6
B) 22.99°
C) 65.21°
Determine the sign of the trigonometric function.
35) cos(-401°)
A) Positive
D) 26.89°
35)
B) Negative
For the given function value determine the quadrants in which the terminal side of the angle can lie.
36) cos = -0.5
A) II, III
B) II, IV
C) I, IV
D) I, III
36)
Determine the quadrant containing the terminal side of
37) tan < 0 and sin < 0
A) Quadrant IV
B) Quadrant III
37)
under the given conditions.
C) Quadrant I
D) Quadrant II
Find the missing parts of the triangle. (Find angles to the nearest hundredth of a degree.)
38) a = 8.9
b = 13.4
c = 15.9
A) A = 32.03°, B = 57.41°, C = 90.56°
B) A = 34.03°, B = 57.41°, C = 88.56°
C) No triangle satisfies the given conditions.
D) A = 36.03°, B = 55.41°, C = 88.56°
Find the missing parts of the triangle.
39) A = 48°30'
B = 36°20'
a = 10.53
A) C = 96°10', b = 8.33, c = 14.00
C) C = 95°10', b = 8.33, c = 14.00
38)
39)
B) C = 96°10', b = 14.00, c = 8.33
D) C = 95°10', b = 14.00, c = 8.33
6
Solve the problem.
40) A beam of light is partly reflected, and the remainder of the beam passes straight through the
surface. Find the angle (angle O) between the surface and the part that passes through.
42°
A) 42°
B) 48°
C) 87°
7
D) 132°
40)