Republic of the Philippines
Department of Education
Region VIII
Division of Calbayog City
CALBAYOG CITY NATIONAL HIGH SCHOOL
Calbayog City
FINAL EXAMINATION
In
PRECALCULUS
Strand & Grade:
Name:
Date: 1.Q_l_/2016 Score:
Rating:
%
Test I. MULTIPLE CHOICE. Select only the letter that represent your best answer and write it in CAPITAL
letter on the space provided before the answer. Write your solutions on separate sheet. Erasure means wrong.
I.A function whose domain is the set of positive integers or the set {1, 2, 3, . . . . , n} is called:
a. senes
b. sequence
c. arithmetic sequence
d. geometric sequence
e. neither of these
2. A sequence in which each term after the first is obtained by multiplying the preceding term by a constant (called
the common ratio) is called:
a. geometric sequence
b. arithmetic sequence
c. sequence
d. series
e. neither of these
3. A sum of numbers which is separated by "+" or "-"sign is called:
a. arithmetic sequence
b. geometric sequence
c. senes
d. sequence
e. neither of these
4. A sequence in which each term after the first is obtained by adding a constant (called the common difference) to the
preceding term is called:
a. sequence
b. arithmetic sequence c. geometric sequence
d. series
e. neither of these
5. The first five terms of the sequence {1 + n a. -1,1,5,11,19
b. -l,-l,-5,-11,-19
n
2
} are:
c. l,-l,5,-11,19
6. The associated series of { 1 · 2 · 3 · · · n } are:
a. 102
b. 135
d. 1,1,-5,11,-19
e. neither of these
d. 153
c. 120
e. neither of these
n
.
I:.t(iJ .
d
express10n i=m
is rea as:
7.
The
a. the series off(i) from i = m to n
c. the summation of f(i) from i = m to n
b. the sigma notation of f(i) from i = m to n
d. the total off(i) from i = m to n
G
Jn
n + 1 is approximately equal to:
8. The equivalent value of the expression
a. 2.527
b. 2.54
c. 2.52
d. 2.25
e. neither of these
d. 64
e. neither of these
5
Li is equal to:
9. The equivalent sum of the expression
0
a. 61
b. 62
'=
c. 63
10. The sigma notation of the expression 1 - 2 + 3 - 4 + 5 - 6 + . . . - 10 is:
10
a.
kxk
k= l
b. 2.__) -l)k-1
k=I
n
10
10
/;
c. 2= ( 2 1 + :3)
i=
1
d.
2.: ·rj
e. neither of these
j= l
11. These are the properties of the so called Pascal 's Triangle. Which of these are TRUE?
I. There is symmetry of the numbers in each row.
III. Each row begins and ends with 1.
II. Each row has n + 1 numbers.
IV. The second and second to the last number of each row
correspond to the row number.
a. I,
II, III
b. I, II, IV
c. II, III, IV
d. I, III, IV
e. all of these
12. The following numbers , 1 8 28 56 70 56 28 8 1 are coefficients in a row of Pascal's Triangle. What is its row
number?
a. 6
b. 7
c. 8
d. 9
e. neither of these
13. Which of the following are the coefficients of the 9th row of the Pascal 's Triangle?
a. 1 9 34 84 126 126 84 34 9 1
b. 1 9 36 84 126 126 84 34 9 1
c. 1 9 36 84 126 126 84 36 9 1
d. 1 9 34 86 126 126 86 34 9 1
e. neither of these
14. Which of the following are the coefficients of the 5th row of the Pascal 's Triangle?
a. 1 5 10 10 5 l
b. 15 10 5 1
c. 1 5 10 20 10 5 1
d. 1 5 5 1
e. neither of these
15. The following numbers , 1 6 15 20 15 6 1 are coefficients in a row of Pascal 's Triangle. What is its row number ?
a. 5
b. 6
c. 7
d. 8
e. neither of these
l l Pa g e
CMOR
16. Which of the following is the sixth coefficient of the 8th row in Pascal's Triangle ?
a. 56 a
5 b3
b. 56 a
3 b5
c. 56 a
4 b4
d. 56 a
6 b2
e. neither of these
17. Which of the following is the sixth coefficient of the 5th row of the expression ( 2:r - 3y) ?
5
a. -243 Y
b. 243 Y
5
c. -243 Y
d. -243 Y
e. neither of
these
18. What is the value of combinations
a. 60, 6720
b. 56, 10
19. What is the value of combinations
a. 66, 35
b. 36,65
, respectivel y?
c. 10, 56
d. 20, 46
e. neither of these
d. 36, 66
e. neither of these
, respectivel y?
c. 66, 36
20. The following refers to angle as used in trigonometr y. Which of these are TRUE?
I. It is formed by rotating a ray about its endpoint.
III. A rotation of a ray, and, therefore , has no limit.
II. It is a union of rays and has measure between 0 and 180
IV. It has positive and negative directions and
measures.
a. I, II, III
b. I, III, IV
c. I, II, IV
d. II, III, IV
e. all of these
21. Which of the following is the accurate value of the subtended angle of 1 radian in degrees, in five decimal places ?
a. 57.29577
b. 57.29576
c. 57.29757
d. 57.29578
e. neither of these
22. Express 75° and 240° in radians, respectivel y.
a. 5rr /12, 4rr I 3
b. 4rr I 3, 5rr /12
c. 12rr /5, 4rr I 3
d. 5rr /12, 3rr I 4
e. neither of these
23. Express rr/8 rad and llrr/6 rad in degrees, respectively.
a. 330, 22
b. 320, 22
c. 330, 22.5
d. 22.5, 330
e. neither of these
24. Find the angle between 0° and 360° that is coterminal of angle -380°.
a. -340
b. 20
c. -20
d. 340
e. neither of these
25. Find the angle between -360° and 0° that is coterminal of angle -380°.
a. -340
b. 20
c. -20
d. 340
e. neither of these
26. Find the angle between 0° and 360° that is coterminal of angle -28°48 '65".
a. 331°10'55"
b. 332° 10'55"
c. 331°11'55"
d. 330° 10'55"
e. neither of these
27. Find the angle between -360° and 0° that is coterminal of angle -400°1'23".
a. 40°1'23"
b. 40°2'23"
c. 40°1'43"
d. 50° 1'23"
e. neither of these
28. Find the length of an arc of a circle with radius 10 m that subtends a central angle of 30°.
a. 4rr I 3
b. 5rr I 4
c. 3rr I 5
d. 5rr I 3
e. neither of these
29. A central angle 8 in a circle ofradius 4 m is subtended by an arc oflength 6 m. Find the measure of 8in radians.
a. 2/3
b. 4/3
c. -3/2
d. 5/2
e. neither of these
30. Find the area of a sector of a circle with central angle 60° if the radius of the circle is 3 m.
a. 3rr I 2
b. 2rr I 3
c. 4rr I 3
d. 3rr I 4
e. neither of these
31. In a circle of radius 7 feet, find the length of the arc that subtends a central angle of 5 radians.
a. 34ft.
b. 35 ft.
c. 36 ft.
d. 37 ft.
e. neither of these
32. A central angle 8 in a circle of radius 20 m is subtended by an arc oflength 15rr m. Find the measure of 8 in degrees.
a. 133°
b. 134°
c. 135°
d. 136°
e. neither of these
33. Find the area of a sector of a circle with central angle that measures 75° if the radius of the circle is 6 m, in sq. m.
a. 7
b. 6
c. 7.5
d. 9
e. neither of these
34. The geometric mean of two numbers is the square root of their product. Find the geometric mean of 1 and 100.
a. 10
b.
± 10
c. 3.16
d. 3.20
these
2 1 Pag e
CM OR
e. neither of
35. The arithmetic mean of two numbers equals one-half their sum. Find the arithmetic mean of 2 and 6.
a. 5
b. 6
c. 8
d. 3
e. neither of these
36. The harmonic mean of two numbers is the quotient of twice their product and their sum. Find the harmonic mean of 2
and 4.
a. 8/3
b. 3/8
c. 6/16
d. 4/8
e. neither of these
37. Geometric mean is also equal to the square root of the product of arithmetic and harmonic mean. Find the geometric
mean of two numbers whose arithmetic mean is 15 and whose harmonic mean is 5/27.
a. 3/5
b. 5/3
c. 4/3
d. %
e. neither of these
38. Find the sum of the first 20 terms of a geometric series if the first term is 1 and r=2.
a. 1,048,575
b. 1,048,574
c. 1,408,575
d. 1,048,576
e. neither of these
39. Find the seventh term of the geometric sequence: 1, Yz, 'l-4, . . . ,
a. 1/32
b. 1/64
c. 1/46
d. 1/23
e. neither of these
40. Which of the following is NOT included in arithmetic sequence?
a. 2, 5, 8, 11
b. 4, 2, 0, -2
c. -7, -3, 1, 5
d. -25, -22, -19, -16
e. neither of these
41. Which of the following is NOT included in geometric sequence?
a. 64, -16, 4, -1
b. 1/16, 1/8, 'l-4, Yz
c. 80, 40, 20, 10
d. -27, 18, -12, 8
e. neither of these
42. Which of the following is an arithmetic sequence?
a. 'l-4, 1/8, 1/12
b. 3, 1, 3/5
c. 9, 12, 15
d. 1/3, 4/15 , 2/9
e. neither of these
43. Which of the following is a geometric sequence?
a. 49, 45, 41
b. 1/3, Yz, 2/3
c.l, 1, -112, 1/4
d. -1, 2, 5
e. neither of these
44. Two gears of radii 2.5 cm and 4.8 cm are adjusted so that the smaller gear drives the larger one. Ifthe
smaller gear rotates counterclockwise through 225°, through how many degrees will the larger gear rotate ?
a. 117
b. 116
c. 118
d. 117.1
e. neither of these
45. Ifthe radius of a circle is doubled and the central angle of a sector is unchanged , how is the AREA of the sector
changed ?
a. doubled
b. tripled
c. quadrupled
d. the same
e. neither of these
46. Ifthe radius of a circle is doubled, how is the LENGTH of the arc intercepted by a fixed central angle changed ?
a. doubled
b. tripled
c. quadrupled
d. the same
e. neither of these
47. Convert 3 radians to degrees.
a. 171 degrees
b. 172 degrees
c. 170 degrees
d. 173 degrees
e. neither of these
48. Find the measurement in degrees of an angle with 1/5 revolution counterclockwise.
a. 71
b. 72
c. 73
d. 70
e. neither of these
49. Find the measurement in degrees of an angle with 1-1/3 revolution clockwise.
a. -480
b. -490
c. -470
d. -500
e. neither of these
50. Convert 40°36' to radians.
a. 1 rad
b. 0.81 rad
e. neither of these
c. 0.91 rad
d. 0.71 rad
Prepar ed by Science, Technology, Engineering and Mathematics (STEM) Facilitators:
CESAR M DEL ROSARIO JR..
CE
SHS T-1
31 Pag e
JEHU ARIBA. E CE
SHS T-1
MER CY DA n1N CHAVEZ.
CE SHS T-1
CM OR