1. Which of the
following are antiderivatives of $f(x)={{\cos}^{3}}x\sin{x}$?
A. $F(x)=\frac{-{cos}^{4}x}{4}$
B. $F(x)=\frac{{sin}^{2}x}{2}-\frac{{sin}^{4}x}{4}$
C. $F(x)=\frac{1-{cos}^{4}x}{4}$
D. all
of these
2. If you wanted to
estimate the true percentage of all voters in Canada who are in favour of
abolition of the senate, and if you wanted your maximum error of estimate to be
6% with a confidence level of 95%, what would the required sample size be?
A. 267
B. 1068
C. 131
D.
4272
3. $\underset{x\to
\infty }{\mathop{\lim }}\,\frac{5{{x}^{2}}+7x-3}{2+3x-11{{x}^{2}}}$ = _____.
A. -3/2
B. -5/11
C. 0
D. It is nonexistent.
4. What is the
horizontal asymptote of this graph?
A. x = 0
B. y = 0
C. x = 2.5
D. y =2.5
B. y = 0
C. x = 2.5
D. y =2.5
5. A building that is
25 m tall casts a shadow of 10 m long. How long is the shadow of a 5-foot girl
standing beside the building?
A. 2 ft
B. 2.5 ft
C. 10 ft
D. 250 ft
B. 2.5 ft
C. 10 ft
D. 250 ft
6. Person M bought two
radial tires at Php49.95 each and two seat cushions at Php16.99 each. The sales tax
where she lives is 6 percent. What was the total amount of the purchase?
A. Php 141.91
B. Php 99.00
B. Php 99.00
C. Php 33.98
D. Php 133.88
D. Php 133.88
7. Find the general
equation of the line which passes through the points (2,-1) and (-3,5).
A. 6x +5y -7 = 0
B. 5x -6y -7 =
0
C. 6x +7y -5 = 0
D. 6x +6y -5 = 0
8. In 4 years, Lynley
will be twice as old as she was 6 years ago. How old is Lynley?
A. 14
B. 15
C. 16
D. 18
B. 15
C. 16
D. 18
9. For the parabola$y={x}^{2}+x-6$,
find the equation of the axis of symmetry.
A. x = -1/2
B. x = -1
B. x = -1
C. x = 1/2
D. x = 1
D. x = 1
10. He is known as the
"Father of Geometry" and had written a book that is considered to be
the greatest piece of historical work in mathematics.
A. Archimedes
B. Euclid
B. Euclid
C. Newton
D. B. Pascal
D. B. Pascal
11. Find all real numbers
that satisfy the equation,$cos(x)=1$.
A. $\left\{ x|x=\frac{\pi
}{2}+2k\pi \right\}$
B. $\left\{
x|x={\pi}+2k\pi \right\}$
C. $\left\{ x|x=\frac{3\pi
}{2}+2k\pi \right\}$
D. $\left\{
x|x=0+2k\pi \right\}$
12. Find all real numbers
that satisfy the equation, $cos(2x)=\frac{\sqrt{3}}{2}$.
A. $\left\{ x|x=\frac{\pi }{6}+k\pi{or}
x=\frac{5\pi }{6}+k\pi\right\}$
B. $\left\{ x|x=\frac{\pi }{12}+k\pi \right\}$
B. $\left\{ x|x=\frac{\pi }{12}+k\pi \right\}$
C. $\left\{ x|x=\frac{\pi
}{12}+2k\pi{or} x=\frac{11\pi }{12}+2k\pi\right\}$
D. $\left\{ x|x=\frac{\pi }{12}+k\pi{or} x=\frac{11\pi }{12}+k\pi\right\}$
D. $\left\{ x|x=\frac{\pi }{12}+k\pi{or} x=\frac{11\pi }{12}+k\pi\right\}$
13. 9i(5 - 6i) = _____.
A. 54 + 45i
B. 45i - 54
B. 45i - 54
C. $45i-54{i}^{2}$
D. none of these
D. none of these
14. If the length of the
radius of a circle is doubled, what happens to the circumference?
A. halved
B. quadrupled
B. quadrupled
C. doubled
D. tripled
D. tripled
15. What is the midpoint
of the line segment joining the points (5, -3) and (-2, -7)?
A. (1/2, -10)
B. (3, -10)
B. (3, -10)
C. (7, 4)
D. (3/2, -5)
D. (3/2, -5)
16. Solve for a: ${\log}_{4}{(3a-4)}=2$
A. a =3
B. a = 4
C. a = 20/3
D. a = 20
B. a = 4
C. a = 20/3
D. a = 20
17. "Which statement
best describes these two functions?
$f(x)={x}^{2}-x+4$
$g(x)=-3{{x}^{2}}+3x+7$
" A. The maximum of f(x) is less than the
minimum of g(x).
B. The minimum of f(x) is less than the
maximum of g(x).
C. The maximum of f(x) is greater than
the minimum of g(x).
D. The minimum of f(x) is greater than
the maximum of g(x).
18. If (14x + 2) units is
the perimeter of a rectangle and (4x + 2) units is its length, how many units
is its width?
A. 2x + 1
B. 3x - 1
B. 3x - 1
C. x
+ 4
D. 2x - 2
D. 2x - 2
19. What is the
y-intercept of the graph of $y=-4{x}^{2}+2x-3$?
A. -3
B. 3
C. -4
D. 4
B. 3
C. -4
D. 4
20. Find all real numbers
in [0, 2p] that satisfy the equation,$\sin{4x}=\frac{\sqrt{3}}{2}$.
A. 0, $\frac{\pi}{4}$, $\pi$
B. $\frac{\pi}{12}$, $\frac{\pi}{6}$, $\frac{2\pi}{3}$, $\frac{7\pi}{12}$,
$\frac{7\pi}{6}$, $\frac{13\pi}{12}$, $\frac{5\pi}{3}$, $\frac{19\pi}{12}$
C. $\frac{\pi}{4}$, $\frac{5\pi}{4}$
D. 0
21. If $f(x)=\left\{
\begin{matrix} {{e}^{x}},x<\ln 2 \\
2,x\ge \ln 2 \\\end{matrix}
\right.$, then $\underset{x\to \ln 2}{\mathop{\lim }}\,f(x)$ = _____.
A. $\frac{1}{2}$
B. $\ln{2}$
C. 2
D. ${e}^{2}$
B. $\ln{2}$
C. 2
D. ${e}^{2}$
22. Find the area of the
triangle, given that $\gamma={105}^{\circ}$, a = 2, and b = 9. Note that $\alpha$,
$\beta$, and $\gamma$ are the opposite angles of the sides: a, b, and c,
respectively.
A. 2.33
B. 8.69
B. 8.69
C. 101.42
D. 34.77
D. 34.77
23. Compute for the
determinant.
\[\left|
\begin{matrix} 1 & 2 & 3 &
4 \\
1 & 4 & 5 & 8 \\ 1 & 1 & 2 & 3 \\ 1
& 3 & 5 & 8 \\\end{matrix}
\right|\]
A. -4
B. -3
B. -3
C. -2
D. -1
D. -1
24. $\frac{5(\cos{{200}^{\circ}}
+ i\sin{{200}^{\circ}})}{4(\cos{{50}^{\circ}} + i\sin{{50}^{\circ}})}$ =
______.
A. $-2+2\sqrt{3}i$
B. $-\frac{1}{2}+\frac{\sqrt{3}}{2}i$
C. $-10+10\sqrt{3}i$
D. $-\frac{5\sqrt{3}}{8}+\frac{5}{8}i$
25. Which of the
following is equal to ${\log}_{3}{(243)}=5$?
A. ${5}^{4}=243$
B. ${243}^{\frac{5}{3}}$
C. ${3}^{5}=243$
D. $\sqrt[3]{243}=5$
26. The earliest known
use of the equals symbol ( = ) is by Robert Recorde in what year?
A. 1409
B. 1452
B. 1452
C. 1508
D. 1557
D. 1557
27. If one side of a
square is doubled in length and the adjacent side is decreased by two
centimeters, the area of the resulting rectangle is 96 square centimeters
larger than that of the original square. Find the dimensions of the rectangle.
A. 17 x 24
B. 24 x 24
B. 24 x 24
C. 10 x 24
D. 6 x 16
D. 6 x 16
28. The smallest angle of
a triangle is two-thirds the size of the middle angle, and the middle angle is
three-sevenths of the largest angle. Find all three angle measures.
A. 30°, 60°, 90°
B. 45°, 45°, 90°
B. 45°, 45°, 90°
C. 35°, 45°, 110°
D. 30°, 45°, 105°
D. 30°, 45°, 105°
29. What is the area of
the largest rectangular garden that can be fenced off with 50m of fencing
materials?
A. 156.25 sq m
B. 175.5 sq m
B. 175.5 sq m
C. 475.75
sq m
D. 625 sq m
D. 625 sq m
30. If tan x = 2/3 and
tan y = 3/4, what is the value of tan (x + y)?
A. 1/6
B. 4/5
C. 1
D. 17/6
B. 4/5
C. 1
D. 17/6
31. How many terms are
there in a geometric series if the first term is 3, the common ratio is 4, and
the sum of the series is 1,023?
A. 4
B. 5
C. 6
D. 23
B. 5
C. 6
D. 23
32. Sampling that subdivides the population into subgroups
is called a _____ sampling.
A. cluster
B. stratified
B. stratified
C. systematic
D. random
D. random
33. A, B, and C are 3
consecutive numbers. If A > B > C, what is the value of (A - B)(A - C)(B
- C)?
A. -2
B. -1
B. -1
C. 1
D. 2
D. 2
34. arcsec $\left(\sqrt{2}\right)$
= _____.
A. $\frac{7\pi}{4}$
B. $\frac{3\pi}{4}$
C. $\frac{\pi}{4}{\pm}2{\pi}n$ , $\frac{7\pi}{4}{\pm}2{\pi}n$
D. $\frac{\pi}{4}$
D. $\frac{\pi}{4}$
35. In a Filipino test,
eight students obtained the following scores: 10, 15, 12, 18, 16, 24, 12, 14.
What is the median score?
A. 14
B. 14.5
B. 14.5
C. 15
D. 15.5
D. 15.5
36. Two angles of a
triangle measure 4 cm and 7 cm. What is the range of values for the possible
lengths of the third side?
A. 4 < x < 7
B. 3 < x < 11
B. 3 < x < 11
C. 7 < x < 11
D. 11 < x < 15
D. 11 < x < 15
37. A wood frame for
pouring concrete has an interior perimeter of 14 meters. Its length is one
meter greater than its width. The frame is to be braced with twelve-gauge steel
cross-wires. Assuming an extra half-meter of wire is used at either end of a
cross-wire for anchoring, what length of wire should be cut for each brace?
A. 6 m
B. 7 m
B. 7 m
C. 8 m
D. 12 m
D. 12 m
38. Which of the
following statements is true?
A. A rectangle is a square.
B. A parallelogram is a trapezoid.
B. A parallelogram is a trapezoid.
C. A rhombus is a rectangle.
D. A square is a rhombus.
D. A square is a rhombus.
39. Which expression
represents the result of the following subtraction? $\frac{3x-1}{x+2}-
\frac{x-2}{x-1}$
A. $\frac{2x+1}{3}$
B. $\frac{2x+1}{{x}^{2}+x-2}$
C. $\frac{3{{x}^{2}}-4x+5}{3}$
D. $\frac{2{{x}^{2}}-4x+5}{{x}^{2}+x-2}$
40. Adrian Rice has
written in Historia Mathematica about _____.
A. the London Mathematical Society
B. the
Brazilian Mathematical Society
C. the Mathematics of Ancient Egypt
D. the
Mathematics of Macedonia
41. At which of the
following points is the graph of $f(x)={x}^{4}-2{x}^{3}-2{x}^{2}-7$ decreasing
and concave down?
A. (1, -10)
B. (2, -15)
B. (2, -15)
C. (3, 2)
D. (-1, -6)
D. (-1, -6)
42. Rodia can
cross-stitch a design for 10 days while Vessy can do the same job in 15 days.
How long will they finish the job is they help each other?
A. 5 days
B. 6 days
B. 6 days
C. 8 days
D. 10 days
D. 10 days
43. Evaluate: $\left(
{{\log }_{3}}4 \right)\left( {{\log }_{2}}3 \right)$
A. 2
B. 3
B. 3
C. 4
D. 5
D. 5
44. There are how many
inversions in the permutation (1, 5, 3, 2, 4)?
A. 1
B. 2
B. 2
C. 3
D. 4
D. 4
45. Which of these is a
root of $f(x)={x}^{3}-3{{x}^{2}}-4x+12$ ?
A. -3
B. 3
B. 3
C. 4
D. 12
D. 12
46. How many unique
diagonals can be drawn in a pentagon?
A. 5
B. 6
B. 6
C. 7
D. 10
D. 10
47. Find the value of x: ${\log}_{2}{x}=5$
A. 2.5
B. 3.2
B. 3.2
C. 10
D. 32
D. 32
48. A German expert known
as 'Princeps Mathematicon' meaning the "Prince of Mathematicians".
A. Archimedes
B. Euclid
B. Euclid
C. C. Gauss
D. B. Pascal
D. B. Pascal
49. "Which quadrants
contain the solutions to the following system of inequalities?
\[\left\{
\begin{align} & y-2x\le -3 \\ & 3y+x\ge -4 \\\end{align} \right\}\]
A. quadrants I and IV
B. quadrants II and III
B. quadrants II and III
C. quadrants III and IV
D. quadrants II, III, and IV
D. quadrants II, III, and IV
50. (9 - 4i)(2 + 6i) =
_____.
A. 42 - 46i
B. 42 + 46i
B. 42 + 46i
C. -6 - 62i
D. none of these
D. none of these
51. Write an equation to
represent the following: "Eigtheen is ten less than twice some number,
x."
A. 2x - 10 = 18
B. 2x - 18 = 10
B. 2x - 18 = 10
C. 10 - 2x = 18
D. 18 - 10 = 2x
D. 18 - 10 = 2x
52. Solve the triangle,
given that a = 8.9, b = 13.2, and c = 16.1. Note that $\alpha$, $\beta$, and $\gamma$
are the opposite angles of the sides: a, b, and c, respectively.
A. $\alpha={31.5}^{\circ}$, $\beta={55.0}^{\circ}$,
$\gamma={93.4}^{\circ}$
B. $\alpha={35.5}^{\circ}$, $\beta={53.0}^{\circ}$,
$\gamma={91.4}^{\circ}$
C. $\alpha={33.5}^{\circ}$, $\beta={55.0}^{\circ}$,
$\gamma={91.4}^{\circ}$
D. no solution
53. How many liters of
water should be added to 8 liters of 70% solution to make it 60% of the acid?
A. 1 1/3
B. 2 1/2
B. 2 1/2
C. 3
D. 3 2/3
D. 3 2/3
54. It is the set of
points in a plane such that the sum of the distances of each point from two
fixed points is a constant.
A. parabola
B. circle
B. circle
C. ellipse
D. hyperbola
D. hyperbola
55. Which expression is
equivalent to $\sqrt{-6}(\sqrt{-4}-\sqrt{3})$
?
A. $2\sqrt{6}+3\sqrt{2}$
B. $-24-6i\sqrt{3}$
C. $2\sqrt{6}-3i\sqrt{2}$
D. $-2\sqrt{6}-3i\sqrt{2}$
56. Simplify: $5\sqrt{12}-3\sqrt{27}+7\sqrt{48}$
A. $2\sqrt{5}$
B. $9\sqrt{6}$
C. $29\sqrt{3}$
D. $3\sqrt{7}$
B. $9\sqrt{6}$
C. $29\sqrt{3}$
D. $3\sqrt{7}$
57. Given the following
scores of 70, 95, 60, 80, and 100, what is the mean absolute deviation?
A. 11.7
B. 13.2
B. 13.2
C. 14.6
D. 15.9
D. 15.9
58. Which expression is
equivalent to ${(4i)}^{3}$ ?
A. -12i
B. 12i
B. 12i
C. -64i
D. 64i
D. 64i
59. Which of the
following exhibits an odd permutation?
A. 5, 2, 4, 1, 7, 9
B. 1, 4, 3, 2, 6, 5
B. 1, 4, 3, 2, 6, 5
C. c, a, g, b, d
D. 6, 1, 4, 3, 5, 2
D. 6, 1, 4, 3, 5, 2
60. ${\csc}^{-1}\left({2}\right)$
= _____.
A. ${{60}^{\circ }}$
B. $-{{30}^{\circ }}$
C. ${{420}^{\circ }}$
D. ${{30}^{\circ }}$
61. _____ is 20% more
than 50.
A. 110
B. 55
B. 55
C. 60
D. 72
D. 72
62. What is the sum of
the measures of the interior angles of an icosagon?
A. 3100
B. 3140
B. 3140
C. 3240
D. 2850
D. 2850
63. $-15+20i$ = _____.
A. 25(cos 126.9° + i sin 126.9°)
B. 25(cos 306.9° + i sin 306.9°)
B. 25(cos 306.9° + i sin 306.9°)
C. 25(cos 53.1° + i sin 53.1°)
D. 25(cos 233.1° + i sin 233.1°)
D. 25(cos 233.1° + i sin 233.1°)
64. What is the measure
of an interior angle of a regular dodecagon?
A. 120 degrees B. 130 degrees
C. 140
degrees D. 150 degrees
65. Find all solutions to
the following systems of linear equations.
\[\left( \begin{align} & x+y+3z=3 \\ & -x+y+z=-1 \\ & 2x+3y+8z=4 \\ \end{align} \right)\]
\[\left( \begin{align} & x+y+3z=3 \\ & -x+y+z=-1 \\ & 2x+3y+8z=4 \\ \end{align} \right)\]
A. x =1; y = 2; z = 4
B. x =1; y = 2; z = 6
B. x =1; y = 2; z = 6
C. x =1; y = 2; z = 8
D. there are no solutions
D. there are no solutions
66. $\sqrt{-25}$ = _____.
A. 5i
B. -5i
C. $-i\sqrt{5}$
D. $\pm5$
67. At a large
university, the probability that a student takes calculus and statistics in the
same semester is 0.0125. The probability that a student takes statistics is
0.125. Find the probability that a student is taking calculus, given that he or
she is taking statistics.
A. 0.1
B. 0.1125
B. 0.1125
C. 0.0016
D. 0.1375
D. 0.1375
68. If $f(x)={x}^{2}-1$
and $g(x)=x-1$ , what is the value of $(\frac{f}{g})(x)$ ?
A. x - 1
B. x + 1
C. $\frac{1}{x-1}$
D. $\frac{1}{x+1}$
69. Given the matrix, \[A=\left(
\begin{matrix} 1 & 1 & 1 \\ 1
& 2 & t \\ 1 & 4 & {{t}^{2}} \\\end{matrix} \right)\], for what values of t is matrix A invertible?
A. A is invertable for $t\ne{3}$, $t\ne{0}$.
B. A is invertable for$t\ne{2}$, $t\ne{1}$.
C. A is invertable for$t\ne{-2}$, $t\ne{-1}$.
D. A is not invertable at all values of t.
70. if the sum of the
interior angles of a regular polygon is 1980 degrees, how many sides does it
have?
A. 11
B. 12
C. 13
D. 14
B. 12
C. 13
D. 14
71. If$f(x)=(1+6x)(1-6x)$,
what are the zeros of the function f?
A. 0, -1/6
B. 1/6. 1/6
B. 1/6. 1/6
C. -1/6,
1/6
D. 6, -6
D. 6, -6
72. Find the magnitude
and direction angle of the vector, <$\sqrt
{21}$. -1>. Give the measure of the direction angle as an angle in
[0°, 360°).
A. 22; 347.7°
B. 22; 102.3°
B. 22; 102.3°
C. $\sqrt{22}$; 347.7°
D. $\sqrt{22}$; 282.3°
D. $\sqrt{22}$; 282.3°
73. A boat sails 40 miles
north, 60 miles west, and 40 miles north again. How many miles is it from the
starting point?
A. 100
B. 120
B. 120
C. 140
D. 150
D. 150
74. Which among the
measures of central tendency is not influenced by outliers?
A. mean
B. weighted mean
B. weighted mean
C. median
D. mode
D. mode
75. 3(cos 30° + i sin
30°) · 2(cos 90° + i sin 90°)
A. $2\sqrt{6}-\sqrt{2}i$
B. $-3+3\sqrt{3}i$
C. $-6-6\sqrt{3}i$
D. $3-12\sqrt{3}i$
76. The mass of a
radioactive sample is given by $M(t)={{M}_{0}}{{10}^{-kt}}$ , where t is the
time in years, ${M}_{0}$ is the initial mass, and k is a constant. If 400 grams
of this material decays to 40 grams in 10 years, what is the value of k?
A. 1
B. -1
C. 0.1
D. -0.1
B. -1
C. 0.1
D. -0.1
77. What measure of
central tendency can best describe the size of t-shirts commonly used by
teenagers?
A. mean
B. median
C. mode
D. both a and c
78. The price of a
magazine rises from Php5.00 to Php15.00. What is the percent increase in price?
A. 100%
B. 150%
B. 150%
C. 180%
D. 200%
D. 200%
79. In a senior class of
100 students, 60 are taking Spanish as a foreign language, while 70 are taking Japanese.
If 40 are taking both Spanish and Japanese, and if these are the only foreign
languages courses offered in the school, how many are not taking any foreign
language courses?
A. 5
B. 8
B. 8
C. 10
D. 30
D. 30
80. Solve the triangle,
given that $\gamma={65.7}^{\circ}$, a = 4.42, and b = 17.5. Note that $\alpha$,
$\beta$, and $\gamma$ are the opposite angles of the sides: a, b, and c,
respectively.
A. c = 18.5, $\alpha={16.4}^{\circ}$, $\beta={40.1}^{\circ}$
B. c = 12.7, $\alpha={18.4}^{\circ}$, $\beta={38.1}^{\circ}$
B. c = 12.7, $\alpha={18.4}^{\circ}$, $\beta={38.1}^{\circ}$
C. c = 15.6, $\alpha={20.4}^{\circ}$, $\beta={36.1}^{\circ}$
D. no solution
D. no solution
81. If tan x = 2/3 and
tan y = 3/4, what is the value of tan (x + y)?
A. 1/6
B. 4/5
B. 4/5
C. 1
D. 17/6
D. 17/6
82. How many sides does a
regular polygon have if the exterior angle is ${15}^{\circ}$?
A. 15
B. 24
B. 24
C. 30
D. 48
D. 48
83. Find the banker's
interest to the nearest cent. Principal: Php 2500.00; rate: 9%; time: 180 days
A. Php 104.32
B. Php 109.75
B. Php 109.75
C. Php 112.50
D. Php 110.96
D. Php 110.96
84. Which of the
following is true for all acute angles?
I. ${\cos}^{2}\theta=1-{\sin}^{2}\theta$
II. $\cos\theta\tan\theta=\sin\theta$
III. ${\sec}^{2}{\cot\theta}=\csc\theta$
A. I only
B. II only
B. II only
C. I and II
D. I, II, and III
D. I, II, and III
85. Find all real numbers
that satisfy the equation, $cos(x)=1$.
A. $\left\{ x|x=\frac{\pi
}{2}+2k\pi \right\}$
B. $\left\{
x|x={\pi}+2k\pi \right\}$
C. $\left\{ x|x=\frac{3\pi
}{2}+2k\pi \right\}$
D. $\left\{
x|x=0+2k\pi \right\}$
86. 3(cos 30° + i sin
30°) · 2(cos 90° + i sin 90°)
A. $2\sqrt{6}-\sqrt{2}i$
B. $-3+3\sqrt{3}i$
C. $-6-6\sqrt{3}i$
D. $3-12\sqrt{3}i$
87. Find all solutions to
the following systems of linear equations.
\[\left(
\begin{align} & x-2y+2z=5 \\ & x-y=-1 \\ & -x+y+z=5 \\ \end{align}
\right)\]
A. x =1; y = 2; z = 4
B. x =1; y = 2; z = 5
B. x =1; y = 2; z = 5
C. x =1; y = 2; z =3
D. there are no solutions
D. there are no solutions
88. If x and y are real
numbers, what is the simplified radical form of ${{\left( {{x}^{2}}{{y}^{5}}
\right)}^{\frac{1}{5}}}$ ?
A. $y\sqrt[5]{{{x}^{2}}}$
B. $y\sqrt{{{x}^{5}}}$
C. $\left| y
\right|\sqrt[5]{{{x}^{2}}}$
D. $\left| y \right|\sqrt{{{x}^{5}}}$
89. Which of the
following equations is a graph of a
point?
A. ${x}^{2}+{y}^{2}-4x+10y+29=0$
B. ${x}^{2}+{y}^{2}+8x-6y+30=0$
C. ${x}^{2}+{y}^{2}-6x-8y+9=0$
D. $4{x}^{2}+4{y}^{2}-81=0$
90. Mr. L worked at three
jobs in 3 days. In the first day, he earned Php 310.00. In the next day, he was
paid Php 334.00. In the third day, he was paid Php 307. What average per day
did Mr. L earn for these 3 days?
A. Php 951.00
B. Php 317.00
B. Php 317.00
C. Php 978.00
D. Php 326.00
D. Php 326.00
91. Let f be a function
such that, $\underset{h\to 0}{\mathop{\lim }}\,\frac{f(5+h)-f(5)}{h}=3$. Which
of the following must be true?
A. f(5) = 3
B. f'(5) = 3
C. f is continuous and differentiable
at x = 5.
D. both B and C
92. What is the set of
approximate y-values of the relative minimum and maximum of this graphed
function?
A. {2}
B. {-1, 2}
B. {-1, 2}
C.
{-1, 3}
D. {-2, 1, 3}
D. {-2, 1, 3}
93. What is the maximum
number of books, each 1.4 cm thick that can be put vertically in a shelf which
is 64 cm long?
A. 44
B. 45
C. 46
D. 64
B. 45
C. 46
D. 64
94. Which expression represents the
quotient of the following? $\frac{4{{x}^{2}}y}{8x{{y}^{2}}}\div
\frac{12x{{y}^{2}} }{8{{x}^{6}}{{y}^{3}}}$
A. $\frac{{{x}^{5}}}{3}$
B. $\frac{3}{{{x}^{5}}}$
C. $\frac{{{x}^{6}}}{3}$
D. $\frac{3}{{{x}^{6}}}$
95. The earth revolves ${360}^{\circ}$
of longitude in one day. How many minutes does it take to revolve through ${15}^{\circ}$?
A. 30
B. 60
B. 60
C. 90
D. 120
D. 120
96. How many vertical
asymptotes does the graph of $y=\frac{x-2}{{x}^{2}+4}$ have?
A. 0
B. 1
B. 1
C. 2
D. 4
D. 4
97. If ${x}^{2}$ is
proportional to ${y}^{3}$, and if x = 1 when y = 4, find x when y = 3.
A. $\frac{3\sqrt{3}}{8}$
B. $\frac{4\sqrt{2}}{5}$
C. $\frac{6\sqrt{3}}{7}$
D. 12
98. If $f(x)=x-\frac{1}{2}$
and $g(x)=-2$ , which graph corresponds to the function $(fg)(x)$ ?
A. line R
B. line S
B. line S
C. line T
D. line U
D. line U
99. What is the value of
x in this rational equation, $\frac{2}{x-1}=\frac{3}{x+1}$ ?
A. 2
B. 3
C. 4
D. 5
B. 3
C. 4
D. 5
100. What is the converse
of the statement, "If a, then b"?
A. If not a, then b.
B. If
b, then a.
C. If not b, then a.
D. If
not a, then not b.
101. Evaluate: $\frac{{{a}^{2}}}{ab}* \frac{3{{b}^{2}}}{2a}$
A. 3/2a
B. b/a
B. b/a
C. 3b/2
D. b/2
D. b/2
102. In a photograph,
Bianca is 9 cm tall and her brother Tristan is 10 cm tall. Bianca's actual
height is 153 cm. What is Tristan's actual height?
A. 148 cm
B. 156 cm
B. 156 cm
C. 168 cm
D. 170 cm
D. 170 cm
103. Which of the following
must be always positive?
A. The product of three negative
numbers.
B. The sum of two negative numbers.
C. The sum of a positive and a negative
number.
D. The product of two negative numbers.
104. $10+\sqrt{-81}$ =
_____.
A. 1
B. 10 - 9i
B. 10 - 9i
C. 10 + 9i
D. 10 + i
D. 10 + i
105. Which of the following
must be true if points L, M, N, and O are coplanar points and a line segment
drawn from L to M passes through N while a line segment drawn from N to M
passes through O?
A. LN + NO = LM
B. LO + NO = LN
C. Point N is the midpoint of segment
NO.
D. Points L, M, N, and O are collinear.
106. If the height of a
triangle is five inches less than the length of its base, and if the area of
the triangle is 52 square inches, find the base(b) and the height (h).
A. b=13, h=8
B. b=12, h=9
B. b=12, h=9
C. b=11, h=7
D. b=13, h=4
D. b=13, h=4
107. A triangle has a
perimeter of 50. If 2 of its sides are equal and the third side is 5 more than
the equal sides, what is the length of the third side?
A. 5
B. 10
C. 15
D. 20
B. 10
C. 15
D. 20
108. Find the magnitude and
direction angle of the vector, <0, -18>. Give the measure of the
direction angle as an angle in [0°, 360°).
A. 324; 270°
B. 18; 90°
B. 18; 90°
C. 18; 180°
D. 18; 270°
D. 18; 270°
109. Find the component
form for the vector v with the given magnitude and direction angle θ. |v| =
153.8, θ = 121.6°
A. <131.0, 80.6>
B. <80.6, 131.0>
B. <80.6, 131.0>
C. <-80.6, 131.0>
D. <131.0, -80.6>
D. <131.0, -80.6>
110. Find the area of
the figure below.
A. 25.02 sq ft
B. 6.26 sq ft
B. 6.26 sq ft
C.
12.51 sq ft
D. 14.69 sq ft
D. 14.69 sq ft
111. What is the solution set of this system of equations?
\[\left\{
\begin{align} &
{{x}^{2}}+y-1=0 \\ & x-y+1=0 \\\end{align} \right\}\]
A. {(-1,-1), (-1,0)}
B. {(-1,0), (-1,1)}
B. {(-1,0), (-1,1)}
C. {(-1,0), (0,1)}
D. {(1,0), (1,1)}
D. {(1,0), (1,1)}
112. What are the vertical
and horizontal asymptotes of $f(x)=\frac{{x}^{2}-9}{16-{x}^{2}}$
?
A. x = $\pm4$, and y = -1
B. y
= $\pm4$, and x = -1
C. x = $\pm4$, and y = 1
D. y
= $\pm4$, and x = 1
113. Find the inverse of
the matrix, \[B=\left[
\begin{matrix} 1 & 0 & 4 \\ -1
& 1 & -1 \\ -1 & 0 & -3 \\\end{matrix} \right]\]
A. 1
B. \[{{B}^{-1}}=\left[
\begin{matrix} - 4 & 2 & 1 \\
-1& 5 & -1 \\ -6 & 8 & -1 \\\end{matrix} \right]\]
C. \[{{B}^{-1}}=\left[ \begin{matrix} -3 & 0 & 4 \\ -2
& 1 & -3 \\ 1 & 0 & 1 \\\end{matrix} \right]\]
D. the
matrix is not invertible
114. If the smallest and
largest numbers is set Q are removed, what is the median of set Q? Q = {10, 9,
2, 6, 3, 4, 1, 7, 5, 2}
A. 4
B. 4.5
B. 4.5
C. 5
D. 5.5
D. 5.5
115. The Vitamin C content
of a particular brand of vitamin supplement pills is normally distributed with
mean 490 mg and standard deviation 12 mg. What is the probability that a
randomly selected pill contains at least 500 mg of Vitamin C?
A. 0.0525
B. 0.1123
B. 0.1123
C. 0.2033
D. 0.7967
D. 0.7967
116. Which set of three
numbers can be the measures of the sides of right triangle?
A. 5, 12, 13
B. 4, 8, 12
B. 4, 8, 12
C. 7, 13, 15
D. 6, 7, 8
D. 6, 7, 8
117. Which of these
observations is a model of population growth?
A. The population started out large,
decreased in size, then became large again.
B. The population is observed to
increase at a faster rate as time passes.
C. The population is observed to
increase steadily over time.
D. The population grew very quickly but
then declined.
A. a
B. a + b
B. a + b
C. 2a
D. a + 2b
D. a + 2b
119. How many ways can a
committee of 4 people be selected from a group of 7 people?
A. 35
B. 70
B. 70
C. 140
D. 210
D. 210
120. What are the
coordinates at the minimum point of $f(x)={{x}^{2}}-4x+3$ ?
A. (-1,2)
B. (-1,2)
B. (-1,2)
C. (2, -1)
D. (2, 1)
D. (2, 1)
Answer Key
1. D
2. A
3. B
4. B
5. A
6. A
7. A
8. C
9. A
10. B
11. D
12. D
13. A
14. C
15. D
16. C
17. B
18. B
19. A
20. B
21. C
22. B
23. C
24. D
25. C
26. D
27. C
28. D
29. A
30. D
31. B
32. B
33. D
34. D
35. B
36. B
37. A
38. D
39. D
40. A
41. A
42. B
43. A
44. D
45. B
46. A
47. D
48. C
49. A
50. B
51. A
52. C
53. A
54. C
55. D
56. C
57. B
58. C
59. A
60. D
61. C
62. C
63. A
64. D
65. B
66. A
67. A
68. B
69. B
70. C
71. C
72. C
73. A
74. C
75. B
76. C
77. C
78. D
79. C
80. B
81. D
82. B
83. D
84. C
85. D
86. B
87. A
88. A
89. A
90. B
91. D
92. C
93. B
94. C
95. B
96. A
97. A
98. D
99. D
100. B
101. C
102. D
103. D
104. C
105. D
106. A
107. D
108. D
109. C
110. C
111. C
112. A
113. C
114. B
115. C
116. A
117. B
118. A
119. A
120. C
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