MATHEMATICS-1
1. What is the equation normal to the curve x2 + y² = 25 thru (2, 1)?
A. 2x + y = 25 B. x+2y= 5
C. x-2y=0 D. x+y=3
2. A man standing on a 48.5 m high building has an eyesight height of 1.5m from the top of the building,
took a depression reading from the top of another nearby building and nearest wall, which are 50° and
80° respectively. Find the height of the nearby building in meters and both buildings lie on the same
horizontal plane.
A. 39.49
C. 30.74
D. 42.55
B. 35.5
Which of the following is divisible by 9?
A. 10 2019 +6
C. 10 2019 +7
D. 10 2019 +9
B. 10 2019 +8
The area bounded by the curve y² = 12x and the line x = 3 is revolved about the line x = 3. What is the
volume generated?
A. 382.644pi
C. 76.529pi
D. 180.956pi
B. 288pi/5
5. What is the curve describe by the equation Ln zil = 2?
A. Ellipse
C. Circle
D. Parabola
B. Hyperbola
6. A pendulum 1m long oscillates at an angle of 10 degrees. Find the length of the arc subtended.
a. (1/6)pi
C. (1/36)pi
D. (1/18)pi
B. (1/6)pi
7. An arch is in the form of an inverted parabola and has span of 12 feet at the base and a height of 12
feet. Determine the equation of the parabola and give the vertical clearance 4 feet from the vertical
centerline.
A. 7.33 ft
C. 5.33 ft
B. 6.00 ft
D. 6.67 ft
8. Evaluate In(3+j4)
A. 1.46+j0.102
C. 1.77 + j0.843
D. 1.95+j0.112
B. 1.61+j0.927
9. The value of a house is P185,000. A community which has an assessment of property at 85% of the
value. The tax rate is P24.85 per thousand of pesos. How much is the total tax of the house?
C. P3,907.66
D. P1,480
A. P4,597.25
B. P1,850
10. 14 is 30% of what number?
C. 46.67
A. 4.2
B. 214.286
D. 12.45
11. Find the weight of the heaviest right circular cylinder that can be cut from a 100 kg solid iron shot.
C. 75 kg
A. 50 kg
B. 86.6 kg
D. 57.7 kg
12. Three circles externally tangent with each other has radii 3cm, 4cm, and 5cm. Find the maximum
angle formed by the triangle connecting the centers of the circle.
A. 270 deg.
C. 73.4deg.
D. 48.2 deg.
B. 286.6 deg.
13. What is the curve describe by the equation Im (z²) = 4?
A. Ellipse
C. Circle
B. Hyperbola
D. Parabola
14. Points A and B, 1000m apart are plotted on a straight highway running east and west. From A, the
bearing of the tower C is 32°W of N and from B, the bearing of C is 26°N of E. Approximate the shortest
distance of the tower C to the highway.
A. 374 m
B. 770 m
C. 241m
D. 1033m
15. Find the limit of z 2/(z+z+3) as z approaches e to the (i/2).
A. 3/16 B. (-4+1)/17
C. (8/-76)/365 D. (51+6)/287
16. Which of the formulas below is incorrect?
A. cos20 = 2cos20-1
B. c2a2+ b²-2abcosC
C. sin20 1-2sin20 D. sec²0 = tan20 +1
17. The sum of the 3 positive integers is 51. Find the greatest possible product of these numbers.
A. 7362
C. 5624
B. 4913
D. 9625
18. Find k in the equation of the line 5x-2y + k = 0 that is tangent to y = 6 + x2
A. 25/8
C. 23/4
B. 5/12
D. 71/8
19. The tenth's and the unit's digit of a number are x and y respectively. Write the number in terms of its
digits.
A. 10x + y
B. x+10/y
C. 10y + x
D. y + x/10
20 An object falls from rest in a medium offering resistance. The velocity of an object before the object
reaches the bottom is given by the differential equation dV/dt + V/10 = 32, ft/sec. What is the velocity of
the object one second after it falls?
A. 40.54 B. 38.65
C. 30.45 D. 34.12
21. Evaluate sin4x if sinx = 2.
A. j42
B. 33
C. 73
D.-j56√3
22. Obtain the differential equation of the family of circles with center on the y-axis.
A. (y)3-xy" + y' = 0
B. xy" (y')^3-y' = 0
C. y"-xyy" + y = 0
D. (y)+(y")²+xy = 0
23. The product of the slopes of the equation of 2 lines is -1 One of the line is
A. Non-intersecting
B. Parallel
C. Perpendicular D. Skew
24. Two perpendicular chords of a circle are cut thru 2 and 6 and the other chord at 3. Find the radius of
the circumscribing circle?
A. 4 B. 3
C. 7 D. 5
25. A triangular corner lot has perpendicular sides of lengths 90m and 60m. Find the dimensions of the
largest rectangular building that can be constructed on the lot with sides along the streets. 25.
A. 45mx30m B. 45mx75m
C. 75mx25m D. 18mx75m
26. Postal regulations require that a parcel post package to be no greater than 3m in the sum of its
length and girth (perimeter of the cross section). What is the volume in cu.m of the largest package
allowed by postal regulations if the package is to be rectangular in shape and has square ends? 26.
A. 3 cu. m B. 2 cu. m
C. 1/3 cu. m
D. 1/4 cu. M
27. Evaluate the integral of x³dx over(e^x-1) limits from zero to infinity. 27.
A. 2(4pi - e)/3 B. (pi^4)/15
C. 19-4pi D. (pi^2)/6
28. What equation best represents the statement Rodel (R) has 3 candies and ate one.
C. R=3-1
A. R=3R-R
B. R 3/R-1/R
D. R=3R-1
29. Find the angle between adjacent faces of a regular octahedron
C. 35.340
D. 1050
A. 45.50
B. 109.470
30. Find the general solution of (D2-D + 2)y = 0.
A. y = C,e-²+ Ce¹
C. y = C,e Acos() + Bsin()]
D. y = C,e Acos()t + Bsin()]
31. Ben gives 1/4 of his candies to Charlie. Charlie in turn gave 1/5 of what he received to Dennis. If
Dennis received 2. How much candy has Ben?
A. 10
C. 30
D. 40
B. 20
32. Evaluate tan3x if sinx = 2.
A. 115 √3
B. -j26 √3/45
D. 156 √3
C. 6√3
33. What is 75% of 450?
A. 600
C. 337.5
D. 325
B. 250.4
34. Jose is 5' 6' in height while Pedro is 6' 5" in height. Pedro is
taller than Jose?
A 9 inches B. 13 inches
C. 11 inches D. 12 inches
35 Evaluate the integral of sink+cosx, from 0 to pi/2
A 1/60
C. 1/40
B. 1/20 D. 1/50
36 Evaluate the expression: 12[cos45+ jain45) + 3[cos15+ jsin15)
C. 4√2-j3
A 4√2+j3
B.2√3 +j2
D. √3-j2
37. What is a solution of the first-order differential equation y(h+1) = y(h) +5
A y(h)=h-5/h
C. y(h) C-h, C is a constant
D. y(h) = 20+ 5h
B. y(h) 5+ (1-5y-h
38. Find the area in [cm] of a regular octagon inscribed in a circle of radius 10cm.
A 283
C. 298
B. 289
D. 238
39. Find the general solution of dy/dx = ysecx.
A. y=C (secx+ tanx)
C. y= Insecx+C
D. y=- InCcosx
B. y secxtanx = C
40. Find the change in volume of a sphere whose diameter increased from 4 in by 0.1in.
A 2.5133 B. 2.6282
C. 2.5766 D. 2.4967
41. The sides of a right triangle are in arithmetic progression. The sides of a triangle are
A. 2, 4, and 6
B. 4, 6, and 8
C. 3, 4, and 5
D. 5, 7, and 9
42. The area bounded by the curve y=x and the line x-4=0
A. 11 B. 31/3
C. 10 D. 32/3
43. Find the volume generated by rotating a circle x²+y²+6x+4y+12=0 about the x-axis..
A. 6pi^2
D. 5
44 What is the value of log to base 10 of 1000 33
A. 10.9
C. 99
D. 9.5
B. 999
45. Find the limit of (x-4)/(x-2) as x approaches 2. A. 2
C. O
B. 4
D. indeterminate
46. Bobby is two years younger than twice as old as Ellen. The sum of two times the age of Bobby and
three times the age of Ellen is 66. How old is Bobby?
A. 10 B. 12
C. 18
D. 15
47. Carmela gives 1/4 of her cookies to Charly. In turn Charly gave 1/5 of what he received to Dennis. If
Dennis received 2. How many cookies has Carmela?
A. 50 B. 20
C. 30
D. 40
48. 120 is 20% of what number?
A. 240
B. 480
C. 60
D. 600
49. If logx 10= 0.25, what is the value of log10 X?
A. 2
B. 4
C. 6
D. 8
50 A wheel 5 feet in diameter rolls down an inclined plane 300 with the horizontal. How high is the
center of the wheel when it is 5 ft. from the base.
A. 5 ft.
B. 3 ft.
C. 4 ft.
D. 2.5 ft.
51. What is the curve of r = 6?
A. line
B. parabola
C. circle
D. ellipse
52. What conic section, B2-4AC = 0?
A. Circle
C. Parabola
D. Hyperbola
B. Ellipse
53. Jose is 5' 11" in height while Pedro 6' 5" in height. Pedro is taller than Jose.
A. 8"
C. 1'6"
B. 6"
D. 1'
54. A 3-4-5 triangle is inscribed in a circle. Find the diameter of the smallest circle that can circumscribe
it.
A. 6
C. 8
B. 5
D. 10
55 14.5 is 29% of what number?
A. 51.667
B. 48.333
C. 4.205
D. 50.0
56 A circle with center at the origin has a radius of 5. Find the equation of a parabola opening to the
right that has its vertex on the circle and crossing the points of intersection of the circle and y-axis.
A. 5x+25=y
C. 5y+ 55 x
B. 5x-25-y
D. 5y-25= x²
57. Find the ratio of the angles of a triangle if the product of their sines is maximum.
A. 1:1:1
C. 1:1:2
D. 1:2:3
B. 1:2:2
58. Find the area between x²-4x+y-40 and 3x²-12x+2y-8=0
A 40/3
B. 64/3
D. 32/3
C. 16/3
59. Evaluate sin (A + B); sin A=-3/5 quad 4; cot B=4 quad 3.
A. 8/5 √17
C. - 16/5 √17
B. 16/5 17
D. -8/5 √17
60. What is the coordinate of the vertex of the curve y 2 = 8x?
A 0,0
C. 2, 0
D. 8, 0
B. 0, 2
61. What is the coordinate of the focus of the curve y 2 = 8x?
A. 0, 0
C. 2,0
D. 8, 0
B. 0,2
62. Find the limit
X->2
X-2
x^2+3x-10
A. 1/8
B. 1/6
C. 1/5
D. 1/7
63. Evaluate sin3x if sinx = 2.
A. 4
C. 16
D. -26
B.-3
64. What is the equation of the tangent line of the circle x² + y² = 5 thru (1, 2)
A. x+2y-5=0
B. 5x-8y+11=0
C. 3x-4y+5=0
D. 2x-3y+4=0
65. Given the tangent lines, x + 2y -5=0 at (3, 1) and 2x-y-10=0 at (4, -2) of a circle. Find the
equation of the circle.
A. (x-4)+(y-1)=1
C. (x+1)² + (y +2)² = 25
D. (x-11)²+(y-2)² = 65
B. (x-2)+(y+1)=5
66. The distance of a point from a pole is called
A. abscissa
B. y-intercept
C. x-intercept
D. radius vector
67. The equation |z-3|+|z+3| = 10 represents what kind of a curve?
A. Parabola
B. Ellipse
C. Hyperbola
D. Circle
68. Evaluate sin^5x cos^3x dx
A. 2.3873
B. 4.0493x10-9
C. 0.04167
D. 0.1524
69. The distance of a point from the y-axis is called
A. abscissa
C. x-intercept
D. ordinate
B. y-intercept
70. The distance of a point from the x-axis is called
A. abscissa
C. x-intercept
D. ordinate
B. y-intercept
71. What is the centroid of a semi-circular area of radius R?
A. 2R/T
B. 4R/T
C. 4R/3π
D. 3R/8
72. What is the centroid of a hemisphere of radius R?
A. 2R/T B. 4R/T
C. 4R/3π
D. 3R/8
73. Evaluate the double integral of dx dy/(x - y) with the outer limit 2y to 3y and inner limit 0 to 2.
A. In2
C. In3
D. In4
B. In1/2
74. What is the equation of the circle that passes thru the vertex and latus rectum of the curve y^2=8x?
A. (x-4)2 + y² = 20
B. (x-5)²+ y² = 25
C. (x-2)2 + y² = 16
D. (x-3)2 + y² = 17
75. Find the moment of inertia with respect to the x-axis of the area bounded by the parabola y^2=4x
and the line x = 1.
A. 2.03
C. 2.13
B. 2.33
76. What is the maximum rectangular area that can be fenced in 20 ft using two perpendicular corner
sides of an existing wall?
C. 100 ft 2
D. 120 ft 2
A. 310 ft
B. 250 ft 2
77. Find the area enclosed by the lemniscate of Bernoulli r = a cos 20.
C. a^2 D. a 2/3
78. A hand soap manufacturer introduced a new liquid, lotion-enriched, antibacterial soap and
conducted an extensive consumer survey to help judge the success of the new product. The survey
showed 40% of the consumers had seen an advertisement for the new soup, 20% had tried the new
soap, and 15% had both seen an advertisement and tried the new soap. If a randomly selected
consumer has seen an advertisement for the new soap, what is the probability that this consumer has
tried the new soap?
A. 72%
C. 40%
D. 37.5%
B. 25%
C. n-6
80. Which of the following is equal to n^-4* n^4?
A. 1
B. n
D. 0
81. Jason made 10 two-point baskets and 2 three-point baskets in Friday's basketball game. He did not
score any other points. How many points did he score?
A. 22
B. 12
C. 26
D. 24
81. Evaluate √1- cos xdx
A. 2√2 cos x + C
B. -2√2 cos x/2 + C
C. - 2√2 cos x + C
D. 2√2 cos x/2 + C
82. If the graph of y = f(x) is transformed into the graph of 2y-6=-4f(x-3), point (a, b) on the graph
of y = f(x) becomes point (A, B) where A and B are expressed as :
A. A= a+ 4, B = 2b+3
C. A a +3, B = -2b+3
D. A= a +2, B = 2b-3
B. A a +6, B = 2b +6
83. From past experience, it is known 90% of one-year old children can distinguish their mother's voice
from the voice of a similar sounding female. A random sample of 20 one-year olds are given this voice
recognition test. Find the probability that all 20 children recognize their mother's voice.
D. 0.122
A. 0.222
C. 1.000
B. 0.500
84. Find the radius of curvature of the parabola y² - 4x = 0 at the point (4,4).
C. 25.36
A. 22.36
B. 20.36
D. 27.36
85. Find all differential equation of the family of lines passing through the origin.
C. ydx + x dy = 0
A. x dx + y dy = 0
B. x dy - y dx = 0
Dy dx-x dy = 0
86. Find the point on the line 3x + y + 4 = 0 that is equidistant from the points (-5, 6) and (3,2).
https://www.toppr.com/ask/question/find-the-point-on-the-straight-line-3xy40-which-is-equidistantfrom-the-points-56/
A. (-2,2)
B. (-2,3)
C. (-2,-2)
D. (2,2)
87. Find all real solutions to the logarithmic equation In (x^2-1) -In (x − 1) = ln 4.
https://www.toppr.com/ask/question/find-all-the-real-solutions-to-thelogarithmicequationlnx21lnx1ln4/
A. 0 87.
C. 5
B. 3
D. 2
88. Gabby cuts a piece of rope into three pieces. One piece in 5 inches long, one piece is 4 inches long,
and one piece is 3 inches long. The longest piece of rope is approximately what percent of the original
length before the rope was cut?
A. 55%
C. 33%
D. 50%
B. 42%
89. What is the result when 6ab + 3b is subtracted from -6ab - 3b?
C. 18ab
A. 12ab+6b
B. -12ab-6b
D. O
Find 60% of 390.
A. 134 B. 190
C. 180 D. 243
Find the area bounded by y = x^3, the x-axis and the lines x=-2 and x = 1.
A. 0.43 B. 2.45
C. 1.25 D. 4.25
The table shows the number CD players sold in a small electronics store in the years 1989-1999 as
follows; 92. 22
YEAR 1989
CD PLAYERS SOLD
545 675
1990 1991
665
1992
665
1993
600
1994
550
85.
86.
89.
90.
91.