Mathematics and Surveying 2010-2012 zherrinore 1) after the price of petrol went up by 10%, pedro reduced his petrol consumption by the same percent. By what percent would his petrol bill be changed? a) decrease by 10% b) Decrease by 1% c) Increase by 1% d) increase by 5% e) Increase by 2% 2) A square of side A is inscribed in a circle, find the area between the circle and the square a) a2(π/2-1) b) ¼( π-1)a2 c) (π-1)a2 d) (π/4-1)a2 e) (π+2)a2 3) It is between 3 and 4 oclock, and in twenty minutes, the minute hand will be as much after the hour hand as it is by now behind it. What is the time? a) 3:05 4/11 b) 3:04 4/11 c) 3:06 4/11 d) 3:07 4/11 e) 3:08 4/11 4) If 1/x, 1/y, 1/z are in A.P. find the value of y a) x+z/xz b) 2xz/x+z c) z-x d) z/1(x+z) e) 2x+2z 5) the quotient of a two digit number divided by the sum of its digit is 4. if the number is subtracted from the sum of the squares of its digits, the difference is 9, find the number a) 36 b) 33 c) 30 d) 28 e) 34 6) the length of a side of rhombus is 5cm. if the shorter diagonal is of length 6cm, find the area of the rhombus? a) 32 b) 24 c) 28 d) 36 e) 12 7) there are three short questions in math exams. for each question, 1 mark will be awarded for a correct answer and no work for a wrong answer. if the probability that mary correctly answers a question in a test is 2/3, determine the probability that mary gets 2 marks in the test. a) 8/27 b) 2/9
c) 1/27 d) 5/9 e) 4/9 8) Maria is 36 yrs old. Maria was twice as old as Anna was when Maria was as old as Anna is now. how old is Anna now? a) 22 b) 25 c) 24 d) 23 e) 4 9) the standard deviation of two numbers x and y, where x>y is. a) x+y/2 b) x2+y2/2 c) x-y/2
10)
11)
12)
13)
d) √ e) x2-y2/2 determine the length of the line in meters if there were 3 tallies, 8 pins and the last pin was 9m from the end of the line. the tape used was 50 m. long a) 1875 b) 1713 c) 1584 d) 1236 e) 1909 this sides of a square lot having an area of 2.25 hectares were measured using a 100 m tape that was .04 m too long. compute the error in the area in sq. meters a) 18 b) 10 c) 15 d) 13 e) 16 if 1/x=a+b and 1/y=a-b find x-y a) 2b/b2-a2 b) 2a/b2-a2 c) b2+a2/b d) b2-a2/a e) b2+a2/a one side of a field measuring 75 meters is parallel to the center line of the adjoining road. the other two sides which are both perpendicular to the road are 125 and 150 m respectively. if the field is to be divided into two parts of two equal areas by another perpendicular line, determine the length of the line. a) 129.415 b) 125.415 c) 145.544 d) 138.067 e) 156.354
Mathematics and Surveying 2010-2012 zherrinore 14) in what ratio must tea costing 24 per kg be mixed with tea costing 34 per kg so that a profit of 20% is made by selling the mixture at 36 per kg a) 2:3 b) 3:2 c) 1:2 d) 5:3 e) 4:6 15) a line 100 m long was paced by a surveyor four times with the following data, 142, 145, 145.5, and 146. then another line was paced for four times again with the following results, 893, 893.5, 891, and 895.5 a) 635.685 b) 617.236 c) 654.158 d) 628.424 e) 689.598 16) in a two-peg test method od a dumpy level, the following observations were taken, Instrument Set up near A 1.505
Instrument Set up near B .938
Rod reading on A Rod reading 2.054 1.449 on A if the line of sight is not in adjustment, determine the correct rod reading on A with the instrument still set up at B a) .919m b) .526 c) .825 d) .665 e) .715 17) transform r2 sin 2θ=6 into Cartesian coordinates a) xy=2 b) xy=3 c) xy=4 d) xy=5 e) xy=6 18) the height of the cone is U. it contains water to a depth of 2/3H. determine the ration of the volume of water to that of the cone a) 19.27 b) 26.27 c) 8:27 d) 1:27 e) 5:27 19) a boy at 8:00 am started to walk at a rate of 4 km/hr for 2 hrs and 45 mins, after which a man followed to overtake him with a rate of 4.5 km/hr for the first gour, 4.75 km.hr for the second hour and so on, increasing his rate by a quarter of km each hour. find the time when the man overtook the boy a) 6:45 PM
20)
21)
22)
23)
24)
25)
26)
b) 7:45 PM c) 8:45 PM d) 9:45 PM e) 6:25 PM let f(x)=(x+3)(x-4)+4. when f(x) is divided by (x-k), the remainder is k. find k a) -2 or 4 b) -1 or 3 c) -3 or 5 d) -1 or 2 e) -1 or 6 the daily wage of a technician and an apprentice are in the ratio 2:1. in a day a technician has to work 8 hours but an apprentice only in 6 hrs. the hourly wages of a technician and an apprentice is in a ratio a) 4:3 b) 8:3 c) 2:1 d) 3:2 e) 5:3 a circular rotunda passes through the three points A(-4,3), B(2,1) and C(-2, -5). determine the radius of the circular rotunda. a) 5.58 b) 3.26 c) 6.15 d) 7.15 e) 4.27 find the equations of the tangents to the circle x2+y2=5 which make an angle 45 degrees with the xaxis a) x+y=±√10 b) x-y=±√10 c) x-y=√10/2 d) x2+y2=±√10 e) x2-y2=±√10 the point of intersection of the perpendicular bisector of the sides of the triangle a) circumcenter b) centroid c) eulers line d) circul circle e) non of these the angle of a sector is 60° and the radius is 2 cm. what is the area of the section a) 4/3 π b) 60/ π c) 2/3 π d) 120 e) 150 the table shows the number of students in two classes of a school and their average marks in a test. Class No of students Average mark a 40 65 b x 50
Mathematics and Surveying 2010-2012 zherrinore if the average mark of the two classes is 58, find x a) 35 b) 42 c) 28 d) 32 e) 52 27) using polar coordinates, find the polar equation of the path of a point which is equidistant from the points whose polar coordinates are (2a, 0) and (a. π/2) a) r=3a/2(2cosθ-sinθ) b) r=3a/ (2cosθ-sinθ) c) r=3a/2(2cos2θ-sin2θ) d) r=3a/(2cosθ-sinθ) 28) a fruit vendor goes to market to buy fruits for resale at her store. she spends half her money for mangoes, and 1/3 of which remains for bananas. she spends P150 for other fruits and still has P200 left from the amount she originally had. how much money did she have at the start? a) 1150 b) 1250 c) 1050 d) 1110 e) 1025 =y find the value of y a) y=x log10x b) y=x2log10x c) y=x2 log10(log10x) d) y=x log10(log10x) e) y=x log10 30) a hawker sold 100 egss. 80 of them were sold at a profit of 30% while the rest were sold at a loss of 40%. what is the percentage gain or loss on the whole stock? a) a gain of 16% b) a gain of 10% c) a loss of 8% d) a loss of 10% e) a loss of 5% 31) the capacities of two hemispherical tanks are in the ratio of 64:125. if 4.8 kg of paint is required to paint the outer surface of the smaller tank. then how many kg of paints would be needed to paint the outer surface of the larger tank? a) 6.4 b) 5.3 c) 8.6 d) 9.6 e) 7.5 32) the bearing of a line from A to B was measured as S. 16°30’ W. it was found that there was local attraction at both A and B and therefore a forward and backward bearing were taken between A and a point C which there was no local attraction. if the
33)
34)
35)
29)
x
36)
37)
38)
bearing at AC was S 30°10’E and that of CA was N28°20’W, what is the corrected bearing of AB? a) S 18 24’W b) S 18 15’ W c) S18 25’W d) S 18 22’W e) S 18 20’W In a throw of two dice, what is the probability of obtaining a total of 10 or 12? a) 1/6 b) 1/9 c) 1/12 d) 1/8 e) 1/10 the wheel of a car revolves n times while the car travels x km. thr radius of the wheel in cm is equal to ________ a) 50000x/πn b) 2πnx c) 20000x/πn d) 5πnx e) 30000x/πn a Quonset 18m long has a parabolic cross section. its base is 12 m and its height at the center is 6m. a flat horizontal ceiling 3.70 m above the base is to be constructed inside the hut. if the ceiling will consist of wooden boards 25 mm thick, how many cubic meters of ceiling boards will be required assuming that 10% of the materials is wasted during construction? a) 4.524 b) 2.365 c) 5.458 d) 3.715 e) 6.326 find the sum of the series 1+3+5+7+...+(2n-1) a) (2n-1)2 b) n2+2n c) ½(n2+2n) d) n2 e) n+2n a conical funnel is 20 cm wide at the top and 50 cm dee. liquid is flowing in at 200 cm3/sec and flowing out at 30 cm3.sec. find the speed with which the liquid surface is rising when it is 25 cm deep. a) 9.715 b) 5.112 c) 6.152 d) 7.485 e) 8.658 a polygon having 1000 sides a) quindecagon b) chillagon c) nonagon d) enneagon
Mathematics and Surveying 2010-2012 zherrinore
39)
40)
41)
42)
43)
44)
45)
e) icosagon the line kx+(3-k)y+3(1=k) passes through a fixed point P for a ny value k, find the coordinates of P a) 3,2 b) 4,1 c) 4,2 d) 3,1 e) 2,2 find the equation of the sphere whose center is (-2, 4, -3) and which passes through (5, -1, 3) a) x2+y2+z2+4x-8y+6z-81=0 b) x2+y2+z2+2x-4y+3z-49=0 c) x2+y2+z2+6x-12y+8z-81=0 d) x2+y2+z2+3x-5y+6z-46=0 e) x2+y2+z2+5x-5y+6z-50=0 ABCD is a parallelogram in clockwise direction. A line QPD as drawn with point P along the side AB. the line QPD is the bisector of angle ADC and angle QPB is 40°. find the angle BCD. point Q is outside the parallelogram a) 80 b) 60 c) 100 d) 120 e) 40 determine the equation of two lines passing through (-2,4) and forming with the axes of a triangle with area 9 a) x+y=3, 8x+y+12+0 b) x+2y=6, 6x+y+13+0 c) x+3y=6, 8x+y+15+0 d) x+y=6, 8x+2y+12+0 e) x+2y=6, 8x+y+12+0 a certain printer charges P100 for every thousand books per page. if only 2000 books are printed. for every thousand in excess of 2000 it will charge 2 less. thus if 3000 are ordered, the price is 98/thousand, for 4000 the price is 96/thousand, etc. find the total number of books it should print for maximum income? a) 25000 b) 26000 c) 24000 d) 27000 e) 28000 AOB is a sector of a circle having a radius of 4 cm.
46)
47)
48)
49)
50)
51)
a) x2+y2+z2-10x-2y-4z=0 b) x2+y2+z2-12x-y-2z=0 c) x2+y2+z2-15x-5y-6z=0 d) x2+y2+z2-13x-3y-8z=0 e) x2+y2+z2-11x-4y-2z=0 if (-2, -4) is the midpoint of (6, -7) and (x,y), determine the value of x a) 9 b) 8 c) -10 d) -15 e) 10 (x-4)2+y2=25 is the equation of a circle and (1,4) is the point at one end of the diameter. find the coordinate of the ether end of the diameter a) 6,-4 b) 5,-3 c) 8,-3 d) 4,-5 e) 7,-4 there a re 4 white balls and 6 red balls in a box, if two balls are taken out successfully, the first ball is not replaced what is the probability that the balls are of different colors. a) 7/15 b) 3/17 c) 8/15 d) 5/27 e) 6/19 a right circular cone is divided into 3 portions A,B and C by planes parallel to the base. the height of each portion is H and the base radius of the cone at A is r. determine the ration of the volume of A to that of B. a) 1/7 b) 7/19 c) 1/3 d) 3/5 e) 3/10 A stone contractor has his quarry 10 km from P, the nearest point on a straight railway. The railroad company agrees to haul his stone to S 30 km along the straight track from P for 5 centavos per ton per kilometre. If the cost of hauling by car from quarry to the railroad track is 12 centavos per ton per kilometre, to what point at then railway shoul he haul his stone so that the cost of transportation from the quarry to s be minimum a) 2.36 b) 4.59 c) 3.48 d) 5.58 e) 6.28 Another term for quadrilateral or quadrangle a) Hexagon
Mathematics and Surveying 2010-2012 zherrinore
52)
53)
54)
55)
56)
57)
b) Tetragon c) Pentagon d) Trapezium e) Trapezoid 5,2,-1 ...are in A.P. find the sum of the progression from the 11th term to 20th term a) 425 b) 235 c) 525 d) 485 e) 385 A steel girder 8 m long is moved on rollers along a passageway 4.0 m wide and into a corridor at right angles to the passageway. Neglecting the width of the girder how wide must the corrider be? a) 2.6 b) 2.8 c) 1.8 d) 2.2 e) 3.25 Water flows through a pipe of internal diameter 4 cm at the rate of 60 cm/sec to a rectangular tank whose base has a dimension of 180 cm x 264 cm. Find the time in seconds required to raise the water level by 2cm use π=22/7 a) 190 b) 126 c) 93 d) 64 e) 156 The top of a ladder 6 m long rests on a vertical wall while the bottom rests on a horizontal floor. If the to slides down at a constant rate of .60 m/sec determine the rate at which the angle the ladder makes with the horizontal changes when the lower end is 3.6 m from the wall a) -1/4 rad/sec b) -1/7 rad/sec c) -1/5 d) -1/8 e) -1/6 Prietto and ancheta at a distance of D km apart start simultaneously and travel to meet each other. If their speeds are x kph and y kph, find the time taken in hours before they meet. a) 2D/x-y b) D/x-y c) D/x+y d) 2D/x+y e) D/xy One ship was sailing north at 8 knots, another cast at 10 knots at 10:00 AM, the second crossed the course of the fisrt at the point where the first was at 8:00 A.M. at what rate was the distance between the ships changing at 9:00 A.M
58)
59)
60)
61)
a) -4.48 knots b) -5.48 c) -3.28 d) -2.81 e) -1.23 A ship anchored in 7.2 m of water. The anchor chain passes through an opening in the ships bow 3.6 m above the water surface. If the chain is pulled in at the rate 75 mm/sec, how fast is the ship moving when 18 m of chain are out? a) 90.47 mm/sec b) 85.44 c) 92.15 d) 96.57 e) 93.75 A boy 1.2 m tallis walking directly away from a lamp post at the rate of .90 m/sec. If the lamp is 6m above the ground, find the rate at which his shadow is lenghthening a) .562 b) .415 c) .158 d) .225 e) .336 If the surface area of a sphere increases by 21%, its volume is increased by? a) 13.31% b) 33.1% c) 30% d) 34% e) 23.2% Find the minimum distance from the point (6,0) to the parabola y2=8x a) 4 2 b) 3 2 c) 2 2 d) 4 2 2
e) 5 2 62) In a group of 70 students, 35 are taking mathematics, 25 are taking design and 15 are taking both subjects. If a student is chosen at random, what is the probability that he is taking design but not mathematics? a) 2/5 b) 1/7 c) 3/5 d) 2/7 e) 3/7 63) A triangle with all interior angles less than 90 a) Acute triangle b) Obtuse triangle c) ]right triangle d) Scalele triangle e) Scalene
Mathematics and Surveying 2010-2012 zherrinore 64) Find the length of the common chord of two circles of radii 25 cm and 26 cm respectively if the distance between their centers is 17 cm a) 48 b) 45 c) 56 d) 62 e) 50.12 65) The surface areas off two spheres are 24 cm2 and 96 cm2 respectively. Find the ration of their volume a) 1/6 b) 1/5 c) ¼ d) 1/8 e) 1/9 66) The sum to the nth term of a sequence 8is given by S(n)=n(n-3). What is the nth term of the sequence? a) 3n-2 b) 2n-4 c) 2n+2 d) 2n+4 e) 3n+2 67) The mark price of a chair is x pesos, 30% of this price is the profit. If the chair is sold at a discount of 20% compute the net profit a) .o9x b) .24x c) .10x d) .04x e) .08x 68) Find the length of the common external tangent to two circles of radii 5cm and 12 cm respectively. If the distance between their centers is 25 cm a) 26 b) 28 c) 20 d) 22 e) 24 69) Peter bought two cars, one for 60000 and the other for 40000. He sold the first at a gain of 10n% and the second at a loss of 12%. What is the total percentage loss or gain? a) 6%loss b) 2.5%gain c) 1.2%gain d) 2$loss e) 1.8%gain 70) A chord is 24cm long and its midpoint is 8 cm from the midpoint of its shorter arc. Find the radius of the circle a) 15 b) 12 c) 10 d) 14 e) 13
71) Simplify (1/sinϴ-1/tanϴ)(1+cosϴ). a) Cos ϴ b) sinϴ+tanϴ c) cosϴ+1 d) tan ϴ e) sinϴ 72) a cyclic uadrilateral ABC is inscribed in a circle ha ing a diameter C .AB is arallel to C . f the angle AB is 40:, find the angle A B. a) 20 b) 10 c) 12 d) 30 e) 25 73) One side of a parallelogram is 10 cm and its diagonals are 16 cm and 24 cm respectively. Find its area a) 169.4 b) 146.1 c) 133.7 d) 158.6 e) 173.2 74) Two circles of equal radii r intersect each other. If the ceneter of the circle lies on the circumference of the other, find the perimeter of the resulting figure a) 7/4πr b) 3/8πr c) 4/7πr d) 8/3πr e) 4/9πr 75) The sides of a triangle are 5,7 and 10 respective;y, find the radius of the circumscribed circle a) 5.39 b) 4.56 c) 6.75 d) 7.45 e) 3.32 76) ow many sides has an e uiangular olygon if each of its interior angles is 165:? a) 24 b) 22 c) 20 d) 26 e) 30 77) The nth term of an A.p. is 3n+1 where n is a natural number. The number of terms of the progression each of which is less than 82 is a) 78 b) 6 c) 8 d) 27 e) 52 78) ABCD is a rectangle. The length of the diagonal is 30 cm and the acute angle between them is 50:. Find the length of the shortest side of the rectangle
Mathematics and Surveying 2010-2012 zherrinore
79)
80)
81)
82)
83)
84)
85)
a) 13.42 b) 10.42 c) 9.56 d) 8.15 e) 12.68 The following are the height in cm of 9 boys, 190.180,180,110,130,100,200,150 and 270. What is the median of the distribution a) 130 b) 100 c) 110 d) 180 e) 150 The sum of three consecutive odd integers is 75. Find the largest integer a) `32 b) 19 c) 42 d) 38 e) 27 A semi circle of radius 14 is formed by a piece of wire. If it is bent into a re4ctangle with one side equal to x and the other side, find the value of x a) 14.5 b) 17.5 c) 12.5 d) 16.5 e) 18.5 Z varies directly as x and inversely as y2. If x=1 y=2 and z=2. Find z when x=3 and y=4 a) 2/3 b) 3/2 c) ¾ d) 4/3 e) ½ Find the side of a regular octagon inscribed in a circle of radius 10cm a) 4.15 b) 5.69 c) 6.12 d) 7.65 e) 3.45 1/3, 1/33, 1/35......is a GP what is the sum to infinity? a) 9/10 b) 3/8 c) 9/8 d) 5/8 e) 3/10 A sector of a circle has a radius R=9cm. The sector has a central angle of 60:. A small circle is inscribed in a sector. Determine the radius of the small circle a) 5 b) 3 c) 4 d) 2
86)
87)
88)
89)
90)
91)
e) 6 The length of a side of a square is increased by 100%. Its perimeter is increased by: a) 100% b) 400% c) 25% d) 200% e) 50% Mary is three times as old as ricky. Three years ago, she is four times as old as ricky. Find the sum of their ages. a) 38 b) 30 c) 36 d) 42 e) 40 A piece of wire of length 52 cm is cut into 2 parts. Each part is then bent to form a square. It is found that the total area of the two squares is 97cm2. Find rthe difference in length of the sides of the two squares. a) 5 b) 8 c) 4 d) 10 e) 12 The areas of the three faces of a cuboid are 10, 14 and 35. Find the volume of a cuboid? a) 140 b) 49 c) 10 d) 350 e) 240 A class of 40 students took examination in English and Chinese. If 30 passed in English, 36 passed in Chinese and 2 failed in both subjects, determine the number of students passing in both subjects a) 24 b) 18 c) 26 d) 28 e) 32 Four military recruits whose respective shoe sizes are 7,8,9, and 10 report to the supply clerk to be issued boots. The supply clerk selects one pair of boots in each of the four required sizes and hands them at random to the recruits. What is the probability that all recruits will receive boots of incorrect sizes? a) .38 b) .25 c) .45 d) .61 e) .75
Mathematics and Surveying 2010-2012 zherrinore 92) Three spheres has radii of (r+1), r, (r-1) respectively. Find the total volume of the three spheres. a) (r2+2r-3.5)π b) 4π(r3+2r) c) 3π(r3+r) d) R3+r-2)π e) 2π(r+2r) 93) The obelisk of a certain rizal monument rises to some height above the dais, the angles of elevation of the top and bottom of the obelisk from the two stations A and B on the same horizontal plane as the base of the dais are 45: and 30: res ecti ely, the corresponding horizontal angles to the common center of both dais and obelisk from the ends of the base line a-b 2.5m long are 75:and 60: res ecti ely. Find the height of the obelisk a) 10.86 b) 9.15 c) 8.75 d) 7.46 e) 15.26 94) A wooden cone of altitude h is to sawed into two parts of equal weight. How far from the vertex should the cut parallel to the base be made? a) .336h b) .415h c) .648h d) .526h e) .794h 95) Find the volume of a right circular cone whose base radius is 8cm and whose altitude is 15 cm a) 260π b) 240π c) 280π d) 320π e) 300π 96) The sum of the first n terms of a sequence is 2n=2-4. Find the value of the 6th term of the sequence a) 142 b) 162 c) 128 d) 158 e) 136 97) A job can be finished by peter alone in x dats or by jack alone in y days. If peter and jack work together, the number of days they will take to finish the job is a) x/x+y b) y/x+y c) x+y/xy d) xy/x+y e) x+y/y 98) from a tower 100 m high, two objects A and B in the plane of the base are found to have angles of depression of 15 and 12 degrees respectively. The
horizontal angle subtended by A and B at the foot of the tower is 48:. Find the distance from A to B. a) 345.25 b) 305.56 c) 324.72 d) 354.49 e) 331.15 99) The distance between the points (sinϴ, cos ϴ) and (cosϴ, -sinϴ) is equal to a) 2 b) c) 2sinϴ d) 2 e) 2cosϴ 100) The number of cars entering a toll plaza on a bridge during the hour after midnight follows a poisson distribution with a mean of 20. What is th probability that 17 cars will pass throght the toll plaza during that hour on any given night? a) .12 b) .16 c) .23 d) .076 e) .48 1. a rectangular sheet of paper measures 16 cm. x 24 cm. circles are to be cut from the paper, each with a radius of 4 cm. what is the max. no. of circles that can be cut from the given paper. 2. a pyramid has a square base of side 8 cm. and is 20 cm. high. if it is cut parallel to and 7 cm. from the base, determine the ratio of the volumes of the smaller pyramid formed to the original pyramid. 3. a spherical sector has a central angle of 30° at the center of the sphere having a radius R. find the radius R if the volume of the segment is 231 cu.m. 4. the diameter of two spherical bearings are in the ratio 2:5. what is the ratio of their volume? 5. a frustum of a sphere has the following diameters 12.6 cm. and 20.4 cm. the frustum is 3.6 cm. thick. A. find the volume of the frustum of the sphere. B. fine the radius of the sphere. C. find the area of the zone thus formed. 6. a triangle has the following given parts: A = 0.65, B = 0.75, C = 78.9° A. compute the value of c. B. compute the value of b. C. compute the value of a. 7. from his office window of a building, a man tried to make vertical angular measurements of a utility tower
Mathematics and Surveying 2010-2012 zherrinore in a distant field. using crude instruments, he measured the angle of depression of the foot of the tower and recorded it be 6.4°. he then looked at the top of the tower and calculated an angle of elevation off 42.6°. if the ground is generally level from the foot of the building to the foot of the tower and the man’s eyes was approximately 3.2 m. above the ground, what is the height of the tower?
16. if 8 men can chop down 28 trees in one day, how many trees can 20 men chop down in one day?
8. two instruments were set up at A and B to measure the height of a flagpole. B is 54.1 m. closer to the flagpole, than A and they are all along the same line. if the angle of elevations from A and B are 26.7° and 60.8° respectively, find the height of the flagpole in meters.
19. ab = 1/8, bc = 6 and ac = 3. if all the above statements are true, what is one possible value of abc?
9. a regular pentagon has a side 23.2 cm. long. a certain cross-section is formed by two circles, one circumscribing the pentagon and the other inscribed in it. find the area of the cross section. 10. to determine the height of a distant mountain two observation points were set up at A and B, which is 290 m. closer to but 25 m. lower in elevation than A. The angles of elevations from both points are 24.45° and 35.45° respectively. if the elevation at A is 550.45m., find the elevation of the top of the mountain. 11. two insects fly from the same point but towards different directions. one was flying at a speed of 12.2 m/min., while the other was flying at 17.4m/min. the angle between their fight direction is 84.1°. how many meters are they apart after 2.1 minutes. 12. a triangular lot was surveyed with a steel tape and found to have the following side lengths. 23.56 m., 38.54 m. and 33.40m. determine the angle opposite the 38.54 m. side. 13. two values A and B are related to each other in an inverse manner such that when one increases, the other decreases, always with a constant inverse proportionality, when the value of A is 1200, B is recorded to have a value of 144720. find the value of A when B reaches 256,000. 14. it takes 3 hours and 15 minutes to fly from city A to city B at constant speed. Find how long the journey takes if: A. the speed is 1½ that of the original. B. the speed is ¾ of the original. C. the speed is 3.25 times the original. 15. if 481/N = 2 x 31/N, find the value of N.
17. what is the equation in slope-intercept form of the equation 5x + 2y - 8 = 1. 18. if 2x – 7y = 12 and – 8 + 3y = 2, what is the value of x – y?
20. if xyz = 4 and y2z = 5, what is the value of x/y? 21. a metallic tube has an outside diameter of 8 cm. and an inside diameter of 6 cm. it has a total length of 4 m. what is the total volume of the metal needed to make the tube? 22. a metal sphere weighing 24 kg is melted down and recast into a solid cone which has a base with a radius of 8 cm. the metal used has a density of 8000 kg/m3, 15% is lost in the recasting process. the perpendicular height of the cone is not readily known. what is the diameter of the metal sphere? 23. a loud speaker diaphragm is in the form of frustum of a cone. the end diameters measures 28 cm. and 6 cm. and the vertical distance the ends is 30 cm. the curve surface of the speaker is made of felt composite material. calculate the area of felt composite material needed to cover the curved surface. 24. a metal sphere with a specific gravity of 8000 kg/m 3 originally weighs 24 kg. it underwent a process of recasting and was formed into a solid cone with a base having a radius of 8 cm. assuming 15% of the metal was lost in the procedure, what is the perpendicular height of the new cone. 25. a rectangular block of alloy has the following dimensions: 4.3 cm. by 7.2 cm. by 12.4 cm. it was melted and recast into a frustum of a square pyramid, 10% of the metal being lost in the process. if the end of the frustum are square of 3 cm. and 8 cm. respectively, determine the height of the frustum. 26. a cone has a diameter of 80 mm and a perpendicular height of 120 mm. calculate the volume. 27. a water tank has a cylindrical shape with a diam. of 2 m. and a perpendicular height of 3 m. since it was already old and leaking, it is to be replaced by another tank of the same capacity but in the form of a frustum of a cone. the diameters of the ends of the frustum are
Mathematics and Surveying 2010-2012 zherrinore designed to be 1 m. and 2 m. respectively. what must be its height. 28. the absolute value of x is greater than the absolute value of y. which of the following must be true? 29. a man can run x km in y hours. how long will it take him to run z km.? 30. cokoy can do a job in 1 hour. paul can do the same job in 2 hours and praxy can do the job in 3 hours. how long does it take them to do the job working together? 31. determine the ratio of the area of a circle to the radius of the circle. 32. calculate for the surface area of a frustum of a sphere if the diameter of its ends are 80 cm. and 120 cm. and the thickness is 30 cm. 33. what is a non-zero solution to the equation 2x5 – 30x4 = 0. 34. if the sum of seven consecutive integers is zero, what is the smallest of the seven integers? 35. the area of a park on the map is 500 mm2. if the scale of the map is 1:40000, determine the true area of the park in hectares. 36. a gasoline tank is composed of a cylindrical portion 5 km. long with hemispherical sections attached at each end. the cylinder and hemispheres have the same diam. of 1.2 m. what is the capacity of the fuel tank in liters? 37. if a cone has a height perpendicular to its base is 120 cm. and its base has a diameter of 80 cm. what is its curved surface area? 38. if ab – cde is positive, which of the following must be true? 39. an angle of 125° is subtended by an arc of a circle of radius 8.4 cm.: A. find the length of the minor arc. B. find the length of the major arc. C. find the area of the circle. 40. if f(x) = x5 – 2x2 + 3/x, then f(-1) must be equal to: 41. if f(x) = x(2x), then f(x) should be equal to:
42. a particle is travelling along the x-axis. its position is given by x(f) = 1 – t2 at time t > 0. t + 3 find the instantaneous rate of change of x with res ect to “t” when t = 1. 43. Mario has 4 more hats than alex and half as many hats as Miguel. if the three together have 24 hats, how many hats does Miguel have? 44. a shipment of 3200 items is divided into 2 portions such that the difference between the portions is one half of their average. what is the ratio of the smaller to the larger portions? 45. three distinct positive integers have a sum of 15 and a product of 45. what is the largest of these integers? 46. ohm’s law sti ulates that electric current, while flowing is a fixed resistor is directly proportional to the voltage applied. when 30 volts is applied across a certain resistor, the current which flows through the resistor is 2.4 x 10-3 amperes. Find the following: A. the constant of proportionality between voltage and current. B. the current when the voltage applied is 52 volts. C. the voltage required if a current of 3.6 x 10-3 amperes is required. 47. f(x) = 3x2 – 6x -9/ x2 – x -2 will have a vertical asymptotes at _______. 48. given that lim (1 – Cos x) = 0 then the x x0 lim (3x2 + 5 Cos x – 5) must be equal to: 2x x0 49. find the 10th term of the series: 5, 10, 20, 40. . . . . . . 50. determine the sum to the first 7 terms of the series: 0.25, 0.75, 2.25, 6.75 . . . . . . . . . 51. the first term of a geometric progression is 4 and the 6th term is 128. what is the 11th term? 52. which of the following functions grows the fastest? A. B. C. D.
t(u) = 200 eu h(u) = u100 + u99 g(u) = 4u K(u) = 3u + u3
53. simplify sec2 θ – 1 =?
Mathematics and Surveying 2010-2012 zherrinore D. y + x 54. e aluate ∫ CSC x cot x dx PLEASE CHECK THE BOOK 55. a conical tank is full of water. it has a diameter of 10 cm. find the work done in N,m in pumping all the water our of the top of the tank if it has a depth of 20 cm. 56. a cycling tract is in the form of an ellipse, the axes being 250 m. and 150 m. respectively for the inner boundary and 270 m. and 170 m. for the outer boundary. calculate the area of the track. 57. if fencing cost P8 per meter, find the cost of enclosing an elliptical plot of land which has a major and minor diameter lengths of 120 m. and 80m. 58. Charles law states that for a given mass of gas at constant pressure, the volume is directly proportional to its thermodynamic temperature. a certain gas is contained in a vessel having a volume of 2.25 liters at a temp of 360° K. A. what is the constant of proportionality? B. what is the volume of the gas at 420° K while keeping the pressure constant? C. what is the temperature when the volume is expanded to 2.635 liters? 59. a number line is divided by 10 evenly spaced thick mark. the length between each tick mark equals x, and x is a prime number. what is the total length of the line number. 60. if ab = | a | b | which of the following relation is true. A. a = b (nothing suggest that a =b) (not ok) B. a > 0 and b > 0 (-1)(-1) = | - 1 | -1 | not ok because a > 0 and b >0 C. ab > 0 1(1) > 0 absolute value of any number is > 0 (ok) D. a – b > 0 -1 – (-1) = 0 (not ok) therefore ab > 0 is true 61. if x, y, z and z are integers, and x and y are both even, which of the following could be an odd integer? A. xy +z B. y – xz C. xy + y
62. if ab is positive and cde is negative, which of the following must be true. A. ab – cde > 0 ab – (-cde) > = 0 ab + cde > 0 (ok) B. ab – (cde)(cde) > 0 ab – (-cde)(-cde) > 0 ab – (cde)2 < 0 (not ok) C. ac + de < 0 (not ok D. ab/cde < -1 (not ok) 63. there are 37 applicants for civil engineering aide positions in a construction company, consisting of an odd number of male applicants. if an equal number of male and female engineers shall be hired for gender equality, 3 ladies will left out. how many men applied? 64. if 3 < x < 7 and 5 > x > 2 which of the following best describes. A. B. C. D.
3
65. a music school produced a number of musicians which includes 3 drummers, 4 trumpet players and 5 pianists. how many different jazz trios can be formed from this batch of musicians if each trio consists of a drummer, a trumpet player and a pianist? 66. x, y, r, and t are integers such that xy is negative and rt is positive. if it is not a multiple of 2, then which of the following statements must be true? A. B. C. D.
y is a multiple of 2 xr > 0 x–r<0 xt > 0
67. a certain curve has the equation y = sin A. in comparison to this curve, which of the following has twice the amplitude and half the period. 68. a sphere has a diameter of 32 mm. a frustum of the sphere is created by passing two parallel planes, one 12m mm from the center and the other 10 mm and on the opposite side of it. compute the volume of the frustum.
Mathematics and Surveying 2010-2012 zherrinore 69. a train 180 m. long is chugging along a railroad track going north. along another railroad tract, very near and parallel to the first, another train 100 m. long is trying to overtake the first at 180 km/hr and its tail end is exactly 500 m. ahead of the front of the second train, then find the following: A. how many meters have the first train travelled when the front end of the second train caught up with its tail end? B. how many meters have the second train travelled when its front end caught up with the tail end of the first train? C. how many seconds would have elapsed from the initial position when the second train has completely and clearly overtake the first train. 70. a tank contains 100 liters of brine with 60 kg of salt in solution. brine containing 1.0 kg per liter of slat flows into the tank at the rate of 2 liters per minute, kept uniform by stirring, flows out at the rate of 3 liters per minute. find the amount of salt in the tank at the end of one hour. 71. the time taken by a terminal fee collector to collect terminal fees from passengers entering NAIA is an exponential distribution with a mean of 23 seconds. what is the probability that a random passenger will be processed in 25 seconds or more (that is, will take more than 25 seconds). 72. a backhoe component exhibits a negative exponential failure distribution with a mean time to failure of 1000 hours. The maximum operating time such that the reliability remains above 99% is most probably ________ 73. a vehicle velocity check is conducted in a stretch of highway in northern Luzon. On a regular weekday, the speeds were found to have a normal distribution with a mean of 46 and a standard deviation of 3. The daily average speed for the same highway on consecutive normal weekdays were determined by sampling 25 vehicles each day. What is the upper two-standard deviation average speed? 74. LED lamps are packages in boxes of 200. If the production line is known to produce 1.5% defective lamps on the average, determine the probability that a box chosen at random will contain: A. No defective LED lamps. B. 2 defective LED lamps. C. More than 3 defective lamps. 75. solve yn – 4y1 - 12 = 0
1. Given a certain acute angle A, such that cos A is equal to 4/5. What should be the value of Cos (2A)? 2. A circle has its center at (-4, 3) on the xy plane and passes through the point (2, 5). What is the equation of the circle? 3. In a certain city in the Philippines, all seven digit telephone numbers begin with 350. How many telephone numbers maybe assigned to that city if the last four digits should not begin or end in zero? 4. A school chess team has six members, one of which is the team captain. If they are to complete in 6 simultaneous games board 1 to 6, how many arrangement can they make if the team captain should always be in board 1. 5. Given the value of y which is a positive acute angle. It is predetermined that Sin y is equal to 0.50. calculate the value of Sin 2y. 6. Given two angles x and y such that Sin x = 4/5 and Tan y = 5/12. Both angles are in quadrant 1. What is the value of Sin (x + y)? 7. A triangular piece of land has vertices A, B and C and is surveyed producing the following data: A = 30:, C = 50: and AC = 13 m. What should be the length of side AB? 8. From appoint A, the angle of elevation of the top of the pole is measured as 37.1:. Measured from the point B on the opposite side but along the same straight line, the angle of elevation of its top is 35.9:. if points A and B are 124 m. Apart, find the height of the pole. 9. A straight line is defined by the equation y = 3x – 4. Another line is drawn in such a way that the two will never meet even if extended indefinitely. Which of the following maybe the equation of the line. 10. A certain circle has the equation of x2 + y2 + 8x – 2y + 8 = 0. What is the coordinate of the center of the circle? 11. In the order of direct proportionality, x : y as 7.5 : 9.5 on the other hand y : z as 125. : 3.5. if z has an original value of 76.48, find the value of x.
Mathematics and Surveying 2010-2012 zherrinore 12. A sandwich is made by putting cheese and ham between two pieces of bread. You are given five types of cheese, two kinds of ham and three choices of bread. How many different sandwiches can you made?
21. A water tank is in the form of a sphere. It is filled with water to a depth of 30 cm. The inner diameter of the tank is 45 cm., what is the volume of water in it in liters.
13. Given an expression which is (3x)-2 where x is not equal to zero, the equivalent expression is _____.
22. Find the trigonometric function asked of certain angles in standard position of the given points are on the terminal side of the angles.
14. Given an original expression x2 + 9x + 14 + 3x + 6 X2 – 49 x2 + x -56
23. A sub-atomic particle with a mass of 100 ___ has a velocity of (25i + 4j – 5k) m/s, where i, j and k are unit vectors in the x, y and z directions. It hits another atomic particles which is stationary and which as a mass of 40 ___ merging into one composite mass
15. A certain radio wave takes the form of sine curve and is expressed by the equation y = 5 Sin 2x. What is the period of this radio wave? 16. The politicians filed the certificate of candidacies (COC’s) to run for town mayor of Baguio. A survey is taken a month before the election asking 400 registered voters which candidate they will vote for in the elections. The results of the survey are as follows: Candidates votes Garnered A 150 B 130 C 120
No. Of
after the impact and proceeding in the new trajectory. A. What is the x-component of their common velocity after the impact? B. What is the y-component of their common velocity after the impact? C. What is the z-component o their common velocity after the impact? 24. The parametric equation of a function are x = 2 Cos3, y = 2 Sin3 C. Find the equation of the normal at the point where C = π/4. 25. A circle has is center at (-4, 3) on the x – y plane and passes through the point )2, 5). The equation of the circle maybe written in the form.
------400 17. A steel structural member has a mass of 400 kg. If each of its dimensions are reduced by 30%, determine its new mass. 18. Which of the following is the product of an even prime number and odd prime number. Solution: Odd prime number = 3, 5, 11 Even prime number = 2 19. Given an angle A such that (Sec A – 2) (2 SecA – 1) = 0 20. What is the slope of the line which is defined by the equation 4y = 3x + 16.
26. Light bulbs having a mean life of 2400 years and standard deviation of 62 hours are used for a consignment of 4000 bulbs. A. Determine the number of bulbs likely to have a life in excess of 2500 lbs. B. Determine the percentage of bulbs with a life length between 2300 hrs to 2500 hrs. C. Determine the probability of any bulb having a life of 2500 hrs. 27. A certain function variable x is nearly normally distributed with a mean of 6 and a standard deviation of 2. A. Approximately what percentage of the observation in x will be greater than 4. B. Approximately what percentage of the observation in x will be greater than 12. C. Approximately what percentile of the observation in x corresponds to 2.
Mathematics and Surveying 2010-2012 zherrinore 28. A rectangle ABCD is given such that AB is 5 units of measure while BC is 2 units. A solid is to be formed by rotating the rectangle around side AB. Determine its volume in square units. 29. A cylinder has a height of 10 units of measure and is constructed such that its volume numerically equals its lateral surface area. Find its total surface area. 30. In the following mathematical expression, select whether the expression describe is positive, negative, imaginary or can be determine by the given terms. A. The product of 3 negative numbers. -3 (-2) (-2) = 8. Ans. negative B. The quotient of one negative and one positive number. -6/2 = 3. Ans negative C. xy, given that x < 0 and y is not equal to zero. x=5 y=4 xy = -5(4) xy = -20 ans. Negative
C. determine the value of tan (-7π/6) 37. A. If cos x = 3/5 and csc x < 0, find the secant x. B. if tan x = -8/3 and csc x < 0, find the sine of x. C. if sin x = 2/3 and cos x < 0, find the tangent of x. 38. If y inversely proportional to x and y = 15.3 when x = 0.6. A. Determine the coefficient of porpoortionalit. B. Determine the value of y when x = 105. C. Determine the value of x when y = 27.2. 39. A 4 cm. By 6 cm. Rectangular pyramid of perpendicular height 12 cm. What is the volume? 40. A 4.2 cm by 4.2 cm. Square pyramid with a lateral edge of 15 cm. What is the volume? 41. The volume of a square prism is equal to its lateral surface area. Its height is not the same as the measure of its base. Calculate the unit length of the side of the base.
31. find the angle between the curves x2 + y2 =4 and 5x2 + y2 + 5 at their point of intersection for which x and y are positive.
42. A parallelogram ABCD has the following given vertices. A(3, 1), B(2, -1), C(-1, -1) and D(0, 1). Find the area.
32. Obama and Romney are 20 km apart and walk towards each other in a straight line direction. Obama walks at a fairly constant rate and he walks faster than Romney by 1 kph. Romney walks at a constant rate of 5 kph. Obama left his original location first, then Romney started walking 24 min. After. When they eventually meet, how far has Romney walked from his original position.
43. Which of the following ilnes is parallel to the line y = 5x – 1.
33. If x = 1 + Sin 2C, y = 1 + Cos C + Cos 2C. Find the equation of the tangent at C = 60. 34. A civil engineer walks along Roxas Blvd with his girlfriend for half an hour at an average speed of 3 kph. They waited 10 min. For a taxi which brought them back to their starting point at 3:15 PM. If they started walking at 2:25 P.M. that afternoon, what was the average speed of the taxi? 35. The measurements of a rectangular are 12 m. And 16 m. What is the area of the smallest circle that can cover this rectangle entirely? 36. A. Determine the value of tan 11π/6. B. Determine the value of tan π
44. Given the following information: A. The average of A and B is 50. B. The average of B and C is 80. 45. Given the sets of numbers. 1st – 1 2 3 4 2nd – 7 7 10 10 3rd – 11 14 19 19 4th – 23 24 24 26 1st quartile = 4 2nd quartile = 10 3rd quartile = 19 46. From a building across the street, the angle of depression of the foot of an edifice is measured as 13.7: and the angle of elevation of the top is 45.8:. if the observers eye is 14.7 m. From the ground level, find the height of the edifice. 47. There exist a value of x such that the tangent of an expression 2x + 18 is equal to the cotangent of the expression 4x – 12. Find the value of x.
Mathematics and Surveying 2010-2012 zherrinore 48. You are given the equation of a curve y = x2 – 16x + 63 which is a parabola. Find its vertex.
volume of the solid generated if triangle OAB is rotated around the x-axis, O being teh origin.
49. If a solid metal ball is immersed in a apol of paint, it will displace 288π cu. Cm. Of the paint. If the ball will be painted, what is the total area that required painting.
59. A square ABCD has the following x – y coordinates. A(-3, 0), B(0, 3), C(3, 0) and D(0, 3). What is the volume of the solid generated by rotating the square about the y-axis.
50. In a three dimensional space using an x – y – z coordinate system, a line is connected between (0, 0, 7) and (4, 1, 0). Determine the length of the line.
60. Given the equation 5x2 – 2x + 1 = 0. Determine the characteristics of the roots of the equation.
51. Actual measurements of a triangular lot ABC shows the following data. AB = 240, BC = 180 and CA = 16. Calculate the angle at B in degrees. 52. Given the original terms 1 + 1 where x is X+1 x not equal to zero and not equal to – 1, express the terms into a single fraction. 53. Divide the expression 2/3x2 + ½ by the tern x/2 and express the answer in its simplest form. 54. A telephone operator asked 20 of her friends what the memory size of their flash disks are. She found out 12 of her friends have only 8 MB flash disks, 5 have both 8 Mb and 16 MB flash disks. The rest of her friend have only 16 MB flahs disk. How many of her friend have 16 MB flash disks. 55. In measuring a distance by break chaining, the tape was not accurately levelled and was actually 0.95 m. lower at one end. If the distance recorded was 25.60 m., what is the correct distance. 56. To determine the elevation of an inaccessible point x, two observation station were set up at Z and at B, which is 280.5 m. nearer to station A but 35 m. Lower in elevation than A. .the respective angle of elevations from A and B are 25.2: and 45.6: respectively. If the elevation of A is known at 9.89 m. Find the elevation of the distant inaccessible point. 57. What is the volume generated by rotating rectangle ABCD around AD, CD has a length of 2 m. while BC has a length of 5 m. 58. Point A and B has the following Cartesian coordinates A (0, 3) and B (5, 0). Find the
61. If arc Sin (3x – 4y) = 1.571 and arc Cos (x – y) = 1.047. 62. A circle having a radius of 9 cm. Circumscribes a right triangle whose area is 43.23 sq. cm. If one of the sides is 18 cm. long., another side is __________. 63. A boat makes 25 mph in still water. It is headed N. 45: E. In a 7.5 mph water current flowing east. Find the direction of the course of the boat. 64. You are directed to formulate the equation of a line that is slope must be three and the intercept must be -2, what is the equation? 65. Three numbers are in direct proportion in the following manner. A is to B as 34.5 is to 21, while B is to C as 36 is to 14. If C = 41.7, what is the value of A. 66. Expand the expression: (x – 3)2 3 2 67. A sine wave being emitted is monitored on a laboratory diagram and is found to follow the function f(t) = π Sin 2t 4 3 A. Calculate its amplitude B. Compute its period C. Compute its frequency 68. Humbler and haide are running 1 km. race, since Hembler can run faster than Haide he gave her a 12 sec. head start. If Hembler and Haide run at 5 m/s respectively, in how many seconds can Hembler catch up with Haide? 69. The distance “S” meters from a fixed oint of a vehicle travelling in a straight line with constant acceleration “a” is gi en by the formula S = ut at2 where “u” is the initial elocity in m/s, and
Mathematics and Surveying 2010-2012 zherrinore “t”, the time in seconds. Gi en S = 42 m. when t = 2 sec., and S = 144 m. when t = 4 sec. 70. Given the following set of numbers: Set 1 : (9, 11, 16) Set 2 : (21, 4.6, R) If the two sets have identical average, compute for R. 71. Determine the vertex of the graph of y = (x + 1)2 + 7. 72. A salesman gets a P1000 commission on a small scale, one of the many that he accomplished in a period of time. This P1000 commission raised his average commission by P150. If the salesman’s new a erage commission is now P400, how many sales did he make? 73. You are given 8 numbers which add up to 168. One of the numbers is 28. Calculate the average of the other 7 numbers. 74. The average of 11 numbers is 10. One number is eliminated leaving only 10 numbers. The average of the remaining number is 7.5. what number was eliminated? 75. Let A represents a number line such that -1 < a < 5. Let B represents a number line such that 6 < b < 10. If A were shifted by 5 in the positive direction and B were shifted by 2 in the positive direction, how many common integers would the new A and new B share? 76. A right circular cylinder has a height of 10 cm. and radius of 4 cm. a point A lies on the surface of the cylinder and another point B lies on the same surface of the cylinder. If point A and point B are to be far apart as possible from each other, what is the maximum distance between A and B?
