Ce Board November 2017 (mathematics)
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BE S
AV
IL LA
REFERENCE BOOKS (Mathematics)
CE BOARD NOV 2017
BE S
AV
IL LA
Evaluate the integral of x Cos (4x) dx with lower limit of 0 and upper limit of π/4.
CE BOARD NOV 2017
BE S
AV
IL LA
. A circular lake is located at a certain barangay in Tagaytay. An existing road runs tangential to a circular lake. Twelve kilometers from the point of tangency, along the existing road, a new road of 8 km length is constructed to the periphery of the lake at B. The new road is extended to cross the lake. Compute the length of the bridge needed to cross the lake.
CE BOARD NOV 2017
BE S
AV
IL LA
. A quadrilateral ABCD is inscribed in a given circle. The angle ADC = 75° and angle ACD = 45°. If the arc BC is only one-half of arc CD, find the value of angle BCA.
CE BOARD NOV 2017
BE S
AV
IL LA
Find the volume of the parallelipiped whose edges are represented by A = 2i – 3j + 4k B = i + 2j – k C = 3i – j + 2k
CE BOARD NOV 2017
BE S
AV
IL LA
Throughout history many people have contributed to the development of . Mathematics. These mathematicians include Pythagoras, Hypatia, Euclid, Euler, Einstein, Fibonacci, Agnesia and Pascal. What is the probability that a mathematician’s name selected at random from those listed will start with either the letter E or the letter A?
CE BOARD NOV 2017
BE S
AV
IL LA
. . Find the
CE BOARD NOV 2017
BE S
AV
IL LA
. What is the slope of the curve y = 2x4 – 3x2 + x1/2 – 290 at x= 3?
BE S
AV
IL LA
CE BOARD NOV 2017
CE BOARD NOV 2017
BE S
AV
IL LA
. that w varies directly as the product of x and y and inversely as the square Given of z, and that w = 4 when x = 2, y = 6 and z = 3. Find the value of w when x = 1, y = 4 and z = 2.
CE BOARD NOV 2017
BE S
AV
IL LA
The. distance from point A ( 6 Cos θ, 2 Sin θ) to the center of ellipse is equal to 2. If the equation of ellipse is 2x2 + 6y2 = 12, find the value of θ.
CE BOARD NOV 2017
BE S
AV
IL LA
. Pacific airplane travels in a direction of N.30°W at an air speed of 600 kph. Cebu If the wind has a speed of 80 kph on a direction of N.40°E, what is the ground speed of the plane?
CE BOARD NOV 2017
BE S
AV
IL LA
. is the equivalent of 630° in the centesimal system? What
CE BOARD NOV 2017
BE S
AV
IL LA
A plane . flies 465 miles with the wind and 345 miles against the wind in the same length of time. If the speed of the wind is 20 mph, find the speed of the plane in still air?
REFERENCE BOOKS
BE S
AV
IL LA
(Surveying/Transportation/Ports and Harbor)
CE BOARD NOV 2017
BE S
AV
IL LA
. A spiral 80 m. long connects a tangent with a 6.5° circular curve. Determine the deflection angle at the first quarter point.
CE BOARD NOV 2017
BE S
AV
IL LA
. are the two components in stopping sight distance? What
CE BOARD NOV 2017
BE S
AV
IL LA
A differential leveling was conducted from BM1 to BM2 30 km apart. BM1 is at elevation . 124.08 m. The backsight distances averages 150 m in length and the foresight distances averages 100 m. The recorded elevation of BM2 was 274.11 m. If the level used is out of adjustment such that when the bubble was centered the line of sight was inclined 0.003 m upward in distance of 100 m. What would be the corrected elevation of BM2?
REFERENCE BOOKS
BE S
AV
IL LA
(Surveying)
CE BOARD NOV 2017
BE S
AV
IL LA
. on the map is 1: x. A lot having an area of 640 sq.m. is represented by an The scale area of 25.6 cm2 on the map. What is the value of x?
CE BOARD NOV 2017
BE S
AV
IL LA
. The common tangent of a compound curve makes an angle of 12° from the tangent passing thru the P.C. and 18° from the tangent passing thru the P.T. If the radius of the second curve is 180 m, find the radius of the first curve if the length of the common tangent is 70 m. long.
CE BOARD NOV 2017
BE S
AV
IL LA
A 50 m.. tape weighing 1.075 kg has a standard pull of 8 kg. The tape’s crosssectional area and modulus of elasticity are 0.05 cm2 and 200 GPa respectively. What pull (normal tension) is required in order that the effect of sag will be eliminated when the tape is supported at the end points only?
BE S
AV
IL LA
CE BOARD NOV 2017
REFERENCE BOOKS
BE S
AV
IL LA
(Economics and Physics)
CE BOARD NOV 2017 Slick oil Company is considering the purchase of a new turbo-generator set that will last 5 years with a cost of P50,000. Maintenance will cost P6000 the first year, decreasing by P1000 each year to P2000 the 5th year. If the interest rate is 8% per year, . compounded annually, how much money should the company set aside for this machine?
BE S
AV
IL LA
Single-payment compound amount factor (F/P, 8%, 5) = 1.4693 Uniform series compound amount factor (F/A, 8%, 5) = 5.8668 Uniform series capital recovery factor (A/P, 8%, 5) = 0.25046 Gradient series factor (A/G, 8%, 5) = 1.8465
BE S
AV
IL LA
CE BOARD NOV 2017
CE BOARD NOV 2017
BE S
AV
IL LA
Talisay .City is considering a new P50000 street cleaner. The new machine will operate at a savings of P600 per day compared to the present equipment. Assume the MARR is 12%, and the machine life is 10 years with zero resale value at that time. How many days per year must the machine be used to justify the investment?
CE BOARD NOV 2017
BE S
AV
IL LA
A fixed .capital investment of P10 M is required for a proposed manufacturing plant and an estimated working capital of P2,000,000. Annual depreciation is 10% of the fixed capital investment. If the annual profit is P2,500, what is the rate of return?
CE BOARD NOV 2017
BE S
AV
IL LA
How long . must a temporary warehouse last to be desirable investment if it costs $16,000 to build, has annual maintenance and operating cost of $360, provides storage space-valued at $360 per year and if the company MARR is 10%?
CE BOARD NOV 2017
BE S
AV
IL LA
A block. weighing 500 N is dropped from a height of 1.3 m upon a spring whose modulus is 20 N/mm. What velocity will the block have at the instant the spring is deformed 100 mm?
REFERENCE BOOKS
BE S
AV
IL LA
(Transpo and Ports)
CE BOARD NOV 2017
BE S
AV
IL LA
Waves .which fall forward since the forward velocity of the crest exceed the velocity of propagation of the wave itself. In deep water, this normally occurs when the wave velocity L is less that 7 times the wave height.
CE BOARD NOV 2017
BE S
AV
IL LA
The ratio . of the wave height to its wave length is called:
DO NOT .
STUDY HARD, STUDY SMART.
Handouts and Quizzes
NOT INCLUDED
AV
IL LA
REFERENCE BOOKS (Mathematics)
CE BOARD NOV 2017
BE S
AV
IL LA
Evaluate the integral of x Cos (4x) dx with lower limit of 0 and upper limit of π/4.
CE BOARD NOV 2017
BE S
AV
IL LA
. A circular lake is located at a certain barangay in Tagaytay. An existing road runs tangential to a circular lake. Twelve kilometers from the point of tangency, along the existing road, a new road of 8 km length is constructed to the periphery of the lake at B. The new road is extended to cross the lake. Compute the length of the bridge needed to cross the lake.
CE BOARD NOV 2017
BE S
AV
IL LA
. A quadrilateral ABCD is inscribed in a given circle. The angle ADC = 75° and angle ACD = 45°. If the arc BC is only one-half of arc CD, find the value of angle BCA.
CE BOARD NOV 2017
BE S
AV
IL LA
Find the volume of the parallelipiped whose edges are represented by A = 2i – 3j + 4k B = i + 2j – k C = 3i – j + 2k
CE BOARD NOV 2017
BE S
AV
IL LA
Throughout history many people have contributed to the development of . Mathematics. These mathematicians include Pythagoras, Hypatia, Euclid, Euler, Einstein, Fibonacci, Agnesia and Pascal. What is the probability that a mathematician’s name selected at random from those listed will start with either the letter E or the letter A?
CE BOARD NOV 2017
BE S
AV
IL LA
. . Find the
CE BOARD NOV 2017
BE S
AV
IL LA
. What is the slope of the curve y = 2x4 – 3x2 + x1/2 – 290 at x= 3?
BE S
AV
IL LA
CE BOARD NOV 2017
CE BOARD NOV 2017
BE S
AV
IL LA
. that w varies directly as the product of x and y and inversely as the square Given of z, and that w = 4 when x = 2, y = 6 and z = 3. Find the value of w when x = 1, y = 4 and z = 2.
CE BOARD NOV 2017
BE S
AV
IL LA
The. distance from point A ( 6 Cos θ, 2 Sin θ) to the center of ellipse is equal to 2. If the equation of ellipse is 2x2 + 6y2 = 12, find the value of θ.
CE BOARD NOV 2017
BE S
AV
IL LA
. Pacific airplane travels in a direction of N.30°W at an air speed of 600 kph. Cebu If the wind has a speed of 80 kph on a direction of N.40°E, what is the ground speed of the plane?
CE BOARD NOV 2017
BE S
AV
IL LA
. is the equivalent of 630° in the centesimal system? What
CE BOARD NOV 2017
BE S
AV
IL LA
A plane . flies 465 miles with the wind and 345 miles against the wind in the same length of time. If the speed of the wind is 20 mph, find the speed of the plane in still air?
REFERENCE BOOKS
BE S
AV
IL LA
(Surveying/Transportation/Ports and Harbor)
CE BOARD NOV 2017
BE S
AV
IL LA
. A spiral 80 m. long connects a tangent with a 6.5° circular curve. Determine the deflection angle at the first quarter point.
CE BOARD NOV 2017
BE S
AV
IL LA
. are the two components in stopping sight distance? What
CE BOARD NOV 2017
BE S
AV
IL LA
A differential leveling was conducted from BM1 to BM2 30 km apart. BM1 is at elevation . 124.08 m. The backsight distances averages 150 m in length and the foresight distances averages 100 m. The recorded elevation of BM2 was 274.11 m. If the level used is out of adjustment such that when the bubble was centered the line of sight was inclined 0.003 m upward in distance of 100 m. What would be the corrected elevation of BM2?
REFERENCE BOOKS
BE S
AV
IL LA
(Surveying)
CE BOARD NOV 2017
BE S
AV
IL LA
. on the map is 1: x. A lot having an area of 640 sq.m. is represented by an The scale area of 25.6 cm2 on the map. What is the value of x?
CE BOARD NOV 2017
BE S
AV
IL LA
. The common tangent of a compound curve makes an angle of 12° from the tangent passing thru the P.C. and 18° from the tangent passing thru the P.T. If the radius of the second curve is 180 m, find the radius of the first curve if the length of the common tangent is 70 m. long.
CE BOARD NOV 2017
BE S
AV
IL LA
A 50 m.. tape weighing 1.075 kg has a standard pull of 8 kg. The tape’s crosssectional area and modulus of elasticity are 0.05 cm2 and 200 GPa respectively. What pull (normal tension) is required in order that the effect of sag will be eliminated when the tape is supported at the end points only?
BE S
AV
IL LA
CE BOARD NOV 2017
REFERENCE BOOKS
BE S
AV
IL LA
(Economics and Physics)
CE BOARD NOV 2017 Slick oil Company is considering the purchase of a new turbo-generator set that will last 5 years with a cost of P50,000. Maintenance will cost P6000 the first year, decreasing by P1000 each year to P2000 the 5th year. If the interest rate is 8% per year, . compounded annually, how much money should the company set aside for this machine?
BE S
AV
IL LA
Single-payment compound amount factor (F/P, 8%, 5) = 1.4693 Uniform series compound amount factor (F/A, 8%, 5) = 5.8668 Uniform series capital recovery factor (A/P, 8%, 5) = 0.25046 Gradient series factor (A/G, 8%, 5) = 1.8465
BE S
AV
IL LA
CE BOARD NOV 2017
CE BOARD NOV 2017
BE S
AV
IL LA
Talisay .City is considering a new P50000 street cleaner. The new machine will operate at a savings of P600 per day compared to the present equipment. Assume the MARR is 12%, and the machine life is 10 years with zero resale value at that time. How many days per year must the machine be used to justify the investment?
CE BOARD NOV 2017
BE S
AV
IL LA
A fixed .capital investment of P10 M is required for a proposed manufacturing plant and an estimated working capital of P2,000,000. Annual depreciation is 10% of the fixed capital investment. If the annual profit is P2,500, what is the rate of return?
CE BOARD NOV 2017
BE S
AV
IL LA
How long . must a temporary warehouse last to be desirable investment if it costs $16,000 to build, has annual maintenance and operating cost of $360, provides storage space-valued at $360 per year and if the company MARR is 10%?
CE BOARD NOV 2017
BE S
AV
IL LA
A block. weighing 500 N is dropped from a height of 1.3 m upon a spring whose modulus is 20 N/mm. What velocity will the block have at the instant the spring is deformed 100 mm?
REFERENCE BOOKS
BE S
AV
IL LA
(Transpo and Ports)
CE BOARD NOV 2017
BE S
AV
IL LA
Waves .which fall forward since the forward velocity of the crest exceed the velocity of propagation of the wave itself. In deep water, this normally occurs when the wave velocity L is less that 7 times the wave height.
CE BOARD NOV 2017
BE S
AV
IL LA
The ratio . of the wave height to its wave length is called:
DO NOT .
STUDY HARD, STUDY SMART.
Handouts and Quizzes
NOT INCLUDED
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