Ce Board May 2018 Mathematics To Be Updated
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BE S
AV
IL LA
REFERENCE BOOKS (Mathematics)
CE BOARD MAY 2018
BE S
AV
IL LA
At how many minutes after 3 PM will the hands of a clock be perpendicular to each other for the first time after 3 PM?
CE BOARD MAY 2018
BE S
AV
IL LA
Two perpendicular chords both 5 cm from the center of the circle, which divides into four parts. If the radius of the circles is 13 cm, find the area of the smallest part.
CE BOARD MAY 2018
BE S
AV
IL LA
The height of the cone is h. It contains water to a depth of 2/3 h. What is the ratio of the volume of water to that of the cone?
BE S
AV
IL LA
CE BOARD MAY 2018
CE BOARD MAY 2018
BE S
AV
IL LA
A spherical triangle ABC has an angle C = 90°, and sides a = 50° and c = 80°. Find the angle of side b in degrees.
CE BOARD MAY 2018
BE S
AV
IL LA
Find y’ if x = 2 arc cos 2t and y = 4 arc sin 2t.
BE S
AV
IL LA
CE BOARD MAY 2018
CE BOARD MAY 2018
BE S
AV
IL LA
ABCD is a square of side 10 cm. Four congruent isosceles triangles are cut off from the four corners so that the remaining portion is a regular octagon. Compute the equal sides of the isosceles
CE BOARD MAY 2018
BE S
AV
IL LA
The coordinate axes are asymptotes of the equilateral hyperbola whose vertex in the first quadrant is 3 2 units from the origin. What is the equation of the hyperbola?
REFERENCE BOOK
BE S
AV
IL LA
(Surveying/Transportation/Ports and Harbor)
CE BOARD MAY 2018
BE S
AV
IL LA
The observed interior angles of a quadrilateral and their corresponding number of observation are as follows: Corner Angle No. of observations 0 1 67 5 0 2 132 6 3 960 3 0 4 68 4 Determine the corrected angle at corner 3.
BE S
AV
IL LA
CE BOARD MAY 2018
CE BOARD MAY 2018
BE S
AV
IL LA
A school lot has the following dimensions. Find the cost of the lot if it cost P3.1M per hectare. Compute also the distance of line 2 – 3. COURSE BEARING DISTANCE 1–2 N. 57°39’ W 145.16 2–3 ------3–4 S. 44°45’ E 62.10 4–1 N. 31°16’ E 300.00
BE S
AV
IL LA
CE BOARD MAY 2018
CE BOARD MAY 2018 DISTANCE 44.47 137.84 12.83 64.86 107.72
BE S
AV
IL LA
A closed traverse has the following data: LINE BEARING AB ? BC ? CD N 1°45’ E DE N 72°10’ E EA S. 48°13’ E Find the bearing of line BC.
BE S
AV
IL LA
CE BOARD MAY 2018
CE BOARD MAY 2018
BE S
AV
IL LA
A simple curve is to be designed for a maximum speed of 90 kph. The coefficient of friction between the tires and the pavement is 0.40. If the super elevation is limited to 12%, determine the degree of curvature. Use arc basis.
BE S
AV
IL LA
CE BOARD MAY 2018
CE BOARD MAY 2018
BE S
AV
IL LA
Applying full brakes at a speed of 60 kph, the car traveled 40 m until it stopped. Determine the average skid resistance.
REFERENCE BOOK
BE S
AV
IL LA
(Surveying)
CE BOARD MAY 2018
BE S
AV
IL LA
On a railroad, a + 0.8% grade meets a -0.4% grade at sta. 2 + 700 and at elevation 30 m. The maximum allowable change in grade per station is 0.2%. Determine the length of the curve.
CE BOARD MAY 2018
IL LA
With the geometry of the vertical curves shown, some preliminary computations are required before the vertical curves themselves can be computed. Given: Stationing of PV1 = 44 + 00 Elevation of PV1 = 686.45 feet L1 = 600 feet g1 = - 3.34% L2 = 400 feet g2 = + 1.23%
BE S
AV
Calculate the stationing and elevation of BVC and EVC.
BE S
AV
IL LA
CE BOARD MAY 2018
CE BOARD MAY 2018
BE S
AV
IL LA
An existing highway with bearing N.20°E. is to be connected to another highway with bearing of N.80°E by a 4° simple curve. What length of curve is required?
REFERENCE BOOK
BE S
AV
IL LA
(Economics and Physics)
CE BOARD MAY 2018 FC = P600,00 SV = P60,000 Life = 5 years Compute the depreciation on the 3rd year using Modified Accelerated Cost Recovery System Method.
BE S
AV
IL LA
Given:
CE BOARD MAY 2018
BE S
AV
IL LA
Objects A and B with the same mass m = 2 kg undergo a direct central impact. Before the impact, A is moving to the right with a velocity of 4 m/s and B is stationary. Determine the velocity of A after impact if the impact is perfectly plastic.
REFERENCE BOOK
BE S
AV
IL LA
(Transpo and Ports)
CE BOARD MAY 2018
BE S
AV
IL LA
Warn road users of condition on or adjacent to the road that may be unexpected or hazardous.
CE BOARD MAY 2018
BE S
AV
IL LA
The number of vehicles moving in a specified direction on a given lane or roadway that pass a given point during specified unit time and is usually expressed as vehicles per hour or vehicles per day.
CE BOARD MAY 2018
BE S
AV
IL LA
The maximum number of passenger cars that can pass a given point on a lane or roadway during one hour under the most nearly ideal roadway and traffic conditions which can possibly be attained.
CE BOARD MAY 2018
BE S
AV
IL LA
The maximum sustained 15 min. rate of flow, expressed in passenger cars per hour per lane, which can be accommodated by a uniform freeway segment under prevailing traffic and roadway conditions in one direction.
CE BOARD MAY 2018
BE S
AV
IL LA
Waves under the influence of the winds that generated them are called:
CE BOARD MAY 2018
BE S
AV
IL LA
Determine the minimum length of a sag vertical curve between a – 0.7% grade and a + 0.5 grade for a road with 110 kph design speed. The vertical curve must provide 220 m. headlight sight distance.
REFERENCE BOOK
BE S
AV
IL LA
(Algebra)
CE BOARD MAY 2018
BE S
AV
IL LA
Rolls of carpet are stacked in 20 rows with 3 rolls in the top row, 4 rolls in the next row, and so on, forming an arithmetic sequence. Find the total number of carpet rolls if there are 22 rolls in the bottom row.
CE BOARD MAY 2018
BE S
AV
IL LA
As a result of a nuclear accident, radioactive debris was carried through the atmosphere. One immediate concern was the impact that the debris has on the milk supply. The percent y of radioactive material in raw milk after t days is estimated by y = 100(2.7)=0.1t. Estimate the expected percent of radioactive material in the milk after 30 days.
CE BOARD MAY 2018
BE S
AV
IL LA
The maximum weight that a rectangular beam can support varies jointly as its width and the square of its height and inversely as its length. If a beam is 1/3 ft. wide, ½ ft. high and 11 ft. long can support 20 tons, find how much similar beam can support if the beam is ¼ ft. wide, ¼ ft. high and 17 ft. long.
REFERENCE BOOKS
BE S
AV
IL LA
(Probability and Statistics)
CE BOARD MAY 2018
BE S
AV
IL LA
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?
Problems from Refresher and Coaching that came out are NOT INCLUDED here
…a good Review Center too
AV
IL LA
REFERENCE BOOKS (Mathematics)
CE BOARD MAY 2018
BE S
AV
IL LA
At how many minutes after 3 PM will the hands of a clock be perpendicular to each other for the first time after 3 PM?
CE BOARD MAY 2018
BE S
AV
IL LA
Two perpendicular chords both 5 cm from the center of the circle, which divides into four parts. If the radius of the circles is 13 cm, find the area of the smallest part.
CE BOARD MAY 2018
BE S
AV
IL LA
The height of the cone is h. It contains water to a depth of 2/3 h. What is the ratio of the volume of water to that of the cone?
BE S
AV
IL LA
CE BOARD MAY 2018
CE BOARD MAY 2018
BE S
AV
IL LA
A spherical triangle ABC has an angle C = 90°, and sides a = 50° and c = 80°. Find the angle of side b in degrees.
CE BOARD MAY 2018
BE S
AV
IL LA
Find y’ if x = 2 arc cos 2t and y = 4 arc sin 2t.
BE S
AV
IL LA
CE BOARD MAY 2018
CE BOARD MAY 2018
BE S
AV
IL LA
ABCD is a square of side 10 cm. Four congruent isosceles triangles are cut off from the four corners so that the remaining portion is a regular octagon. Compute the equal sides of the isosceles
CE BOARD MAY 2018
BE S
AV
IL LA
The coordinate axes are asymptotes of the equilateral hyperbola whose vertex in the first quadrant is 3 2 units from the origin. What is the equation of the hyperbola?
REFERENCE BOOK
BE S
AV
IL LA
(Surveying/Transportation/Ports and Harbor)
CE BOARD MAY 2018
BE S
AV
IL LA
The observed interior angles of a quadrilateral and their corresponding number of observation are as follows: Corner Angle No. of observations 0 1 67 5 0 2 132 6 3 960 3 0 4 68 4 Determine the corrected angle at corner 3.
BE S
AV
IL LA
CE BOARD MAY 2018
CE BOARD MAY 2018
BE S
AV
IL LA
A school lot has the following dimensions. Find the cost of the lot if it cost P3.1M per hectare. Compute also the distance of line 2 – 3. COURSE BEARING DISTANCE 1–2 N. 57°39’ W 145.16 2–3 ------3–4 S. 44°45’ E 62.10 4–1 N. 31°16’ E 300.00
BE S
AV
IL LA
CE BOARD MAY 2018
CE BOARD MAY 2018 DISTANCE 44.47 137.84 12.83 64.86 107.72
BE S
AV
IL LA
A closed traverse has the following data: LINE BEARING AB ? BC ? CD N 1°45’ E DE N 72°10’ E EA S. 48°13’ E Find the bearing of line BC.
BE S
AV
IL LA
CE BOARD MAY 2018
CE BOARD MAY 2018
BE S
AV
IL LA
A simple curve is to be designed for a maximum speed of 90 kph. The coefficient of friction between the tires and the pavement is 0.40. If the super elevation is limited to 12%, determine the degree of curvature. Use arc basis.
BE S
AV
IL LA
CE BOARD MAY 2018
CE BOARD MAY 2018
BE S
AV
IL LA
Applying full brakes at a speed of 60 kph, the car traveled 40 m until it stopped. Determine the average skid resistance.
REFERENCE BOOK
BE S
AV
IL LA
(Surveying)
CE BOARD MAY 2018
BE S
AV
IL LA
On a railroad, a + 0.8% grade meets a -0.4% grade at sta. 2 + 700 and at elevation 30 m. The maximum allowable change in grade per station is 0.2%. Determine the length of the curve.
CE BOARD MAY 2018
IL LA
With the geometry of the vertical curves shown, some preliminary computations are required before the vertical curves themselves can be computed. Given: Stationing of PV1 = 44 + 00 Elevation of PV1 = 686.45 feet L1 = 600 feet g1 = - 3.34% L2 = 400 feet g2 = + 1.23%
BE S
AV
Calculate the stationing and elevation of BVC and EVC.
BE S
AV
IL LA
CE BOARD MAY 2018
CE BOARD MAY 2018
BE S
AV
IL LA
An existing highway with bearing N.20°E. is to be connected to another highway with bearing of N.80°E by a 4° simple curve. What length of curve is required?
REFERENCE BOOK
BE S
AV
IL LA
(Economics and Physics)
CE BOARD MAY 2018 FC = P600,00 SV = P60,000 Life = 5 years Compute the depreciation on the 3rd year using Modified Accelerated Cost Recovery System Method.
BE S
AV
IL LA
Given:
CE BOARD MAY 2018
BE S
AV
IL LA
Objects A and B with the same mass m = 2 kg undergo a direct central impact. Before the impact, A is moving to the right with a velocity of 4 m/s and B is stationary. Determine the velocity of A after impact if the impact is perfectly plastic.
REFERENCE BOOK
BE S
AV
IL LA
(Transpo and Ports)
CE BOARD MAY 2018
BE S
AV
IL LA
Warn road users of condition on or adjacent to the road that may be unexpected or hazardous.
CE BOARD MAY 2018
BE S
AV
IL LA
The number of vehicles moving in a specified direction on a given lane or roadway that pass a given point during specified unit time and is usually expressed as vehicles per hour or vehicles per day.
CE BOARD MAY 2018
BE S
AV
IL LA
The maximum number of passenger cars that can pass a given point on a lane or roadway during one hour under the most nearly ideal roadway and traffic conditions which can possibly be attained.
CE BOARD MAY 2018
BE S
AV
IL LA
The maximum sustained 15 min. rate of flow, expressed in passenger cars per hour per lane, which can be accommodated by a uniform freeway segment under prevailing traffic and roadway conditions in one direction.
CE BOARD MAY 2018
BE S
AV
IL LA
Waves under the influence of the winds that generated them are called:
CE BOARD MAY 2018
BE S
AV
IL LA
Determine the minimum length of a sag vertical curve between a – 0.7% grade and a + 0.5 grade for a road with 110 kph design speed. The vertical curve must provide 220 m. headlight sight distance.
REFERENCE BOOK
BE S
AV
IL LA
(Algebra)
CE BOARD MAY 2018
BE S
AV
IL LA
Rolls of carpet are stacked in 20 rows with 3 rolls in the top row, 4 rolls in the next row, and so on, forming an arithmetic sequence. Find the total number of carpet rolls if there are 22 rolls in the bottom row.
CE BOARD MAY 2018
BE S
AV
IL LA
As a result of a nuclear accident, radioactive debris was carried through the atmosphere. One immediate concern was the impact that the debris has on the milk supply. The percent y of radioactive material in raw milk after t days is estimated by y = 100(2.7)=0.1t. Estimate the expected percent of radioactive material in the milk after 30 days.
CE BOARD MAY 2018
BE S
AV
IL LA
The maximum weight that a rectangular beam can support varies jointly as its width and the square of its height and inversely as its length. If a beam is 1/3 ft. wide, ½ ft. high and 11 ft. long can support 20 tons, find how much similar beam can support if the beam is ¼ ft. wide, ¼ ft. high and 17 ft. long.
REFERENCE BOOKS
BE S
AV
IL LA
(Probability and Statistics)
CE BOARD MAY 2018
BE S
AV
IL LA
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?
Problems from Refresher and Coaching that came out are NOT INCLUDED here
…a good Review Center too
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