CE Board Examinations - Mathematics and Surveying November 2003

Find the maximum area of a rectangle inscribe in a triable with sides: a = 4.25, b = 8.62, c = 9.61. The least dimension of the rectangle lying along side a.

630° equal to _____ in centesimal system.

Round-off 102.48886 to four significant figures.

The sum of two numbers is k. If the product of the first number multiplied by the cube of the other is maximum, find one number.

Find the height of a tetrahedron given a total surface area of 170 sq. cm.

Given the general equation of the curve Ax² + By² + F = 0 which passes through points (0,3) and (4,0). Determine what type of curve. 

Calculate the effective rate that corresponds to nominal rate of 6% compounded continuously.

In a spherical triangle with B = 81°50' C = 91°40', c = 90°. Find angle A. 

When you divide x⁴ + Ax³ + 5x² + Bx + 6  by (x - 2), the remainder is 16. When you divide by (x+ 1), the remainder is 10. Find B.

Find the perimeter of the curve r = 4(1 - \(\sin\theta\))

If x = t³ and y = 2t², where x and y are in meters and t in seconds, find the velocity at t = 2 seconds.

If versed sin A = 0.148, find A. 

Compute the magnitude of the vector r = 2i + 5j + 6k

Find the volume of the spherical wedge given a central angle of 1.25 radians. Radius of the sphere is 2 units.

The lateral area of a right circular cone os 240 cm². Find its altitude if the diameter is half of its altitude.

The distance from (x, 4, 5) to (-3, 7, 1) is 13. Find the value of x.

Calculate the difference of the future amount of annuity due and ordinary annuity. Given that the periodic payment is P 10 000 with interest rate of 12% compounded annually for 20 years.

An equipment costing P 420 000 has a salvage value of P 50 000 at the end of 6 years. If the depreciation charge after 1st year was P 105 714.29, what method of depreciation was used?

Find the area of a hexagon inscribed in a circle with area of 33.16 cm^2.

Compute the area of the surface generated by revolving the arc x² = 16 - 8y in the first quadrant about the y-axis.

The following are bearings and distances taken on a closed traverse. (See attached picture)

A line from vertex A to F on the side BC divides the traverse and makes area ABF to be 280 00o m². Find the length of the line AF.

The cross section notes below are for a ground excavation of a 10 m roadway

\({9.8\over2.4},{0\over x},{7.4\over1.2}\)

Find the value of x so that the area of the cross section will be 33.10 m². Slope of the roadway is 2:1.

A block of 15 kg mass is resting on a horizontal surface and is acted by a 40 N force making an angle of 50° from the coefficient of friction between the block and the surface when the block starts to slide. 

A block moving at 22 m/s stops after it has traveled 100 m on a horizontal surface. Compute the coefficient of kinetic friction between the block and ground surface.

Find the distance between points P₁ (-5, 4, 8) and P₂ (-10, 4, 4).

A particle moves on a circular pa.th of radius 2.5 m, compute the normal acceleration when the angular speed is 10 rad/min

In triangle ABC, BC = 36 cm, AC = 57 cm and B = 102.7°. Compute the length of side AB.

The line of sight was inclined at 4°30' with the horizontal. It intercepts the staida rod with the length of 1.8 m. The stadia interal factor is 100 and stadia constant is 0.3. COmpute the vertical distance of the point sighted above the instrument.

A compound curve has a common tangent equal to 140 m. First curve has a radius equal to 194 m and has subtended angle of equal to 24° while the second curve has central angle of 34°. What is the degree of the second curve?