MATH 2019 PART 1

If each item in the sequence below is-4 times the previous term, then the value of xy is _____

x, y, -64, 256,...

-64

3 multiple choice options

The polar coordinates of a point are (-4, 270°). Which ordered pair represents the same point in Cartesian coordinates?

A. (-4,-4)

3 multiple choice options

What is the period of the trigonometric function given by f(x) = 2 sin(5x)

2𝝿/5

3 multiple choice options

Evaluate the differential of tan Φ

sec² Φ dΦ

3 multiple choice options

What market situation exists where there are few sellers and few buyers?

Bilateral Oligopoly

3 multiple choice options

The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 4.6m away from the wall. The length of the ladder is _____

9.2m

3 multiple choice options

The corners of a cubical block touch the closed spherical shell that encloses it. The volume of the box is 2744 cc. What volume in cc, inside the shell is not occupied by the block?

4721 cu. cm.

3 multiple choice options

lim ((x² - 16) / (x - 4))

x->4

Simplify the expression below:

8

3 multiple choice options

The spherical excess of the triangle ABC given a = 56°, b = 65° and c = 78° is _______

33°33'

3 multiple choice options

The value of 2x (-3x) is ____

-6x^2

3 multiple choice options

(9x+a) (x+b) is equal to_____

x² +(a + b)x + ab

3 multiple choice options

What is the amplitude of f(x) = 4 sin(x) cos(x)?

4

3 multiple choice options

"When one of the factors of production is fixed in quantity or is difficult to increase, increasing the other factors of production will result in a less than proportionate increase in output". This statement is known as the:

Law of supply and demand

3 multiple choice options

Simplify: 3^log3^ (-5) is equal to ______

undefined

3 multiple choice options

Line Ab is parallel to line CD, and line GH is perpendicular to lines AB and CD. The diagram is rot to scale. If line CD is 25 units from line AB, and the measure of angle IKD is 135 degree, then the length of line segment IK is_____

see fig 6.

25√2 units

3 multiple choice options

The volume of a cube is reduced by _____ if all sides are halved.

1/8

3 multiple choice options

A triangular section has coordinates of A(2,2), B(11,2), and C(5,8). Find the coordinates of the centroid of the triangular section.

(6, 4)

3 multiple choice options

The volume in m^3 of a regular octahedron with an edge 2m is

3.77

3 multiple choice options

The area of a spherical triangle ABC whose parts are A = 93° 40', B = 64° 12', C = 116° 51' and the radius of the sphere is 100m is _____

16531 sq. m.

3 multiple choice options

The region in the first quadrant, which is bounded by the curve x² = 4y, the line x = 4, is revolved about the line x = 4. Locate the centroid of the resulting solid revolution.

0.8

3 multiple choice options

_____ is the acute angle between the lines y = 3x +2 and y = 4x + 9.

4.4°

3 multiple choice options

Given r = 10.8 in, Φ = 210°, what is the length of an arc on a circle of radius r intercepted by central angle Φ? (Round answers to one decimal place.)

39.6 in

3 multiple choice options

The volume of water in a spherical tank having a diameter of 4m. is 5.236 cu. m. Determine the depth of the water on the tank.

1.0

3 multiple choice options

What is the component form of vector AB, if it has initial point A, (-4, 2), and terminal point B, (3, -5)?

(-7, 7)

3 multiple choice options

A young engineer borrowed P 10,000 at 12% interest and paid P 2,000 per annum for the last 4 years. What does he have to pay at the end of the fifth year in order to pay off his loan?

P 6,922.93

3 multiple choice options

The inequality corresponding to the statement: "the price is no less than 100 dollars" is ___

x > 100

3 multiple choice options

______ is the surface area of a sphere whose volume is 36 cu. m.

52.7 m²

3 multiple choice options

Find the slope of the tangent to the curve y² = 3x² + 4 through point (-2, 4)

-3/2

3 multiple choice options

Shell Philippines, a multinational company, has a total gross income for a particular year of P 50,000,000. If the taxable income after taking all deductions except for depletion is P 18,500,000 then the allowable depletion all allowance for that particular year is ____ taking percentage of gross income for oil as 22%

P 9,250.00

3 multiple choice options

What is the radius of curvature at point (1, 2) of the curve 4x - y^2 = 0?

5.66

3 multiple choice options

____ is the value of (a√b) (-ab) if a = 1/3 and b = 9.

1

3 multiple choice options

The average value of g(x) = (x-3)^2 in the interval (1, 3) is _____

8/3

3 multiple choice options

Find the centroid of the area bounded by the curve y = 4 - x^2, the line x= 1 and the coordinate axes.

(0.48, 1.85)

3 multiple choice options

Find the volume of the solid formed if we rotate the ellipse 0.11x^2 + 0.25y^2 = 1 about the line 4x + 3y = 20

40 𝝿2m3

3 multiple choice options

The volume of the water in a spherical tank is 1470.265 cu. m. Determine the depth of water if the tank has a diameter of 30 cm.

6

3 multiple choice options

If 7a + 20b = 28-b, then the value of a in terms of b is _______

4-19/4 b

3 multiple choice options

A student plans to deposit P1,500 in the bank now and another P3, 000 for the next 2 years. If he plans to withdraw P5,000 three years from after his last deposit for the purpose of buying shoes, what will be the amount of money left in the bank after one year of his withdrawal? Effective annual interest rate is 10%.

P1,549.64

3 multiple choice options

Lines AE, BF, GD and ray OC all intersect at point 0 (not labeled), and line AE is perpendicular to ray OC. If the measure of angle 3 is 5x - 3 and the measure of angle 4 is 15x + 7, then the sum of angles 5 and 6 ____________

157°

3 multiple choice options

If the sum of the interior angles of a polygon is equal to the sum of the exterior angles, then ______

The polygon has 6 sides

3 multiple choice options

A point moves on the x-axis in such a way that its velocity at time 𝑡 (𝑡>0) is given by 𝑣=ln𝑡𝑡. As such, ______ is the value of "𝑡" when "𝑣" attains its maximum.

𝑒

3 multiple choice options