2017

The equation lim┬(x→π/2)⁡〖cosx/(x- π⁄2)〗is equal to _______ A. 0 B. -1 C. infinity D. 1

B. -1

The center of gravity of a solid cone lies on the axis at the height _______ A. Three eight of the total height above the base B. One third of the total height above base C. One half of the total height above base D. One fourth of the total height above base

D. One fourth of the total height above base

______ is a definite integral which is not equal to zero A. ∫_0^π cos x dx = 0 B. ∫_-π^x cos^3 x dx = 0 C. ∫_-π^π cos^3 x dx = 0 D. ∫_-π^π x² sin x dx = 0

B. ∫_-π^x cos^3 x dx = 0

________ is used to evaluate (m + 3) (m + 2) A. a² - b² = (a + b)(a - b) B. (x + a) (x - b) = x² + (a + b)x + ab C. (a + b)² = a² + 2ab + b² D. (a - b)² = a² - 2ab + b²

C. (a + b)² = a² + 2ab + b²

The suitable identity to find (x + 3)(x + 3) is ________ A. a²-b² B. (ab)² C. (a+b)² D. (x+a)(x+b)

C. (a+b)²

A man invested P110,000 for 31 days. If the net interest after deducting 20% withholding tax is P890.36 then the rate of return annually is ________ A. 12.32% B. 11.95% C. 11.75% D. 11.50%

C. 11.75%

Given the equations below, the value of ab is ________ 10b - 9a = 6 b - 1 = 1 A. -7 B. 1 C. 12 D. -12

C. 12

The length of a rectangle is four less than twice its width. If x is the width of the rectangle, then the perimeter of the rectangle would be _________ A. 6x - 4 B. 6x - 8 C. 6x + 4 D. 3x - 4

B. 6x - 8 W = x L = 2x -4 Perimeter = 2(L + W) = 2(2x - 4 + x) = 4x - 8 + 2x Perimeter = 6x - 8

In a shower 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is ______ A. 7500 cu.m. B. 750 cu.m C. 75 cu.m. D. 75000 cu.m.

B. 750 cu.m.

The expression in one variable is A. x + y B. x + x² + 1 C. x + 9y D. xyz

B. x + x² + 1

If fg + 2f - g = 2 - (f + g), then the value of g in terms of f is __________ A. (2-f)/f B. 4/f C. 1/f D. -1

A. (2-f)/f

ln ((x-1)^2) = 2 ln (x-1) for all x in the interval __________ A (-infinity, 1) u (1, -infinity) B. (1, +infinity) C. (-infinity, +infinity) D. (0, +infinity)

A (-infinity, 1) u (1, -infinity)

The graph of y = 5x^4 - x^5 has a point of inflection at A. (3, 162) only B. (4, 256) only C. (0, 0) and (2, 162) D. (0, 0) only

A. (3, 162) only

The exact value of tan 165d using a half angle identity is A. -2 ± √3 B. 2 ± √3 C. 2 - √3 D. -2 - √3

A. -2 ± √3

Subtracting 7x + y from - x + y gives ________ A. -8x B. 8x + 2y C. 8x D. 6x + 2y

A. -8x -x + y - (7x +y) -x + y - 7x - y (cancel y) - x - 7x = -8x

Mr. Quirisit borrowed money from the bank. If he received from the bank P1842 and promised to repay P2000 at the end of 10 months then the rate of simple interest is _______ A. 10.23% B. 12.03% C. 12.19% D. 11.54%

A. 10.23% F = P (1 + in) 2000 = 1842 (1 + (i)(10/12)) i = 10.29% or 10.23%

If y = tan u, u = v - 1/v, and v = lnx then the value of dy/dx at x = e is ______ A. 2/e B. 1 C. e/2 D. -1

A. 2/e

If a cube has side 6cm then the total surface area should be ________ A. 216 sq. m. B. 226 sq. m. C. 214 sq. m. D. 236 sq. m

A. 216 sq.m.

__________ is the value of (x^-y)(2x^y)(3y^x) if x = 2 and y = 2 A. 24 B. 6 C. 8 D. 12

A. 24

______ is the distance of the line 3x + 4y + 15 = 0 from the origin A. 3 B. 4 C. 2 D. 1

A. 3

If a cylindrical gasoline lying horizontally has 0.50 radius and 3m long is filled to a depth of 0.60m then it can still contain ______ gallons of gasoline A. 360 B. 250 C. 270 D. 300

A. 360

If f(2x + 3) = 2x -1, then f(3x + 4) is equal to _______ A. 3x B. 9x + 15 C. 6x + 11 D. 6x + 7

A. 3x

One degree on the equator of the earth is equivalent to ______ A. 4 minutes B. 1 minute C. 1 hour D. 30 minutes

A. 4 minutes 1 degree x (1 hr/15degrees) x (60 mins/1 hr)

______ is the distance from the point (2, 3) to the line 3x + 4y + 3 = 0 A. 4.2 B. 5.4 C. 5 D. 5.8

A. 4.2

______ is the distance in nautical miles between Manila and San Francisco given that Manila is located 14d36m N latitude and 121d05m E longitude while San Francisco is situated at 37d48m N latitude and 122d24m W longitude. A. 6046.2 nautical miles B. 6326.2 nautical miles C. 5896.2 nautical miles D. 7856.2 nautical miles

A. 6046.2 nautical miles

A right circular cone with an altitude of 9 meters is divided in two segments: one is a smaller circular cone having the same vertex with an altitude of 6m. with there, the ratio of the volume of the two cones is _______ A. 8:27 B. 1:3 C. 19:27 D. 2:3

A. 8:27

The inverse of the function given below is _________ fx = ∛(x/5) - 2 A. F^(-1) (x) = 5(x + 2)³ B. F^(-1) (x) = (5(x + 2)³ C. F^(-1) (x) = 5(x³ + 2) D. F^(-1) (x) = 15(x + 2)

A. F^(-1) (x) = 5(x + 2)³

The domain of f(x) = ln (2 - x) + ln (3 - x) is given by A. ( -infinity, 3) B. ( -infinity, 2) C. (2, 3) D. ( -infinity, 7)

B. ( -infinity, 2)

_________ is the centroid of a triangle whose vertices are (2,3) (-4,6) (2,-6) A. (1, 0) B. (0, 1) C. (-1,0) D. (0,-1)

B. (0,1) Xcentroid = (x1 + x2 + x3)/3 Ycentroid = (y1 + y2 + y3)/3

The equation ∫_0^(-π/4) tan²θ dθ us equal to _______ A. 1/3 B. (π/4) - 1 C. (π/4) + 1 D. 1 - (π/4)

B. (π/4) - 1

Using identity a² - b² = (a + b) (a - b), 4^x - 6^x is _________ A. 20 B. -20 C. 12 D. -12

B. -20

If the distance between the points (8, 7) and (3, y) is 13, then the value of y is _______ A. -19 B. 19 or -5 C. 5 D. 5 or -19

B. 19 or -5 d = √[(x2 - x1)² + (y2 - y1)²] backsubsti or shift solve

The area enclosed by the graph r = 5 cos(40) is _______ A. 25π/4 B. 25π/2 C. 25π D. 10

B. 25π/2

Two ships are sailing in the sea on the two sides of a lighthouse. the angle of elevation of the top of the lighthouse is observed from the ships are 30d and 45d respectively. If the lighthouse is 100m high, the distance between two ships is ______ A. 200 B. 273 C. 173 D. 300

B. 273

The value of expression a(a² + n + 1) if a^1 = 0 is _______ A. -5 B. 5 C. A + 5 D. 6

B. 5

Given the right spherical triangle whose given parts are a = 82d, b = 62d and c = 90d. The value of the side opposite the right angle is ________ A. 84d45m B. 86d15m C. 84d30m D. 85d15m

B. 86d15m

_______ is an amount which a willing buyer will pay to a seller for the property where each has equal advantage and is used for compulsion to buy or sell A. Use Value B. Market Value C. Book Value D. Fair Value

B. Market Value

A market situation where there is only one seller with many buyer is known as ______ A. Monophony B. Monopoly C. Oligopoly D. Perfect Competition

B. Monopoly

If the edge of a cube is doubled, ______ statement is INCORRECT. A. The diagonal is doubled B. The weight is doubled C. The volume is increased 8 times D. The lateral area will be quadrapled

B. The weight is doubled

Given f(x) = x² + 2x = 4, ________ following statement is NOT true A. The graph of f has no x-intercept B. f(x) has a maximum value C. The graph of...... D. The graph of f is not a line

B. f(x) has a maximum value

A leading shoe manufacturer produces a pair of Lebron James signature shoes at a labor cost of P900.00 a pair and a material cost of P800.00 a pair. The fixed charges on the business are P5,000,000 a month and the variable costs are P400.00 a pair. Royalty to Lebron James is P1000 per pair of shoes sold. If the shoes sell at P5000.00 a pair then there is a need to produce _____ pairs each month for the manufacturer to break even A. 2890 B. 2590 C. 2632 D. 2712

C. 2632

_________ is the distance from the center of a sphere of a radius 10 cm, a plane should be passed so that the ratio of the areas of two zones is 3x7 A. 6 cm B. 3 cm C. 4 cm D. 5 cm

C. 4 cm

The frustrum of a triangular pyramid has equilateral triangles for its bases, and the lower and upper base edges are 9m and 3m, respectively. If the volume is 118.2 cu.m. then the bases are ______ apart A. 10 m B. 9 m C. 7 m D. 8 m

C. 7 m

_________ is the suitable identity to evaluate 99^x A. 10201 B. 10199 C. 9801 D. 10901

C. 9801 let x = 2 99² = 9801

The Geodetic Engineers of the Philippines Inc (GEPI) is planning to put up its own building. Two proposal being considered are: A. The construction of the building now to cost P400,000 B. The construction of a smaller building now to cost P300,000 and at the end of 5 years, an extension to be added to cost P200,000 Proposal "B" is more economical than proposal A by _______ if interest rate is 20% and depreciation to be neglected A. P19423.69 B. P19518.03 C. P19624.49 D. P19122.15

C. P19624.49 F = P ( 1 + i)^n = 200000 (1 + .20)^5 F = 80375.51 80375.51 + 300000 = 380375.51 M = 400000 - 380375.51 M = P19624.49

given the equations below, the value of x-y is __________ (x + y)/3 = 8 2x - y = 9 A. 1 B. -24 C. 0 D. -2

D. -2

The equation ∫(x/√(9 - x²)) dx is equal to ________ A. 2√(9 - x²) +c B. 1/2 ln √( 9 - x² + c) C. -1/4 √(9 - x²) + c D. -√(9 - x²) + c

D. -√(9 - x²) + c

If (1/2)x + 6 = - x - 3, then the value of -2x is _________ A. -3 B. -12 C. -6 D. 12

D. 12

A ship on certain day is at latitude 20d N and longitude 140d E sailing for 150 hours at a uniform speed along a great circle ... reaches a point at latitude 10d S and longitude 170d E if the r... the earth is 3959 miles, find the speed in miles per hour. A. 16.4 B. 17.4 C. 15.4 D. 19.4

D. 19.4

A college freshman borrowed P2000 from a bank for his tuition fee and promised to pay the amount for one year. If he received only the amount of P1920 after the bank collected the advance interest of P80 then the rate of discount is ________ A. 4.15% B. 4.25% C. 3.67% D. 4.00%

D. 4.00% I = Prt 80 = 2000 r (1) r = 4%

The sum of the series 2 - 1 + 1/2 - 1/4 + 1/8 - ... is _______ A. 3/4 B. 3/2 C. 5/4 D. 4/3

D. 4/3 s = a/(1-r) = (2 - 1)/{1 - [(1/2 - 1/4)/(2 -1)]} s = 4/3

If the edge of a cube is increased by 30% then ________ ... surface area A. 63 B. 65 C. 67 D. 69

D. 69

If a cone was formed by rolling a thin sheet of metal in the form of a sector of a circle 72 cm in diameter with a central angle of 150d then the volume of the cone in cc is _________ A. 7722 B. 7733 C. 7744 D. 7711

D. 7711

The equation of the line through (-3 , -5) parallel to 7x + 2y - 4 = 0 A. 2x + 7y + 30 = 0 B. 7x - 2y + 30 = 0 C. 7x - 2y - 4 = 0 D. 7x + 12y + 31 = 0

D. 7x + 12y + 31 = 0

_______ is the rate of interest compounded annually which is the same as the rate of interest on 8% compounded quarterly. A. 8.12% B. 8.07% C. 8.16% D. 8.24%

D. 8.24%

___________ is the equation of the perpendicular bisector of the joining (5, 0) and (-7, 3) A. 8x - y + 11 = 0 B. 8x + 2y + 11 = 0 C. 8x + y + 11 = 0 D. 8x - 2y + 11 = 0

D. 8x - 2y + 11 = 0

A man standing at a point P is watching the top of the tower which makes an angle of elevation of 30d with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 60d. The distance beween the base of the tower and the point P would be ________ A. 8 units B. 12 units C. 42 units D. Data inadequate

D. Data inadequate height of the tower is not given

_________ defines a function "i" for which f(-x) = -f (x) A. F(x) = log x B. F(x) = cos x C. F(x) = x² D. F(x) = sin x

D. F(x) = sin x

The place where buyers and sellers come together is known as ______ A. Store B. Bargain C. Port D. Market

D. Market

If a, b, c, d, and e are real numbers and a not equal to 0 then the polynomial equation ax² + bx² + cx² + dx + e = 0 has __________ A. No positive real roots B. Only one real root C. At least one real root D. No real roots

D. No real roots

The expression in (x - 2) < 0 is true if and only if ________ A. 2 < x < 3 B. x > 2 C. x > 3 D. x < 3

D. x < 3

If an amount of P 1000 became P1409.41 after 4 years compounded bimonthly then the minimal interest is _________ A. 12% B. 12.08% C. 11.27% D. 12.32%

WALANG SAGOT!

_________ is an equation of a curve that intersects at right angles every curve of the family y = 1/x + k (where it takes all real values)

y = (x^3)/3