Republic of the PhilippinesBATANGAS STATE UNIVERSITY

Alangilan, Batangas City

COLLEGE OF ENGINEERING, ARCHITECTURE, FINE ARTS& COMPUTING SCIENCES

PETROLEUM ENGINEERING DEPARTMENT

COMPREHENSIVE EXAMINATION

Name:______________________________ Date:______________________Section:_____________________________ Time:______________________

Directions: Encircle the correct answer. Show your solutions. Cheating in any form will be penalized according to the student’s norm of conduct.

Engineering Mathematics

Evaluate (2x – 5y)3

a. 2x3 + 30x2y + 75xy2 + 50y3

b. 2x3 – 30x2y + 75xy2 – 50y3

c. 8x3 – 60x2y + 150xy2 – 125y3

d. 8x3 – 15x2y + 70xy2 + 50y3

If A={f,a,c,e,t} and B={a,t,e}, is B a proper subset of A?a. Yes, because A has more elements than B.b. Yes, since each element of B is an element of A.c. No, because it is A that is the subset of B.d. No, since A is not equal to B.

Solve for k. 3 (9)2k = (35)k

a. 0b. 1c. 2d. 3

Remove the parenthesis and collect similar terms in the expression.7(-2c – 9u + 3p) – 8(-4c – 7u + 6p)

a. 14 + 7u + 27pb. -14 + 7u + 27pc. 18c + 7u + 27pd. 18c – 7u - 27p

Find the value of k that will make the statement identity.(x – k) (x + 2k) = x2 – 3x - 18 a. -1b. -2c. -3d. -4

If the half-life of a medical substance is 5 days, then the amount remaining after n days is approximately (0.87)n. How much will remain after 4 days?

a. 0.57b. 0.498c. 4.25d. 3.84

Which among the following trinomials is not factorable?a. 7x2 – 12x + 4b. 6x2 – 13x + 6c. 15x2 + 11x – 12

d. 3x2 – 10xy – 8y2

Find the value of |-3 + 8| - |-2| + 6 + |4(-3)|.

a. 21b. 22c. 23d. 24

Subtract the sum of 2a + 3p + 5x and 3a + 2p - 6x from 6a + 4p + x.a. 5a + 5p - xb. 5a - 5p - xc. a + p + 2xd. a – p + 2x

If A = {2, 4, 6, 8, 10, 12} and B = {3, 6, 9, 12} find A ∩ Ba.A ∩ B = {2, 3, 4, 6, 8, 9, 10, 12}b. A ∩ B = {2, 4, 8, 10}c. A ∩ B = {6, 12}d. A ∩ B = {3, 9}

Solve the inequality: 4(6x – 5 ) > 2(8x + 1)a. x > 9/4b. x > 10/4

c. x > 11/4 d. x > 12Find the product. (3x + 2)(7x2 + 5x + 4)

a. 21x3 + 29x2 + 22x + 8b. 21x3 + 15x2 + 12x + 10c. 21x3 - 15x2 - 12x – 10 d. 21x3 + 12x2 + 14x + 8

Solve 6 – 3( t + 1 ) > 5t + 7

a. t < -12

b. t < 12

c. t < −32

d. t < -34

.Expand (x – 2)3 – 8y3

a. (x – 2y – 2)[( x – 2)2 + 2y( x – 2 ) + 4y2]b. (x + 2y – 2)[(x – 2)2 + 2y (x – 2) + 4y2]c. ( x- 2y + 2)[(x – 2)2 + 2y(x – 2) + 4y2]d. ( x – 2y -2)[( x – 2)2 – 2y(x – 2) + 4y2]

Simplify: 3x2 – {2x2 – xy – [x(x – y) – y(2x – y)] + 4xy} – 3y2

a. 2x2 + 6xy – 2y2

b. 2x2 – 6xy + 2y2

c. 2x2 – 6xy - 2y2

d. 2x2 + 6xy + 3y2

A recipe of 16 brownies requires 2/3 cup of flour. How much flour is needed to make one dozen brownies?

a. 1/3 cupb. 1/5 cupc. 1/7 cupd. ½ cup

Factor the expression ( x4 – y4 ) as completely as possible:a. ( x + y) ( x2 + 2xy + y2)b. ( x2 + y2) ( x + y )( x – y )c. ( x2 + y2 ) (x2 – y2)d. (1 + x2) ( 1 + y) ( 1- y2)

Find the product (3x – 2y)(2x – 5y)a. 6x2 + 19xy – 10y2

b. 6x2 – 19xy + 10y2

c. 6x2 – 11xy - 10y2

d. 6x2 + 11xy + 10y2

Simplify the exponential expression:(a3n+1 b2n-1 )4

a6n+4 b2n-5a.

a7n+5 b6n-5

a6n+4 b2n-5

b.a6n b6n+1

c. an+3 b2n-3

a6n+4 b2n-5

d. a6n b6n-1

Reduce the complex fraction

1+ 1

1 + 1x - 1

1

1 - 1x + 1

a. 3x - 1x + 1

b. x - 1x + 1

c. 2x - 1x - 2

d. 2x - 1x + 1

Remove the grouping symbols and combine terms in the expression.3a – [4b + 2(6a – b) – 3(a – 5b – 3) – 7] a. -3a + 17b + 3b. 3a – 17b - 3c. -6a – 17b - 2d. 6a – 17b – 2

Simplify the expression √49x2 a. 3xb. 5xc. 7xd. 9x

Obtain the product of x2 - 3x+22x2+ 3x-2

2x2+ 5x -3 x2 - 1

and 3x2+ 6x2x -4

a. 3x(x - 3)2(x - 1)

b. 3x(x+3)2(x+1)

c. 2(x+3)3x(x+1)

d.2(x+1) 3x(x+3)

Three bars of iron weigh 3 2/5, 5 ½, and 7 3/10 kilograms. Find their average weight.a. 4.40b. 5.40c. 6.40d. 7.40

Simplify( -5a)4

a. -20a4

b. 20 (a4)c. -625a4

d. 625 (a4)

a<b or a=b or a>b, is what property?a.Additive inverse property b.Transitive property of equality c.Identity property of additiond.Trichotomy property

2(xy)=(2x)y, is what property?a.Associative property of multiplicationb.Closure property of substraction

c.Associative property of addition d.Distributive property of additionIf a=37 and 37=b, then a=b,is what property? a.Additive inverse property

b.Transitive property of equality c.Identity property of addition d.trichotomy property3/7 + (-3/7) = 0, is what property?

a.Additive inverse propertyb.Transitive property of equalityc.Identity property of additiond.Trichotomy property

Solve 3r ≤ 12.a. r ≤ 4b. r ≤ 3c. r ≤ 2 .d.r ≤ 1

Solve 4x-3>2x+5.a.x>1 c.x>3b.x>2 d.x>4

Solve 5y+8≤7+6y.a.y≥0 c.y≥1b.y≥2 d.y≥3

Evaluate:2(5rs)2

a.50r2s2 c.40r2s2

b.45r2s2 d.35r2s2

Evaluate the polynomial 3r3-r2-8r-9 at r=-1a.-6 c.-4b.-5 d.-3

The residents of a town attempted to raise $25,000 for charity. They raised $ 22,500. What fraction of their goal was raised?

a.9/10 c.7/10b.8/10 d.6/10

If apples cost 68 cents per pound, how much will 2 ¾ pounds cost?a.$1.87 c.$3.87b.$2.87 d.$4.87

. A share of stock was worth $43 1/8 per share on Friday. On Monday it was worth $41 ½. How much did the stock fall?

a.$1.25 c.$2.18b.$1.63 d.$3.18

. A dump truck is loaded with 10 tons of gravel. It dumps 2 ¾ tons at the first stop, and 3 ½ tons at the second. How much gravel is left in the truck?

a.1.75 tons c.3.75 tonsb.2.75 tons d.4.75 tons

Of 6000 fires in a city, 2250 were caused by smoking in bed. What fraction of the 6000 fires were caused by smoking in bed?

a.1/8 c.3/4b.1/2 d.3/8

A carpenter cuts two pieces of lengths 5 ½ feet and 6 7/8 feet from an 18-foot board. Find the length of the piece that remains.

a.5.625ft c.7.625 ftb.6.625ft d.8.625 ft

Evaluate: |-8| - |-2|a.4 c.6b.5 d.7

A furniture store sold two rugs at a loss of $27 per rug, three paintings at a loss of $13 per painting, and seven lamps at a profit of $32 per lamp. Determine the net profit on the 12 sales.

a.$128 c.$135b.$131 d.$137

A clothing store sold three blouses at a loss of $2 per blouse, four skirts at a loss of $3 per skirt, and six dress at a profit of $30 per dress. Determine the net profit on the 13 sales.

a.$162 c.$168b.$164 d.$172

If the number a-6/8=0.001, find a.a.100 c.10b.1,000 d.10,000

Solve for the value of (43.2)3.a.602,238.783 c.602,248.763b.602,247.883 d.602,245.673

Factor the expression 3x3+3x2-18x as completely as possible:a.3x(x+2)(x-3) c.3x(x-2)(x+3)b.3x(x-3)(x+6) d.(3x2-6x)(x-1)

How many significant digits do the 20,540.00 have?a.5 c.6b.7 d.4

How many significant digits do the 0.001964 have?a.4 c.5b.6 d.7

Evaluate i76

a.1 c.ib.0 d.-1

Solve 53m=(5m)2for m.a.1 c.3b.2 d.4

The length of the latus rectum of the parabola y2 = 4px is:a. 4p c. pb. 2p d. -4p

The center of the ellipse 4x2 + y2 - 16y - 6x - 43 = 0 is at :a. (2, 3) c. (1, 9)b. (4, -6) d. (-2, -5)

The area of the ellipse is given as A = 3.1416 a b. Find the area of the ellipse 25x2 + 16y2 – 100x + 32y = 284.

a. 86.2 sq. unitsb. 62.8 sq. unitsc. 68.2 sq. unitsd. 82.6 sq. units

The equation x2 + Bx + y2 + Cy +D = 0 is:a. Hyperbolab. Parabola c. Ellipsed. Circle

The general second degree equation has the form Ax2 + Bxy + Cy2 + Dx + Ey +F = 0 and describe an ellipse if :

a. B2 – 4AC = 0b. B2 – 4AC > 0c. B2 – 4AC = 1

d. B2 – 4AC < 0Find the equation of the tangent to the circle x2 + y2 – 34 = 0 through point (3, 5).

a. 3x + 5y – 34 = 0b. 3x – 5y – 34 = 0c. 3x + 5y + 34 = 0d. 3x – 5y + 34 =0

The semi conjugate axis of the hyperbola is :a. 2 c. 3b. -2 d. -3

Find the equation of the tangent to the curve x2 + y2 = 41 through (5, 4)a. 5x + 4y =41b. 4x – 5y = 41c. 4x + 5y = 41d. 5x – 4y 41

What is the equation of the tangent to the curve 9x2 + 25y2 – 225 = 0 at (0, 3).a. y + 3 = 0b. x + 3 = 0c. x – 3 = 0d. y – 3 = 0

What is the radius of the sphere with center at origin and which passes through the point (8, 1, 6)?

a.10 c. b. 9 d. 10.5

Find the center of the circle .a. (3, -2) c. (-3, 2)b. (3, 2) d. (-3, 2)

The diameter of a circle described by 9x2 + 9y2 = 16 is:a. 16/ 9 c. 4b. 4/3 d. 8/3

Find the point of segment jointing (7, -2) and (-3, 5).a. (2, 3/2) c. (2, 2/3)b. (3, 2) d. (2, 3)

The intersection of the major and minor axis.a. Focib. Centerc. Tangent d. Chord

The two points that define the ellipse.a. Minor axis b. Major axisc. Focid. Center

Equal to the tangent of its angel of inclination.a. Coordinatesb. Axis c. Sloped. Segment

It is the complete set of possible values of the independent variable in the function.a. Interceptb. Domainc. Ranged. Symmetry

It is the complete set of possible resulting values of the dependent variable of a function.a. Interceptb. Domainc. Ranged. Symmetry

Is a line that a graph gets closer and closer to, but never touches or crosses it.a. Interceptb. Asymptote c. Ranged. Symmetry

The set of all points on a plane whose distance from two fixed points add up to a constant.a. Interceptb. Asymptotec. Ellipsed. Symmetry

What is the slope of the line 2x-y+7?a.1b.2c.3d.4

What is the equation of the line that is parallel to the line 3x + 7y = 10 and passes through the point (4, 8)?a. 7x – 3y = 46 b. 3x + 7y = 44 c. 9x + 21y – 184 = 0 d. 3x + 7y = 68At what quadrant does point (4,-3) lies?a. I b. II c. III d. IVDetermine the points of intersection of y=2x2-3 and y = 2x -3a. (0,1), (1,1) b.(0,-3), (1,-1) c. (3,0),(2,-3) d.(0,1),(0,-1)Determine the center and radius of the circle given by the equation x2 – 4x +y2 + 2y = -1:a.(2,-1),2 b. (2,1),2 c.(1,2),1 d.(-1,2),1Determine the x and y intercepts of the graph y = x2 4x +3.a. y=1,x=1,2 b. y=1,x=-1,-2 c. y=3,x=-1,-3 d. y= 2,x=2,1The diameter of the circle described 9x2+9y2=16 are:a. 16/9 b. 4/3 c. 4 d. 8/3What is the radius of the circle with the following equation: x2-6x+y2-4y-12=0a. 3.46 b. 5 c. 7 d. 6The intercept form for the algebraic straight-line equation is:a. a/x +y/b =1 b. y=mx + b c. Ax + By + C=0 d. x/a + y/b =1Find the slope of the line defined by y-x=5a. 1 b. -1/2 c. ¼ d. 5+xThe two straight line 4x – y +3=0 and 8x – 2y +6 =0a. intersects at the origin b. are coincident c. are parallel d. are perpendicularOn what quadrant does point A are x is negative and y intercept is positive.a. I b. II c. III d. IVThe segment from (-1,4) to (2,-2) is extended three times its own length. The terminal point is:a. (11, -18) b. (11, -24) c. (11,-20) d. (-11,-20)Find the cancroids of a triangle whose vertices are (2,3),(-4,6) and (2,-6)a. (0,1) b. (0,-1) c. (1,0) d. (-1,0)Find the distance between the points (4,-2) and (-5,1)a. 4.897 b. 8.947 c. 7.149 d. 9.487If the distance between A(4,-3) and (-2,5)a. 11 b. 8 c. 9 d. 10If the distance between the points (8,7) and (3,y) is 13 what is the value of y?a. 5 b. -19 c. 19 or -5 d. 5 or -19Find the slope of the line 3x-y=1?a. 1 b. 2 c. 3 d. 4Find the slope of the line 3x +2y +5 =0a. -2/3 b. -3/2 c. 3/2 d. 2/3Find the slope of the curve whose parametric equation is y= 5-3t and x=2 +ta. 3 b. -3 c. 2 d. -2Find the slope of the curve whose parametric equation are x=-1 +t and y=2ta. 2 b. 3 c. 1 d. 4Which of the following is perpendicular to the line x/3 +y/4 =1?a. x -4y -8=0 b. 4x -3y -6=0 c. 3x-4y-5=0 d. 4x+3y-11=0

The equation of the line through (1,2) and parallel to the line 3x -2y + 4=0a. 3x -2y +1=0 b. 3x -2y -1=0 c. 3x+2y+1=0 d. 3x +2y -1=0If the point (-3,-5), (x,y) and (3,4) lie on a straight line, which of the following is correct?a. 3x +2y-1=0 b. 2x +3y+1=0 c. 2x +3y -1 =0 d. 3x -2y -1 =0A line which passes through (5,6) and (-3,-4) has an equation of?a. 5x +4y +1 =0 b. 5x -4y -1 =0 c. 5x-4y +1 =0 d. 5x +y -4=0Find the equation of the line with slope of 2 and y-intercept of -3a. y= -3x +2 b. y= 2x -3 c. y= 2/3x +1 d. y=3x-2The equation of a line that intercepts the x-axis at x=4 and the y-axis at y=-6 is:a. 2x -3y =12 b. 3x +2y=12 c. 3x -2y=12 d. 2x -3y=12What is the radius of a circle with the following equation, x2-6x +y2-4y -12 =0?a.3.46 b. 5. c. 7 d. 6Find the center of a circle x2 + y2 -6x +4y -23=0a. (3,-2) b. (3,2) c.(-3,2) d. (-3,-2)At which quadrant lies the point (15,-2)?a. I b. IV c. II d.IIIThe number of board feet in plank 3 in. thick, 1 ft. wide and 20 feet long is:A. 30 C. 120B. 60 D. 90A rectangle has a length of twice its width. If diagonal of rectangle is 45 cm. Find its width.

A. 10 cm C. 20 cmB. 15 cm D. 25 cm

A square and a rectangle has a total area of 300 sq. m. If the area of square is one half of the rectangle, find the perimeter of the square.

A. 10 m C. 30 mB. 20 m D. 40 m

A semi- circle below has a radius of 15 cm. Find the area of shaded part.A. 180.41 cm2 C. 186.46 cm2

B. 173.43 cm2 D. 164.21 cm2

A chord is shaped into a circle whose radius is 15 cm. It is then reshaped to a square. Find its side.A. 60 π C. 7.0πB. 6.5 π D. 7.5 π

The area of a circle is 89.42 in2 .wahat is the circumference?A. 35.33 in C. 33.52B. 32.25 in D. 35.55

A circle has a radius of 50 cm. A 50 cm chord has it ends along the circle perimeter. Find the distance from the center to the chord.

A. 25.42 cm C. 38.65 cmB. 43. 30 cm D. 82.46 cm

Two concentric circle was formed a ring. A chord 10 cm long is drawn tangent to inner circle and the ends at the perimeter of big circle. Find the area of ring.

A. 25π C. 18πB. 26π D. 28 π

The area of a circle is 81π m2. Find the circumference of the circle.A. 18π C. 20πB. 19π D. 21π

The perimeter of a sector is 24 ft. and its radius is 6 ft.. What is the area of sector?A. 72 ft2 C. 76 ft2

B. 74 ft2 D. 78 ft2

A sector having a radius of 20 cm has a central angle of 70 degrees. What is the length of sector?A. 25.68 cm C. 24.43 cmB. 24.83 cm D. 26.54 cm

Solve the length of the hypotenuse of a right triangle if the lengths of the two legs are 7 m and 16 m.A. 17.46 m C. 5.84 mB. 10.84 m D. 7.54 m

The equal sides of an isosceles triangle is 4 inches longer than the base. If the perimeter of a triangle is 23 inches, find the length of its base.

A. 2 inches C. 4 inches B. 3 inches D. 5 inches

The area of a triangle whose sides are are 25, 39 and 40 is :A. 486 C. 648B. 846 D. 468

Arectangle has a length of 150 % its width, If diagonal is 50 m, find the length of rectangle.A. 41.60 m C. 48.58 mB. 27.73 m D. 36.54 m

A square and a rectangle has a total area of 500 square meter. If the area of a square is one third of the rectangle , find the perimeter of square.

A. 12.61 m C. 16.84 mB. 35.52 m D. 44.72 m

A chord is shaped to enclosed a square whose area is 225 in2. If is then reshape to enclosed a rectangle whose length is 20 in. Find the area of rectangle.

A. 100 in2 C. 300 in2

B. 200 in2 D. 400 in2

Chord is the form of a square has a diagonal og 32 in. If it is then reshaped to form a ring, find the diameter of the ring.

A. 28.81 in. C. 20.45 in.B. 24.86 in. D. 26.85 in.

What is the area of a circle inscribed in as square that has a perimeter of 64 cm?A. 16 π C. 48 πB. 32π D. 64`π

The circumference of a circle is 20 π . Find the eare of the circle. A. 50π C. 80πB. 60π D. 100π

As shown below, find the diameter of the circle.A. 4 in. C, 6 in.B. 5in. D. 7 in

A parallelogram whose adjacent sides are equal.A. Rhombus C. RectangleB. Rhomboid D. Trapezoid

A prism whose lateral faces are rectangles that are perpendicular to its bases.A. Right prism C. Truncated PrismB. Oblique prism D. Rectangular prism

Is a polyhedron of which the base is a polygon of n number of sides and other faces of triangles with a common vertex.

A. Regular pyramid C. FrustumB. Pyramid D. Cone

Is a solid bounded by a conical surface and the plane intersecting all the elements.A. Cone C. PyramidB. Frustum D. Prism

A polyhedron whose parallel bases are polygons and the lateral faces triangles or trapezoids.A. Prismoid C. Cylindrical WedgeB. Sphere D. Spherical Zone

A cube has an edges of 10inches. If the side will increased by 5 inches, what is the increase in volume?A. 2375 in³ C.3426 in³B. 4265 in³ D. 1425 in³

If one edge of a cube measures 12cm, calculate the surface area of the cube and the volume of the cube.

A. 945 cm², 6754 cm³ C. 125 cm², 1540cm³B. 894 cm², 1728 cm³ D. 864 cm², 1728 cm³

A cylindrical tank has its height twice its radius. If the tank volume is 128π, find the tank radius.A. 4m C. 6mB. 5m D. 7m

A cylindrical tank with 10 m height has capacity of 900 cubic meters. Determine the surface area of the tank.

A. 336.3 m² C. 254.4 m²B. 286.6 m² D. 624.7 m²

A cylindrical tank 5 m diameter and 7 m height is filled with water to height of 3m from the top. Find the volume of water in the tank.

A. 12π C. 23πB. 22π D. 25π

A pipe lining material of silicon carbide used in conveyance of pulverized coal to fuel a boiler, has a thickness of 2cm and inside diameter of 10cm. find the volume of the material for pipe length of 6m.

A. 64,289 cm³ C.10, 240 cm³B. 48, 654 cm³ D. 45, 239 cm³

if the volume of sphere is 345 cm³, solve for its diameter.A. 8.02 cm C. 8.70 cmB. 9.81 cm D. 9.42 cm

A spherical solid material has a radius of 3 in is melted down to form a solid shaft that has a diameter of 2 in. Find the shaft length.

A. 7 in C. 36 inB. 8 in D. 10 in

If the LPG sphere of Shell Company has an inside diameter of 15 m and it could safely be filled to 75% of its volume, compute for the volume of LPG that could safely be contained in the sphere.

A. 1,462.38 m³ C. 8,254.61 m³B. 1, 746.32 m³ D. 1,325.36 m³

A spherical water tank is filled with 10m³ of water. If the water level of the tank is 80 cm from the bottom, determine the tank radius.

A. 5.24m C. 7.84mB. 6.25m D. 9.95m

A 10m diameter spherical tank is filled with water to a height of 7m. Find the volume of water in the tank.

A. 400.10m³ C. 390.46m³B. 360.60m³ D. 410.50m³

A conical tank has a volume of 200m³. If the height is twice the diameter, determine the tank diameter.A. 2.5cm C. 3.5cmB. 3.0cm D. 7.25cm

if the cone has a base radius of 35 cm and an altitude of 45cm, solve for the total surface area. A.10115.93cm² C. 34261cm²B. 2046.75cm² D. 82541cm²

An inverted conical tank has a diameter of 10m and 8m height. Find the tank volume.A.200m³ C. 283m³B.210m³ D. 254m³

A pyramid with square base has an altitude of 25 cm. If the edge of the base is 15cm, calculate for the volume of the pyramid.

A. 1264cm³ C. 1875cm³B.1285cm³ D. 2465cm³

A frustum of a cone has a lower base radius of 10in and an upper radius of 5in. Determine the volume if the height is 12in.

A. 400π C.600πB. 50π D.700π

A cube has edges of 12inches. If the edge will decrease by 4 inches, find the percent decrease in volume.A. 70.30% C.65.42%B. 80.44% D.50.21%

What is the side of a cube if total surface area is 384in²?A. 8in C. 4inB. 6in D. 2in

A cylindrical tank has a lateral surface area of 400m². if the tank height is 12m, find the tank diameter.A. 10.61m C. 14.61mB. 12.48m D. 16.84m

A cylindrical tank 6m diameter and 9m height is filled with water to 2/3 of its height. Find the volume of water in the tank.

A. 184.65m³ C. 169.65m³B. 175.65m³ D. 154.65m³

A steam pipe is 10m long and has an internal diameter of 50 cm. If the pipe has 10 cm thick, find the volume of metal in the pipe.

A.16, 850,000cm³ C. 20,850,000cm³B. 18, 850,000cm³ D. 22,850,000cm³

A cubical tank has an edge of 5m is full of water. The water is poured into a cylindrical tank that has a radius of 2m, find the height of water in the cylindrical tank.

A. 8m C. 12mB. 10m D. 14m

A sphere has a volume of 300 in³, find its diameter.A. 4.15 in. C. 6.42 in.B. 8.30 in. D. 5.25 in.

A spherical solid metal has a radius of 5inches is melted down to form a hollow shaft with outside diameter of 2in. Find the shaft length.

A. 13.11ft C.11.11ftB. 41.67ft D. 14.11ft

A spherical water tank is to be filled at a capacity of 90% of its volume. If the tank radius is 5m, Find the volume of water in the tank.

A. 523.59m³ C. 420.63m³B.471.23m³ D. 580.23m³

The study of the properties of triangles and trigonometric functions and their applications.a. Algebra c. Analytic Geometryb. Calculus d. Trigonometry

Defined as the union of two rays with a common endpoint.a. Angle c. Vertexb. Ray d. Vector

An angle more than 90° but less than 180°.a. Oblique angle c. Related angleb. Obtuse angle d. Reflex angle

An angle that differs from another by some multiple of 90°.a. Oblique angle c. Related angleb. Obtuse angle d. Reflex angle

What is the angle of πand less than 2π?a. Oblique angle c. Related angleb. Obtuse angle d. Reflex angle

An angle more than 180° but less than 360°.a. Oblique angle c. Related angleb. Obtuse angle d. Reflex angle

An angle less than 90°.a. Acute angle c. Related angleb. Obtuse angle d. Reflex angle

An angle whose sum is 90°.a. Complementary angle c. Related angleb. Supplementary angle d. Reflex angle

An angle whose sum is 180°.a. Complementary angle c. Related angleb. Supplementary angle d. Reflex angle

Is a number that can be written in the form a + bi , where a and b are real numbers and i = √−1a. Complex number c. Imaginary numberb. Real number d. Rational number

An equation in which the variable is in the exponent.a. Exponential equation c. Logarithmic equationb. Trigonometric equation d. None of the above

Naperian logarithms have base closest to which number?a. 153 c. 2.72

b. 162 d. 10The logarithm of a negative number is

a. Real c. imaginaryb. Irrational d. rational

The logarithm of 1 to the base isa. Intermediate c. infinityb. Zero d. One

Log n√ x = log(x)1/n is also equal to:a. Log (nx) c. log(x)/nb. Log (x)n d. n log (x)

The sum of the squares of the sine and cosine of an angle:a. 0 c. 2b. 3 d. 1

Solve for x: log5 x = 3a. 115 c. 125b. 120 d. 130

Find the value of 3log3

7

a. 4 c. 6b. 5 d. 7

Solve for x: logx 5 = - 12

a. 1/25 c. 1/27b. 1/26 d. 1/28

Solve ln x3 = 12a. 54.600 c. 52.289b. 53.289 d. 51.289

Find the value of csc θof an angle in standard position whose terminal passes through the point (8, 15).a. 13/15 c. 17/15b. 14/15 d. 19/15

Solve ln(ln x) = 0a. 1 c. eb. 0 d. Infinity

For a right triangle ABC, a = 12 and A = 45°. Find side b.a. 10 c. 12b. 11 d. 13

Simplify sin (π – θ).a. sin θ c. cos θb. cot θ d. tan θ

Simplify sec2 x – 1.a. sin2 x c. cos2 xb. tan2 x d. cot2 x

Solve for x: log4 x = - 32

a .16

c. 18

b .17

d.19

Log12 x = 2, x = ?a. 144 c. 524b. 414 d. 425

Find the value of x if 2x^3 = 256a. 2 c. 8b. 6 d. 4

Find x if log x = 0.8995a. 6.934 c. 8.934b. 7.934 d. 9.934

Solve for x: 32x = 5a. 0.532 c. 0.732

b. 0.632 d. 0.832 In a triangle, find the side c if angle C=100°, side b = 20 and side a = 15.

a. 28 c. 29b. 27 d. 26

Simplifying the expression sin2ɵ(1 + cot2ɵ) will give the value equal to:a. 1 c. sin2ɵ sec2ɵb. Sin2ɵ d. cos2ɵ

Simplifying the expression secɵ - (secɵ)(sin2ɵ) will give the value equal to:a. Cos2ɵ c. sin2ɵb. cosɵ d. sinɵ

Simplify: cos2ɵ(1 + tan2ɵ)a. Tan 2ɵ c. sin 2ɵb. 1 d. cos2ɵ

Sin (x+y) = 0.9659, sin x = 0.5, Find cos y.a. 0.425 c. 0.707b. 0.816 d. 1.0

Sin 2α = ?a. 2 sinαcosα c. cos2α – sin2αb. sinαcosα d. 2sin2αcosα

The identity of cos2ɵ - sin2ɵ is:a. 2cos ɵ c. 2cos2ɵ - 1b. 1 – cos ɵ d. 2sin2ɵ - 1

Name the two angles, one is positive and the other is positive that are coterminal to 15°.a. 375, 735° c. 375, 725°b. 375, 456° d. 375, 635°

Name the two angles, one is positive and the other is positive that are coterminal to 165°.a. 573°, 525° c. 763°, 525°b. 885°, 525° d. 973°, 525°

Name the two angles, one is positive and the other is positive that are coterminal to -100°.a. 260°, 620° c. 260°, 630°b. 260°, 640° d. 260°, 650°

For a right triangle ABC, c = 18 and A = 30°. Find side a.a. 9 c. 11b. 10 d. 12

Express cos 145° as a function of an acute angle.a. -cos35° c. –cos55°b. –cos45° d. –cos65°

Name the Quadrant of ɵ. Sin ɵ > 0, cos ɵ < 0a. I c. IIIb. II d. IV

Name the Quadrant of ɵ. Sin ɵ < 0, cos ɵ < 0a. I c. IIIb. II d. IV

Name the quadrant of ɵ. cosɵ < 0, tanɵ > 0a. I c. IIIb. II d. IV

Given the quadrant of ɵ. Cos ɵ = - 1213

, 0° < ɵ < 180°

a. I c. IIIb. II d. IV

Name the quadrant of ɵ. Sin ɵ = - 34

, tanɵ > 0

a. I c. IIIb. II d. IV

An angle equal to 180°.a. Supplementary angle c. related angleb. Right angle d. straight angle

An angle equal to 90°.

a. Supplementary angle c. related angleb. Right angle d. straight angle

This is the angle above the horizontal plane of the observer.a. Angle of elevation c. Angle of depressionb. Angle of difficulty d. Angle of hardness

Prepared by:

Engr. Melannie Pinlac Adante