Mathematics Set 1 (Q&A)

a

Which of the following quadratic equations will give a sum and product of the roots equal to 4 and 7 respectively?

a. x² - 4x + 7 = 0

b. x² - 2x + 8 = 0

c. x² - 5x + 10 = 0

d. x² - 10x + 15 = 0

b

The unit "gross" means

a. 100 pieces

b. 12 dozens

c. 100 dozens

d. 120 pieces

a

If x = y and y = x. This illustrates what axiom in Algebra?

a. symmetric axiom

b. reflexive axiom

c. transitive axiom

d. inverse axiom

a

Eight men can dig 150 ft. of trench in 7 hrs. Three men can backfill 100 ft. of trench in 4 hrs. How long will it take 10 men to dig and fill the 200 ft. of trench?

a. 9 hrs and 52 min

b. 8 hrs and 40 min

c. 10 hrs and 3 min

d. 7 hrs and 34 min

d

Solve: dy/dx = 8x⁷y

a. y = 8Cx⁸eˣ⁷

b. y = Cex⁸eˣ⁷

c. y = Cex⁸

d. y = Ceˣ⁸

a

Besavilla's age in 20 years will be the same as Terry's age is now. Ten years from now, Terry's age will be twice of Besavilla's. How old is Terry now?

a. 20

b. 30

c. 10

d. 25

b

If eccentricity, e, of a conic is equal to one, the conic has

a. 2 vertices

b. one vertex

c. greater than 2 vertices

d. no vertex

b; c

What is the multiplicative inverse of x?

a. -x

b. 1/x

c. 1/x

d. x²

a

Solve the inequality

(3x - 2 ) ≤ ( 5x - 12 )

a. x ≥ 5

b. x < 5

c. x > 5

d. x ≤ 5

d

Jake has 300 grams of 20% hydrochloric acid solution. He wishes to drain some off and replace it with an 80% solution so as to obtain a 25% solution. How many grams must he drain and replace with the 80% solution?

a. 20

b. 12

c. 23

d. 25

b

The rule stating that the limit of the ratio of two functions of the same variable x as x approaches a value is equal to the limit of the ratios of their derivatives with respect to x.

a. Newton's Rule

b. L'Hopital's Rule

c. De Gias' Rule

d. Leibniz Rule

c

The conic is symmetric with respect to its

a. latus rectum

b. major axis

c. principal axis

d. minor axis

c

Dodecagon is a polygon with ____ sides.

a. 20

b. 14

c. 12

d. 16

d

One nautical mile is equivalent to

a. 5,280 feet

b. 1,256 statute mile

c. 6,280 feet

d. 1.854 kilometers

c

How many cubic meters is 100 gallons of liquid?

a. 0.1638 m³

b. 1.638 m³

c. 0.3785 m³

d. 3.7850 m³

c

1° is equivalent to __ minutes.

a. 30

b. 90

c. 60

d. 180

d

Numbers which are considered as the counting numbers.

a. Cardinal Numbers

b. Whole Number

c. Ordinal Numbers

d. Natural Numbers

d

4² = 16, the number 16 is called the ____.

a. Base

b. Exponent

c. Index

d. Answer

c

What is the fourth term of the expansion of (x+x²)¹ºº?

a. 161700x¹ºº

b. 167100x¹º³

c. 161700x¹º³

d. 167100x¹ºº

c

e⁻³ is equal to:

a. 0.048787

b. 0.049001

c. 0.049787

d. 0.048902

d

The logarithms of the quotient and the product of two numbers are 0.352182518 and 1.556302501, respectively. Find the first number?

a. 12

b. 11

c. 10

d. 9

c

The set of values of the independent variable(s) for which a function or relation is defined.

a. Asymptote

b. Set

c. Domain

d. Function

c

The major axis of the elliptical path in which the earth moves around the sun is approximately 186,000,000 miles and the eccentricity of the ellipse is 1/60. Determine the perigee of the earth.

a. 93,000,000 miles

b. 94,335,000 miles

c. 91,450,000 miles

d. 94,550,000 miles

b

The sum of the numerical coefficient in the expansion (x - 2y + 3z)³²³.

a. 1.7 x10⁻⁹⁷

b. 1.7 x10⁹⁷

c. 1.803 x10⁶⁷

d. 1.7 x10⁸⁷

a

In the quadratic equation Ax² + Bx + C = 0, the product of the roots is

a. C/A

b. -C/A

c. -B/A

d. B/A

d

Finn and Jake traveled at the same time at the rate of 20 m/min, from the same point on a circular track of radius 600 m. If Finn walks along a circumference and Jake towards the center, find their distance after 10 minutes.

a. 193 m

b. 202 m

c. 241 m

d. 258 m

a

At 2:00 pm, an airplane takes off at 340 mph on an aircraft carrier. The aircraft carrier moves due south at 25kph in the same direction as the plane. At 4:05 pm, the communication between the plane and aircraft carrier was lost. Determine the communication range in miles between the plane and the carrier.

a. 656 miles

b. 557 miles

c. 785 miles

d. 412 miles

b

An aeronautical engineer was told that a survey had been made on a certain rectangular field but the dimension had been lost. An assistant remembered that if the field had been 100 ft. longer and 25 ft. narrower, the area would have been increased by 2,500 sq. ft., and that if it had been 100 ft. shorter 50 ft. wider, the area would have been decreased by 5,000 sq. ft. What was the area of the field?

a. 25, 000 sq. ft.

b. 20, 000 sq. ft.

c. 15, 000 sq. ft.

d. 22, 000 sq. ft.

c

There are seven arithmetic means between 3 and 35. Find the sum of all terms.

a. 169

b. 167

c. 171

d. 173

b

How many permutations can be made out of the letters in the word "PHILIPPINES"?

a. 1,801,000

b. 1,108,800

c. 1,108,000

d. 1,801,800

d

By moving or changing the orientation of one of the following digits, the equation 62 - 63 = 1 will be correct. Which digit must be moved?

a. 1

b. 2

c. 3

d. 6

c

What is the area of a triangle given the length of sides of 4, 5, and 6?

a. 0

b. 122

c. 10

d. 7.5

d

The perpendicular distance of a point from the vertical axis.

a. Circumcenter

b. Vertex

c. Ordinate

d. Abscissa

b

300 knots is equivalent to ___ m/s.

a. 506

b. 154

c. 345

d. 440

a

Find the area of the sector of a circle that has an arc of 70 degrees and a radius of 6 feet.

a. 22 ft²

b. 23 ft²

c. 24 ft²

d. 25 ft²

a

√(4x + 21) = x + 6. Solve for x.

a. x = -3, -5

b. x = 5, -3

c. x = 9, 7

d. x = -9, 7

b

The angle of inclination of the road is 32. What is the angle of inclination in mils?

a. 35.6

b. 568.89

c. 125.36

d. 456.23

a

Find the distance between given lines 4x - 3y = 12 and 4x - 3y = - 8.

a. 4

b. 5

c. 3

d. 1

a

What is the sum of interior angles of a heptagon?

a. 900

b. 540

c. 720

d. 1080

d

Determine the radius of the circle given the equation 4x² + 4y² -20x + 4y - 55 = 0

a. 20.25

b. 2.12

c. 2.25

d. 4.5

a

What is the remainder of 2x³ - 5x² + 6x - 3 divided by x - 2?

a. 5

b. 3

c. 2

d. 8

d

a² = y is equivalent to ___.

a. log₂y = a

b. log₁₀y = 2a

c. logᵧa = 2

d. logₐy = 2

c

Calculate the work done to taxi an Airbus A380 if the aircraft needs to be displaced 2,000 meters from its starting point with thrust per engine of 80,000 N.

a. 160,000 J

b. 160,000,000 J

c. 640,000,000 J

d. 320,000,000 J

d

Solve for x and y: x + 3y - 32 = 0 and 3x+ 5y = 10

a. 32.5 & -21.5

b. 67.5 & 33.5

c. -67.5 & -33.5

d. -32.5 & 21.5

b

Which of the following is a possible

root of the polynomial: x⁴ + 5x³ + 5x² - 5x - 6 = 0

a. 3

b. -2

c. 0

d. 4

c

The equation 3x⁴ - 7x³ + 5x² - 7x + 2 = 0 has two rational roots, both of which are positive. Find the larger of these two roots.

a. 1

b. 3

c. 2

d. 4

c

What is the remainder of the polynomial x³ + 4x² - 3x + 8 when divided by x - 5?

a. 208

b. 283

c. 218

d. 305

b

Find the 15th term in the arithmetic sequence: 1,3,5,7...

a. 25

b. 29

c. 27

d. 31

b

Find the 12th term in the geometric series: 3,9,27...

a. 59,049

b. 531,141

c. 177,147

d. 1,594,323

a

Subtract 60º10" - 27º34‟52"

a. 32º25‟18"

b. 32º35‟18"

c. 32º35‟8"

d. 32º25‟"