Mathematics

2

What is the lowest common factor of 10 and 32?

4

Two friends Adrian and Melvin are respectively 5 and 8 years old. In how many years will the ratio of their ages be 3:4?

42.31

The arithmetic mean of 80 numbers is 55. If two numbers namely 250 and 850 are removed, what is the arithmetic mean of the remaining numbers?

15

Determine the sum of the positive valued solution to the simultaneous equations:

xy = 15, yz = 35, zx= 21

200 and 180

Seven carpenters and 5 masons earn a total of 2,300 per day. At the same rate, of pay 3 carpenters and 8 masons earn 2,040. What are the wages per day of a carpenter and a mason?

25 kg

Determine how much water should be evaporated from 50 kg of 30% salt solution to produce a 60% solution. All percentages are by weight.

4 km/hr.

A boat going across a lake 8 km wide proceeds 2 km at a certain speed and then completes the trip at a speed of ½ km/hr. faster. By doing this, the boat arrives 10 minutes earlier than if the original speed had been maintained. Find the original speed of the boat.

357

A bookstore purchased a best-selling price book at Php 200.00 per copy. At what prize should this be sold so that, giving a discount, the profit is 30%?

305.9 ft

Gravity causes a body to fall 16.1 ft in the first second, 48.3 in the 2nd second, 80.5 in the 3rd second. How far did the body fall during the 10th second?

18

In the “Gulf War” in the Middle East, the allied forces captured 6400 of Saddam’s soldiers and with provisions on hand it will last for 216 meals while feeding 3 meals a day. The provision lasted 9 more days because of daily deaths. At an average, how many died per day?

1/11

Find the 4th term of the progression ½, 0.2, 0.125,…

7, -7/6

Determine x so that: 𝑥, 2𝑥 + 7, 10𝑥 − 7 will be a geometric progression.

-2, 4/8

The seventh term is 56 and the twelfth term is -1792 of a geometric progression. Find the common ratio and the first term. Assume the ratios are equal.

20

In a benefit show, a number of wealthy men agreed that the first one to arrive would pay 10 centavos to enter and each later arrive would pay twice as much as the preceding man. The total amount collected from all of them was P104, 857.50. How many wealthy men paid?

250 ft

A rubber ball is made to fall from a height of 50 feet and is observed to rebound 2/3 of the distance it falls. How far will the ball travel before coming to rest if the ball continues to fall in this manner?

-7^a

Simplify: 7^a+2 − 8(7)^a+1 + 5𝑏² − 4𝑏 + 16(7)^a + 49(7)^a-2

21 days

Two workers A and B together can complete a job in 7 days. A works twice as fast as B. How many days would it take B to do the job working alone?

284

The sum of the digits of a three digit number is 14. The units digit is half the tens digit. If the digits are reversed, the resulting number is 198 more than the original number. Find the original number.

12

A realtor bough a group of lots for $90, 000. He then sells them at a gain of $3, 750 per lot and has a total profit equal to the amount he received for the last 4 lots sold. How many lots were originally in the group?

1:45.73 PM

A man left Manila for Baguio City at past 9 AM. Between 4 to 5 hours, he arrived at Baguio and noticed the minute and hour hands of his wrist watch interchanged in position. At what time did the man arrive at Baguio?

2.41

A passenger train x times as fast as a freight train takes x times as long to pass overtaking the freight train as it takes to pass when the two trains are going in opposite directions. What is the value of x?

12 min

A tank can be filled separately in 10 and 15 minutes respectively by two pipes. When a third pipe was used simultaneously with the first two pipes, the tank can be filled in 4 minutes. How long would it take the third pipe alone to fill the tank?

0.50

A 2.5 liter container has a mixture of 25% alcohol. How many liters of the mixture must be drained out and replaced with pure alcohol in order to obtain a mixture containing 40% alcohol?

680 km

On a trip, a man noticed that his car averaged 21 km per liter of gasoline except for the days he used the air conditioning and then it averaged only 17 km per liter. If he used 91 liters of gasoline to drive 1, 751 km on how many of those kilometers did he use the air conditioning?

15

Mary is twice as old as Ann was when Mary was as old as Ann is now. If Mary is 20 years old now, how old is Ann now?

0.40 L

From a 2 liter vessel containing water, a certain amount was drained and replaced with pure alcohol. Later from the mixture, the same amount was drained and again replaced with pure alcohol. What amount was removed each time if the resulting mixture has 36% alcohol?

40

If a man was left with 10 hectares than 40% of his land after selling 6 hectares more than 70% of his land, how many hectares of land did he initially own?

15

A boy is 2 years more than twice as old as his younger brother. The two boys together are 17 years older than their sister whose is 7 years younger than the older boy. How old is the sister?

5

The 3rd term of a harmonic progression is 15 and the 9th term is 6. Find the 11th term.

13 m/s

It takes 10 seconds for two trains to pass each other when moving in opposite direction. If they move in the same direction, the faster train could completely pass the slower train in 2 minutes. If the faster train is 120 meters long and the slower train is 130 meters long, find the rate of the faster train.

6.43 hr

A man can do a job in 8 hours, a boy can do the same job in 12 hours and a girl can do it in 16 hours. How long will it take them to do the job if the man and the boy work together for one hour and then the boy and the girl finish the job? 

5

A piece of work can be done by women in 11 days and 30 men in 7 days. In how many days can the work be done by 22 women and 21 men?

144 cm

The bob of a pendulum swings through an arc of 24 cm long on its first swing. If each successive swing is approximately 5/6 the length of the preceding swing, find the approximate total distance it travels before coming to rest.

9 kph

A boat travels 12 km downstream and 16 km upstream in 12 hours. If the rate of the current is 3 kph, what is the rate of the boat in still water?

0.447

If the cosine of angle x is 3/5, then the value of the sine of x/2 is

10 deg

If 82° + 0.35x = Arctan(cot 0.45x), find x.

If sec A = -5/4, A in quadrant II, find tan 2A.

√(a²+b²)

If ysinx = a and ycosx = b, find y in terms of a and b.

1/3

If tan(Arctanx + Arctan ¼) = 7/11, find x.

1/3

If tan 𝜃 = √3, θ in quadrant III, find the value of 1+cosθ / 1 -cosθ

9.11

What is the diameter of the circle that is circumscribed about an isosceles triangle whose vertical angle is 8 degrees and the sum of the two equal sides 18 units?

837.62

The diagonals of a quadrilateral are 34 and 56 intersecting at an angle of 67°. Find its area.

67.83 cm

Find the radius of a circle in which is inscribed a regular nonagon whose perimeter is 417.6 cm

18

If each interior angle of a regular polygon has a measure of 160degrees, how many sides has the polygon?

½ (a + b - c)

The sides of a right triangle are a, b, and c where c is the hypotenuse. Find the radius of the circle that is inscribed in the triangle.

47.65

Two sides of a parallelogram are 20 and 30 and the included angle is 36 degrees. Find the length of the longer diagonal.

14

What is the greatest common factor (GCF) of 70 and 112?

18

What is the greatest common factor of 324, 666, and 756?

Rational Number

The number 0.123123123… is:

5/22

What is the equivalent to 0.22727272727

-120

Evaluate √−64√−225

(x² - 1)(x + 1)

Find the factor of x³ + x² – x – 1.

(1 + x⁴)(1 + x²)(1 + x)(1 − x)

Which of the following is the factor of the expression (1 − x⁸)?

All of these

Solve the value of x:

x^2/3 + x^-2/3 = 17/4

4

If log_x 10 = 1/4, what is log₁₀ x?

-√70

Evaluate √−7√−10

4

The number 0.005328 has how many significant digits?

Real Number

Which of the following best describe 7+0i?

27719

Which of the following is the smallest number that when divided by 11 gives a remainder of 10, when divided by 10 gives a remainder of 9, and when divided by 8 gives a remainder of 7, and so on, down to a remainder of 1 when the number is divided by 2?

360

If red bulbs flash every 8s, blue bulbs every 9s, and green bulbs every 10s, how many seconds pass before they all flash simultaneously again?

All of these

Which of the following is equal to 100 grads?

135 deg

How many degrees of ¾ π of radians?

1/cosθ

Simplify cosθ/sinθ+1 + tan θ

2sinx/secx

What is an equivalent expression for sin2x?

0.250

If sin A = 2.571x, cos A = 3.06x, and sin 2A = 3.939x, find the value of x?

-1

cos 1°+ cos 2°+ cos 3°+…+ cos 180° is equal to

The cosine is negative

Which is true regarding the signs of the natural functions for angles between 90 deg and 180 deg?

90

If the angles of a triangle are in the ratio of 2:4:6. find the largest angle.

9:4

The corresponding sides of the two similar triangles are in the ratio 3:2. What is the ratio of their areas?

810 deg

What is the measure of 2.25 revolutions counter clockwise?

124.64 m

Given the triangle ABC in which A = 30°30', b = 100 m and c = 200 m. Find the length of the side a.

geometric

The cotangent of the angles pi/3, pi/4, and pi/6 are in _ progression.

2.87 km

When a helicopter is 1.2 km above one end of an island, the angle of depression to the other end of the island is 22.7 deg. Find the approximate length of the island.

3.897

Find the area of an equilateral triangle with a perimeter of 9.

parabola

Which conic is represented by the equation x²+y²-2xy+20x+10=0?

Hyperbola

Which of the following is represented by the equation 2xy-x+y-3=0?

10 centered at (2, -1)

Find the center and the diameter of the equation x² + y² - 4x + 2y - 20 = 0.

x² + y² - 4x - 2y - 45 = 0

Find the equation of the circle passing through (-3, 6), (-5, 2). and (3,-6).

The coefficients A and C preceding the x² and y² terms in the general form of the equation are equal.

Which of the following statements is FALSE for all noncircular ellipses Ax2 + Bxy + Cy2 + Dx + Ey + F = 0? A. The eccentricity, e, is less than one.

(-2, 2) & (0, 2)

Find the location of the vertex of the hyperbola 16x² - 9y² + 32x + 36y - 36 = 0.

(1, 0)

Which of the following points ( 1,0 ), (-1, 0) , (4, 4) and (9, 7) belong to the equation y = x²-x?

y² + 8x- 6y + 25 = 0

Determine the equation of a parabola with vertex (-2,3) and focus at (-4,3).

whose eccentricity is 2.52

The equation 16x² - 3y² - 32x + 12y - 44 = 0 represents a hyperbola

1.25

Find the eccentricity of the hyperbola whose equation is 9x² - 16y² + 18x + 64y - 91 = 0.

C (1, 1) & 2

Find the center and semi-major axis of ellipse x² + 4y² - 2x - 8y + 1 = 0.

7.48

The length of the tangent from (4,8) to the circle x² + (y - 1)² = 32 is:

0.75

Compute the eccentricity of the given curve 9𝑥² + 4𝑦² − 24𝑦 + 144 = 0.

(4, -5)

Find the center of the conic whose equation is 16x² - 9y² - 128x - 90y - 113 = 0.

(-2, 2) & (0, 2)

Find the location of the vertex of the hyperbola 16x² - 9y²+ 32x + 36y - 36 = 0.

147,272.21

A steam boiler is purchased on the basis of guaranteed performance. A test indicates that the operating cost will be Php 15,000 more per year that the manufacturer guaranteed. If the expected life of the boiler is 20 years, and the money is worth 8%, what amount the purchaser should deduct from the purchase price to compensate for the extra operating cost?

Php 5650

How much money must you invest today to withdraw Php 1000 per year for 10 years if the interest rate is 12%?

3940 per month

The president of a growing engineering form wishes to give each of 50 employees a holiday bonus. How much is needed to invest monthly for a year at 12% nominal interest rate, compounded monthly so that each employee will receive a P1000 bonus?

P 1,435,493.83

A house and lot is being sold and the payments are on installment basis of P 400,000 each year for 5 years. If the payments are to be made at the beginning of each year, how much is the cash price of the property? Assume that money is worth 20% compounded annually?

5

Determine the x – intercept of the line passing through (1, 4) and (4,1).

-4/5

If the slope of a line 3x + y – 5 + k(x + 2y – 3) = 0 is 11/3 find k.

7x + 2y + 31= 0

Find the equation of the line parallel to 7x + 2y – 4 = 0 and passing through (-3 , -5).

2x + 5y – 13 = 0

Find the equation of the line through (-1, 3) and is perpendicular to the line 5x – 2y + 3 = 0.

4

Find the area of a triangle whose vertices are (1, 1), (3, -3) and ( 5, -3).

5x + y – 4 = 0

Find the equation of the line passing through points (0,4) and (1,-1)

1

If points (3, 2) and (x, 5) lie on a line whose slope is -3/2, then what is the value of x?