Q1

Find the constant remainder when 3x4-4x3+5x2-5x+1 is divided by x +1. a. 18 b. 81 c. 77 d. 16

a

Find the 5th term in the expansion of (x2-2y3)8 a. 2011x8y12 b. 1120x8y12 c. -1120x8y12 d. 2110x8y12

b

25. How many sides and diagonals have an equiangular polygon if each its interior angles is 165 degrees? a. 24, 252 b. 42, 522 c. 34, 282 d. 14,152

a

A ball is dropped from a height of 128 cm. Each time it strikes the ground, it rises to ½ of the height from where it falls. Find the total distance travelled by the ball until it stops. a. 384 cm b. 483 cm c. 348 cm d. 438

a

A man piles 150 logs in layers so that the top layer contains 3 logs and each layer has one more log than the layer above. How many logs are at the bottom? a. 17 b. 16 c. 19 d. 81

a

A tank can be filled in 30 min by two pumps working together. If the larger pump takes 25 min less time than the smaller pump to fill the tank, what is the time needed by the larger pump to fill the tank? a. 50 min b. 75 min c. 45 min d. 30 min

a

Find the radius of the circle that circumscribed a triangle with sides 8, 10, 12 cm respectively. a. 6.05 cm b. 2.65 cm c. 5.68 cm d. 4.65 cm

a

Find two numbers such that their difference is equal to their product and the sum of their reciprocals is 5. a. ½, 1/3 b. 2, 3 c. 3/2, 2 d. 2/3, 3

a

Find two numbers whose arithmetic mean is 20 and whose geometric mean is 16. a. 8, 32 b. 10, 30 c. 12, 28 d. 6, 34

a

How many grams of alloy containing 35% nickel must be melted with an alloy containing 65% nickel in order to obtain 20 grams of an alloy containing 41% nickel? a. 16 b. 18 c. 14 d. 15

a

If 4 men take 6 days to assemble 8 machines, how many days will it take 3 men to assemble 10 machines? a. 10 b. 12 c. 11 d. 15

a

If the 3rd term of a GP is 20 and the 8th term is 640, find the 10th term a. 2560 b. 2650 c. 5620 d. 2065

a

On a trip, James noticed that his car averaged 21 km per liter of gasoline except for the days he used the aircon, and then it averaged only 17 km per liter. If he used 91 liters of gasoline to drive 1751 km, on how many km did he use the air-con? a. 680 b. 860 c. 780 d. 870

a

Pedro can do a job in 6 hrs and Jose can do the same job in 10 hrs. If Pedro work 2 hrs and Jose joined him, how many hrs more will the two boys finish the job together? a. 2 1/2 b. 3 ½ c. 2 ¼ d. 2 1/6

a

The 9th term of an AP is 5 times the 2nd term and the 11th term exceeds the 6th term by 20. Find the 13th term. a. 51 b. 15 c. 71 d. 81

a

The sides of a triangle are 5, 7, and 10 respectively. Find the radius of the inscribed and circumscribed circle. a. 1.48, 5.39 b. 2.48, 6.39 c. 3.48, 7.39 d. 4.48, 8.39

a

The sides of a triangle are 5, 8 and 10 respectively. Find the length of the median line through the side 10. a. 4.42 b. 4.24 c. 6.82 d. 8.70

a

A car traveling at 75 kph leaves town A for town B. Two hours earlier, a truck left town A at a speed of 45 kph. How far from town A will the car overtakes the truck? a. 252 km b. 225 km c. 552 km d. 215 km

b

A policeman is pursuing a thief who is ahead by 72 of his own leaps. The thief takes 6 leaps while the policeman is taking 5 leaps, but 4 leaps of the thief are as long as 3 leaps of the policemen. How may leaps were made by the policeman until he caught the thief? a. 648 b. 540 c. 450 d. 230

b

A room has a dimension of 5x4x3m. An ant is located at one corner of the ceiling in the room. If it will travel on the walls and the floor, find the length of the shortest path it should travel to reach the opposite corner on the floor. a. 9.5m b.8.6m c. 9.8m d. 8.3m

b

At noon, ship A is sailing on a course eastward at the rate of 20 knots. At the same instant, another ship B, 100 nautical miles east of ship A is sailing on a course N30OW at the rate of 10 knots. How far away from each other are the ships after one hour? Note 1 knot = 1 nautical mile/hr. a. 55.7 nm b. 75.5 nm c. 57.5 nm d. 65.7 nm

b

Determine the value of k so that the sum of the roots of 3kx2 + 3k2 -4kx = 5- 3x exceeds the product of the roots by 3. a. 2 b. -2 c. -4 d. 3

b

Find the angle (in rad) between the minute hand and hour hand of a wall clock at 3:25 pm. a. 0.892 rad b. 0.829 rad c. 0.982 rad d. 0.928 rad

b

Find the angle whose supplement exceeds 6 times its complement by 20 deg. a. 67 deg b. 76 deg c. 27 deg d. 54 deg

b

Find the area of a regular hexagon if each side is 8 cm long. a. 316.37 b. 166.28 c. 133.37 d. 313.73

b

From a point on a level ground, the angle of elevation of the top of a building is observed to be twice the angle of elevation of the window one third of the way up the building. Find the angle of elevation of the top of the building. **** a. 56 deg b. 60 deg c. 65 deg d. 48 deg

b

If the rth term of (x^2-2y^3)^8 is kx^8y^12, find the value of k. a. 2011 b. 1120 c. 2110 d. 1210

b

John's rate of doing work is three times as fast as Bill. On a given day John and Bill work together for 4 hrs then Bill was called away and John finishes the rest of the job in 2 hrs. How long would it take Bill to do the complete job alone? a. 18 hrs b. 22 hrs c. 15 hrs d. 31 hrs

b

Solve for the value of y from the system of equations ysinx=3 and ycosx=4. **** a. 7 b. 5 c. 25 d. 1

b

The difference in area between the pentagram and the circumscribed circle with radius 10 cm is nearest to. a. 201 sq m b. 202 sq m c. 205 sq m d. 204 sq m

b

What is the greatest distance on the surface of the earth that can be seen from the top of a mountain which is 2.4 km high if the radius of the earth is 6370 km. a. 157.9 km b. 174.8 km c. 179.7 km d. 189.7 km

b

A certain solution should contain 8% alcohol. It was mistakenly mixed to contain 6% alcohol; how much must be drawn from a filled 5-liter tank and replaced by 10% alcohol solution to provide the proper concentration? a. 5.2L b. 2.7L c. 2.5L d. 2.8L

c

A man at a certain distance measure the angle of elevation of a tower. He then walks 20m on a level ground towards the tower. The angle of elevation from this second station was then the complement of the former angle. The man again walks 5m nearer to the tower in the same line and found the angle of elevation to be doubled the first angle. How high is the tower? a. 29.12m b. 22.19m c. 22.91m d. 27.7m

c

A man rows upstream and back in 12 hours. If the rate of the current is 1.5 kph and that of the man in still water is 4 kph, what was the time spent downstream? a. 1.75 hr b. 2.75 hr c. 3.75 hr d. 4.75 hr

c

A plane was scheduled to fly from city A to city B. The flight was against the head wind of 10 kph. Threat of mechanical failure forced the plane to turn back and it returned to city A with a tail wind of 10 kph landing 1.5 hrs after it had taken off. If the plane has a uniform speed of 150 kph, how far had it gone before turning back? a. 121 km b. 211 km c. 112 km d. 122 km

c

An equilateral triangle has its side 20 cm. Smaller equilateral triangle are formed by connecting the midpoints of the sides of each of the other equilateral triangles and so on indefinitely. Find the sum of the perimeters of all the triangles. a. 210 cm b. 230 cm c. 120 cm d. 150 cm

c

An observer on top of a cliff 45.8 m high observes the angles of depression of two ships, which are due north of him to be 20'12' and 47'39'. Find the distance between ships. **** a. 273.82m b. 87.32m c. 82.73m d. 83.72m

c

At a point A south of a tower, the angle of elevation of the top of the tower is 50 deg. At another point B, 200 m east of A, the angle of elevation is 22 deg. Find the height of the tower. **** a. 84m b. 85m c. 86m d. 87m

c

Find the area covered by the pentagram in sq cm if the pentagon formed at the center has a side of 10 cm. **** a. 565.76 b. 655.67 c. 556.76 d. 556.67

c

Find the value of k in the quadratic equation (2k+2)x2 + (4-4k)x +k -2 = 0 so that the roots are reciprocal of each other a. 4 b. 2 c. -4 d. 3

c

If the sum to infinity of 1/x, 1/4x, 1/16x... is 2/3, find x. a. 3 b. 5 c. 2 d. 4

c

In a family of 8 children, two are twins. The youngest is 3 yrs old and the eldest is 21 yrs old. Their ages are in AP. There are 3 children younger than the twins. How old are the twins? a. 8 b. 10 c. 12 d. 6

c

The base of a parallelogram is 57.5cm and its diagonals make angles of 24"20' and 42"26' with the base. Find the length of the longest diagonal. a. 56.16 cm b. 28.08 cm c. 83.04 cm d. 41.52 cm

c

Without expanding (2x+y)^13 , find the numerical coefficient of the 9th. a. 41,481 b. 41,841 c. 41,184 d. 41,418

c

An airplane is flying at an altitude of 1 km directly away from an observer on the ground has an angle of elevation of 48 deg at a certain instant and an angle of elevation of 20 deg one minute later. The speed of the plane is nearest to. a. 115 kph b. 112 kph c. 140 kph d. 111 kph

d

An inscribed angle is radian and the chord of the circle subtended by this angle is cm. Find the radius of the circle. a. 15 cm b. 14 cm c. 13 cm d. 12 cm

d

From a point outside an equilateral triangle the distances of the vertices are 10 meters 18 meters and 10 meters respectively. Find the length of the side of the triangle a. 16.95m b. 17.95m c. 18.95m d. 19.95m

d

Identical spheres are piled to form a pyramid with square base having 8 pieces on each side until a sphere on top. How many spheres are on the pile? a. 240 b. 230 c. 210 d. 204

d

The angle of elevation 10m from a tree of the top of the tree is three times the angle of elevation at a point 50m from it. Find the height of the tree. **** a. 25m b. 23m c. 21m d. 19m

d

The centers of two circles of radii 41cm each are 80 cm apart. Find the length of their common chord. a. 14 cm b. 15 cm c. 16 cm d. 18 cm

d

The sum of the squares of the two digits of a positive integral number is 89. The number itself is 7 more than 6 times the sum of its digits. Find the number. a. 58 b. 38 c. 49 d. 85

d