ACLC COLLEGEBALANGA CITY, BATAAN

ALGEBRA1. Factor the expressions 12a3 – 24a2 – 48a2. Factor the expressions 24x4 – 16x3. Factor the expressions 25a2 – 14. Evaluate -2-1 – 20 – 2-2

5. Factor the expressions X2 - 10AX - 11A2

6. Factor the expressions 16X2 – 16BX + 3B2

7. Fill in the missing term to make the expression a perfect square trinomial.

____ - 180yz + 100z2 8. Factor 12x2 + 7x – 129. Find the Least Common Multiple (LCM) of 12x2yz3, 28x3y2z, 30x4y4z10.Perform the indicated operation.

b2

(b−4)2− 16

(b−4)2

11.Evaluate [ 4a2b3 c46a5b2 c3 ]3

12.Simplify 3√54m4n10 p17

13.Simplify this rational expression p3−8p2−4

14.Simplify [-92 ÷ (-3)] √ 9 - 58 ÷ 2

15.Perform the indicated operation. 43√54 + 3 3√250 - 6 3√128

16.Solve for x using quadratic formula. 10x2 + 11x = 6

17.Given the equation 2(2x + 1) – 3x/2 = -3(4 + x)/2, solve for X

18.Subtract 5x + 3y – 4 from the sum of -9x + 7y – 8 and -2x – 9y + 10.

19.Perform the operation.

4 x2−12x2−5 x−3

. x2+ x−12

4 x2−8 x+3. 2x

2+3 x−9x2+7 x+12

20.A rectangular field has a perimeter of 104 meters. The length of the field is 12 meters more than its width. Find the length and the width of this field.

21.Solve for the positive value of X in the expression X2 - X – 3022.One number is 5 less than the other. If their sum is 135. What are the

numbers.23.The sum of two numbers is 21 and one number is twice the other. Find the

number24.If 8 is added to the product of a numerical number, the sum is seventy one.

Find the unknown number25.Find the 6th term of the sequence 55, 40, 28 19, 13 ….

TRIGONOMETRY1. Two triangles have equal bases. The altitude of one triangle is 3 units more

than its base and the altitude of the other triangle is 3 units less than its base. Find the altitudes if the areas of the triangles differ by 21 square unit.2. Two cars are on 2 straight roads which cross at right angles. If the cars are 20m and 99m from the intersection, how far apart are they?

3. A tree is broken 3m above the level ground. The top strikes the ground 4m from the foot, while the other end of the broken part remains attached to the stump. How high is the tree?

4. On the way to the office, Boy Bayo was told that when she stands 123 ft from the base of the building, the angle of elevation of its top is 26°30’. If her eyes are 5 ft above the ground, find the height of the building.

5. A 98 ft extension ladder has just reached the top of the building. It has a ladder truck 11 ft. from the ground. When the angle of elevation of the ladder is 73°, how high up the building?

6. A ladder 42 ft. long is placed so that it will reach a window 30 ft. on one side of the street, if it turned over, its foot being held imposition, it will reach a window 25 ft. high on the other side of the street. How wide is the street from building to building?

7. From the top of the cliff 52m high, the angle of depression of the 2 ships due east are 36° and 24° respectively. Find the distance between the ships.

8. An antenna is on top of a TV transmission tower. At a point 236 m from the base of the tower, the angles of elevation of the top of the antenna TV transmission tower are 42˚ 20’ and 44˚ 10’ respectively. Find the height of the tower and the antenna.

ANALYTIC GEOMETRY1. Find the distance of points (6,3) (4,3).2. Find the midpoint of a line segment (4,8) (-4,-3).3. Find the perimeter of a triangle whose vertices are A (3,0) , B (5,2) , C (7,6).4. Show that the quadrilateral whose vertices are (-2,6) (4,3) (1,-3) and (-5,0) is a

square. Find the area.5. Find the slope of the line through points (3,-5) (-6,-2).6. Find the coordinates of the point which is one-fourth of the way from the point

(2,1) to the point (5,5).7. Find the equation of the line through points (5,1) (3,6).8. A line which passes through (5,6) and (-3,-4) has an equation of:9. Find the equation of the line with slope 2 and y-intercept of -3.10.Find the equation of the line with x-intercept 4 and y-intercept -6.11.A line passes through (-2,-7) and has its intercept numerically equal but opposite

sign. Find its equation.12.Write the equation of the line 3x + 6y – 2 = 0 in the slope intercept form and find

the slope and y-intercept.13.Give the standard form of the equation of the circle with center (2,6) and radius 5.14.What is the radius of the circle with the following equation x2 – 6x + y2 – 4y 12 = 0 15.Find the center of the circle x2 + y2 – 6x + 4y – 23 = 016.Write the equation of the circle, the line segment joining A (0,0) and B (-8,6) as a

diameter.17.What is the length of the latus rectum of parabola x2 = -12y.18.Find the equation of the directrix of parabola y2 = 16x.19.Find the coordinates of the Foci (FF’), major axis (VV’) and minor axis (BB’) of

the curve ellipse y2/25 + x2/16 = 1. 20.What is the equation of the asymptote of the hyperbola 36x2 – 64y2 = 4.21.Find the transversal axis (VV’), conjugate axis (BB’), Foci (FF’) of the hyperbola

9y2 – 4x2 = 36.

STATISTICS

1. In the Philippine 6/45 lottery, how much will I spend if I were to bet on all the possible combinations. ( prize per combination is 10 pesos ).

2. In a class of 40 students, 27 like calculus and 25 like circuits. How many like both calculus and circuit.

3. A card is drawn from a deck of 52 playing cards. Find the probability of drawing a picture ( king, queen jack ) or a black card.

4. Roll two dice once. What I the probability that the sum is 6?hn5. In how many ways can you invite one or more of your five friends in a

party?6. In Mathematics examination, a student may select 7 problems from a set

10 problems. What are the possible choice of combinations?

7. A card is drawn from a deck of 52 playing cards. Find the probability of drawing an even number or a diamond card.

A mental ability test was administered to 1000 randomly selected high school students. The mean was 100 and the standard deviation was 15. Assume a normal distribution of the scores, answer the following questions: ( questions 9-11 )

8. How many students scored below 90?9. How many students got a score of above 100?10. How many students scores between 90 and 110?

11. In how many ways can 9 passengers be seated in a bus if there are only 5 seats available?

In how many ways can 4 boys and 4 girls be seated in a row of 8 chairs if:

12. they can sit anywhere?13. the boys and the girls are to be seated alternately?

A box contains 2 red, 5 blue, 5 yellow balls. In how many ways can three balls be drawn from the box such that:

14. they are all blue?15. There are no blue balls?16. 2 are red and 1 is yellow?17. They are of different colors?

A box contains 4 blue chips and 5 red chips:

18. If one chip is drawn at random, what is the probability that is blue?19. If two chips are drawn at random, what is the probability that both are red?20. If two chips are drawn at random, what is the probability that one is blue and the

other is red?

SOLID MENSURATION

1. Calculate the volume of a conical frustum container with a height of 100 cm if the radius of the lid is twice of the base. ( radius of base is 36 cm )

2. If I used 40 meters to fenced a 100 square meter rectangular lot, what is the dimension of the lot?

3. Derive the formula for the AREA of a regular Octagon.4. What is area of a 9 sided regular polygon if its side is 10 units.5. Given a cylindrical tin can with height of 10 inches. Find the Total Surface

Area of the can if the volume is 100 cubic inches.6. Find the volume of a square base pyramid with side equal to 50 meters and

height 40 meters.

7. A 3 meters square base chimney is to be made using a quick dry cement. The base is twice as large as the tip. If the chimney exhaust dimension is 1x1 from top to bottom and its base is 3 meters, how much cement is used to build the chimney

DISCRETE MATHEMATICSFALSE IF TRUE AND TRUE IF FALSE.Consider the sets A= {1, 2, 3, 4} B= {2, 4, 6, 8, 10} C= {1, 3, 5, 7, 9} D= {1, 2, 3, 4, 5,…., 100}

1) D ⊂ A2) B=C3) Ø ⊂ B4) 4ϵ D5) {8} ∉ B

6) List all the elements of set M is the set of months having exactly 30 days.

7) How many subset in set P = {a, b, c, d}

Given : U = {F,A,C,E,B,O,K}A = {F,A,C,E}B = {B,E,A,K}C = {B,A,K,E}D = {A,C,E]E = {A}

Find:

8) (C'⋂ D) ⋂ B9) (A⋂ B)’10) (A’ – B)’11)(B’ – A)’12)(A⋃C)’ ⋃ D’

Solve the following using Venn diagram, answer the questions that follow:

An engineering professor conducted a survey regarding the favorite subjects of 100 students. The following data were gathered:

15 students like all the three subjects5 likes both algebra and physics10 likes both calculus and physics15 likes both algebra and calculus60 students like algebra50 students like calculus45 students like physics

13)How many had no favorite at all?14)How many likes algebra only?15)How many likes physics and algebra only?16)How many likes physics only?17)How many likes both algebra and calculus only?

18) Draw the truth table of (A + B) + AC

If A + B is 0 and A.C is 1, what is:

19)(A B) (A + C)

20)A (B C)

21)(A + B) C

Draw the logic circuit of the following:

PROCTOR WILL PROVIDE THE EXPRESSION:

ACLC COLLEGEBALANGA CITY, BATAAN

DIFFERENTIAL CALCULUS

1) Simplify the expression: limx→ 4

x2−16x−4

2) Evaluate the limit: limx→1

x2−1x2+3 x−4

3) Evaluate the limit x−4

x2−x−12 as x approaches 4.

4) Find dydx if y=5

2x+1

5) Find the derivative of x+5x2−1

with respect to x.

6) Find the derivative of ( x+1 )3

x

7) Evaluate the first derivative of y = 4x3 + 2x2 – 5x + 6 if x = 2.

8) Find the second derivative of y = x+1x+2

9) What is the derivative of y = x2 sinx

10)Given the function y = (x2+2x+1 )3 , find the first derivative.

11)What is the derivative of y = 3√2x−7

12)Differentiate -5x-6 + 4x-3 + 4x-1 + 6

13)What is the derivative of y = sinxcosx

14)Differentiate y = x2+x−1

sinx+cos x

15)Differentiate y = [ 4 x−12x+3 ]3

16)Find dydx

if y = (6 x2−5 x+3 )−1 /4

17)Find the third derivative of y = sin4x + x2

18)Find the slope of the line tangent to the curve y = x3 – 2x + 1 at x = 1

19)Find the slope of the tangent to the curve y = x4 – 2x2 + 8 through point (2,16).

20)Find the equation of the tangent line of the curve y = x2 + 3x + 4 through points (1,8).

INTEGRAL CALCULUS1) Evaluate ∫102x dx

2) Evaluate ∫ 4e2x dx

3) Evaluate ∫√e4 x dx

4) Evaluate ∫ dx

e1−2x

5) Evaluate ∫3e5x−2 dx

6) Integrate (12x5 + 5x4 + 6x2 + 2x – 4) dx

7) Evaluate: ∫√2−3x dx

8) What is the integral of ∫ x4+2 x2−1√ x

dx

9) Find the integral of ∫ x2 (2x3−1 )4 dx

10) Integrate: 5x3−2x2−18 x−10

x+2 dx

11) Evaluate: ∫ 4 x2+3 x−9x+2 dx

12) Find the integration of ∫ 6 x3−5 x2−8 x+33x2+2 x−1

dx

13) Find the integral of ∫ (4 sinx−5 cosx ) dx

14) What is the integral of ∫ cscx−cotxcosx dx

15) Evaluate: ∫1

3

(3 x2+ 4x2 ) dx

16) Evaluate ∫0

2

(x3−3x2−x+3 ) dx

Express each without the symbol ∑, evaluate when n = 10

17)∑i=1

n

(8i−3 )

18)∑i=1

n

i (i−1 ) ( i+1 )

DIFFERENTIAL EQUATION

1. A nominal interest of 3% compounded continuously I given on the account. What is the accumulated amount of P 10,000.00 after 10 years?

2. The sum of P 10,000.00 is invested at the rate of 5% per year compounded continuously. When will the amount be P 20,000.00

3. The population of a country doubles in 50 years. How many years will it be five times as much? Assume the rate of increase is proportional to the number of inhabitants.

4. Radium decomposes at a rate proportional to the amount present. If half of the original amount disappear after 1000 years, what is the percentage lost in 100 years.

5. The sum of two positive numbers is 50. What are the numbers I their product is to be the largest possible.

6. A farmer has enough money to build only 100 meters of fence. What are the dimensions of the field he can enclose the maximum area?

7. Find the minimum amount of tin sheet that can be made into a closed cylinder having a volume of 108 cu. Inches.

8. A box is to be constructed from a piece of zinc sq. in by cutting equal squares from each corner and turning up the zinc to form the side. What is the volume of the largest box that can be so constructed?

PHYSICS1. Determine the X and Y components of each of the forces shown below. A=

100N 35o from x axis, R= 120N 35o from x axis, W= 150N 45o from x axis, I= 111N along y- axis, N= 60N 50o from x axis. Also, compute for the Resultant Force and its Direction.

A R

3

9

4

6

5

2. The wooden block is acted upon by its weight W=300 Lbs, a horizontal force F= 800 Lbs and the pressure P ( at 15 degrees from the vertical ) exerted by the inclined plane. Determine P that will stop the block from sliding

3. Determine the X and Y components of each of the forces shown below. A= 150N, B= 200N, C= 98N , D= 69N. Also, compute for the Resultant Force and its Direction.

N IW

40o 20o

W

F

P

B

C

8

A

3

6

D

4. Manny Pacquiao threw a punch with a force of 85 Newtons at 73° angle. What are the x and y components of the force?

5. A truck travels 137.50 miles heading north then it turns east and covers a distance of 85.2 miles. What is the magnitude and direction of the truck’s displacement?

6. A mountaineer climbed a 225 feet distance and then rest. He ascended to a distance of 96 feet then he suddenly slipped and rolled down to a distance of 35 feet. What is the total distance covered by the mountaineer?

7. A truck with a velocity of 130 km/hr collides with a bus with a velocity of 85 km/hr. What is the resultant velocity if the angle between the two vehicles is 60°?

8. Determine the horizontal force needed to accelerate a 1.5-lbs box from rest to 0.4-ft/s in 3 seconds if the coefficient of friction between the box and the floor is 0.40. (15 points)

300 lb

400 lb

RIGID BODIES ( STATIC MECHANICS )1. The bell crank shown below is supported by a bearing at A. A 100 pound

force is applied vertically at C, rotation being prevented by the force P acting at B. Compute the value of P and the bearing reaction at A.

2. A system of knotted cords shown below support the indicated weights. Compute the tensile force in each cord.

13.67

D

C

B

30o

105o

30o

75o

C

A8

75o

45o

100 Lb

B

P RA

90o

A