ARITHMETIC AND NUMBER THEORY

1. An airplane flying at 15,000 meters climbs 3,000 meters to avoid a storm. Then in drops 4,000 meters and finally climbs 2,000 meters. What is its final altitude?

A. 24,000 m B. 6000 m C. 16,000 m D. 14,000 m

2. Given the set of numbers{−8 ,−6 ,−1 ,1 ,4 }, what is the smallest product that can be obtained by multiplying two numbers of the set?

A. -1 B. -4 C. -24 D. -48

3. Simplify: {2−[3+4 (5−3 )+7 ]+8}

A. -11 B. -8 C. 21 D. 22

4. Susan has Php 1,000 in a bank. She withdrew money to buy her twin nieces a present that cost Php 274.50 and Php 195.50. She received Php 250.00 from her mother as her allowance and deposited half that money in her account. How much money did she have in a bank?

A. Php 655 B. Php 595 C. Php 1,125 D. Php 250

5. [(−32 + 14 )÷ 58 ]

A.−15

B. -2 C.−2532

D. 2

6. On a number line, what is the distance between -7 and 8?

A. −1 B. 1 C. 15 D. -15

7. What us the GCF of 16, 24, 40?

A. 4 B. 2 C. 8 D. 6

8. What is the LCM of 16, 24, 40?

A. 240 B. 960 C. 15360 D. 8

9. Two Filipino families migrated to Australia. They came home regularly as “balikbayans”. The Garcia family comes back to the country every two years and the Dizon family every three years. If they came together last year (1998), when will they come home again?

A. 2000 B. 2001 C. 2004 D. 2010

10. A certain supermarket repacks rice in smaller bags from big sacks of about 50 kg. Whether they use 2 kg or 3 kg bags, they still have 1 kg of rice left in the sack. How many kg of rice does a sack contain?

A. 50kg B. 55 kg C. 48 kg D. 49 kg

11. Janice has several small boxes that she wants to pack in bigger boxes. If she packs 4 or 5 small boxes in a bigger box, she has 2 left over. If she packs 6 of them together, none is left over. How many small boxes does she have?

A. 42 B. 60 C. 22 D. 122

12.If a is divided by 2, there’s a remainder of 1, divided by 3, a remainder of 2; divided by 4, a remainder of 3, and so on up to the number divided by 9 which gives a remainder of 8. What is the number?

A. 2517 B. 2518 C. 2519 D. 2520

13.Which of the given numbers is both divisible by 2 and 3?

A. 27 B. 30 C. 200 D. 23

14.Which of the given numbers is divisible by 11?

A. 1211 B. 1021 C. 2101 D. 1120

15.Which of the following numbers is divisible by 8?

A. 518 B. 632 C. 416 D. 832

16.For a given number126.3_8 what number may be placed in the blank to make it divisible by 3.

A. 0 B. 1 C. 2 D. 3

17.Given 25_3_9, what numbers may be placed in the blank to make it divisible by 9?

A. 8 &9 B. 10 &7 C. 5&4 D. 6&3

18.Find the largest three-digit number that is divisible by 22 and the sum of whose digit is 11.

A. 209 B. 920 C. 290 D. 902

19.In one section, the ratio of boys to girls is 4:3. If there are 42 students in class, how many are girls?

A. 18 B. 6 C. 24 D. 36

20.A hospital charges a patient Php 78.00 for 12 capsules. How much should it charge for 18 capsules?

A. Php 111 B. Php 114 C. Php 117 D. Php 120

21.A Magnolia bar contains 200 calories. How many bars would you need to eat to get 500 calories?

A. 1 ½ B. 2 C. 2 ½ D. 3

22.The distance between two cities on a road map is 11cm. Actually, the cities are 308 km apart. The distance between two other cities is 15 cm. How far apart are the cities?

A. 420 km B. 3388 km C. 4620 km D. 312 km

23.Lyn has 25 m ribbon. If she needs 3 dm to tie a certificate, how many certificates can she prepare with the ribbon?

A. 7 B. 8 C. 9 D. 10

24.Two people take 12 days to repair a sidewalk. How many people are needed to complete the repair in 4 days?

A. 2 B. 4 C. 6 D. 8

25. Three numbers are in the ratio of 2:4:6. The middle number is 68, what is the sum of the three numbers.

A. 196 B. 200 C. 204 D. 208

26.If a certain amount of food will last 50 days for 200 soldiers, how long will it last if 50 soldiers are added at the end of 20 days?

A. 24 days B. 26 days C. 28 days D. 30 days

27. 90 is what percent of 450?

A. 2% B. 5% C. 20% D. 50%

28. 79.2 is 16.5% of what number?

A. 13.068 B. 66.132 C. 4.8 D. 480

29. 6.2% of 98 is_________?

A. 6.076 B. 60.76 C. 607.6 D. 6076

30. If x is 125% of y, then y is what percent of x?

A. 75% B. 80% C. 85% D. 90%

31.The cost of an electric fan was Php 1053 including 8% sales tax. What was the price of the electric fan without tax?

A. Php 968.76

B. Php 975 C. Php 975.50 D. Php 980

32.In a group of 100 students, 48 have black pens, 32 have blue pens and 20 have red pens. What percent of the students have either black or red pens?

A. 8% B. 32% C. 48% D. 80%

33.A jacket on sale at Php 480 is 60% of the regular price, what is the regular price?

A. Php 288 B. Php195 C. Php800 D. Php768

34.A room is 10 m by 7 m. There is a 7.5 m by 5 m carpet in the middle. What percent of the room is uncovered?

A. 46.4% B. 53.6% C. 26.5% D. 73.5%

35.What is the area of the largest circle which can be cut from a rectangle whose length and width are 40 cm and 30 cm respectively?

A. 1256 cm2 B. 706.5 cm2 C. 2826 cm2 D. 94.2 cm2

36.Two empty tanks are being filled with water. The first tank fills at the rate of 60 liter per minute for 2 minutes before the water to the second tank is turned on. The second tank

fills at the rate of 80 liters per minute. How many minutes will it take until the second tank has the same amount of water as the first tank.

A. 4 B. 5 C. 6 D. 7

37. A faucet starts dripping into a 120 milliliter glass. The first minute it drips 1 milliliter, the second minute it drops 2 milliliters, the third minute 3 milliliters, and so on. How many minutes will it take to fill the glass.

A. 10 B. 100 C. 15 D. 120

38.How many circles of radius 5 cm can be cut from a piece of cartolina 52 wide by 71 cm long?

A. 47 B. 35 C. 78 D. 117

39. A picture 10 cm by 8 ½ cm is mounted on a piece of hard cardboard. If there is a margin of 2 ½ cm around the picture, what is the perimeter of the cardboard used?

A. 37cm B. 47cm C. 57cm D. 67cm

40. A picture 25 cm by 35 cm is to be framed. If the width of the wood is 2 cm, how long would be the piece of wood needed for the frame?

A. 128cm B. 136cm C. 120cm D. 875cm

BASIC AND ADVANCE ALGEBRA

1. Simplify : 2(3r-7t) – 5(2r + 3t) + (5r + t)

A. r+28t B. 28t-r C. –r-28t D. r-28t

2. If five times the smaller of 2 consecutive integers is added to 3 times the larger, the result is 59. Find the smaller integer.

A. 7 B. 8 C. 9 D. 10

3. If (28-27) (25-24)=2x, what is x?

A. 1 B. 2 C. 11 D. 28

4. What is the real value of x such that if 64x-1 is divided by 4 x-1 the quotient is 2562x.

A.13 B.

−13

C. 3 D. -3

5. What must be subtracted from 5x3-4x2+3x-5 to get 2x3-8+5x-2x2?

A. 3x3-2x2-2x+3 B. 3x3-2x2-2x-3 C. 3x3+2x2+2x+3 D. 3x3-2x2+2x+3

6. Multiply and simplify 3ab2(3a2+3b)-2b(a3b-ab2)

A. 11a3b+7ab3 B. 7a3b+11ab3 C. 11a3b-7ab3 D. 7a3b+11ab3

7. If the replacement set is the set of positive integers, find the solution set of 4 x3

−2<3−3 x4.

A. X< 24 B. {…−1,0,1,2 } C. {1,2 } D. {1,2,3 }

8. If y=3-4x and -5 ≤ x≥, find the range of y.

A. -17≤ y≤23 B. -23≤ y≤17 C. 23≤ y≤17 D. 17≤ y≤23

9. Two candles of the same height are lighted at the same time. The first is consumed in 4 hours and the second in 3 hours. Assuming that each candle burns at a constant rate, in how many hours after being lighted was the first candle twice the height of the second?

A. 2 B. 2.2 C. 2.4 D. 2.6

10.A kerosene tank is 57 full. Mother used

35 of it and the remainder is 9 liters. How many

liters does the tank contain?

A. 6.85 B. 78.75 C. 21 D. 31.5

11.An open box is made from a rectangular sheet of metal by cutting 2 cm square from each corner. If the perimeter of the base of the box must be 40 cm. What is the maximum possible volume of the box?

A. 100cm2 B. 200cm2 C. 300cm2 D. 400cm2

12.Find the length of a rectangular garden with a perimeter of 124 m such that its area is a maximum.

A. 31cm B. 32cm C. 33cm D. 34cm

13.One quarter, a student received 22 grade points for making A or B in each of the 6 subjects he studied. If each A was worth four grade points and each B was worth 3 grade points, in how many subjects did he make A?

A. 1 B. 2 C. 3 D. 4

14.Fred thinks of three numbers. If they are added in pairs the result are 38, 44 and 52. Find the largest of the three numbers.

A. 15 B. 23 C. 29 D. 31

15.A child’s age increased by 3 years gives a perfect square. The age decreased by 3 years gives the square root of that perfect square. What is the child’s age.

A. 1 B. 23 C. 29 D. 31

16.If a, b and c are positive integers, the radical √a+ bc and a√ bc are equal when and only

c=____?

A. b(a2−1)a

B. a2b−b C. b(a2+1)a

D. b (a2−1)

17.The sum of the squares of two numbers is 225 and the squares of their sum is 441. What is their product?

A. 108 B. 216 C. 250 D. 300

18.By what expression of lowest degree can (2x2-x-6) (x2+x-6) be multiplied to make it a perfect square.

A. 2x2-9x-9 B. 2x2+9x+9 C. 2x2+9x-9 D. 2x2-9x+9

19.The fraction (5 x−11)

(2 x2+x−6) was obtained by adding to fractions

A(x−2) and

B(2 x−3). Find the

value of B.

A. -2 B. -1 C. 0 D. 1

20.Factor completely: 4x3-12x2-x+3

A. (x+3)(4x2-1) B. (x+3)(4x2+1) C. (x-3)(2x+1)(2x+1) D. (x-3)(2x+1)(2x-1)

21.Simplify

1

1+1

1+11+1

A. 1 B. ½ C. 3/5 D. 5/3

22.x, y and z satisfies the equation 1x= 1y+ 1z . What is the value of y when x=

13 and z=

14?

A. 1/12 B. 12 C. -1 D. 1

23.If 2a(3b)(5c)=180, find the positive values for a, b and c.

A. a=2,b=2,c=1 B. a=2,b=1,c=2 C. a=1,b=2,c=2 D. a=1,b=1,c=2

24.(x1/2+ a1/2)2 is identical to

A. X+a B. (x2+a2)1/2 C. X+√2ax+a D. X+2√ax+a

25.Simplify : x2

(1−x2 )3 /2+ 2

(1−x2 )1/2

A. (2−x2)¿¿

B. (x2−2)¿¿

C. (x2+2)¿¿

D. (−x2−2)¿¿

26. Simplify [4 t (l+t 2 )−1 /2−2 t 3 (l+t 2 )−3 /2 ]÷ t

√l+t 2

A. 2(l+t2)¿ B.2 [2 (l+t 2 )−t 2 ]

l+t 2

C. 2(l+t2)[2(l+t 2)−t2 ]D.2 [2 (l+t 2 )−t 2 ]

(l+t 2 )−l

27.Express (12+√−16)+ (3+√−25)in the form a + bi.

A. 15-i B. 15+i C. 15-9i D. -15-i

28.Simplify i9+i7+i5+i3+i.

A. 1 B. -1 C. i D. -i

29.Multiply (3-2i)(3+2i)

A. 9-4i B. 13 C. 9-6i D. 4i

30.Perform the indicated operations and simplify (3+2 i)2

4−5 i.

A.−64+4 i9 B.

649

+ 4 i9 C.

−649

+ 4 i9 D.

649

−4 i9

31. Find the quadratic equation with the integer coefficient in which one root is 3-i√2.

A. X2+6x+11 B. X2-6x-11 C. X2-6x+11 D. X2+6x-11

32.If the half life of a certain radioactive substance is 1690 years. What fraction of an original amount of the substance will remain after 6760 years.

A. ½ B. 1/3 C. ¼ D. 1/5

33.If the value of a diamond necklace appreciates exponentially at a yearly rate of 18%, how much will be its cost in 5 years time if the initial cost of the necklace is Php 25,000.

A. 57,194 B. 47,500 C. 60,175 D. 147,500

34.Solve for x: log10 (x2−3 x+6 )=1.

A. 1 B. 4 C. 1 and 4 D. 1 or 4

35.If log10m=b−log10 n , find the value of m

A. 10b/n B. 10bn C. 10/n D. 10n

36.Solve for x: (3 x−2)4

<(2x+7)2

A. X>16 B. X>-16 C. X<16 D. X<-16

37.Solve for x: x2-5x+6> 0.

A. x=3 or x=2 B. x>3 or x>2 C. x>3 or x<2 D. 2<x<3

38.An 8 cm square picture is to be surrounded by a matting that is the same width on all sides, the total area of the picture plus the matting must not exceed 225 cm. how wide can the matting be?

A. -23≤ x≤7 B. 0≤ x≤7 C. 0¿ x≤7 D. -23≤ x≤0

39.Find the value of k so that 8k+4, 6k-2 and 2k-7 will form an arithmetic progression.

A. ½ B. 2 C. -½ D. -2

40.If a clock strikes the appropriate number of times on each hour, how many times will it strike in one day

A. 300 B. 156 C. 78 D. 9

41.In a geometric progression 18, -12 and 8, which term is 512759?

A. 6 B. 7 C. 8 D. 9

42.A man accepts a position at Php 3,600 with the understanding that he will receive a 2% increase every year. What will his salary be after 10 years of service?

A. 4,388 B. 4,320 C. 4,302 D. 4,300

43.Find the constant variation if u varies directly as v and w; u=2 when v=15 and w= 23

A. 5 B. 1/5 C. 10 D. 1/10

44.The period of a pendulum varies directly as the square root of the length of the pendulum. If a pendulum 2 m long has a period of 1.5 seconds, find the period of the pendulum 8 m long?

A. 3 B. 4.5 C. 6 D. 7.5

45.The illumination from the source of light on a surface varies inversely as the square of the distance. A table light is 40 cm from a book. How far should the light be so that the book receives twice as much illumination.

A. 20 cm B. 20√2cm C. 40√2cm D. 80cm

46.If z varies jointly as x2 and y and z= 24 when x=2 and y=3 find the value of z when x=3 and y=5.

A. 45 B. 15 C. 90 D. 180

47.The stiffness of a beam varies jointly as its breadth and depth inversely as the square of the length. What is the change in the stiffness if each of the three dimensions is increased by 10%?

A. Increased by 10% B. decreased by 10% C. increased by D. none

5%

48.If (x-2) is a factor of x3-2x2-ax+8, what is the value of a?

A. -4 B. -2 C. 0 D. 4

49.How many possible rational roots does the equation 4x5-16x4+17x3-19x2+13x-3=0.

A. 4 B. 6 C. 10 D. 12

50.Find the zeroes of f(x)=x3-6x2+3x+10 if (x-2) is one of the factors.

A. -1,-2,5 B. -1,2,5 C. -1,2,-5 D. -1,-2,-5

PLANE GEOMETRY1. K, L and M are collinear points. K has coordinate 12 and L has coordinate -6. If L is

between K and M, and KM =25. What is the coordinate of M.

A. 13 B. 37 C. -13 D. -37

2. If AB=36 and C is the midpoint of AB, what is the coordinate of point C if the coordinate of A is 5?

A. 13 B. 18 C. 22 D. 31

3. Through a given external point, there is _______ line parallel to a given line.

A. Only 1 B. Two C. Three D. infinite

4. In a plane through a point on a given line, there is ____ line perpendicular to the given line.

A. infinite B. Three C. Only 1 D. Two

5. If one angle of a linear pair is obtuse, the other angle is ________.

A. Acute B. Right C. Obtuse D. straight

6. What is the supplement of the complement of an angle 38°?

A. 142° B. 128° C. 90° D. 52°

7. What is the equation od the perpendicular bisector of the segment whose endpoints are (-2,3) and (4,-1)?

A. 3x+2y-5=0 B. 3x-2y+1=0 C. 3x-2y-1=0 D. 3x-2y-2=0

8. ABCD id a trapezoid such that AB is parallel to CD. Points M and N are the midpoints of AD and BC respectively. If the altitudes of ABCD is 3 cm and the length of the bases are 5 cm and 9 cm, what us the area of the quadrilateral ABNM.

A. 16cm2 B. 18cm2 C. 21cm2 D. 9cm2

9. In Triangle ABC, ∠ Ais greater than ∠C. The bisector of angles A and C meet at point D. Which of the following is true?

A. ICDl>IADI B. ICDl=IADI C. ICDl<IADI D. ICDl≤IADI

10.Which of the following cannot describe just one triangle?

A. Acute and scalene

B. Acute and equilateral C. Right and isosceles D. Right and equilateral

11.If two sides of the triangles are of lengths of 7 & 10, how long must the third side be?

A. Between 3 &10

B. Between 7 &17 C. Between 3 &17 D. Greater that 3

12. A man travels 7 km due north, 3 km due east and then 3 km due south. How far is the he from his starting point?

A. 13 km B. 7km C. 5km D. 4km

13.ABCD is a square, triangle XCD is equilateral. How many degrees is ∠BXC?

A. 100° B. 75° C. 90 ° D. 60°

14.In a parallelogram, two adjacent angles differ by 70°. Find the measure in degrees of the largest angle.

A. 55° B. 12° C. 130° D. 125°

15.EF is the median of the trapezoid ABCD. If AD// BC, AD=5 cm and EF= 9 cm. Find BC

A. 13cm B. 10cm C. 9cm D. 4cm

16.The angles of a certain convex polygon have an average of 150°. How many sides does the polygon have?

A. 9 B. 10 C. 11 D. 12

17.Find the measure of each angle of a regular pentadecagon.

A. 90° B. 108° C. 120° D. 156°

18. Find the sum of the measure of the five angles at points of this star.

A. 180° B. 360° C. 540° D. 900°

19.A circle has a radius of 8 cm. what is the radius in cm of a circle which has four times its area?

A. 32cm B. 16cm C. 256cm D. 8cm

20.Two circles with centers at A and C intersect at B and D. If each circle has radius 5, what is the perimeter of the quadrilateral with vertices A, B, C, and D?

A. 5 B. 10 C. 15 D. 20

21.If the chords AB and AC of a circle are of equal length and divide the circle into 3 arcs according to the ratio 2:5:2, then ∠BAC equals

A. 80° B. 100° C. 120° D. 200°

22.Mr. Heintz brought his geometry class a portion of a circular plate. Suppose that the students were given that AB=8; AC=BC=5. What would be the diameter of the plate?

A. 416 B. 8

13 C. 8

16 D. 1

16

23.BC and DE are secants intersecting at A. if mEC=115 and m ∠ A=37 °. Find mBD

A. 41° B. 78° C. 152° D. 30°

24.Which of the following is not a congruence theorem.

A. ASA B. SAA C. SAS D. SSA

25.∆ LET ∆RAN . Let LE=8, ET=6, LT=11 and AN=24. What is the perimeter of ∆ RAN ?

A. 25 B. 49 C. 80 D. 90

26.The floor plan for Sally’s living room has a scale of 1 inch=4 feet. The actual dimension of the living room are 13 ft by 23 t. what are the dimensions of the floor plan?

A. 3.25in by 5.75in B. 32.5in by 57.5in C. 52in by 92in D. 3.25ft by 5.75ft

27.Find the area of a right triangle, given that the altitude to the hypotenuse separates it into segments of lengths 9 and 16.

A. 72 B. 150 C. 96 D. 54

28.Two similar triangles have areas k and 16k. what is the ratio of corresponding sides?

A. 1:8 B. 1:16 C. 1:4 D. 1:2

29.Find the length of the wire needed to brace the two poles if the angles made by the wire with the ground are congruent.

A. 20m B. 25m C. 30m D. 32m

30.In ∆ BOY , m∠B=45 °, m∠O=30 ° and YX⊥BO. If XY=4, what is the perimeter of ∆ BOY ?

A. 12+8√6 B. 20√6 C. 8+48√2+4√3 D. 12+4√2+4√3

ANALYTIC GEOMETRY1. Find the slope of the line passing through (2,3) and (4,-6).

A. -2 B. -1 C. – ½ D. ½

2. Find the slope of a line whose equation is y=-8

A. 0 B. 1 C. -8 D. undefined

3. Find the equation of a line whose slope is -2 and y-intercept is 5.

A. 2x+y-5=0 B. -2x+y-5=0 C. 2x-y-5=0 D. 2x+y+5=0

4. Find the equation of the line with slope of ½ passing through the point (-2,3).

A. x+2y+8=0 B. x-2y-8=0 C. x-2y+8=0 D. –x-2y+8=0

5. Find the equation of a line passing through the points (1,4) and (6,8)

A. 4x+5y+16=0 B. 4x-5y+16=0 C. 4x-5y-16=0 D. -4x-5y-16=0

6. Find the slope of the line parallel to 4x – 3y – 5=0.

A. 4 B. -4 C. -4/3 D. 4/3

7. Find the equation of the line with y-intercept of 10 and parallel to 2x-5y+1=0.

A. 2x-5y-50=0 B. 5x-2y-50=0 C. 2x+5y+50=0 D. 2x-5y+50=0

8. Find the slope of the line perpendicular to y+4x+2=0.

A. -4 B. 4 C. ¼ D. – ¼

9. Find the equation of the line perpendicular to x+2y-6= and passing through the origin.

A. 2x+y=0 B. 2x-y=0 C. -2x-y=0 D. X+2y=0

10.Find the distance between the pair of points (3,-1) and (6,-5).

A. 5 B. -5 C. 25 D. 12.5

11.Find the distance between the line 2x + 4y -3=0 and the point (-2,5).

A.1320 B. 13√5

20C.

1310 D. 13√5

10

12.Find the equation of the lines 7x +12y=4 and 8x-y=4 and through the point (2,1).

A. X+2y+1=0 B. X-2y-1=0 C. X-2y+1=0 D. -X-2y-1=0

13.Find the midpoint of the segments that has endpoints (-1,3) and (-2,-7).

A. (−32 ,2) B. ( 32 ,2) C. (−32 ,−2) D. ( 32 ,−2)14.One endpoint is (3,1), the midpoint is (1,5), find the other endpoint.

A. (-1,9) B. (1,9) C. (-1,-9) D. (1,-9)

15.A point P(x,y) is on the line passing through A (-2,5) and B(4,1). Find the coordinates of P if it is twice as far from A from B.

A. (10,3) B. (10,-3) C. (-10,3) D. (-10,-3)

16.The points A (2,-4), B (8,4) and C (0,6) are vertices of a triangle. Find the coordiantes of

the point on each median which is 23 of the way of the vertex to the midpoints of the

opposite side.

A. (2 , 103 ) B. ( 103 ,2) C. (−2 , 103 ) D. (2 ,−103 )17.Find the center of the circle whose equation is (x+2)2+(y-3)2=6.

A. (2,-3) B. (-2,-3) C. (2,3) D. (-2,3)

18.The equation x2-2x+y2-16y=p represents a circle with radius 2. Find p.

A. -61 B. 61 C. 65 D. -63

19.A circle is tangent to the line 2x-y+1=0 at the point (2,5), and the center is on the line x+y=9. Find the equation of the circle.

A. (x+6)2+(y+3)2=20 B. (x-6)2+(y-3)2=20

B (x-6)2+(y+3)2=20 D. (x+6)2+(y-3)2=20

20.Find the equation of the circle which passes through the points P(1,-2), Q(5,4) and R (10,5)

A. (x+9)2+(y+3)2=65 B. (x-9)2+(y-3)2=65

B (x+9)2+(y-3)2=65 D. (x-9)2+(y+3)2=65CIRCULAR AND TRIGONOMETRIC FUNCTIONS

1. Express 11π6 radians in degree measure.

A. 330° B. 660° C.180π

D. 350°

2. Evaluate sin30°+cos60°-tan45°

A. 1 B. -1 C. 0 D. √2

3. Find sin(-420° ¿

A. – ½ B. -√3/2 C. √3/2 D. ½

4. Covert to radians: 1.5°

A.π120 B.

9π4 C.

23π36 D.

π150

5. Triangle ABC is a right triangle with right angle at C. if tan A=2/3, find secB

A. √13/3 B. √3/2 C. 3/√3 D. 2/√3

6. What is the area in square cm of a sector of a circle of radius is 6cm. if the central angle is 30° .

A.π2

B. 12π C. 3π D. 540

7. Find secθ if sinθ=−√32

and tan θ=√3

A. -2 B. 2 C. ½ D. – ½

8. Solve for the hypotenuse of an isosceles right triangle one of whose legs has length 20.

A. 10 B. 10√2 C. 20√2 D. 40

9. Express tan θ+cotθsec θ in terms of sinθonly

A. B. C. D.

10.A wheel having 3 ft diameter is rotating on its axis at a speed of 280 rad/ sec. how far has a point on the rim of the wheel travelled after 1 minute?

A. 420ft B. 840ft C. 25,200ft D. 50,400ft

11.The length of an arc of a circular sector is 17π3

cm. If the radius is 6 cm, what is the

central angle in degrees.

A. 170 ° B. 340° C. 270° D. 430°

12.The point P (13, y) where y<0 is on the unit circle. Find tanθwhere θ is an angle in standard

position whose terminal side intersects the unit circle at point P.

A. -2√2 B. -2 C. -2/√3 D. 2√2

13.At a certain time of a day, a 100 ft tree casts a 23 ft shadow. What is the angle of elevation from the tip of the shadow to the top of the tree when rounded to the nearest degree?

A. 13° B. 43° C. 76° D. 77°

14.To four decimal places, find csc172°

A. 0.1392 B. -0.1392 C. 7.1853 D. -7.1853

15.Find the exact value of cot θif the terminal side of θis in QIII and cos θ=−38

A. -5/8 B. 5/8 C. 3/√55 D. -3/√55

16.How high is a building whose horizontal shadow is 45m. when the angle of elevation of sun is 55.6°?

A. 60.5m B. 65.7m C. 67.5m D. 55.7m

17.What is the period of y=2cos4x?

A. 8π B. 4π C. π D. π /2

18.Evaluate without the use of calculator: arcsin1

√2

A. π /4 B. π C. π /2 D. 2π

19.In triangle ABC, a=4, b=√106 and c=5√2. Using Law of Cosines, the measure of angle B is:

A. -π /4 B. π /4 C. 2π /3 D. 3π /4

20.Let sin A=35 and sinB ¿−

45 where A & B have terminal sides in QII and QIII respectively.

Then sin(A-B) is equal to;

A. -1 B. 1 C. -7/25 D. 7/25

21.From the top of a house, the angle of depression of a point on the ground is 25°. The point is 35m from the base of the building. How high is the building? (Round to the nearest meter).

A. 16 B. 17 C. 18 D. 15

22.Assuming the earth’s radius to be 4000 miles, find the linear speed of a point on the equator in mph.

A. 1047 B. 947 C. 1147 D. 1247

23.Find the degree measure of an angle formed by a rotation of: 1732 revolution

counterclockwise.

A. 191° 15 B. 181° 15 C. 180° 15 D. 190° 15

24.A tractor wheel has a diameter of 2m. how far will the tractor travel as the wheel makes 5.4 revolutions.

A. 30m B. 35m C. 33.9m D. 23.9m

25.Find the circumference of a circle whose diameter is 4.2m. (Use 3.14 for π ¿

A. 13m B. 44m C. 12m D. 15m

PROBABILITY AND STATISTICS1. A die is tossed. What is the probability of tossing an odd number?

A. ½ B. 1/3 C. ¼ D. 1/5

2. A single card is drawn from a deck of cards. What is the probability that the card id either a queen or a spade?

A. 13/52 B. 4/52 C. 2/13 D. 4/13

3. A coin is tossed three times. What is the probability that not all three tosses are the same?

A. 1/8 B. 3/8 C. ¼ D. ¾

4. Two cars are drawn from a deck of 52 cards with the first card replaced before the second card is drawn. What is the probability that neither card is a spade.

A. 9/16 B. ¾ C. 1/16 D. 19/34

5. How many three-letter words composed from the 26 letters of the alphabet are possible. No duplication of letters is permitted.

E. 13,600 F. 15,600 G. 600 H. 156

6. Evaluate: 7 !6 !

A. 1 B. 7 C. 13 D. 42

7. In how many ways can a fountain and a mountain be chosen from 8 fountains in Rome and 5 mountains in Canada.

A. 13 B. 3 C. 40 D. 8/5

8. Evaluate: P(9,3)

A. 27 B. 3 C. 504 D. 124

9. If 20 people won prizes in a state lottery, how many ways were there for these 20 to win 1st, 2nd , 3rd and 4th prizes. Assume there were no ties.

A. 180200 B. 5120 C. 1168 D. 116280

10.How may 3-digit numbers are there using 1,3,5,7 and 9.

A. 125 B. 225 C. 325 D. 23

11.When people are seated at a circular table, we consider only their positions relative to each other and are not concerned with the particular seat that a person occupies. How many arrangements are there for seven people to seat themselves around a circular table.

A. 620 B. 120 C. 720 D. 820

12.A supermarket manager who wants to study “traffic” in her store finds that 295, 1002, 941, 768 and1283 persons entered the store during the past 5 days. Find the mean number of persons who entered the supermarket during these 5 days.

A. 856 B. 858 C. 859 D. 855

13.In a factory, the time during working hours in which a machine is not operating as a result of breakage or failure is called a downtime. The following distribution shows a sample of the length of the downtime of a certain machine:

Downtime (minutes) Frequency0-9 2

10-19 1520-29 1730-39 1340-49 3

Find the standard deviation.

A. 9.90 B. 8.90 C. 7.90 D. 9.80

14. The following are the response time of a smoke alarm after the release of smoke from a fixed source: 12, 9, 11, 7, 9, 14, 6 and 10 seconds. Find the range.

A. 8 B. 9 C. 10 D. 12

15.In fifteen days, a restaurant served breakfast to 40, 52, 55, 38, 40, 48, 56. 56, 60, 37, 58, 63, 46, 50 and 61 customers. Find the median.

A. 50 B. 51 C. 52 D. 56

16.The following are the range of thirty persons empaneled for jury duty by a court, 42,45,51,39,32,61,27,62,53,51,48,40,34,37,28,58,55,43,29,39,40,22,58,28,31,31,52,44, 38 and 36. Find their mean age.

A. 31.8 B. 21.8 C. 41.8 D. 51.8

17.In a biology class, there are 20 freshmen, 18 sophomore and 12 juniors. If the freshmen averaged 68 in an examination; the sophomores averaged 75 and the juniors averaged 86 what is the mean grade of the entire class.

A. 70.84 B. 74.84 C. 84.84 D. 74.74

18.From a bag containing 8 black ball, 6 white balls and 4 red balls, one ball is drawn at random. What is the probability that the ball drawn is not red?

A. 4/9 B. 8/18 C. 6/18 D. 7/9

19.The 1960 graduating class of a cetain college composed of 200 aged 21 and 100 aged 22. According to the CSO table, approximately how many should be alive at the 50 th

reunion?

A. 152 B. 142 C. 132 D. 122

20.From an ordinary deck of cards, M has drawn a card, say, the jack of diamonds. Without replacing this card, he draws another. What is the probability that the second card will be a card of lower rank than jack.

A. 12/17 B. 1/52 C. 4/52 D. 1/17

BUSINESS MATHEMATICS1. Find the amount of discount for a dining set with a list price od P5,350 and a discount

rate of 10%.

A. P53.50 B. P535 C. P635 D. P5350

2. Mr. Cruz is a sales representative of Realty Appliance Company. He is given 20% of the total sales he makes every week. What is his earnings if he sales total P67,850

A. P1357 B. P6780 C. P13570 D. P135.70

3. Find the simple interest in the amount of P1,000 at 5% for 10 months.

A. I=P41.67S=P1041.67

B. I=P45 S=P1045

C. I=P105 S=P1105

D. I=P17.50 S=P1017.50

4. At what rate of simple interest will P2,000 amount to P2110 in one year?

A. 4% B. 5% C. 4 ½ % D. 5 ½ %

5. How long will it take any sum of money to double itself by 5% simple interest.

A. 10 years B. 15 years C. 20 years D. 25 years

6. Find the simple discount on a debt of P1,500 due in 9 months at a discount rate of 6%.

A. P67.50 B. P57.50 C. P77.50 D. P87.50

7. What is the value today of bond coupons totalling P1,200 which fall due in one month money worth 6% simple interest?

A. P1,090 B. P1,194.03 C. P1,295.05 D. P1,145.05

8. Find the compound amount of P10,000 for 20 years at 5% compounded monthly.

A. P2,712.62 B. P2,7126.4 C. P2,712 D. P27,155

9. Find the present value of P300,000 due in 8 years, 10 months if money is worth 4% compounded quarterly.

A. P21,073 B. P21,1073 C. P21,1730 D. P211.073

10.In buying a house, Y pays P100,000 cash and agrees to pay P75,000 two years later. At 6% compounded semi-annually, find the cash value of the house.

A. P16,663.65 B. P156,636.5 C. P166,636.5 D. P166,500

11.At what discount rate was a stereo sold if the marked price was P7,250 and the selling price was P5,945.

A. 18% B. 12% C. 15% D. 82%

12.Mr. Cortez receives a commission of 15% on sales. He received a commission of P891 on his sales in July. What are his sales?

A. P5,940 B. P1,336 C. P1,683 D. P594

CALCULUS

1. Find the limit of the function: f(x)=x−4

3(√3−2), ≠4 as x tends ¿ 4

A. ¾ B. 5/4 C. 4/3 D. 4/5

2. Given f(x)=x2. Find the derivative, f1(x)

A. 2 B. 2x C. 4 D. 4x

3. Find the derivatives: f(x)= x2−1x2+1

A.4 x

(x2+1 )2 B. x2+1x2−1

C.2x−12x+1 D.

4 xx−1

4. Evaluate: lim =3 x+25x+4

A. ½ B. 3/5 C. ¾ D. 2/5

5. Evaluate: lim =(3)√n

A. 1 B. -1 C. 0 D. 2

6. Find the derivative of : x2+3x-4

A. 2x+3 B. 3x-4 C. 2x2+3x D. 4x+3

7. Fid the value of f(x) for the given value x: f(x)=(x2+2x+3)2/3, x=-1

A. 1 B. 2 C. 3 D. 0

8. The difference between two numbers is 20. Select the numbers so that the product is as small as possible.

A. 5,4 B. 10,2 C. 10,-10 D. -5,-4

9. Find the coordinated of the point or points on the curve y= 2x2 which are closest to the point (9,0)

A. (1,2) B. (2,3) C. (3,4) D. (-1,0)

10.Water is flowing into a vertical cylindrical tank of radius 2ft. at the rate of 8ft 3/min. how fast is the water level rising?

A. 4ft/min B.2πft/min C.

3πft/min D. ½ ft/min

KEY CORRECTIONS

ARITHMETIC AND NUMBER THEORY BASIC AND ADVANCE ALEGBRA

1 C 21 C 1 D 26 B2 D 22 A 2 A 27 A3 B 23 B 3 C 28 C4 A 24 C 4 B 29 B5 B 25 C 5 A 30 D6 C 26 A 6 B 31 C7 C 27 C 7 C 32 C8 A 28 D 8 A 33 A9 C 29 A 9 C 34 D

10 D 30 B 10 D 35 A11 A 31 B 11 B 36 B12 C 32 D 12 A 37 C13 B 33 C 13 B 38 C14 C 34 A 14 C 39 A15 D 35 B 15 D 40 B16 B 36 D 16 A 41 D17 A 37 C 17 A 42 A18 D 38 B 18 B 43 B19 A 39 C 19 B 44 A20 C 40 A 20 D 45 B

ANALYTIC GEOMETRY 21 C 46 C1 C 11 D 22 C 47 D2 A 12 C 23 A 48 A3 B 13 C 24 D 49 D4 C 14 A 25 A 50 B

5 B 15 BCIRCULAR AND TRIGONOMETRIC FUNCTIONS

6 D 16 B 1 A 13 D7 A 17 D 2 C 14 C8 C 18 A 3 B 15 C9 B 19 C 4 A 16 B

10 A 20 D 5 B 17 DPROBABILITY AND STATISCTICS 6 C 18 A

1 A 11 C 7 A 19 D2 D 12 B 8 C 20 A3 D 13 A 9 A 21 A4 A 14 A 10 C 22 A5 B 15 B 11 A 23 A6 B 16 C 12 A 24 C7 C 17 B 25 A8 C 18 D9 D 19 C

10 A 20 A 0

BUSINESS MATHEMATICS1 B 7 B2 C 8 B

3 A 9 B4 D 10 C5 C 11 A6 A 12 A

CALCULUS1 C 6 A2 B 7 D3 A 8 C4 B 9 A5 C 10 B