Math Talino

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SECOND CACPRISAA MATHEMATICS CONTESTS

August 23, 2007

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August 23, 2007

Grade One

Easy (15 sec / 1 pt)

What is 45 increased by 9 + 17?

A. 19 B. 26 C. 45 D. 71

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August 23, 2007

Grade One

Average (30 sec / 2 pts)

1. What is the largest 3-digit number?

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August 23, 2007

Grade One


2. Write 4 tens, 7 ones and 9 hundreds in symbols.

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August 23, 2007

Grade One

Difficult (60 sec / 3 pts)

1. Vince had P23.00. His mother gave him P18.00 and his father gave him P29.00. How much money had Vince then?

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August 23, 2007

Grade One


2. One Saturday morning, Aiko woke up at 6:15. She did her usual morning routine: She took a bath, ate her breakfast and brushed her teeth. She finished at 8:00. How many minutes in all did she spend in her morning routine?

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August 23, 2007

Grade One


3. I am a 2-digit number. The sum of my digits is 9. My ones digit is 3

more than my tens digit. Who am I?

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August 23, 2007

Grade One

Clincher Round (60 sec)

1. Leo bought 47 bananas; Randy bought 19 bananas. How many more bananas did Leo buy than Randy?

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August 23, 2007

Grade One


2. How many months are there in 3 ½ years?

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August 23, 2007

Grade One


3. Isay can save P25.00 in a day. How much can she save in 7

days?

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August 23, 2007

Grade One


4. On Monday, Sandra solved 34 math problems. She solved 15 more math problems on Tuesday than on Monday. How many math problems did she solve on two days?

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August 23, 2007

Grade One


5. A square blackboard is 6 feet on each side. What is its

perimeter?

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August 23, 2007

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August 23, 2007

Grade Two


Which of the following is a prime number?

A. 73 B. 74 C. 75 D. 77

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August 23, 2007


1. How many hundreds are there in 2,537?

Grade Two

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August 23, 2007


2. What is thrice 17 increased by 9?

Grade Two

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August 23, 2007


1. Crizel bought 2 ¼ dozens of apples. How many apples did she buy?

Grade Two

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August 23, 2007


2. Mark has 130 marbles. He has several boxes. Seven marbles can fill each box. How many boxes can Mark fill with his marbles?

Grade Two

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August 23, 2007


3. I am thinking of a number. If I add 28 to it, the sum is equal to 9 x 13. What is my number?

Grade Two

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August 23, 2007


1. How many weeks are there in 343 days?

Grade Two

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August 23, 2007


2. A clown in a carnival had 36 balloons. He gave 1/3 of them in the morning. He gave ½ of those remained in the afternoon. How many balloons were left?

Grade Two

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August 23, 2007


3. How many prime numbers are there between 30 and 40?

Grade Two

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August 23, 2007


4. Add: 375 + 249 + 168.

Grade Two

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August 23, 2007


5. What is 49 in Roman Numerals?

Grade Two

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August 23, 2007

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August 23, 2007

Grade Three


If September 15 is Saturday, What day is September 23?

A. Friday C. SundayB. Saturday D. Monday

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August 23, 2007


1. By what can 85 be decreased to make it 37?

Grade Three

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August 23, 2007


2. How many 5-peso coins equal P200-bill?

Grade Three

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August 23, 2007


1. A box is 10 cm long, 8 cm wide and 6 cm high. What is its volume?

Grade Three

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August 23, 2007


2. Jun and Rey went to see a movie. It lasted for 1 hour and 45

minutes. It ended at 9:15pm. What time did the movie begin?

Grade Three

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August 23, 2007


3. Elma has a picture album. She puts 8 pictures in each page. If 19 pages are full and there are 5 pictures on the

20th page, how many pictures are in her album?

Grade Three

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August 23, 2007


1. The park is 50 meters long and 35 meters wide. If you walk

around it twice, how many meters will that be?

Grade Three

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August 23, 2007


2. What is the sum of the first ten counting numbers?

Grade Three

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August 23, 2007


3. I am thinking of two factors of 60 whose sum is 17. What are the two factors?

Grade Three

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August 23, 2007


4. Given the digits 2, 5, 7, and 9. What is the difference between the largest and smallest 4-digit numbers that can be formed from the given digits?

Grade Three

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August 23, 2007


5. Ian has a P1000-bill, two P500-bills, three P100-bills, four P50-bills and

five P20-bills in his wallet. How much money has he in his wallet?

Grade Three

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August 23, 2007

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August 23, 2007

Grade Four


What is the greatest common factor of 22 and 55?

A. 11 B. 22 C. 55 D. 110

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August 23, 2007


1. Fill in the blank with a digit to make 76,98__ divisible by 9.

Grade Four

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August 23, 2007


2. Round off 3,689 and 765 to the nearest hundreds and

then find their difference.

Grade Four

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August 23, 2007


1. The perimeter of an isosceles triangle is 68 cm. If the base is 29 cm long, how long is each of the equal sides?

Grade Four

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August 23, 2007


2. Vicky got scores of 91, 90, 85 and 90. What was her average score?

Grade Four

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August 23, 2007


3. How many 0.25-kg bags of rice can be filled from a 50-kg bag?

Grade Four

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August 23, 2007


1. The area of a rectangle is 42 sq cm. If one side of the rectangle is 3 cm, what is its perimeter?

Grade Four

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August 23, 2007


2. How many thousandths are there in 3.03?

Grade Four

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August 23, 2007


3. What is the least common multiple of 72 and 108?

Grade Four

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August 23, 2007


4. Joan bought half dozen of doughnuts at P180 per dozen and 5 cans of juice at P15 per can. How much did she spend in all?

Grade Four

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August 23, 2007


5. A can of paint is needed for 50 sq m of wall. If a wall is 40 meters long and 3.75 meters high, how many cans of paint must be bought?

Grade Four

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August 23, 2007

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August 23, 2007

Grade FiveEasy (15 sec / 1 pt)

If 6:7 = 42:x, what is x?

A. 36 B. 43 C. 49 D. 56

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August 23, 2007


1. Multiply: 5 5/6 x 5 1/7.

Grade Five

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August 23, 2007


2. Round off to the nearest thousands and estimate the sum of: 34,569 + 22,437 + 58,621.

Grade Five

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August 23, 2007


1. Lorna bought two blouses at P115.75 each and two pairs of socks at P32.50 a pair. If she gave a P1,000-bill to the cashier, how much change did she

get?

Grade Five

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August 23, 2007


2. Denji’s grades in his first four tests in math are 92, 91, 89, and 88. What

must his score in the fifth test be so that his average in the five tests is 90?

Grade Five

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August 23, 2007


3. The ratio of the angles of a triangle is 2:3:4. What is the measure of the largest angle of this triangle?

Grade Five

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August 23, 2007


1. During a sale, Alex bought a pair of pants marked P475. If he got a discount of 12%, how much did he pay for it?

Grade Five

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August 23, 2007


2. The scale of a map is 1/4 inches for 30 km. If two towns are 210 km apart, how far apart are they in the map?

Grade Five

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August 23, 2007


3. Mito multiplied a certain number by 25 on a calculator when he should have divided it by 25. He got the answer

9,375. What should have been the correct answer?

Grade Five

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August 23, 2007


4. A box is 2 meters long, 2 meters wide and 1 meter high. How many pieces of plastic containers, 25 cm by 25 cm by 40 cm, can be placed in the box?

Grade Five

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August 23, 2007


5. Angel bought 3 apples for P37.50. At the same rate, how much would one and a half dozens cost?

Grade Five

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August 23, 2007

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August 23, 2007

Grade Six


What is a multiple of 80 closest to 995?

A. 800 B. 960 C. 980 D. 1040

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August 23, 2007


1. Write 0.45454545... as a ratio of two whole numbers in lowest term.

Grade Six

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August 23, 2007


2. What is the next term in this sequence: 1, 4, 10, 19, 31, 46, ____ ?

Grade Six

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August 23, 2007


1. The height of a 6-year old boy is about 6 times the distance from the bottom of his chin to the top of is head. The height of an adult man is about 8 times this distance. The distance on a certain

man was 22 cm. On a boy it was 19 cm. How much taller was the man?

Grade Six

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August 23, 2007


2. Kasaysayan Integrated School has an average of 28

students per class. It has 20 classes. The number of students in Kalayaan Academy, Kalikasan Institute and Karunungan Montessori are 614, 555 and 598, respectively. How much greater is the average number of students in these three schools than the number of students in Kasaysayan Integrated School?

Grade Six

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August 23, 2007


3. How many terms would be in the set of numbers below:

{4, 13, 22, 31, . . . , 400}?

Grade Six

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August 23, 2007


1. A person’s hair grows about 15 cm each year. A child’s hair was 31 cm long on her fourth birthday. She cut off 5 cm of hair on her fifth birthday and 7 cm on her seventh birthday. How long was her hair on her

ninth birthday?

Grade Six

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August 23, 2007


2. Five girls ran in a 100-m dash. Lia finished ahead of Ophel, and Ophel was not last. Gem finished far ahead of Ophel, and Laya finished just behind Gem. If Missy finished last, which girl finished next to last?

Grade Six

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August 23, 2007


3. The sum of the digits of a three-digit number is 17. The tens digit of the number is two-thirds of the hundreds digit and the hundreds digit is four and a half times the units digit. Find the number.

Grade Six

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August 23, 2007


4. Rica is now twice as old as Mike but 6 years ago she was 5 times as old as he was. How old is Rica now?

Grade Six

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August 23, 2007


5. A jar contains 10 red marbles and 30 green ones. How many red marbles must be added to the jar so that 60% of the marbles will be red?

Grade Six

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August 23, 2007

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August 23, 2007

First Year – Elementary Algebra


Eric has 12 Los Angeles Lakers basketball cards. Randy has 3 times as many Lakers cards as Eric. Paul has 16 fewer Lakers cards than Randy. Which of these expressions could correctly represent how many Los Angeles Lakers basketball cards Paul has?

A. 16 – (3 x 12) C. (3 x 16) – 12 B. 3 x (16 – 12) D. (12 x 3) – 16

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August 23, 2007


1. The ordered pair of point A is now (2,2). What is the new ordered pair if point A is moved 5 units to the left and 3 units up?


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August 23, 2007


2. Find the value of the variable y.

x – y = yx = 8


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August 23, 2007


1. A test is composed of 25 questions. The score of an examinee is obtained by giving him 4 points for each correct answer and subtracting 1 point for each wrong answer. If an examinee answered all the questions and obtained a score of 70, how many questions did he answer correctly?


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August 23, 2007


2. A man wants to cover a distance by car in 20% less time than he usually takes. By what percent must he

increase his driving speed?


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August 23, 2007


3. The average of a set of numbers is 22. If 29 is included in the set, the new average becomes 23. How many numbers are in the original set?


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August 23, 2007


1. The sum of the ages of Pete and Alice is 34 years. The product of their ages is 264. If Pete is older than Alice, how old is he in years?


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August 23, 2007


2. It takes 40 minutes for Jack to clean the yard, and Jill 60 minutes to do it. One morning Jack started cleaning their yard. After 20 minutes Jill joined him. In how many minutes after Jill joined Jack will the cleaning of the yard be finished?


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August 23, 2007


3. The sum of the digits of a two-digit number is 7. If 9 is added, the resulting number has the same digits as the original but in the

reverse order. Determine the product of the digits.


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August 23, 2007


4. Neb spent ½ of his earnings last month for living expenses and saved 1/3 of the remainder. Of his earnings last month, Neb paid twice as much in taxes as he saved. If Neb saved P6,000 of his earnings last month, how much did Neb earned last month?


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August 23, 2007


5. A bakery opened yesterday with its daily supply of 40 dozen rolls. Half of the rolls were sold by noon, and 80 percent of the remaining rolls were sold between noon and closing time. How many dozen rolls had not been sold when the bakery closed yesterday?


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August 23, 2007

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August 23, 2007

Second Year – Intermediate Algebra


If p/q < 1, and p and q are positive integers, which of the following must be greater than 1?

A. p/q2 C. q/p2 B. p/2q D. q/p

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August 23, 2007


1. a/b = 5/8 and the greatest common factor of a and b is 1. If a and b are positive integers, what is the value of a + b?


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August 23, 2007


2. If (x2 + 6x + 9) + 6(x + 3) + 9 = 0, then x = ____.


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August 23, 2007


1. In a school canteen, the average revenue was P4,000 a day over a 10-day period.

During this period, if the average daily revenue was P3,600 for the first 6 days, what was the average daily revenue for the last 4 days?


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August 23, 2007


2. If the operation © is defined by x © y = √xy for all positive numbers x and y, then (5 © 45) © 60 = ____.


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August 23, 2007


3. If y is an integer, what is the least possible value of │23 – 5y│?


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August 23, 2007


1. If the sum of two positive integers is 24 and the difference of their squares is 48, what is the product of the two

integers?


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August 23, 2007


2. In a class of 30 students the average on a certain test is p. If the teacher

decides to raise each grade 10 points, what will the new average be?


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August 23, 2007


3. In a certain sequence, the first term is 1, and each successive term is 1 more than the reciprocal of the term that immediately precedes it. What is the fifth term of the

sequence?


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August 23, 2007


4. x is a positive integer. x divided by 100 has a remainder of 30. x divided by 110 has a remainder of 30. What is the tens digit of x?


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August 23, 2007


5. How many integers n are there such that 1 < 5n + 5 < 25?


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August 23, 2007

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August 23, 2007

Third Year – Geometry

Easy (15 sec / 1 pt)In the figure, line l1 is parallel to line l2. y = 50 and z =130. What is the value of x?

A. 30 C.50B. 40 D.130

zo

yo

xol2

l1

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August 23, 2007


1. In the figure, how many of the points on line segment PQ have coordinates that are both integers?


P (0, 30)

Q(50, 0)

y

Ox

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August 23, 2007


2. The dimensions of a rectangular floor are 16 feet by 20 feet. When a rectangular rug is placed on the floor, a strip of floor 3 feet wide is exposed on all sides. What are the dimensions of the rug, in feet?


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August 23, 2007


1. The volume of a sphere with radius r is (4/3)πr3 and the surface area is 4πr2. If a spherical balloon has a volume of 972π cubic centimeters, what is the surface area of the balloon in square centimeters?


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August 23, 2007


2. A square playground has the same area as a rectangular playground that is 30 meters longer but 20 meters narrower. What is the length, in meters, of a side of the square playground?


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August 23, 2007


3. In ΔABC, what is x in terms of z?


37o

B

A

zo

xo

C70o

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August 23, 2007


1. In the figure, 2 is complementary to 3, and m1 = 141. What is m7?


1 2 3 4

5 6 7 8

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August 23, 2007


2. If ABCD is a parallelogram, ADC = 45, BEF = 90, BE = 1, BF = ?


A

D C

BE

F

45

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August 23, 2007


3. Each of the circles A, B, and C are tangent to the other two. AB = 7, AC = 9 and BC = 10. What is the radius of circle C?


C

AB

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August 23, 2007


4. Adelle wants to put up fencing around three sides of her rectangular yard and leave a side of 20 feet unfenced. If the yard has an area of 680 square feet, how many feet of fencing does she need?


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August 23, 2007


5. The cost of a gold paint needed to cover a cube of edge 3 centimeters is P240. At the same cost per square centimeter, what is the cost of gold paint needed to cover the surface of a cube of edge 6 centimeters?


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August 23, 2007

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August 23, 2007

Fourth Year (Trigonometry, Statistics,Business Math and Advance Algebra)


A retail appliance store priced a video recorder at 20 percent above the wholesale cost of P2,000. If a store employee applied the 10 percent employee discount to the retail price to buy the recorder, how much did the employee pay for the recorder?

A. P1,900 C. P2,200 B. P2,160 D. P2,300

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August 23, 2007


1. Sixty percent of the members of a study group are women, and 45 percent of those women are lawyers. If one member of the study group is to be selected at random, what is the probability

that the member selected is a woman lawyer?


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August 23, 2007


2. If x = y + 4 and x = 20 – y, then what is the value of x2 – y2?


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August 23, 2007


1. If tan (3 - 10o) = cot (4 - 5o), then = ______.


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August 23, 2007


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


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August 23, 2007


3. Twelve persons gather in a room for a meeting. Before the meeting begins, each person shakes hands with every other person in the room

exactly once. How many handshakes is there altogether before the meeting begins?


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August 23, 2007


1. If log10x + log108 = log1016, then x is equal to ____.


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August 23, 2007


2. After successive discounts of 15 percent and 10 percent have been allowed on the marked price of a certain article, the net

price is P306. What is the marked price?


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August 23, 2007


3. Violy, Lea and Randy each try independently to solve a problem. If their individual probabilities for success are ¼, ½ and 5/8 respectively, what is the probability that Violy and Lea, but not Randy will solve the problem?


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August 23, 2007


4. For the positive numbers n, n + 1, n + 2, n + 4, and n + 8, the mean is how much greater than the

median?


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August 23, 2007

Clincher Round (60 sec)5. A window washer places a 25-foot ladder against

the side of a building that is perpendicular to level ground. Initially, the bottom of the ladder is 7 feet from the base of the building. If the window

washer wants the top of the ladder to be 4 feet lower, how many feet farther from the base of the building must he move the bottom of the ladder?


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Math Talino