2013 MTAP-DepEd Program of Excellence Mathematics Grade 1 Session 1 I. Read the following numbers. 1. 89 2. 106 3. 736 4. 245 5. 899 6. 302 7. 720 8. 1200 9. 5075 10. 7001 II. What is the place value of each underlined digit? Give the value of each underlined digit. Give the answers orally. A B C D E F 1. 601 215 520 1‚364 5‚ 055
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Algorithm is a list of instructions for carrying out some process step by step Flowchart is a diagram representing the logical sequence in which a combination of steps or operations is to be performed Types of Flowcharts Program Flowchart – describes graphically in detail the logical operations and steps within a program and sequence in which these steps are to be executed for the transformation of data to produce the needed output System Flowchart – is a graphic representation of the
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Integer Programming 9 The linear-programming models that have been discussed thus far all have been continuous‚ in the sense that decision variables are allowed to be fractional. Often this is a realistic assumption. For instance‚ we might 3 easily produce 102 4 gallons of a divisible good such as wine. It also might be reasonable to accept a solution 1 giving an hourly production of automobiles at 58 2 if the model were based upon average hourly production‚ and the production had the interpretation
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Algorithms Homework – Fall 2000 8.1-1 Using Figure 8.1 as a model‚ illustrate the operation of PARTITION on the array A = 13 19 9 5 12 8 7 4 11 2 6 21 i j j 6 19 9 5 12 8 7 4 11 2 13 21 i i j j 6 2 9 5 12 8 7 4 11 19 13 21
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sufficient to answer the question asked (E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked‚ and additional data are needed 3. How many years old will Fred be y years from now? (1) Doris is 12 years older than Fred. (2) The sum of the ages of Doris and Fred is y years. (A) Statement (1) ALONE is sufficient‚ but statement (2) alone is not sufficient to answer the question asked (B) Statement (2) ALONE is sufficient‚ but statement (1) alone is not sufficient to answer the question
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Gems from the world of data structures and algorithms Bit-Sum Prime Difficulty level: moderate Every student‚ who has learned programming‚ must have written a program to determine whether a given positive integer is a prime number. Basically in order to determine whether a positive integer n is prime‚ we search for any number in the range [2‚ n − 1] which can divide n. Some of you would have designed a slighly better implementation where you search √ for any divisor of
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Operational Research 153 (2004) 117–135 www.elsevier.com/locate/dsw An integer programming formulation for a case study in university timetabling S. Daskalaki b a‚* ‚ T. Birbas b‚ E. Housos b a Department of Engineering Sciences‚ University of Patras‚ GR-26500 Rio Patras‚ Greece Department of Electrical and Computer Engineering‚ University of Patras‚ GR-26500 Rio Patras‚ Greece Abstract A novel 0–1 integer programming formulation of the university timetabling problem is presented
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Euclidean algorithm In mathematics‚ the Euclidean algorithm‚ or Euclid’s algorithm‚ is a method for computing the greatest common divisor (GCD) of two (usually positive) integers‚ also known as the greatest common factor (GCF) or highest common factor (HCF). It is named after the Greek mathematician Euclid‚ who described it in Books VII and X of his Elements. The GCD of two positive integers is the largest integer that divides both of them without leaving a remainder (the GCD of two integers in general
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than Rs 2000 (B) He gained more than Rs 2000 (C) He lost less than Rs 2000 (D) He lost more than Rs 2000 2. In an examination‚ the average marks obtained by students who passed was x%‚ while the average of those who failed was y%. The average marks of all students taking the exam was z%. Find in terms of x‚ y and z‚ the percentage of students taking the exam who failed. ( z – x) (A) ( y – x) ( x – z) (B) ( y – z) and at the point P‚ forming a loop. The straight line OP divides the loop into two parts
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of which are tagged. Estimate how many deer are in the forest. (2) The coffee beans from 14 trees are required to produce 7.7 kg of coffee. How many trees are required to produce 320 kg of coffee? (3) The sum of the reciprocals of two consecutive even integers is -9/40. Find two integers. (4) Elissa can clean the animal cages at the animal shelter in 3 hours. Bill can do the same job in 2 hours. How long would it take if they work together to clean the cages. (5) Bob can clean a house in 4
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