circumference of the circle? A. 2.5π B. 3π C. 5π D. 4π E. 10π 5. Two sets of 4 consecutive positive integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set? A. 4 B. 7 C. 8 D. 12 E. it cannot be determined from the information given. 6. If f(x) = (x + 2) / (x-2) for all integers except x=2‚ which of the following has the greatest value? A. f(-1) B. f(0) C. f(1) D. f(3) E. f(4)
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represented in the form p/q where p and q are integers and q is not zero. Example: 2/3‚ 1/10‚ 8/3 etc. They can be finite decimal numbers‚ whole numbers‚ integers‚ fractions. Irrational numbers: A number that cannot be represented in the form p/q where p and q are integers and q is not zero. An infinite non recurring decimal is an irrational number. Example: √2‚ √5 ‚ √7 and Π(pie)=3.1416. The rational numbers are classified into Integers and fractions Integers: The set of numbers on the number line‚ with
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Section 4.1 Divisibility and Modular Arithmetic 87 CHAPTER 4 Number Theory and Cryptography SECTION 4.1 Divisibility and Modular Arithmetic 2. a) 1 | a since a = 1 · a. b) a | 0 since 0 = a · 0. 4. Suppose a | b ‚ so that b = at for some t ‚ and b | c‚ so that c = bs for some s. Then substituting the first equation into the second‚ we obtain c = (at)s = a(ts). This means that a | c‚ as desired. 6. Under the hypotheses‚ we have c = as and d = bt for some s and t . Multiplying
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CHAPTER 2 WHOLE NUMBERS What have we discussed? 1. The number 1‚ 2‚ 3… which use for counting are known as natural number. 2. If you add 1 to a natural number‚ we get its successor‚ if you subtract 1 from a natural number‚ you get its predecessor. 3. Every natural number has a successor. Every natural number except 1 has a predecessor. 4. If add the number zero to the collection of the natural numbers‚ we get the collection of whole numbers. Thus‚ the number 0‚ 1‚ 2‚
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KSF 2013 – finalized problems Cadet 3 points # 1. In the picture‚ the big triangle is equilateral and has area 9. The lines are parallel to the sides and divide the sides into three equal parts. What is the area of the shaded part? (A) 1 # 2. It is true that (B) 4 1111 101 (C) 5 (D) 6 = 11. What is the value of (A) 5 (B) 9 3333 101 + (E) 7 6666 303 ? (D) 55 (C) 11 (E) 99 # 3. The masses of salt and fresh water in sea water in Protaras are in the ratio 7 : 193. How many kilograms of
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Damath Introduction: Damath comes from the Pinoys checker board game called “dama” and Mathematics. It blends local culture‚ education and digital technology that aim to make math teaching and learning child-friendly‚ challenging and interactive. DAMATH‚ a patent-pending mathematical board-game invented by five-time national awardees Jesus L. Huenda‚ is coined from the popular Filipino checkerboard game of dama‚ (or lady in Spanish) and mathematics. It started in a Sorsogon National High School
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CYBER OLYMPIAD The actual test paper has 50 questions.Time allowed : 60 minutes.There are 3 sections‚ 15 questions in section I‚ 15 in section II and 20 in section III. SYLLABUS Section – I (Mental ability) : Natural numbers and whole numbers‚ Integers‚ Factors and multiples‚ Ratio‚ Proportion and unitary method‚ Percentage and its applications‚ Algebraic expressions‚ Linear m oom equations in one variable‚ Basic geometrical concepts‚ Line segments‚ Angles‚ Triangles‚ Pairs of lines .cc and
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are undetermined. Analysis – First I need to declare A‚ B‚ C‚ D‚ F and GPA as integers. A = 4‚ B = 3‚ C = 2‚ D = 1‚ F = 0. Each of these numbers will be floated The program will ask for the name of the user User Name: Stephen The program will then ask for the grades. Grades Entered: A‚A‚D The letters corresponding to the integers will be summed ex. A+A+D = 4+4+1 = 9 The program will then divide the sum of the integers by the amount entered. 9/3 = 3.0 = GPA The program will print the students name
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they are false. Assume x is of type int. A. Any bit of x equals 1. B. Any bit of x equals 0. C. Any bit in the least significant byte of x equals 1. D. Any bit in the most significant byte of x equals 0. Your code should follow the bit-level integer coding rules (page 120)‚ with the additional restriction that you may not use equality (==) or inequality (!=) tests. ◆SOLUTIONS◆ A. !!x B. !!~x C. !!(x & 0xFF) D. !!(~ & 0xFF) ------------------------------------------------- 2
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4. The first term of a sequence is 20 and the second term is 8. The third term and each term thereafter is the average (arithmetic mean) of the two terms immediately preceding it. What is the value of the first term in the sequence that is not an integer? (A) (B) (C) (D) (E) 22.6 1.23 24.7 12.5 6.8 5. a‚ 3a‚ ... The first term in the sequence above is a‚ and each term after the first is 3 times the preceding term. If the sum of the first 5 terms is 605‚ what is the value of a ? 6.
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