SAT Math 1 & 2 Subject Tests Jonathan Spaihts Revised by Morgan Chase Cracking the * 2009–2010 Edition PrincetonReview.com Random House‚ Inc. New York The Independent Education Consultants Association recognizes The Princeton Review as a valuable resource for high school and college students applying to college and graduate school. John Katzman‚ Chairman‚ Founder Michael J. Perik‚ President‚ CEO Stephen Richards‚ COO‚ CFO John Marshall‚ President‚ Test Preparation Services
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This page intentionally left blank Now into its eighth edition and with additional material on primality testing‚ written by J. H. Davenport‚ The Higher Arithmetic introduces concepts and theorems in a way that does not require the reader to have an in-depth knowledge of the theory of numbers but also touches upon matters of deep mathematical significance. A companion website (www.cambridge.org/davenport) provides more details of the latest advances and sample code for important algorithms. Reviews
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fractions StatisticsReading Tables and ChartsExponentsPre-Algebra and Algebra Special notation for multiplication and division with variable Algebra word problems Order of operations Simplifying expressions Prime factorization Greatest common factor Least common multiple Factoring Sample algebra problemsCoordinate System Grid graph Slope coordinatesGeometry Basics Squares‚ rectangles‚ circles‚ trianglesMath Definitions | ENGLISH
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remainder theorem were also known to Brahmagupta (7th century)‚ and appear in Fibonacci’s Liber Abaci (1202). A modern restatement of the theorem in algebraic language is that for a positive integer with prime factorization we have the isomorphism between a ring and the direct product of its prime power parts:
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arranged in the form ax2+ bx=0. Strategy: To factor the binomial using the greatest common factor (GCF)‚ set the monomial factor and the binomial factor equal to zero‚ and solve. Ex. 2) 12x2- 18x=0 6x2x-3= 0 Factor using the GCF 6x=0 2x-3=0 Set the monomial and binomial equal to zero x=0 x= 32 Solutions * In some cases‚ the GCF is simply the variable with coefficient of 1. III. To solve an equation in the form ax2+
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because 9 and 12 can both be divided by 3‚ then the person has not chosen the greatest common factor between the numbers. A person looking for the greatest common factor would choose 15‚ and the expression would change to 15(3x+4y) which reveals 3‚ a prime number that cannot be divided into a smaller number‚ and 4‚ which is not divisible by 3. Therefore‚ 15 is the greatest common factor. Week 2 DQ2 To factor x2+bx+c you would need to find the number that is c that when multiplied will equal the number
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My second expression below: 2b – 2 2b² - 8 Rational expression 2 (b) + 2 (-1) 2b² - 8 Factor out GCF of 2 from each term. 2 (b-1) 2b² -8 Factor GCF 2 from 2b-2. 2 (b – 1) 2 (b²) + 2 (-4) Factor out GCF 2 from each term. 2 (b – 1) 2 (b² - 4) Factor out GCF 2 from 2b – 8. 2 (b -1) 2 (b-2) (b+2) each set contains terms that are perfect squares. Factor using the difference
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L A S T U P D A T E D : J U N E 3 0 ‚ 2 0 1 0 G M AT FLASHCARDS Table of Contents 2 Letter from the Founder 3 Test Prep Company Discounts Verbal Flashcards 4 Sentence Correction 26 Critical Reasoning 38 Reading Comprehension Quantitative Flashcards 49 General 74 Data Sufficiency http://www.beatthegmat.com © Beat The GMAT 1 Back to Table of Contents B E AT T H E G M AT Letter from the Founder During my GMAT preparation‚ I made hundreds
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1 10/10/01 Fermat’s Little Theorem From the Multinomial Theorem Thomas J. Osler (osler@rowan.edu) Rowan University‚ Glassboro‚ NJ 08028 Fermat’s Little Theorem [1] states that n p −1 − 1 is divisible by p whenever p is prime and n is an integer not divisible by p. This theorem is used in many of the simpler tests for primality. The so-called multinomial theorem (described in [2]) gives the expansion of a multinomial to an integer power p > 0‚ (a1 + a2 + ⋅⋅⋅ + an ) p = p k1 k2 kn a1 a2
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the office. He never refuses a potential money-making venture because he lacked the time to give it attention. At the time the company was following a downward track‚ Mr. Gordon decided to focus on one of the company’s large customer‚ Genchryfor or GCF‚ and concentrated on gaining an advantage on them. He resorted to calling the owner’s secretary who opens the quotes to know how much is the lowest quote 2. Edwin Andrews is also a partner in The Wolverine Fastener Co. He is the working partner of
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