2003 AMC 10B ws-25.pdf - Which of the following is the same as 2 \u2212 4 6 \u2212 8 10 \u2212 12 14 3 \u2212 6 9 \u2212 12 15 \u2212 18 21(A \u22121(B \u2212 2 3(C 2 3(D 1(E

2003 AMC 10B ws-25.pdf - Which of the following is the same...

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Which of the following is the same as2-4 + 6-8 + 10-12 + 143-6 + 9-12 + 15-18 + 21? (A)-1(B)-23(C)23(D)1(E)14 32003 AMC 10 B, Problem #12003 AMC 12 B, Problem #1“Can you find any common factor in numerator anddenominator .” Difficulty: Easy NCTM Standard: Number and Operations Standard for Grades 9-12: Compute fluently and make reasonable estimates. Mathworld.com Classification: Number Theory > Arithmetic > General Arithmetic
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Al gets the disease algebritis and must take one greenpill and one pink pill each day for two weeks. A greenpill costs1 more than a pink pill, and Al’s pills costa total of546 for the two weeks. How much doesone green pill cost? 2003 AMC 10 B, Problem #22003 AMC 12 B, Problem #2“The cost of each day’s pills is546/14 = 39dollars .” Difficulty: Medium-easy NCTM Standard: Algebra Standard for Grades 9–12: Use mathematical models to represent and understand quantitative relationships. Mathworld.com Classification: Number Theory > Arithmetic > General Arithmetic
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The sum of 5 consecutive even integers is 4 lessthan the sum of the first 8 consecutive odd countingnumbers. What is the smallest of the even integers? (A)6(B)8(C)10(D)12(E)14 2003 AMC 10 B, Problem #3“Thesumofthefirst8consecutiveoddcountingnumbers is 64 .” Difficulty: Medium-easy NCTM Standard: Number and Operations Standard for Grades 9–12: Compute fluently and make reasonable estimates. Mathworld.com Classification: Number Theory > Arithmetic > General Arithmetic Number Theory > Integers > Consecutive Numbers
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Rose fills each of the rectangular regions of her rectangular flower bed with a different type of flower. The lengths, in feet, of the rectangular regions inher flower bed are as shown in the figure. She plants one flower per squarefoot in each region.Asters cost1 each, begonias1.50 each, cannas2 each, dahlias2.50 each, and Easter lilies3 each. What is the leastpossible cost, in dollars, for her garden? 1 5 4 7 3 3 5 6 (A) 108 (B) 115 (C) 132 (D) 144 (E) 156 2003 AMC 10 B, Problem #4 2003 AMC 12 B, Problem #3 “To minimize the cost, Rose should place the most expensive flowers in the smallest region.” Solution Answer (A): To minimize the cost, Rose should place the most expensive flowers in the smallest region, the next most expensive in the second smallest, etc. The areas of the regions are shown in the figure, so the minimal total cost, in dollars, is (3)(4) + (2 . 5)(6) + (2)(15) + (1 . 5)(20) + (1)(21) = 108 . 1 5 4 20 21 4 15 6 7 3 3 5 6 Difficulty: Easy NCTM Standard: Geometry Standard for Grades 9–12: Use geometric models to gain insights into, and answer questions in, other areas of mathematics.
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