New SAT Math Workbook

You should also know how to raise exponential numbers

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Unformatted text preview: | – |2 – 7| = (A) –14 (B) –9 (C) –5 (D) 0 (E) 10 For all integers a and b, where b ≠ 0, subtracting b from a must result in a positive integer if: (A) |a – b| is a positive integer (B) (C) (D) (E) 3. 4. The figure below shows the graph of a certain equation in the xy-plane. 2. ( ) is a positive integer a b (b – a) is a negative integer (a + b) is a positive integer (ab) is a positive integer What is the complete solution set for the inequality |x – 3| > 4 ? (A) x > –1 (B) x > 7 (C) –1 < x < 7 (D) x < –7, x > 7 (E) x < –1, x > 7 Which of the following could be the equation? (A) x = |y| – 1 (B) y = |x| – 1 (C) |y| = x – 1 (D) y = x + 1 (E) |x| = y – 1 5. If f(x) = | x – 3| – x , then f ( 1 ) = 2 (A) –1 1 (B) (C) (D) (E) –2 0 1 2 1 1 www.petersons.com 250 Chapter 15 4. EXPONENTS (POWERS) An exponent, or power, refers to the number of times that a number (referred to as the base number) is multiplied by itself, plus 1. In the number 23, the base number is 2 and the exponent is 3. To calculate the value of 23, you calculate the value of 2 , you multiply 3 by itself three times: 2 = 2 × 2 × 2 × 2 = 16 . 3 3 3 3 3 3 81 An SAT problem might require you to combine two or more terms that contain exponents. Whether you can you combine base numbers—using addition, subtraction, multiplication, or division—before applying exponents to the numbers depends on which operation you’re performing. When you add or subtract terms, you cannot combine base numbers or exponents: ax + bx ≠ (a + b)x ax – bx ≠ (a – b)x Example: If x = –2, then x5 – x2 – x = (A) 26 (B) 4 (C) –34 (D) –58 (E) –70 Solution: The correct answer is (C). You cannot combine exponents here, even though the base number is the same in all three terms. Instead, you need to apply each exponent, in turn, to the base number, then subtract: x5 – x2 – x = (–2)5 – (–2)2 – (–2) = –32 – 4 + 2 = –34 There are two rules you ne...
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This note was uploaded on 08/15/2010 for the course MATH a4d4 taught by Professor Colon during the Spring '10 term at Embry-Riddle FL/AZ.

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