Practice Test 1: Chapter P Fall 2016 MAT 115 Name________________________________________________ Date__________________ I HAVE ABIDED BY THE UNCG Academic Integrity Policy ON THIS ASSIGNMENT. Student's Signature __________________________________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the distance on the number line between the pair of numbers. 1) 11.0, -19.2 A) 30.2 B) 15.1 C) 4.1 D) 8.2 1) Perform the indicated operations. Write answers using only positive exponents. Assume variables represent positive real numbers. 3 x1/2 y3 2) 2) y3/2 A) x3/2 y9/2 3) 8a 3/2 8a -11/2 a4 A) 64 B) x3/2 y9/2 C) x3/2 D) x1/2 y9/2 3) B) 64 a4 C) 8 a5 D) 8a -8 Simplify. Write answers without negative exponents. Assume that all variables represent nonzero real numbers. 2 4p-4q 4) 4) 2 -1m 3 A) 5) 64q8 q m6 2x3y-3 x-2 y3 A) B) 8q2 p4 m 3 C) 64q2 p8 m 6 D) 8 p8 m 6 -5 2x25 y30 5) B) y30 32x25 Find the degree and leading coefficient of the polynomial. 6) -3x3 + 12 - 16x4 + x9 + 17x2 A) Degree: 3; leading coefficient: -3 C) Degree: 4; leading coefficient: -16 C) y30 2x5 D) y30 2x25 B) Degree: 9; leading coefficient: 1 D) Degree: 9; leading coefficient: -3 Perform the indicated operations and simplify. Assume that all variables represent positive real numbers. 7) (- 3 3)(8 15) A) - 72 5 B) -24 3 15 C) -360 D) 72 5 PA-1 6) 7) Perform the indicated operation and express in lowest terms. b 5 6 + 8) 2 b 5 b + b - 25 8) A) 25(b - 6) (b + 5)(b - 5) B) 6b2 - 25b + 150 b(b + 5)(b - 5) C) 25(b + 6) b(b + 5)(b - 5) D) -25(b - 6) b(b + 5)(b - 5) Solve the problem. 9) The volume of a box is 3p4 + 10p3 + 8p2 . The height is p and the width is p + 2. What is the length? A) p2 + 4 B) 3p + 4 C) 3p3 + 4p2 D) 3p2 + 4p 9) 10) The expression 0.60(226 - a - r) + r is used to obtain the target heart rate for a cardiovascular workout for a nonathletic female with age a and resting heart rate r. Find the target heart rate for a 19-year-old nonathletic female with a resting heart rate of 60 beats per minute. A) 136.8 beats/min B) 148.2 beats/min C) 147 beats/min D) 144.6 beats/min 10) Use the properties of real numbers to simplify the expression. 11) 2(3x + 3) - 4(3x - 1) A) -6x - 10 B) -6x + 10 C) -6x + 2 Factor by grouping. 12) 10x6 - 8x3 - 25x3 + 20 A) (2x3 + 5)(5x3 + 4) C) (2x6 - 5)(5x - 4) D) 18x + 10 12) B) (10x3 + 5)(x3 + 4) D) (2x3 - 5)(5x3 - 4) Factor the sum or difference of two cubes. 13) w3x + 8 A) (wx - 2)(w2x - 2wx + 4) C) (wx + 2)(w2 - 2w + 4) 13) B) (wx + 2)(w2x - 2wx + 4) D) (w + 2)(w2x + 2wx + 4) 14) 64p3 - 1 A) (4p + 1)(16p2 - 4p + 1) C) (4p - 1)(16p2 + 4p + 1) 14) B) (64p - 1)(p2 + 4p + 1) D) (4p - 1)(16p2 + 1) Write rational exponents in radical notation and radicals in rational exponential notation. 15) 2434/5 A) 16) 12 5 x18 2434 A) x6 11) B) 2435 B) x2/3 C) 243 C) x3 PA-2 D) 15) 4 2435 D) x3/2 16) Factor the trinomial. 17) x2 + 6x - 16 A) (x - 8)(x + 1) B) (x + 8)(x - 2) Find the product of the complex number and its conjugate. 18) -1 + i 7 A) 8 B) 50 C) (x - 8)(x + 2) D) (x + 16)(x - 1) C) -6 D) -48 Use scientific notation to solve the problem. 19) Radio waves travel at 3.00 108 m/sec, and the distance from Mars to Venus is about 1.197 1011 m. How long does it take a radio wave to travel from Mars to Venus? A) 3.99 102 min B) 3.99 102 sec C) 3.99 103 sec D) 39.9 sec Reduce the rational expression to lowest terms. 8x + 28 20) 10x + 35 A) 4 21) B) 5 4 a-5 a+3 18) 19) 20) C) 1 D) 4 5 a 2 - 25 a 2 + 8a + 15 A) 17) 21) B) a-5 a-3 C) a+5 a-3 D) a+5 a+3 Simplify. 22) -5 -2 + x+5 x-2 22) -5 -2 x-2 x-3 A) -(x - 3) x+5 B) -7x(x - 3) 3x2 + 11x - 20 Evaluate the expression for the given values. 23) (a + b)(a 2 - ab - b2 ), if a = 6 and b = -5 A) 31 Evaluate the indicated power of i. 24) i55 A) 1 B) 41 B) -i Use the order of operations to evaluate the expression. 25) 89 - 10 5 + 285 (-19) A) 24 B) -19 26) 2(4 - 2 1 - 2 ) A) 4 B) 12 C) -7x2 - 1 + 60 -7x2 + 39x - 20 C) 451 D) -7x2 + 21x -7x2 - 48x - 20 D) 91 C) i D) -1 C) -1206 D) 380 C) 0 D) 6 PA-3 23) 24) 25) 26) Find the domain of the rational expression. 6 27) x(2 - x) A) x x C) x x 2 and x 2 0 and x 6 Use the distributive property to find the product. 28) (6y2 - 2y - 4)(y - 7) A) 6y3 - 44y2 + 10y + 28 C) 6y3 + 44y2 + 18y + 28 27) B) x x 2 and x 0 D) All real numbers B) 6y3 + 44y2 + 10y - 28 D) 6y3 - 44y2 + 18y - 28 28) Perform the indicated operations and write the answer in the form a + bi, where a and b are real numbers. 29) (9 + 9i)(3 - 4i) A) -9 + 63i B) 63 - 9i C) 63 + 9i D) -36i2 - 9i + 27 29) Perform the indicated operation and simplify. 9p - 9 10p - 10 30) p 3p2 30) A) 90p2 + 180p + 90 3p3 B) 27p 10 C) 10 27p D) 27p3 - 27p2 10p2 - 10p PA-4 Answer Key Testname: MAT 115 TEST 1P-A FALL 2016 1) A 2) A 3) B 4) C 5) B 6) B 7) A 8) D 9) D 10) B 11) B 12) D 13) B 14) C 15) A 16) D 17) B 18) A 19) B 20) D 21) A 22) B 23) B 24) B 25) A 26) A 27) B 28) A 29) B 30) B PA-5