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Exam Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A) 2) 1) Simplify the expression. -36 -11 -6 11 B) 6 C) 11 D) -66 6 -11 Evaluate the root without using a calculator or note that root is not a real number. 2) 4 0.0081 A) 81 C) 0.3 3) 4) 5) D) Not a real number Evaluate the root without using a calculator or note that root is not a real number. 3 64 125 A) - C) 4 5 4 5 B) 5 4 D) Not a real number 3) 4) Identify the pair of like radicals. A) - 20 and 8 5 B) C) 3 D) 7 and 7 8 and 16 -3 32 and 5 48 5) Simplify the expression. (-14 - 8x)2 A) 14 + 8x 6) B) 3 B) 196 C) - 64x -14 - 8x D) Identify the real and imaginary parts of the complex number. 1 +i 9 A) Real: 0; imaginary: 1 9 B) Real: 1 ; imaginary: 1 9 C) Real: 1; imaginary: 1 9 D) 1 ; imaginary: 0 9 1 Real: –14 - 8x 6) 7) 7) Rationalize the denominator. 16 5 8) A) 16 5 5 B) 256 5 C) 5 5 16 D) Already rationalized x+ 3 A) y = 9) (m - x)3 3 m 3 - x3 z B) y = z C) y = 3m - 3x z D) y = (m - x)3 z 10 in. B) 12 C) in. 14 in. D) D) 81 9) 28 in. 10) Convert the expression to radical form and simplify. 91/2 9 A) 3 B) 2 C) 11) yz = m Find the length of the third side of the triangle by using the Pythagorean theorem. A) 10) 8) Solve for y. Not a real number 11) Simplify the radical expression. x 2 y8 A) x2 y8 12) C) ± xy4 D) xy4 Simplify the expression. Assume that all variables represent positive real numbers. 3 A) 13) B) |x|y4 64a15b6 61a12b3 B) 4a5 b2 C) -4a5 b2 D) 2a3b3 13) Simplify the expression in terms of i. -200 A) 12) 10 2i B) 100i C) 2 2 10i 2 D) -10i 2 14) 15) 14) Simplify. i42 A) 1 B) –i D) –1 15) x A) x-1/5 17) i Write the expression by using rational exponents rather than radical notation. 5 16) C) B) x5 Solve the equation. 3 5x - 2 = x + 26 A) { } C) x-5 D) x1/5 16) B) {1} C) {1, 7} D) {7} Simplify the expression by using the properties of rational exponents. Write the final answer using positive exponents only. Assume all variables represent positive real numbers. q27/7 17) q6/7 A) q3 18) 19) 20) B) q21 C) q D) q33/7 18) Multiply the radical expressions. (4 6 + 2)(2 10 - 3 8) A) 32 15 + 8 5 - 192 3 - 12 C) 16 15 - 12 B) –16 D) 16 15 + 4 5 - 48 3 - 12 19) Simplify the expression in terms of i. -21 A) i 21 B) 21i C) -i 21 D) –21i Simplify the expression. Assume all variables represent positive real numbers. 4 4 ( 14xy) A) 4 14xy B) 14 4 C) xy 3 14xy D) 14xy 20) 21) Simplify the expression by using the properties of rational exponents. Write the final answer using positive exponents only. Assume all variables represent positive real numbers. 81s12r-4 21) 3/4 16s-4r4 A) 22) 3s16r8 2 B) 3s12 C) 2r6 27s12 8r6 D) 27s6 8 The amount of time it takes an object dropped from an initial height of h0 feet to reach a 22) height of h feet is given by the formula h0 - h t= 16 An object dropped from the top of the Sears Tower in Chicago takes 9.5 seconds to reach the ground. Use the above equation to approximate the height of the Sears Tower. A) 990 feet B) 1,170 feet C) 1,520 feet D) 1,444 feet 23) 24) 23) Simplify the radical. 132 A) 4 33 B) 2 C) 2 66 D) 33 Cannot be simplified Simplify the radical. Assume that all variables represent positive real numbers. 24) 99zt 13 A) 25) B) 9t6 C) 11zt 3t 11zt 11 D) 3t6 11zt 25) Multiply the radical expressions. 3 24 A) 26) 3zt6 33t 36 2 B) 2 C) 6 6 2 125y7 C) 3 3 26) Rationalize the denominator. 7 A) D) B) Already rationalized 7 5y D) 25y4 4 7 125y7 125y7 7 5y 5y3 27) 28) Multiply. Write the answer in the form a + bi. (-4 – 9i) (7 + 3i) A) -1 – 75i B) -28 – 27i 27) C) -55 – 75i D) -1 28) Multiply the radical expressions and simplify your answer. 3 3 3 ( 5ab2 )( 2a3 b)( 50a7b10) 3 A) a3b4 29) B) 5a3 b4 3 4a2 b C) 3 5a7b6 4b2 3 D) a7b6 4b2 29) Simplify the expression. 369 369 A) 30) 4a2 b 738 B) 369 C) 38 D) 136,161 On a certain youth league baseball diamond, the bases are 50 ft apart. Assuming home plate and the three bases form a perfect square, find the exact distance from home plate to second base. Then round to the nearest tenth of a foot. A) The distance is 10 3 ft or approximately 17.3 ft. 30) B) The distance is 50 2 ft or approximately 70.7 ft. C) The distance is 5 2 ft or approximately 7.1 ft. D) 31) The distance is 10 2 ft or approximately 14.1 ft. 31) Solve the equation by using substitution. z4 – 16 = 0 A) {2} B) {2, -2, 2i, -2i} C) {2, -2, 4i, -4i} D) {2, -2} 32) Write the coordinates of the vertex and determine if the vertex is a maximum point or a minimum point. f (x) = 15 - (x + 13)2 A) (-15, 13); maximum B) (13, -15); minimum C) (-13, 15); minimum D) (-13, 15); maximum 32) 33) The city of Morgana is 20 miles due west of Vining. Beckett is due north of Morgana. If the distance from Beckett to Vining is 2 miles less than 3 times the distance from Beckett to Morgana, how far apart are Beckett and Morgana? Round to 1 decimal place. A) 7.8 miles B) 5.3 miles C) 6.9 miles D) 11.2 miles 33) 34) Use the discriminant to determine the type and number of solutions. 5x2 + 5x + 2 = 0 A) One rational solution B) Two rational solutions C) Two irrational solutions D) Two imaginary solutions 34) 5 35) Find the vertex of g(x) = A) 36) 37) 38) 5 6 , 6 5 6 5 ,5 6 C) - 6 5 ,5 6 D) - 5 6 ,6 5 36) B) {±3, C) ±4i} {±3i, ±4} D) {± 3, ±4i} 37) C) {1, -125} D) {1, 25} 38) Find the x-intercepts of the function. C) 4x2 – 16x + 16 B) (2, (2, 0) 1 1 , 0 and - , 0 2 2 D) 0) and (–2, 0) None. Find the value of n so that the expression is a perfect square trinomial and then factor the trinomial. x2 + 12x + n A) n = 36; (x + 6)2 B) n C) n = 36; (x + 6)(x - 6) D) D) {1 + 2i 19, 1 - 2i 19} n = 36; (x - 6)2 40) {-2 + 2 19, -2 - 2 19) A catapult is designed to launch circus performers from a raised platform. After launch, the height of the performer in feet is given by h(t) = –16t2 + 80t + 32 where t is seconds after launch. After how many seconds is the performer exactly 100 feet above the ground? Round to the nearest tenth of a second. A) –0.4 and 5.4 seconds B) 5 seconds C) 0.5 and 2.8 seconds D) 1.1 and 3.9 seconds 6 39) = 144; (x + 12)2 Solve the equation by using the quadratic formula. w(w - 2) = -20 A) {1 + 19, 1 - 19} B) {1 + i 19, 1 - i 19} C) 41) 35) Solve the equation by using substitution. z2/3 + 4z1/3 – 5 = 0 A) {1, 125} B) {4, -4} A) 40) B) Solve the equation. x4 + 13x2 - 48 = 0 A) {±3, ±4} h(x) = 39) 62 5 1 x+ - . 3 5 6 41) 42) 43) 44) Solve the equation by using the square root property. 5y2 + 17 = 3y2 - 179 A) {7 2} B) {7i, -7i} C) {7, -7} 42) D) {7i 2, -7i 2} 43) Graph the function. 1 g(x) = (x - 2)2 - 4 4 A) B) C) D) 44) Solve the equation by using substitution. (t + 10)2 – (t + 10) – 12 = 0 A) {-6, -13} B) {6, 13} C) 7 {4, –3} D) {-14, -7} 45) Graph the parabola. Use the graph to write the domain and range in interval notation. f (x) = -3(x - 2)2 A) Domain: (- , ); Range: (- , 0] B) Domain: [- , 2); Range: (- , ) C) 46) D) Domain: (- , ); Range: [0, ) 45) Domain: (- , 0]; Range: (- , ) Simplify the radical. Assume that all variables represent positive real numbers. 46) 270z15 3z4 A) 47) 48) 9z5 10z B) 3z Solve the equation. -6 = -2 + (q – 6)1/3 A) {70} 10z9 C) 3 10z11 D) 47) B) {58} C) D) {-58} {} 48) Identify the pair of like radicals. A) m m and 5 m 3 B) C) 4 3 x 4 2 x D) and 3z5 10z 8 5t and 3 8t -5 3 2 y 3 and 2 y2 49) 49) Rationalize the denominator. 2-4 2 2+1 2 2-8 3 A) 50) 51) 6 2 - 10 D) 6 2 - 10 3 50) A) 5 B) 125 C) 1 125 D) Not a real number 51) Simplify the radical expression. A) 53) C) -5 2 Simplify the expression, if possible. 625-3/4 3 52) B) 2 (-19)3 -19 Solve the equation. 2x - 5 = 2x - 2 32 A) 81 Solve the equation. x2 (x2 - 1) = 90 A) {±10, ±3i} B) -6859 C) 19 D) 6859 52) B) { C) } {0} D) 81 32 53) B) {± C) 10, ±3i} {±10, ±3} D) {±10i, ±3} 54) Solve the equation by using the square root property. 3y2 = –120 A) {2i 10, -2i 10} B) {2 10, -2 10} C) {2 10} D) {2i 30, -2i 30} 54) 55) Solve the inequality. -x2 – 8x – 16 < 0 A) (- , -4) (4, ) C) (- , ) 55) 56) B) { D) } (- , -4) (-4, ) Write the equation of the axis of symmetry of the parabola. f (x) = -10(x + 2)2 + 5 A) x = -2 B) x = 5 C) y = 5 9 56) D) x=2 57) A) 58) 57) Multiply the radical expressions. -5 y ( y + 10) –5y + 10 B) -5y2 C) - 50 y -55 y D) -5y - 50 y Simplify the radical. Assume that all variables represent positive real numbers. 58) 12x7 A) 59) 2 3x7 C) 3x 2x 3x5 D) 4x6 3x The formula for the area of a circle is A = r2, where r is the radius. Solve the formula for r, and use your answer to find the radius of a circle with area 25 feet. Use 3.14 for and round the answer to the nearest tenth of a foot. A A ,r=; 2.8 feet or –2.8 feet A) r = B) r = 60) B) 2x3 A ; 4.0 feet 2 A C) r= D) r = A - ; 4.7 feet ; 2.8 feet 60) Simplify the radical. 6 50 35 A) 59) 6 2 B) 6 2 7 C) 10 6 10 7 D) 12 35 Answer Key Testname: TEST4 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31) 32) 33) 34) 35) 36) 37) 38) 39) 40) 41) 42) 43) 44) 45) 46) 47) 48) 49) 50) A C C A C B A D A A B B C D D B A D A C C D B D C C A B B B B D A D C D C A A B D D C A A D C D C C 11 Answer Key Testname: TEST4 51) 52) 53) 54) 55) 56) 57) 58) 59) 60) A D B A D A D B C B 12