Test bank precalculus; mathematics for calculus 7e ch1

Stewart/Redlin/Watson - Precalculus 7e Chapter Form A List the elements from the given set that are rational numbers  0,  2, 50,  1 , 0.521, 2, 1.23,  , 4,  4  State the property of real numbers being used  2x  y   4z  2x  3 y  4z  Perform the indicated operations 12 1  12 Evaluate each expression 7 (a)   21 3 (b) 3 40 1 (c)   5 2 Evaluate the expression 48 Find the set A  C if A   x | x   and C   x | 2  x   Simplify the expression and eliminate any negative exponents(s) Assume that all letters denote positive numbers r s 64r s Simplify the expression  a 2b5/   1/ /  a b  A hummingbird’s heart can beat 1260 times per minute Estimate the number of times its heart will beat in years State your answer in scientific notation 10 Factor the expression completely     x x   25 x  11 Perform the indicated operation and simplify    x x   x  12 Stewart/Redlin/Watson - Precalculus 7e Chapter Form A 12 Rationalize the denominator 6 13 Find all real solutions of the quadratic equation 16 z2  z  0 25 14 Caitlin drove from Greensville to Bluesburg at a speed of 50 mi/h On the way back, she drove at 75 mi/h The total trip took h of driving time Find the distance between these two cities 15 Solve the absolute value inequality Express the answer using interval notation x   15 16 Two points P and Q are given P  0, 8  , Q  11, 8 (a) Find the distance from P to Q (b) Find the midpoint of the line segment PQ 17 Find the equation of the circle with center  1,  and radius 18 Determine whether the equation represents a circle, a point, or has no graph If the equation is that of a circle, find its center and radius x2  y  x  y  3 19 Test the equation for symmetry and sketch its graph y  x2  16 20 Find an equation for the line that passes through the point  5,1 and is perpendicular to the line x  y  16  21 Find the equation of a line that passes through the point  7, /  and the midpoint of  2,  and  3,  22 Hooke’s Law states that if a weight w is attached to a hanging spring, then the stretched length s of the spring is linearly related to w For a particular spring we have the equation s  0.4w  3.5 , where s is measured in inches and w in pounds How long is the spring when a 5-lb weight is attached? 23 Determine the values of the variable for which the expression is defined as a real number 1/2      x  x  15  Stewart/Redlin/Watson - Precalculus 7e Chapter Form A 24 In a certain city, the property tax collected for a home varies directly to the valuation of the property The tax collected on a $105, 000 home is $2,846 per year What is the value of a home if the tax collected is $1, 735 ? 25 The resistance of a wire varies directly as its length and inversely as the square of its diameter A wire 50 m long and 0.01 m in diameter has a resistance of 25 ohms Find the resistance of a wire made of the same material that is 20 m long and has diameter 0.02 m ANSWER KEY Stewart/Redlin/Watson - Precalculus 7e Chapter Form A 1 0,  2, 50, 0.521, 1.23,  , Associative Property for addition 7 (a)   21  3 33 (b) 40  27 1 (c)   5 48  12  x | 2  x   4r s a10b6 1.32  109     10 x x   25 x    x  1 x  1 x   x   11 12 3x  x  x  x  1 1 13 z  / 14 225 mi 15 (, 5 / 2)  (5 / 4, ) 16 (a) 11  11  (b)  , 8    2 17 x  x  y  14 y  48    18 center   , 1 , radius   2  25 ANSWER KEY Stewart/Redlin/Watson - Precalculus 7e Chapter Form A 20 18 16 14 12 y10 19 -5 -4 -3 -2 -1 -2 -4 -6 -8 y-axis symmetry 20 y  16  x 21 30 y  x  119  22 5.5 inches 23 (, 5)  (3, ) 24 $64, 010 25 2.5 ohms x Stewart/Redlin/Watson - Precalculus 7e Chapter Form B List the elements from the given set that are rational numbers  0,  2, 25,  3,  , , 0.49, 16,  9  State the property of real numbers being used  2x  y   4z  2x  3 y  4z  Perform the indicated operations   10 Evaluate each expression 33 5 (a)   31 3 (b) 50 (c) 1   3 2 Evaluate the expression 50 Find the set A  C if A   x | x   and C   x | 2  x  10  Simplify the expression and eliminate any negative exponents(s) Assume that all letters denote positive numbers r s 81r s Perform the division and simplify x4 x2   x  x  16 x  13 x  10 A hummingbird’s heart can beat 1260 times per minute Estimate the number of times its heart will beat in years State your answer in scientific notation 10 Factor the expression completely    x x   16 x   11 Perform the indicated operation and simplify 1  x x3 Stewart/Redlin/Watson - Precalculus 7e Chapter Form B 12 Rationalize the denominator 6 13 Determine the values of the variable for which the expression is defined as a real number 1/2      x  x  15  14 The approximate distance d (in feet) that drivers travel after noticing that they must come to a sudden x2 , where x is the speed of the car in mi/h If a car travels 120 ft stop is given by the formula d  x  20 before stopping, what was its speed before the brakes were applied? 15 Solve the inequality x  x  20  16 Two points P and Q are given Sketch the line determined by P and Q, and find its equation in slopeintercept form P 1, 10  , Q  2, 4  17 Find the equation of the circle with center  1,5 and radius 18 Determine whether the equation represents a circle, a point, or has no graph If the equation is that of a circle, find its center and radius x2  y  x  y  3 19 Test the equation for symmetry and sketch its graph 9x  y2  20 Find an equation for the line that passes through the point  5,1 and is perpendicular to the line x  y  16  21 Find the equation of a line that passes through the point  7,1 and has slope of 1/ 22 Find the equation of the line in the figure 8,9 10 5 10 Stewart/Redlin/Watson - Precalculus 7e Chapter Form B 23 Alyson drove from Bluesville to Greensburg at a speed of 60 mi/h On the way back, she drove at 45 mi/h The total trip took h of driving time Find the distance between these two cities 24 In a certain city, the property tax collected for a home varies directly to the valuation of the property The tax collected on a $105, 000 home is $2,846 per year What is the value of a home if the tax collected is $1, 735 ? 25 The cost for one print run of a book is jointly proportional to the number of pages in the book and the number of books in the print run Write an equation for the cost of a print run if it costs $20, 000 to print 4000 copies of a 100-page book, and calculate the cost to print 400 copies of 293 page book ANSWER KEY Stewart/Redlin/Watson - Precalculus 7e Chapter Form B 1 , 0.49,  , 0,  2, 25, Associative Property for addition 9/7 5 (a)   31  3   20  x | 2  x   3r s 3 3 x4 (b) x  x  16  x  3x  13x  10 1.32  109     50  27 (c) 1   3  x  5  x  4 3x  2  2 10 x x   16 x    x   x   x   x   11  3x 12 1 13 (, 5)  (3, ) 14 40 mi/hr 15  , 5   4,   16 y  8  x -4 -2 x -2 -4 -6 -8 y -10 -12 -14 -16 -18 2 17 x  x  y  10 y  23  2 9 ANSWER KEY Stewart/Redlin/Watson - Precalculus 7e Chapter Form B   18 center   , 1 , radius   19 y -2.5 -2 -1.5 x -1 -0.5 -2 -4 x-axis symmetry 20 y  16  x 21 y  x  2 22 y  x 3 23 144 mi 24 $64, 010 25 $5860 Stewart/Redlin/Watson - Precalculus 7e Chapter Form D (a) 40 mi/hr (b) 50 mi/hr (c) 70 mi/hr (d) 80 mi/hr 15 Solve the inequality x  x  18  (a)  , 6    3,   (b) ( , 6]  [3,  ) (c)  3,  (d)  6, 3 (e)  6,3 16 Find all real solutions of the quadratic equation z2  z  0 25 3 (a)  , 5 (b)  , (c) (d) (e) none of these 17 Two points P and Q are given P  0, 8  , Q  11, 8 Find the distance from P to Q (a) 11 (b) (c) 19 (d) (e) 18 Find the equation of the circle with center ( 2,1) and radius (a) x  x  y  y   (b) x  x  y  y   (c) x  x  y  y   (d) x  x  y  y   (e) x  x  y  y   19 Test the equation for symmetry to determine the correct graph y  3x  (e) 90 mi/hr Stewart/Redlin/Watson - Precalculus 7e Chapter Form D (b) x-axis symmetry (a) x-axis symmetry 4 y2 2y x -5 -4 -3 -2 x -1 -2 -2 -4 -4 (d) origin- symmetry (c) y-axis symmetry y -4 -2 x y -1 -2 -4 -2 x (e) none 20 Find an equation for the line that passes through the point  1,  and is parallel to the line x  y  (a) y  x  15 x 15  2 (c) y  15  x (b) y  15 (e) y  x  (d) y  x  21 Determine whether the equation represents a circle, a point, or has no graph If the equation is that of a circle, find its center and radius x  y  x  y  18  (a) point (b) no graph (c) center  4, 2  , radius   (d) center   ,  , radius   (e) center  4,  , radius 22 Find the equation of the line in the figure 8,9 10 5 10 Stewart/Redlin/Watson - Precalculus 7e Chapter Form D (a) x  y  (b) x  y  x y 0 (d) y  x  3 (e) The equation of the line cannot be determined (c) 23 Taylor drove from Greensville to Bluesburg at a speed of 50 mi/h On the way back, he drove at 75 mi/h The total trip took h of driving time Find the distance between these two cities (a) 225mi (b) 175mi (c) 185mi (d) 125mi (e) 450 mi 24 The pressure of a sample of gas is directly proportional to the temperature T and inversely proportional to the volume V Write an equation that expresses this fact if 50 L of gas exerts a pressure of 14 kPa at a temperature of 350 K (absolute temperature measured on the Kelvin scale) 2T V 2V P T PV  T 50T P V P  2TV (a) P  (b) (c) (d) (e) 25 The resistance of a wire varies directly as its length and inversely as the square of its diameter A wire 50 m long and 0.01 m in diameter has a resistance of 25 ohms Find the resistance of a wire made of the same material that is 20 m long and has diameter 0.02 m (a) 2.5 ohms (b) 0.02 ohms (c) 50.54 ohms (d) 0.25 ohms (e) 2500 ohms ANSWER KEY Stewart/Redlin/Watson - Precalculus 7e Chapter Form D 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 a c c e a d b c e a d c b b e e a b a b c d a a a Stewart/Redlin/Watson - Precalculus 7e Chapter Form E List the elements from the given set that are rational numbers  0,  2, 50,  1 , 0.521, 2, 1.23,  , (a) 0,  2, 50, 1.23,  (b) 0, 4,  4  , 0.521, 2 ,  , (c) 0,  2, 50, 0.521, 1.23,  , (d) 0, , 2, (e) 0,  2, 50 State the property of real numbers being used  2x  y   4z  2x  3 y  4z  (a) Commutative Property for addition (b) Commutative Property for multiplication (c) Associative Property for addition (d) Associative Property for multiplication (e) Distributive Property Perform the indicated operations  3  10 Which inequality is not true? (a)  1  10 100 (b)  Evaluate each expression 7 (a)   21 3 (b) 33 40 1 (c)   5 2 (c)  1.7 (d)   0.25 (e) all are true Stewart/Redlin/Watson - Precalculus 7e Chapter Form E Find the set A  C if A   x | x   and C   x | 2  x   (a) (b) (c) (d)  x | 2  x    x | 2  x    x|4 x6   x | 2  x   (e) none Evaluate the expression 48 (b) 24 (a) 36 (d) (e) Simplify the expression and eliminate any negative exponents(s) Assume that all letters denote positive numbers (c) 12 r s 81r s A hummingbird’s heart can beat 1260 times per minute Estimate the number of times its heart will beat in years State your answer in scientific notation 10 Simplify the expression  3   1   xy   x y     (a) y3 3x (b) 2 x y (c) xy 11 Perform the subtraction and simplify  x  x  x  15 12 Rationalize the denominator 6 13 Find all real solutions of the equation x2 3x  x  3x  (d) 3y 8x (e) 3 xy Stewart/Redlin/Watson - Precalculus 7e Chapter Form E 14 Factor the expression completely x3  x  10 x  (b)  x   x  12  x    x  1 (c)  x+1 x  5 x  1 (a) (d)  x    x  1 (e) none of these 15 Solve the absolute value inequality Express the answer using interval notation x   15 16 Two points P and Q are given Sketch the line determined by P and Q, and find its equation in slopeintercept form P 1, 10  , Q  2, 12  17 Find the equation of the circle with center  1,  and radius 18 Determine whether the equation represents a circle, a point, or has no graph If the equation is that of a circle, find its center and radius x2  y  x  y  /  19 Test the equation for symmetry and sketch its graph y  x2  16 20 Find the area of the right triangle with base AB , where the vertices are A   3,  , B   2,  and C   2,  21 Find the equation of a line that passes through the point  7, /  and the midpoint of  2,  and  3,  22 Find an equation for the line that passes through the point  5,1 and is perpendicular to the line x  y  16  (a) y  x  (b) y  x  16 (c) y  16  x (d) y  x  15 (e) y  x 3 Stewart/Redlin/Watson - Precalculus 7e Chapter Form E 23 Caitlin drove from Greensville to Bluesburg at a speed of 50 mi/h On the way back, she drove at 75 mi/h The total trip took h of driving time Find the distance between these two cities 24 In a certain city, the property tax collected for a home is directly proportional to the valuation of the property The tax collected on a $105, 000 home is $2,846 per year What is the value of a home if the tax collected is $1, 735 ? (a) (b) (c) (d) (e) $74,866 $834, 289 $175, 010 $64, 010 $85, 259 25 The resistance of a wire varies directly as its length and inversely as the square of its diameter A wire 50 m long and 0.01 m in diameter has a resistance of 25 ohms Find the resistance of a wire made of the same material that is 20 m long and has diameter 0.02 m ANSWER KEY Stewart/Redlin/Watson - Precalculus 7e Chapter Form E c c 5/3 e 7 (a)   21  3 a c 3r s 3 1.32  109 33 (b) 40  10 b 11 2x    x  x  x  15 x  x  15 12 1 13 no solution 14 e 15 (, 5 / 2)  (5 / 4, ) 16 y  8  x -4 -2 x -2 -4 -6 -8 y -10 -12 -14 -16 -18 17 x  x  y  14 y  48    18 center   , 1 , radius   27 1 (c)   5 2  25 ANSWER KEY Stewart/Redlin/Watson - Precalculus 7e Chapter Form E 19 20 18 16 14 12 y10 -5 -4 -3 -2 -1 -2 -4 -6 -8 y-axis symmetry 20 10 21 30 y  x  119  22 c 23 225 mi 24 d 25 2.5 ohms x Stewart/Redlin/Watson - Precalculus 7e Chapter Form F List the elements from the given set that are rational numbers  0,  2, 25,  , 0.49, 3,  , 16,  9  State the property of real numbers being used 3xy  yx3 (a) Commutative Property for addition (b) Commutative Property for multiplication (c) Associative Property for addition (d) Associative Property for multiplication (e) Distributive Property Perform the indicated operations   10 Evaluate the expression 31/ 271/ Simplify the expression and eliminate any negative exponents(s) Assume that all letters denote positive numbers x x Find the set A  C if A   x | x   and C   x | 2  x  10  Evaluate each expression 5 (a)   31 3 (b) (c) 33 50 1   3 2 Simplify the expression x2  x  x2  x  x2  2x x2  x  Stewart/Redlin/Watson - Precalculus 7e Chapter Form F Simplify the expression  27x y  y4 (a) 3x y (b) 27x3 y (c) 3y (d) 9x y3 (e) 9x y 10 Factor the expression completely    x x   16 x   11 Perform the indicated operation and simplify 1  x x3 (a) (b)   x  3 (c) x  x  3 (d)  3x (e) 3x 12 Rationalize the denominator 6 13 Determine the values of the variable for which the expression is defined as a real number 1/2      x  x  24  14 The approximate distance d (in feet) that drivers travel after noticing that they must come to a sudden x2 , where x is the speed of the car in mi/h If a car travels 175 ft stop is given by the formula d  x  20 before stopping, what was its speed before the brakes were applied? 15 Solve the absolute value inequality Express the answer using interval notation x   15 16 Find all real solutions of the quadratic equation 16 z2  z  0 25 Stewart/Redlin/Watson - Precalculus 7e Chapter Form F 17 Two points P and Q are given P  0, 8  , Q  11, 8 Find the distance from P to Q (a) 11 (b) (c) 19 (d) (e) 18 If M  2,1 is the midpoint of the line segment AB , and if A has coordinates   12 ,6  , find the coordinates of B 19 Test the equation for symmetry to determine the correct graph y  3x  (a) x-axis symmetry (b) x-axis symmetry 4 y2 2y x -5 -4 -3 -2 x -1 -2 -2 -4 -4 (d) origin- symmetry (c) y-axis symmetry y y -4 -2 2 x -1 -2 -4 -2 x (e) none 20 Find an equation for the line that passes through the point  5,1 and is perpendicular to the line x  y  16  21 Determine whether the equation represents a circle, a point, or has no graph If the equation is that of a circle, find its center and radius x  y  x  y  18  (a) point (b) no graph (c) center  4, 2  , radius   (d) center   ,  , radius   (e) center  4,  , radius Stewart/Redlin/Watson - Precalculus 7e Chapter Form F 22 Find the equation of the line in the figure 8,9 10 5 10 23 Taylor drove from Bluesville to Greensburg at a speed of 60 mi/h On the way back, he drove at 45 mi/h The total trip took h of driving time Find the distance between these two cities 24 The pressure of a sample of gas is directly proportional to the temperature T and inversely proportional to the volume V Write an equation that expresses this fact if 50 L of gas exerts a pressure of 14 kPa at a temperature of 350 K (absolute temperature measured on the Kelvin scale) (a) P  2T V (b) P  2V T (c) PV  T (d) P  50T V (e) P  2TV 25 The cost for one print run of a book is jointly proportional to the number of pages in the book and the number of books in the print run Write an equation for the cost of a print run if it costs $20, 000 to print 4000 copies of a 100-page book, and calculate the cost to print 400 copies of 293 page book ANSWER KEY Stewart/Redlin/Watson - Precalculus 7e Chapter Form F , 0.49,  ,   x 2/ x1/ 0,  2, 25, b 9/7  x | 2  x   5 (a)   31  3   e  x x  x x 1/3     (b)   1/3 3 50   x 3/  27  1/3  x1/  (c) 1   3 2 10 x x   16 x    x   x   x   x   11 d 1 12 13 (, 3)  (8, ) 14 50 mi/hr 15 (, 5 / 2)  (5 / 4, ) 16 z  17 a 18  / 2, 4  19 a 20 y  16  x 21 c 22 y  x 3 23 144 mi 24 a 25 $5860 x 2 9 ... Stewart/Redlin/Watson - Precalculus 7e Chapter Form C 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 c b d e a a e c e b d a a b d e e c b a c c a d a Stewart/Redlin/Watson - Precalculus 7e Chapter Form D List... Stewart/Redlin/Watson - Precalculus 7e Chapter Form D 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 a c c e a d b c e a d c b b e e a b a b c d a a a Stewart/Redlin/Watson - Precalculus 7e Chapter Form E List... variable for which the expression is defined as a real number 1/2      x  x  15  Stewart/Redlin/Watson - Precalculus 7e Chapter Form A 24 In a certain city, the property tax collected for