Mock Final Exam Name Solve and check the linear equation. 1) (-8x + 8) + 1 = -7(x + 3) 1) A) {- 30} B) {- 6} C) {30} D) {- 28} First, write the value(s) that make the denominator(s) zero. Then solve the equation. 1 2) x + 3 + 5 x - 3 = 30 (x + 3)(x - 3) 2) A) x -3; {3} B) No restrictions; {3} C) x -3, 3; {4} D) x -3, 3; Add or subtract as indicated and write the result in standard form. 3) 1 - (4-6i) - (4-6i) 3) A) -8 + 12i B) -7 + 12i C) -7-12i D) -8-12i Find the product and write the result in standard form. 4) -7i(9i - 9) 4) A) 63 + 63i B) -63 + 63i C) 63i - 63i2 D) 63i + 63i2 5) (3-9i)2 5) A) -72 B) 9-54i + 81i2 C) 90-54i D) -72-54i Divide and express the result in standard form. 4i 6) 5-7i A) 10 37-14 37 i B) - 5 6 + 7 6 i C) 7 6 + 5 14 i D) - 6 37 + 10 37 i 6) Perform the indicated operations and write the result in standard form. -36 - -252 7) 6 7) A) -6 + i 7 B) -6 - i 6 C) 6 + i 7 D) -6 - i 7 Solve the equation by factoring. 8) x2 = x + 30 8) A) {-5, 6} B) {1, 30} C) {5, 6} D) {-5, -6} Solve the equation by the square root property. 9) 7x2 = 112 9) A) {-7, 7} B) {-4 7, 4 7} C) {0} D) {-4, 4} 1
Solve the equation using the quadratic formula. 10) 3x2-5x + 9 = 0 10) A) 5 ± 83 6 B) -5 ± 83 6 C) -5 ± i 83 6 D) 5 ± i 83 6 Solve the linear inequality. Other than, use interval notation to express the solution set and graph the solution set on a number line. 11) 15x + 9 > 3(4x - 1) 11) A) (-, -4) B) (2, ) C) (-4, ) D) [-4, ) Solve the absolute value inequality. Other than, use interval notation to express the solution set and graph the solution set on a number line. 12) 3(x + 1) + 9 12 12) A) (-6, 2) B) (-8, 0) C) [-8, 0] D) [-6, 2] Give the domain and range of the relation. 13) {(5, -7), (-3, 6), (-8, 4), (-8, -5)} 13) A) domain = {-7, 4, 6, -5}; range = {5, -8, -3} B) domain = {5, -8, -3}; range = {-7, 4, 6, -5} C) domain = {5, -8, -3, -18}; range = {-7, 4, 6, -5} D) domain = {5, -8, -3, 8}; range = {-7, 4, 6, -5} 2
Determine whether the relation is a function. 14) {(-9, -3), (-9, -2), (-1, 4), (5, -2), (7, -9)} 14) A) Function B) Not a function Use the vertical line test to determine whether or not the graph is a graph in which y is a function of x. 15) 15) A) function B) not a function 16) 16) A) not a function B) function 3
Use the graph to determine the function's domain and range. 17) 17) A) domain: [0, ) range: [0, ) B) domain: [0, ) range: [2, ) C) domain: [0, ) range: (-, ) D) domain: (-, ) range: [2, ) Evaluate the piecewise function at the given value of the independent variable. 18) 18) -4x - 2 if x < -2 f(x) = 5x + 5 if x -2 Determine f(-6). A) 27 B) 22 C) 24 D) -32 Find the slope of the line that goes through the given points. 19) (-6, 4), (-3, -7) 19) A) - 3 11 B) - 11 3 C) 11 3 D) 1 3 20) (6, 8), (6, 9) 20) A) 0 B) 17 C) - 1 D) Undefined 12 12 Use the given conditions to write an equation for the line in slope-intercept form. 21) Slope = 5, passing through (4, 7) 21) 6 A) y = 5 6 x + 11 3 B) y = 5 6 x + 4 C) y = 5 6 x - 11 3 D) y = mx + 11 3 22) Slope = 4, y-intercept = 2 22) 5 A) f(x) = 5 4 x + 5 2 B) f(x) = 4 5 x + 2 C) f(x) = 4 5 x - 2 D) f(x) = - 4 5 x - 2 4
23) Passing through (8, 2) and (7, 7) 23) A) y = 5x + 42 B) y = mx + 42 C) y = - 5x + 42 D) y - 2 = - 5(x - 8) Graph the equation in the rectangular coordinate system. 24) x = -2 24) A) B) C) D) 5
25) y = -4 25) A) B) C) D) Graph the equation. 6
26) 2x + 3y - 10 = 0 26) A) B) C) D) 7
Find an equation for the line with the given properties. 27) The solid line L contains the point (1, 3) and is perpendicular to the dotted line whose equation is 27) y = 2x. Give the equation of line L in slope-intercept form. A) y - 3 = - 1 (x - 1) B) y - 3 = 2(x - 1) 2 C) y = - 1 2 x + 7 2 D) y = 1 2 x + 7 2 28) The solid line L contains the point (3, 1) and is parallel to the dotted line whose equation is y = 2x. 28) Give the equation for the line L in slope-intercept form. A) y - 1 = 2(x - 3) B) y = 2x + b C) y = 2x - 2 D) y = 2x - 5 8
Begin by graphing the standard quadratic function f(x) = x2. Then use transformations of this graph to graph the given function. 29) g(x) = x2-2 29) A) B) C) D) 9
Begin by graphing the standard square root function f(x) = function. x. Then use transformations of this graph to graph the given 30) h(x) = x + 2 30) A) B) C) D) 10
Begin by graphing the standard absolute value function f(x) = x. Then use transformations of this graph to graph the given function. 31) h(x) = x + 2 + 2 31) A) B) C) D) For the given functions f and g, find the indicated composition. 32) f(x) = x2 + 2x + 3, g(x) = x2 + 2x + 4 32) f[g(2)] A) 169 B) 148 C) 146 D) 171 Find the inverse of the one-to-one function. 33) f(x) = (x + 8)3 33) A) f-1(x) = 3 x + 8 B) f-1(x) = x - 8 C) f-1(x) = 3 x - 8 D) f-1(x) = 3 x - 512 11
Does the graph represent a function that has an inverse function? 34) 34) A) Yes B) No Find the distance between the pair of points. 35) (7, 1) and (-2, -7) 35) A) 1 B) 145 C) 17 D) 72 Find the midpoint of the line segment whose end points are given. 36) (-3, -8) and (-9, -1) 36) A) (-12, -9) B) (- 6, - 9 2 ) C) (3, - 7 ) D) (6, -7) 2 Write the standard form of the equation of the circle with the given center and radius. 37) (3, -6); 11 37) A) (x + 6)2 + (y - 3)2 = 121 B) (x - 3)2 + (y + 6)2 = 11 C) (x - 6)2 + (y + 3)2 = 121 D) (x + 3)2 + (y - 6)2 = 11 Complete the square and write the equation in standard form. Then give the center and radius of the circle. 38) x2 + y2 + 18x - 6y + 90 = 25 38) A) (x + 9)2 + (x - 3)2 = 25 (-9, 3), r = 5 C) (x - 3)2 + (x + 9)2 = 25 (-3, 9), r = 25 B) (x - 3)2 + (x + 9)2 = 25 (3, -9), r = 5 D) (x + 9)2 + (x - 3)2 = 25 (9, -3), r = 25 12
Graph the equation. 39) x2 + y2 + 4x + 8y - 5 = 0 39) A) B) The graph of a quadratic function is given. Determine the function's equation. 40) 40) A) j(x) = -x2 + 2 B) h(x) = -x2-2 C) g(x) = -x2 + 4x + 4 D) f(x) = -x2-4x - 4 Find the coordinates of the vertex for the parabola defined by the given quadratic function. 41) f(x) = (x + 4)2-8 41) A) (4, 8) B) (4, -8) C) (-4, -8) D) (-4, 8) 13
Find the axis of symmetry of the parabola defined by the given quadratic function. 42) f(x) = 11(x - 5)2 + 4 42) A) x = 4 B) x = -5 C) x = 5 D) x = 11 Find the range of the quadratic function. 43) f(x) = (x + 5)2-9 43) A) (-, -5] B) (-, -9] C) [-9, ) D) [-5, ) Use the vertex and intercepts to sketch the graph of the quadratic function. 44) y - 4 = (x + 3)2 44) A) B) C) D) 14
Determine whether the function is a polynomial function. 45) f(x) = 5x + 4x5 45) A) No B) Yes 46) f(x) = 8-2 x5 46) A) Yes B) No Divide using synthetic division. 47) (2x5 +2x4 + -8x3 + x2 - x + 103) (x + 3) 47) A) 2x4-4x3 + 4x2-12x + 33 + 13 x + 3 C) 2x4-4x3 + 4x2-11x - 33 + 7 x + 3 B) 2x4-4x3 + 4x2-12x - 33 + 13 x + 3 D) 2x4-4x3 + 4x2-11x + 32 + 7 x + 3 Use synthetic division and the Remainder Theorem to find the indicated function value. 48) f(x) = x5 + 9x4 + 8x3 + 6; f(-4) 48) A) -774 B) 54 C) 1798 D) 774 Use the Rational Zero Theorem to list all possible rational zeros for the given function. 49) f(x) = -2x3 + 3x2-2x + 8 49) A) ± 1 2, ± 1, ± 2, ± 4, ± 8 B) ± 1 4, ± 1, ± 1, ± 2, ± 4, ± 8 2 C) ± 1 2, ± 1, ± 2, ± 4 D) ± 1 8, ± 1 4, ± 1, ± 1, ± 2, ± 4, ± 8 2 Find the domain of the rational function. 2x 50) g(x) = (x + 6)(x + 4) 50) A) all real numbers B) {x x -6, x -4, x -2} C) {x x -6, x -4} D) {x x 6, x 4} 15
Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. 51) 2x2 + 7x - 15 0 51) A) (-, -5] 3 2, B) -5, 3 2 C) [-5, ) D) -, 3 2 Approximate the number using a calculator. Round your answer to three decimal places. 52) 6-3.6 52) A) 0.302 B) 2176.782 C) -21.600 D) 0.002 The graph of an exponential function is given. Select the function for the graph from the functions listed. 53) 53) A) f(x) = 3x + 2 B) f(x) = 3x - 2 C) f(x) = 3x D) f(x) = 3x - 2 Graph the function. 16
54) Use the graph of f(x) = 3x to obtain the graph of g(x) = 3x + 2 + 2. 54) A) B) C) D) Approximate the number using a calculator. Round your answer to three decimal places. 55) e-1.3 55) A) 0.573 B) -3.534 C) -0.273 D) 0.273 Use the compound interest formulas A = P 1 + r n nt and A = Pe rt to solve. 56) Find the accumulated value of an investment of $20,000 at 8% compounded annually for 12 years. 56) A) $39,200.00 B) $37,600.00 C) $50,363.40 D) $46,632.78 17
57) Find the accumulated value of an investment of $800 at 8% compounded quarterly for 4 years. 57) A) $1088.39 B) $1098.23 C) $1056.00 D) $865.95 58) Find the accumulated value of an investment of $2000 at 8% compounded continuously for 5 years. 58) A) $2800.00 B) $3083.65 C) $2938.66 D) $2983.65 Write the equation in its equivalent exponential form. 59) log 16 = 2 59) b A) 2b = 16 B) b2 = 16 C) 162 = b D) 16b = 2 Write the equation in its equivalent logarithmic form. 60) 5-3 = 1 125 A) log 5 1 125 = -3 B) log 1/5 5 = -3 C) log -3 1 125 = 5 D) log 5-3 = 1 125 60) 61) 3 8 = 2 61) A) log 8 3 = 1 2 B) log 2 8 = 3 C) log 8 2 = 1 3 D) log 2 8 = 1 3 Evaluate the expression without using a calculator. 62) log 5 125 62) A) 125 B) 3 C) 5 D) 15 63) log 2 1 4 63) A) 4 B) 2 C) -2 D) 1 2 Evaluate or simplify the expression without using a calculator. 1 64) log 100 64) A) 2 B) - 1 2 C) 1 100 D) -2 65) 7 10 log 3.5 65) A) 2.45 B) 8.7693 C) 24.5 D) 245 66) ln e10 66) 1 A) B) 1 C) 10 D) e 10 18
Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. 67) log (7 11) 67) 2 A) log 2 7 + log 2 11 B) (log 2 7)(log 2 11) C) log 2 77 D) log 2 7 - log 2 11 68) ln e 4 9 68) A) 4 - ln 9 B) ln e4 - ln 9 C) 4 + ln 9 D) ln e4 + ln 9 69) log X-9 69) A) 9log X B) 9 + log X C) -9log X D) -9 + log X 70) log 2 x2 y8 70) A) 2 log 2 x + 8 log 2 y B) 2 log 2 x - 8 log 2 y C) 8 log 2 y - 2 log 2 x D) 1 4 log 2 (x y ) Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. 71) 1 4 (log 6 x + log6 y) - 3 log6 (x + 5) 71) A) log6 4 xy (x + 5)3 B) log6 4 xy 3(x + 5) C) log6 4 x + 4 y (x + 5)3 D) log6 4 x + y (x + 5)3 Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places 72) log 49.1 72) 12 A) 2.7703 B) 1.5670 C) 0.6382 D) 0.6119 73) log 15 73) 0.2 A) -0.5943 B) 0.4771 C) -1.6826 D) 1.8751 Solve the equation by expressing each side as a power of the same base and then equating exponents. 74) 3(1 + 2x) = 243 74) A) {81} B) {2} C) {6} D) {-2} 75) 3125x = 125 75) A) 3 5 B) 5 3 C) 3 4 D) 3 19
76) ex + 9 = 1 e10 76) A) -1 B) 1 C) 19 D) -19 Solve the exponential equation. Express the solution set in terms of natural logarithms. 77) 4x + 4 = 52x + 5 77) A) {7 ln 5-5 ln 4} B) C) {ln 5 - ln 4} D) ln 5 5 5 ln 5-4 ln 4 ln 4-2 ln 5 44-4 52 Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. 78) 4 x + 6 = 5 78) A) -0.68 B) 1.64 C) 6.86 D) -4.84 79) e2x = 4 79) A) 2.77 B) 0.69 C) 0.17 D) 5.44 Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. 80) log (x - 1) + log (x - 7) = 4 80) 2 2 A) {10} B) {9, -1} C) {-1} D) {9} 81) ln x + 7 = 2 81) e2 A) 2 + 7 B) {e 2-7} C) {e4-7} D) {e4 + 7} 82) log x2 = log (7x + 18) 82) 8 8 A) 9 8 B) {9} C) D) {9, -2} Determine whether the given ordered pair is a solution of the system. 83) (5, -3) 83) x + y = 2 x - y = 8 A) not a solution B) solution 20
Solve the system of equations by the substitution method. 84) 84) x + y = -9 y = 2x A) {(-3, -6)} B) {(-3, 6)} C) {(3, 6)} D) {(3, -6)} Solve the system by the addition method. 85) -6x + y = 8 85) 3x + 3y = -11 A) {(1, -12)} B) 3, - 10 3 C) - 5 3, -2 D) - 2 3, 4 Solve the system by the substitution method. 86) y = (x + 5)2 + 1 86) 2x - y + 10 = 0 A) {(-4, 2), (4, 18)} B) {(-5, 0)} C) {(-4, 2)} D) {(0, 10), (0, 26)} Solve the system by the addition method. 87) x2 + y2 = 16 87) 16x2 + 4y2 = 64 A) {(2, 0), (-2, 0)} B) {(4, 0), (-4, 0)} C) {(0, 2), (0, -2)} D) {(0, 4), (0, -4)} Graph the solution set of the system of inequalities or indicate that the system has no solution. 88) 2x - y -6 88) x + 2y 2 21
A) B) C) D) Give the order of the matrix, and identify the given element of the matrix. 89) 89) 6 1-11 14 9 3 -e -7-15 8-3 -15-1 11 ; a34 1-14 -10 14 6 3 A) 20; 11 B) 5 4; -10 C) 4 4; -15 D) 4 5; -1 Solve the matrix equation for X. 90) 90) Let A = 3-4 0-3 and B = 8-6 -3-4 ; B - X = 3A 8-6 0 7 A) X = 17-18 3-13 24-11 B) X = -1 6 3 5-24 25 C) X = 17-18 3-13 8-11 D) X = -1 6-3 5-24 25 22
Find the product AB, if possible. 91) 91) A = 3-2 1 0 4-2, B = 5 0-2 3 A) 15 0 0 12 B) 15-10 5-6 16-8 C) AB is not defined. D) 15-6 -10 16 5-8 Use Cramer's rule to solve the system. 92) 3x + 3y = 39 92) 2x - 3y = -9 A) {(7, 6)} B) {(-6, -7)} C) {(6, 7)} D) {(-7, 6)} 23