Final Exam Review PDF

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) To solve x2 + 16x = 2 by completing the square, add ______ to both sides of the equation. A) 16 B) -16 C) 8...

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) To solve x2 + 16x = 2 by completing the square, add ______ to both sides of the equation. A) 16 B) -16 C) 8 D) 64 Solve and check the linear equation. 2) (-8x + 6) + 8 = -7(x + 4) A) {- 42} B) {- 26} C) {- 10} D) {42} Add or subtract as indicated and write the result in standard form. 3) (4 + 4i) - (-9 + i) A) 13 - 3i B) -13 - 3i C) 13 + 3i D) -5 + 5i Solve the equation by the square root property. 4) (2x - 1)2 = 9 A) {-1, 2} B) {-2, 1} C) {-4, 2} D) {-2, 4} Solve the equation using the quadratic formula. 5) 16x2 + 1 = 3x 3 ± 55 -3 ± i 55 -3 ± 55 3 ± i 55 A) B) C) D) 32 32 32 32 Give the domain and range of the relation. 6) {(9, 4), (-6, -4), (-7, -1), (-7, -9)} A) domain = {-4, -1, 4, -9}; range = {-6, -7, 9} B) domain = {-6, -7, 9, 7}; range = {-4, -1, 4, -9} C) domain = {-6, -7, 9, -17}; range = {-4, -1, 4, -9} D) domain = {-6, -7, 9}; range = {-4, -1, 4, -9} 1 Express the interval in set-builder notation and graph the interval on a number line. 7) [-4, 1) -10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 A) {x -4 < x ≤ 1} B) {x -4 ≤ x < 1} -10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 C) {x -4 ≤ x ≤ 1} D) {x x < 1} -10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 Solve the problem. 8) The function P(x) = 0.65x - 89 models the relationship between the number of pretzels x that a certain vendor sells and the profit the vendor makes. Find P(600), the profit the vendor makes from selling 600 pretzels. A) $479 B) $511 C) $301 D) $390 Use the given conditions to write an equation for the line in point-slope form. 8 9) Slope = , passing through (4, 3) 9 8 8 8 8 A) y + 3 = (x + 4) B) x - 3 = (y - 4) C) y = x+4 D) y - 3 = (x - 4) 9 9 9 9 Use the given conditions to write an equation for the line in the indicated form. 1 10) Passing through (5, 2) and perpendicular to the line whose equation is y = x + 7; 9 slope-intercept form 1 47 A) y = 9x - 47 B) y = - 9x + 47 C) y = - 9x - 47 D) y = - x- 9 9 Find the domain of the function. 1 11) f(x) = x+6 A) (- ∞, 0) ∪ (0, ∞) B) (-∞, -6) ∪ (-6, ∞) C) (- ∞, ∞) D) (-6, ∞) Find the midpoint of the line segment whose end points are given. 12) (4, 5) and (1, 8) 5 13 3 3 A) (5, 13) B) ( , ) C) (3, -3) D) ( , - ) 2 2 2 2 2 Find the domain and range of the quadratic function whose graph is described. 13) The vertex is (-1, -6) and the graph opens up. A) Domain: (- ∞, ∞) B) Domain: (- ∞, ∞) C) Domain: [-1, ∞) D) Domain: (- ∞, ∞) Range: [-6, ∞) Range: (- ∞, -6] Range: [-6, ∞) Range: [-1, ∞) Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. 14) f(x) = 2(x - 3)(x + 6)4 A) -3, multiplicity 1, touches x-axis and turns around; 6, multiplicity 4, crosses x-axis B) 3, multiplicity 1, crosses x-axis; -6, multiplicity 4, touches x-axis and turns around C) -3, multiplicity 1, crosses x-axis; 6, multiplicity 4, touches x-axis and turns around D) 3, multiplicity 1, touches x-axis and turns around; -6, multiplicity 4, crosses x-axis Use the Rational Zero Theorem to list all possible rational zeros for the given function. 15) f(x) = 5x 4 - x 2 + 2 1 2 1 1 A) ± , ± , ± 1, ± 2 B) ± , ± , ± 1, ± 2, ± 5 5 5 5 2 1 2 1 5 C) ± , ± , ± 1, ± 2, ± 5 D) ± , ± , ± 1, ± 5 5 5 2 2 Find the vertical asymptotes, if any, of the graph of the rational function. x+4 16) f(x) = x(x + 5) A) x = -5 B) x = -4 and x = -5 C) x = 0 and x = -5 D) no vertical asymptote Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. 17) (x - 3)(x + 2) > 0 -10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 A) (-2, 3) B) (-2, ∞) -10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 C) (- ∞, -2) ∪ (3, ∞) D) (- ∞, -3) ∪ (2, ∞) -10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 3 Solve the problem. 18) If y varies directly as x, and y = 6 when x = 5, find y when x = 10. 1 25 A) 3 B) C) 12 D) 3 3 19) The rabbit population in a forest area grows at the rate of 9% monthly. If there are 190 rabbits in April, find how many rabbits (rounded to the nearest whole number) should be expected by next April. Use y = 190(2.7)0.09t. A) 568 B) 542 C) 554 D) 555 Approximate the number using a calculator. Round your answer to three decimal places. 20) e1.6 A) 3.588 B) 4.349 C) 5.253 D) 4.953 Write the equation in its equivalent exponential form. 21) log 2 32 = x A) 2 x = 32 B) x2 = 32 C) 322 = x D) 32x = 2 Write the equation in its equivalent logarithmic form. 1 22) 2 -3 = 8 1 1 1 A) log 2 -3 = B) log =2 C) log 1/2 2 = -3 D) log 2 = -3 8 -3 8 8 Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. x3 23) log 3 y7 3 x A) log 3 ( ) B) 7 log 3 y - 3 log 3 x C) 3 log 3 x + 7 log 3 y D) 3 log 3 x - 7 log 3 y 7 y 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. 24) log 3 (x + 4) = 2 A) {5} B) {13} C) {12} D) {4} 4 Solve the system of equations by the substitution method. 25) 5x - 4y = 147 x = 5y A) {(7, 35)} B) {(35, 7)} C) {(36, 7)} D) {(35, -7)} Solve the system by the addition method. 26) 6x + 7y = 30 6x + 2y = 60 A) {(12, -6)} B) {(-6, 12)} C) {(-12, 6)} D) {(-12, 7)} Solve the problem. 27) You invested $26,000 and started a business selling vases. Supplies cost $17 per vase and you are selling each vase for $30. Let x represent the number of vases produced and sold and write the cost function, C, and revenue function, R. A) C(x) = 17x + 26,000 B) C(x) = 17x + 30 R(x) = 30 R(x) = 26,000x C) C(x) = 17x + 26,000 D) C(x) = 17x + 26,000x R(x) = 30x R(x) = 30x 28) You invested $8800 and started a business selling vases. Supplies cost $12 per vase and you are selling each vase for $23. Determine the number of vases, x, that must be produced and sold to break even. A) 800 units B) 802 units C) 801 units D) 259 units Solve the system by the substitution method. 29) -4x - y = -24 y = x2 - 8 A) {(4, 8), (-8, 56)} B) {(4, 24), (-8, 72)} C) {(-4, 8), (-8, 56)} D) {(-4, 8), (8, 56)} 5 Graph the solution set of the system of inequalities or indicate that the system has no solution. 30) x2 + y2 ≤ 36 8x + 2y ≤ 16 y 10 5 -10 -5 5 10 x -5 -10 A) B) y y 10 10 5 5 -10 -5 5 10 x -10 -5 5 10 x -5 -5 -10 -10 C) D) y y 10 10 5 5 -10 -5 5 10 x -10 -5 5 10 x -5 -5 -10 -10 6 Answer Key Testname: MAC 1105 FINAL EXAM REVIEW 1) A ID: USER-3 2) D ID: CA8Z 1.2.1-4+ 3) C ID: CA8Z 1.4.1-2+ 4) A ID: CA8Z 1.5.2-5+ 5) D ID: CA8Z 1.5.4-8+ 6) D ID: CA8Z 2.1.1-1+ 7) B ID: CA8Z 1.7.1-2+ 8) C ID: CA8Z 2.1.4-9+ 9) D ID: CA8Z 2.3.2-3+ 10) B ID: CA8Z 2.4.1-7+ 11) B ID: CA8Z 2.6.1-8+ 12) B ID: CA8Z 2.8.2-1+ 13) A ID: CA8Z 3.1.1-60+ 14) B ID: CA8Z 3.2.5-1+ 15) A ID: CA8Z 3.4.1-5+ 16) C ID: CA8Z 3.5.3-2+ 17) C ID: CA8Z 3.6.1-1+ 18) C ID: CA8Z 3.7.1-12+ 19) D ID: CA8Z 4.1.1-6+ 20) D ID: CA8Z 4.1.3-1+ 21) A ID: CA8Z 4.2.1-4+ 22) D ID: CA8Z 4.2.2-2+ 23) D ID: CA8Z 4.3.4-3+ 7 Answer Key Testname: MAC 1105 FINAL EXAM REVIEW 24) A ID: CA8Z 4.4.3-2+ 25) B ID: CA8Z 5.1.2-2+ 26) A ID: CA8Z 5.1.3-3+ 27) C ID: CA8Z 5.1.5-18+ 28) A ID: CA8Z 5.1.5-19+ 29) A ID: CA8Z 5.4.2-1+ 30) C ID: CA8Z 5.5.4-11 8