NAME _____________________________________________ DATE ____________________________ PERIOD _____________ Final Exam Multiple Choice Review Chapter 5 Write the letter for the correct answer in the blank at the right of each question. 1. Simplify (3𝑥 0 )2(2𝑥 4 ). A 𝑥4 B 12𝑥 4 C 18𝑥 6 D 18𝑥 4 1. _________________ 3𝑦 2 𝑧 2. Simplify 15𝑦5 . Assume that no variable equals 0. 𝑧 F 5𝑦 3 G 𝑦3𝑧 5 H 5𝑦 3 z J 𝑦7𝑧 5 2. _________________ 3. Shen is simplifying the expression (3𝑥 4 + 4𝑥 2 )( 𝑥 3 – 2𝑥 2 – 1). Which of the following shows the correct product? A 3𝑥 12 – 6𝑥 8 + 4𝑥 6 – 11𝑥 4 – 4𝑥 2 C 3𝑥 7 + 6𝑥 6 – 4𝑥 5 + 11𝑥 4 + 4𝑥 2 7 6 5 4 2 B 3𝑥 – 6𝑥 + 4𝑥 – 11𝑥 – 4𝑥 D 3𝑥 12 – 6𝑥 8 – 11𝑥 4 + 4𝑥 6 – 4𝑥 2 3. _________________ 4. Simplify (5m – 9) + (4m + 2). F 9m – 11 G m – 11 H 9m – 7 J 20𝑚2 – 18 4. _________________ 5. Simplify 3x(2𝑥 2 – y). A 5𝑥 3 + 3xy B 12x – y C 6𝑥 2 – 3y D 6𝑥 3 – 3xy 5. _________________ 6. Simplify (𝑥 2 – 2x – 35) ÷ (x + 5). F 𝑥 2 – x – 30 Gx+5 Hx–7 J 𝑥 3 + 3𝑥 2 – 45x – 175 6. _________________ 7. Which represents the correct synthetic division of (𝑥 2 – 4x + 7) ÷ (x – 2)? A C 7. _________________ B D 8. _________________ 2 8. Factor 𝑚 + 9m + 14 completely. F m(m + 23) G (m + 7)(m + 2) H (m + 14)(m + 1) J m(m + 9) + 14 9. _________________ 9. Simplify At–5 Chapter 5 𝑡2 +𝑡−6 . 𝑡−2 Assume that the denominator is not equal to 0. Bt–2 Ct–3 61 Dt+3 Glencoe Algebra 2 NAME _____________________________________________ DATE ____________________________ PERIOD _____________ 10. Find p(–3) if p(x) = 4 – x. F 12 G4 10. _________________ H1 J7 11. _________________ 11. State the number of real zeros for the function whose graph is shown at the right. A0 C2 B1 D3 For Questions 12 and 13, use the graph shown at the right. 12. Determine the values of x between which a real zero is located. F between –1 and 0 G between 6 and 7 H between –2 and –1 J between 2 and 3 12. _________________ 13. Estimate the x-coordinate at which a relative minimum occurs. A3 B2 C0 13. _________________ D –1 14. Write the expression 𝑥 4 + 5𝑥 2 – 8 in quadratic form, if possible. F (𝑥 2 )2 + 5(𝑥 2 ) – 8 H (𝑥 4 )2 + 5(𝑥 4 ) – 8 2 2 2 G (𝑥 ) – 5(𝑥 ) – 8 J not possible 15. Solve 𝑥 4 – 13𝑥 2 + 36 = 0. A –3, –2, 2, 3 B –9, –4, 4, 9 14. _________________ 15. _________________ C 2, 3, 2i, 3i 16. Use synthetic substitution to find f(3) for f(x) = 𝑥 2 – 9x + 5. F –23 G –16 H –13 D –2, –3, 2i, 3i 16. _________________ J 41 17. One factor of 𝑥 3 + 4𝑥 2 – 11x – 30 is x + 2. Find the remaining factors. A x – 5, x + 3 B x – 3, x + 5 C x – 6, x + 5 D x – 5, x + 6 17. _________________ 18. Which describes the number and type of roots of the equation 4x + 7 = 0? F 1 imaginary root H 1 real root and 1 imaginary root G 2 real roots J 1 real root 18. _________________ 19. Which is not a root of the equation 𝑥 3 – 𝑥 2 – 10x – 8 = 0? A1 B4 C –2 D –1 20. _________________ 20. Find all the rational zeros of p(x) = 𝑥 3 – 12x – 16. F –2, 4 G 2, –4 H4 Chapter 5 19. _________________ J –2 62 Glencoe Algebra 2 NAME _____________________________________________ DATE ____________________________ PERIOD _____________ Chapter 6 Write the letter for the correct answer in the blank at the right of each question. 1. ______________ For Questions 1 and 2, use f(x) = x + 5 and g(x) = 2x. 1. Find (f + g)(x). A 3x + 5 Bx+5 C 2x + 10 D 2𝑥 2 + 5 2. Find (f ⋅ g)(x). F 2𝑥 2 + 5 G 3𝑥 2 + 10x H 2𝑥 2 + 10x J 2x + 10 2. ______________ 3. ______________ 3. If f(x) = 3x + 7 and g(x) = 2x – 5, find g[f(–3)]. A –26 B –9 C –1 D 10 4. ______________ 4. If f(x) = 𝑥 2 and g(x) = 3x – 1 find [ g ◦ f](x). F 𝑥 2 + 3x – 1 H 9𝑥 2 – 1 G 9𝑥 2 – 6x + 1 J 3𝑥 2 – 1 5. ______________ 5. Find the inverse of g(x) = –3x. A 𝑔−1 (x) = x + 1 C 𝑔−1 (x) = x – 1 B 𝑔−1 (x) = –3x – 3 D 𝑔−1 (x) = – 3x 1 6. Determine which pair of functions are inverse functions. F f(x) = x – 4 g(x) = x + 4 H f(x) = x – 4 g(x) = 4x – 1 G f(x) = x – 4 J f(x) = 4x – 1 g(x) = 𝑥–4 4 6. ______________ g(x) = 4x + 1 7. State the domain and range of the function graphed. A D = {x │ x > 2}, R = {y │ y > 0} 7. ______________ B D = {x │ x < 2}, R = {y │ y > 0} C D = {x │ x ≥ 2}, R = {y │ y < 0} D D = {x │ x ≥ 2}, R = {y │ y ≥ 0} 8. Which inequality is graphed? F y ≤ √4𝑥 + 8 8. ______________ G y > √4𝑥 + 8 H y < √4𝑥 + 8 J y ≥ √4𝑥 + 8 9. Simplify √121. A 11 Chapter 5 9. ______________ B –11 D √11 C ±11 62 Glencoe Algebra 2 NAME _____________________________________________ DATE ____________________________ PERIOD _____________ 10. Use a calculator to approximate √224 to three decimal places. F 15.0 G 14.97 H 14.966 J 14.967 C –1 + √5 D –1 – √5 H 10√3 J 7√3 10. _____________ 11. Simplify (2 + √5)(3 – √5). A 1 + √5 B 1 – √5 11. _____________ 12. Simplify √75 + √12. F 21 G √87 12. _____________ 1 13. Write the expression 57 in radical form. 7 A √51 7 5 C √5 B 35 2 D √7 13. _____________ 1 14. Simplify the expression 𝑚5 • 𝑚5 . 5 3 2 2 F 𝑚3 G 𝑚5 H 𝑚25 J 𝑚5 B7 C 21 D Hx<2 Jx>2 14. _____________ 15. Solve √3𝑥 + 4 = 5. A –7 25 3 15. _____________ 16. Solve 2 + √5𝑥 − 1 > 5. Fx>5 G x > –2 17. Gilda used the formula f(x) = Find the inverse of 𝑓 −1 (x). A 𝑓 −1 (x) = 12x 𝑥 144 to convert square inches to square feet. B 𝑓 −1(x) = 144x 5 16. _____________ C𝑓 −1(x) = 144 𝑥 D 𝑓 −1(x) = (12𝑥 2 ) 17. _____________ 1 18. If x is a positive number, then √𝑥 ÷ 𝑥 5 = ? A 𝑥5 1 5 B x C1 D 1 5 18. _____________ 19. If 28 • y = 25 , then y = ? F –2−3 Chapter 5 G –23 19. _____________ 1 J 2−3 H 23 62 Glencoe Algebra 2 NAME _____________________________________________ DATE ____________________________ PERIOD _____________ Chapter 7 Write the letter for the correct answer in the blank at the right of each question. 1. Find the domain and range of the function whose graph is shown. A D = {x | x > 0}; R = {y | y > 0} 1. ____________ B D = {all real numbers}; R = {y | y > 0} C D = {x | x > 0}; R = {all real numbers} 2. ____________ D D = {all real numbers}; R = {y | y < 0} 2. Which function represents exponential growth? 1 𝑥 3 G y = 4𝑥 4 F y = 9( ) 1 𝑥 5 H y = 12( ) J y = 10(3)𝑥 3. ____________ 3. Solve 8𝑥 + 2 = 322𝑥 + 4 . F –2 G –1 H0 J1 4. Write the equation 43 = 64 in logarithmic form. F log 4 3 = 64 G log 3 4 = 64 H log 64 4 = 3 4. ____________ J log 4 64 = 3 5. Write the equation log12 144 = 2 in exponential form. A 1442 = 12 B 122 = 144 6. Evaluate log 2 8. F3 7. Solve log 3 𝑛 = 2. A6 5. ____________ C 212 = 144 D 14412 = 2 6. ____________ G4 H 16 J 64 7. ____________ B5 C8 D9 8. ____________ 8. Solve log 2 2m > log 2 (𝑚 + 5). 5 F {𝑥 | 𝑚 > 3} Chapter 5 G {x | m < 5} H {x | m > 5} 62 J {x | m > –5} Glencoe Algebra 2 NAME _____________________________________________ DATE ____________________________ PERIOD _____________ 9. __________ 9. Use log 5 2 ≈ 0.4307 to approximate the value of log 5 4. A 0.8614 B 0.8980 C 1.3652 D 0.1855 10. Solve log 6 10 + log 6 𝑥 = log 6 40. F 180 G4 J 30 10. __________ H5 11. __________ 11. Solve 4𝑥 = 20. Round to the nearest ten-thousandth. A 0.4628 B 1.5214 C 0.6990 D 2.1610 12. Solve 3𝑥 ≥ 21. Round to the nearest ten-thousandth. F {x | x ≥ 0.8451} G {x | x ≥ 2.7712} H {x | x ≥ 0.3608} 12. __________ J {x | x ≥ 7.0000} 13. Express log 9 22 in terms of common logarithms. A log 22 9 14. Solve ln 3𝑥 = 1. F 20.0855 B log 198 C 13. __________ log 22 log 9 D log 9 log 22 14. __________ G 0.3333 H 0.9061 J 8.1548 15. AUTOMOBILES Lydia bought a car for $20,000. It is expected to depreciate at a continuous rate. What will be the value of the car in 2 years? Use k = 0.105 and round to the nearest dollar. A $16,212 B $16,012 C $19,867 D $18,567 16. ART Martin bought a painting for $5000. It is expected to appreciate at a continuous rate of 4%. How much will the painting be worth in 6 years? Round to the nearest cent. F $6200.00 G $5360.38 H $37,647.68 J $6356.25 Chapter 5 62 15. __________ 16. __________ Glencoe Algebra 2