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Honors Algebra 2 Summer Packet Answer Key A. Simplify/Evaluate – remember order of operation 1. -18 8. 7 11 30 2. 4 9. 3. 48 2 5 10. 4. -96 5 6 11. 5. -17 5 36 12. Simplify using exact answers – no decimals 15 6 1. 4 2 2. 3. 4. 4 y 2 3xy 5 2 6. 9 2 7. 17 30 7 4 B. 5. 2 Simplify using rules of exponents 1 1 1. 2. x9 3. 6 411 a11 or 25,165,824a11 or 5 7776 6 6. 1 7. x6 8. -27y6 6. 7 6 7. 4ab a 4. 27 5. C. 10. -216x21 11. -24x21 12. 324x10 D. Simplify by adding, subtracting, multiplying or dividing 1. -x + 5 2. x2 - 5x – 1 3 2 4. 2.2x – 0.2x – 3.8x + 23 5. -1.8x4 - 0.6x2 – 1.8x + 4.6 7. x2 + 3x – 10 8. x4 – 1 4 2 10. x – 10x + 25 11. x3 + 15x2 + 75x + 125 13. -3x2 + 3x 14. 12x3 + 8x2 + 15x + 10 16. –u4 -2u + 1 19. -3t4 – 4t3 + 1 17. 50x4 – 7x3 + x E. Solve the following equations 1. a = 32 2. x = 9 3. No solution 2 1 8 1 8 0 3 7. 3. 13x – 1 6. -8x4 +24x3 + 20x2 – 4x 9. 4x2 -12x + 9 12. x2 – 13x + 13 12 x 5 2 x 3 5 x 2 8 15. 4 18. 5t2 + 3t - 6 4. x = 12 F. Use the given matrices to solve the problems 1. 2 x 3 2. 3 x 2 3. 3 2 1 4. Not Possible 6. 9. 16a12b4 4 3 5. 8 9 3 1 10 6 10 6 0 4 2 8 G. Solve each equation 1. r = -3 2. t = -12 3. x = 6 4. x = 7 5. x = 1.65 6. a = 2 1 x5 H. Write the linear equation in slope-intercept form 2 1. y = x – 2 2. y = -4x + 3 3. y = -x – 1 3 6. x = 5 I. 7. y = -x + 5 8. y = 4 4. y = 4 2 x+ 5 3 3 5. y = -1 1 10. y = x + 2 3 9. y = 2x + 3 Sketch the graph & state the domain and range 1. D: All Reals R: All Reals 2. D: {3} R: All Reals 4. D: All Reals R: All Reals 5. D: All Reals R: All Reals 6. D: All Reals R: y 1 7. D: All Reals R: y 8 8. D: All Reals R: y 0 9. D: All Reals R: y 0 10. D: All Reals R: y 3 11. 13. 3. D: All Reals R: {-1} 12. 14. J. Solve the system of equations (use graphing, substitution and/or elimination) 1. (2, -4) 2. (17/3, 16/3) 3. (17/3, 2/3) 4. (-12, 11) 5. (3, 0) 6.(4, -1) 7. All Reals 8. No Solution K. Factor the polynomial completely. 2 2 1. 8x (x – 3) 2. 17xy(x5y2 + 2x2y + 3) 4. (x + 3)(x + 2) 5. (x + 7)(x + 4) 7. (x + 12)(x – 6) 8. (x2 – 5)(x2 + 7) 10. (x + 10)(x – 10) 13. (x2 + 4)(x + 2)(x – 2) 16. (3x + 5)(x – 3) 19. 6(3x – 4y)(x + y) 11. (2x + 9)(2x – 9) 14. (x – 3y)(x + y) 17. (3x – 2)(3x + 4) 20. 5x(3x – 4)(x + 1) 3. 16xy2(x5y2 - 2x4y – 3) 6. (x – 3)(x – 5) 9. (x + 10)(x + 10) or (x + 10)2 12. (x2 + y2)(x + y)(x – y) 15. (2x + 1)(x – 4) 18. (3x + 8)(3x – 2) K. Solve the equation. Use any method that will work: square roots, factoring, quadratic Formula. Be sure to check your solutions. 1. x = 7, -3 2. x = 3 3. x = 4/3, 1 4. x = 3, -3 5. x = 1 3 6. x = 2 11 7. x = 21 3 8. x = 0, 2 9. x = 2i, 2