<p>Algebra II Honors BC First Semester Review 2014</p><p>Show your work for solving each problem.</p><p>I. Exponents and Radicals</p><p>Simplify the following: 1. (5x3y2z)3 2. (-7x4y3)2(-2xy2)3 3. (5x0y4)(-2x3y)2</p><p>4. + - 5 5. (3 + )(3 - ) 6. </p><p>II. Matrices</p><p>7. ∙ 8. </p><p>9. 10. Solve for x, y, and z. </p><p>= </p><p>11. Find the inverse. 12. Write as a matrix equation and solve. x – 4y + 5z = 1 -2x + 6y – 3z = 19 7x + 10y + z = 4</p><p>13. For Matrix B to be the inverse of Matrix A, what must be the value of x in Matrix B? A = B = 14. The height, h(t), in feet above the ground, of a ball thrown into the air from the top of a building is given by the function h(t) = -16t2 + 64t + 200, where t is the number of seconds the ball has been in the air. a. How long does it take the ball to reach its maximum height?</p><p> b. What is that maximum height? III. Functions (Ch. 5)</p><p>If f(x) = x2 + 3x – 4 and g(x) = 2x + 1, find the following: 15. f(6) 16. f(-3) 17. g(5a) 18. f[g(-4)]</p><p>19. f[g(x)] 20. g[f(x)]</p><p>21. Find the first 5 terms of the recursive function: f(1) = 3 f(n + 1) = -2f(n) + 4n – 5</p><p>22. Solve for x. a. |-3x + 7| = 22 b. 24 = 3|2x - 6|</p><p>IV. Transformations (Ch. 6)</p><p>23. Find the coordinates of the image point if the point (-5, 2) is reflected across: a. the x-axis b. the y-axis c. the origin d. the line y = x</p><p>24. Given the function f(x) = x2, write the new function g(x) if the following occur: a. stretched vertically by a factor of 2 b. translated 4 units down c. translated 5 units to the right d. Reflected across the x-axis, translated 2 units left and 3 units up</p><p>25. Find the zeros of y = f(x – 4) if f(x) = x2 + 5x + 6. 26. Find the zeros of y = f(x + 5) if f(x) = x2 – 11x + 24.</p><p>V. Systems (Ch. 7)</p><p>27. Solve the following systems of equations. a. 2x + 3y = 28 b. 4x + 5y = 27 c. -2x + 4y – z = 3 3x - y = 9 y = -2x + 3 x + 2y – 3z = 20 6x – y + 2z = 7</p><p>28. Carmony Computer Consultants charges a $255 fee plus $85 per hour for its work. Holliday Computer Works charges a flat rate of $115 per hour. How many hours would it take the companies to work for their fees to be the same?</p><p>29. + = 12 30. x2 – y2 = 4 31. 9x2 + 16y2 = 1 + = 9 y2 = 3x 9x2 – 16y2 = 1</p><p>VI. Conics</p><p>32. Find the center and radius of the circle: x2 + y2 – 4x + 16y – 10 = 0</p><p>33. Find the center, vertices, co-vertices, and foci of the ellipse: 4x2 + 25y2 – 24x + 50y = 39 34. Write the equation of the parabola that passes through the point (-3, 7) and has its vertex at (-1, 3) and opens to the left.</p><p>35. Find the center, vertices, foci, and equations of asymptotes for the hyperbola: x2 – y2 – 6y + 7 = 0</p><p>36. Identify each equation as a circle, ellipse, parabola, hyperbola, or line. a. 9y2 – 8x2 = 72 d. 9y – 8x = 72 b. 9y = (x + 8)2 + 72 e. 9y2 + 9x2 = 72 c. 9y2 + 8y2 = 72 f. 9y – 8x2 = 72</p>