Show Your Work for Solving Each Problem

Algebra II Honors BC First Semester Review 2014

Show your work for solving each problem.

I.  Exponents and Radicals

Simplify the following:

1.  (5x3y2z)3 2. (-7x4y3)2(-2xy2)3 3. (5x0y4)(-2x3y)2

4. 3 + 12 - 527 5. (3 + 7)(3 - 7) 6. 92- 5

II.  Matrices

7. -5410 ∙ 3123-40-12 8. 7-14-5

9. 10-594-81-22-7 10. Solve for x, y, and z.

2x-6143-3y+1-5z/2 = -1214322-5-4

11. Find the inverse. 1-1-35 12. Write as a matrix equation and solve.

x – 4y + 5z = 1

-2x + 6y – 3z = 19

7x + 10y + z = 4

13. For Matrix B to be the inverse of Matrix A, what must be the value of x in Matrix B?

A = 1531025110 B = -134x

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?

b. What is that maximum height?

III.  Functions (Ch. 5)

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)]

19. f[g(x)] 20. g[f(x)]

21. Find the first 5 terms of the recursive function:

f(1) = 3

f(n + 1) = -2f(n) + 4n – 5

22. Solve for x.

a. |-3x + 7| = 22 b. 24 = 3|2x - 6|

IV.  Transformations (Ch. 6)

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

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

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.

V.  Systems (Ch. 7)

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

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?

29. 2x+1 + 5y-1 = 12 30. x2 – y2 = 4 31. 9x2 + 16y2 = 1

5x+1 + 2y-1 = 9 y2 = 3x 9x2 – 16y2 = 1

VI.  Conics

32. Find the center and radius of the circle: x2 + y2 – 4x + 16y – 10 = 0

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.

35. Find the center, vertices, foci, and equations of asymptotes for the hyperbola:

x2 – y2 – 6y + 7 = 0

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