alg II HP final guide

This year's final is much smaller than last year's with only 18 problems.

The final breakdown by unit (# of problems)
unit 1 transformations/ domain and range - 5
conics-2
quadratics/ complex numbers - 4
polynomials-3
radicals - 4


Here is a review guide.

1.     If G(x) = 2x² + 3x -8, then G(-3) =

2.     If f(x) has point (-3, 0) on it, what will the coordinates of the transformed point be if: a. g(x) = 4f(x)   b.   h(x) = f(2x)  c.  m(x)= f(x+1) – 5

3.     If f(x) = x², then describe all transformations that happen to make

g(x) = -2(x-3)² -9

4.     Describe the solutions to the equation f(x) = 5x² + 19x -1

5.     Solve 5 + 2x² = 12x then write the domain and range.

7.     If 4- 3i and 4 + 3i are the roots, what is the equation?

8.      Simplify i³³

10.  Spiderman jumps from the top of a building to a ledge that is 22 feet off the ground.  His height during the fall is shown by the model g(t) = -16t² + 11 with t standing as time.  At how much time after his jump will he arrive at the ledge?

11. A hunter shoots a dart through a blowgun.  The dart travels by M(t) = – 5t² + 10t + 2 where M(t) is height and t is time in seconds.  He is trying to hit a wild turkey that is in a tree that is 4 meters off the ground.  Will the dart hit the turkey?  Explain your reasoning.

12. What is the maximum height the dart can reach?

13.   Simplify these rational expressions

(a) (-6x)/(3 times the square root of -24)

(b)   (5-3i)/(7+i)

14. Divide using synthetic division:     (3x³ + 4x² -8) divided by (x +4)

15. Solve by factoring:  2x³ + 3x² -8x -12 = 0

16. Write a polynomial with zeros at:

a.     1, -1, 4

b.     -3, 1/2., 1/3

c.      2i and square root of 5  
                                   

17. Draw a graph with root at -3, 1, 4; a y intercept at 12.

18. Draw a graph with root at -1/2, 1, 2; a y intercept at -1.

19. Draw a graph with root at -3, 2 and a double root at 5; and negative even end behavior.

20. Write the new function to f(x) = x³ + 5x² + x-8  if it is transformed by:

a.     a horizontal reflection and a vertical translation of +6

b.     a vertical stretch of 1/3

21.  Write the equation of an ellipse if the coordinates of the foci are (0. 16) and (0, -16) and the length of the major axis is 20. (Hint: Sketch a picture)

22.  Graph:  4(x – 2)² + 16(y+3)²  = 64                 

23.   Put in standard form and graph:   x² + y² -6x -8y + 15 =0

24.  Graph:  y + 1 = -(x-2)²