Review for Final

HONORS ALGEBRA II

Name ______

REVIEW FOR FINAL EXAM

HONORS ALGEBRA II

PART I: QUADRATIC EQUATIONS

For each of the following, calculate the value of the discriminant, and use this to determine the type of roots the equation has.

1. d = ______

roots:______

2. d = ______

roots:______

3. d = ______

roots:______

4. d = ______

roots:______

5. d = ______

roots:______

Graph completely: Identify x and y-intercept(s), the vertex, point symmetrical to y-int and an equation for the axis of symmetry.

vertex: ______

axis: ______

y-int(s): ______

symm pt: ______

x-int(s): ______

vertex: ______

axis: ______

y-int(s): ______

symm pt: ______

x-int(s): ______

vertex: ______

axis: ______

y-int(s): ______

symm pt: ______

x-int(s): ______

vertex: ______

axis: ______

y-int(s): ______

symm pt: ______

x-int(s): ______

10. If the vertex of a parabola is (5, -2), and (1, 3) is a point on the curve, find an equation for the parabola.

11. A rectangle has a perimeter of 50 ft. What dimensions will maximize the area of this rectangle and what is the maximum area?

12. Find two real numbers with sum 14 and product as great as possible. Find both the numbers and the maximum product.

13. A potato farmer has 400 bushels of potatoes that she can now sell for $3.20 per bushel. For every week she waits, the price per bushel will drop by $0.10 but she will harvest 20 more bushels. How many weeks should she wait in order to maximize her income? What will her maximum income be?

14. Consider all pairs of positive integers whose sum is 20. What is the smallest value for the sum of their squares? What pair of integers produces this value?

PART II: EXPONENTS & LOGARITHMS

Evaluate:

1. 2.

3. 4.

5. 6.

7. 8.

Write in simplified radical form:

9. 10.

11. 12.

Solve the following:

13. 16x = 2 14. 4x = 2

15. 10x = 1000 16. 53x – 1 = 25x + 4

17. 1252x – 2 = 253 – x 18. 102x + 4 =

15. Are and inverses? Show.

16. Find the inverse of

Evaluate the following:

21. log10.0001 22. log71

23. 24. log1515

25. log25125 26.

27. log397 28. log5259

29. log64 + 2log63 30. 2(log220 – log25)

31. log516 – 2log510 32.

33. log511 34. log7.385.9

Solve for x:

1. logx16 = ½ 2. log1000x =

3. logx = -2 4. log1001000 = x

5. logx125 = 6 6. log328 = x

7. log5(2x + 5) = 3 8. log3(x2 +17) = 4

9. log10x = log108 + log1081 10. log3x2 = log38 + log310 – log35

11. log3x – log34 = 2log35 12. log6x + log6(x + 5) = 2

13. log32x2 – log3(5x – 9) = 1 14. 7.4-x = 18.6

15. 543x = 19 16.

17. .76(52x) = 29.3 18.

19. 63x – 1 = 28x 20. 42x – 1 = 173x – 1

21. A bacteria culture is found to double in size every 24 minutes. How many minutes would it take for a culture of 320,000 bacteria to grow to 761,000 bacteria?

22. Forty years ago the population of a certain town was 2000. It is now 12,000. Assuming

exponential growth, in how many years will the population be 45,000?

23. Find the value of an investment of $6000 after 1.5 years if the interest is compounded continuously at 8%.

24. How many years ago was $5000 invested in an account paying 8% annual interest compounded quarterly, if the amount presently in the account is $11,500?

Express in logarithmic form: Express in exponential form:

1. e-2 = .135 1. ln .5 = -.693

2. 2. ln .01 = -4.605

Simplify:

1. 2. ln 6 + ln 30 – (ln 5 + 3 ln 2)

3. e2 ln 7 4.

PART III: CONIC SECTIONS

1. Write an equation of the form for the circle with center (0, -4) and radius 5.

2. Find the coordinates for the midpoint and the length of the line segment whose endpoints are (3, -2) and (4, -1).

3. Write an equation for the circle centered at (1, 4) and with a radius of 3.

4. Write an equation for the circle centered at (-9, 3) and with a radius of .

5. Write an equation for the ellipse whose foci lie at ( 5, 0 ) and ( -5, 0 ) and whose vertices lie at ( 9, 0 ) and ( -9, 0 ).

6. Write an equation for the hyperbola whose foci lie at ( 7, 0 ) and ( -7, 0 ) and whose vertices lie at ( 5, 0 ) and ( -5, 0 ).

7. Find the equation of a parabola with focus at (4, 5) and directrix y = 9.

Sketch the graphs of the following conic sections. Provide all “critical” points (i.e: center, vertices, foci)

8. 11.

9. 12.

10. 13.