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HONORS ALGEBRA II
Name _________________
REVIEW FOR FINAL EXAM
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. x 2  5 x  8  0
d = ______________
roots:_________________
2. x 2  3 x  7
d = ______________
roots:_________________
3. 2 x 2  3 x  0
d = ______________
roots:_________________
4. 2x 2  5 x  3  0
d = ______________
roots:_________________
5. 2 x 2  4 x  2  0
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.
6. y   x 2  3
vertex: ________________
axis: ______________
y-int(s): ____________
symm pt: ____________
x-int(s): _____________
HONORS ALGEBRA II
7. x  2  y  2   1
2
vertex: ________________
axis: ______________
y-int(s): ____________
symm pt: ____________
x-int(s): _____________
8. y  2  x  4   5
2
vertex: ________________
axis: ______________
y-int(s): ____________
symm pt: ____________
x-int(s): _____________
9. y  x 2  4 x  5
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.
HONORS ALGEBRA II
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. 7
2
3. 52
3
 2
2.
52
3
2 
4. 10
12
3 2
1
2
5. 9 2
6. 32 5
7. 16

3
4
 3
 125 
8. 

 64 
10

1
3
3 3
HONORS ALGEBRA II
Write in simplified radical form:
9.
11.
4
32 y 6
12
27
10.
6
1
27r 24
12.
4
 49 


 144 
2
Solve the following:
13. 16x = 2
14. 4x = 2
15. 10x = 1000
16. 53x – 1 = 25x + 4
2x – 2
3–x
2x + 4
17. 125
= 25
18. 10
15. Are y 
3
4
x  6 and y  x  8 inverses? Show.
4
3
 1 
=

 100 
x 3
1
16. Find the inverse of y   x  5
4
Evaluate the following:
21. log10.0001
22. log71
23. log 1 128
24. log1515
2
25. log25125
26. log 6 36 6
HONORS ALGEBRA II
27. log397
28. log5259
29. log64 + 2log63
30. 2(log220 – log25)
1
log 2 27
3
1
31. log516 – 2log510
2
32. 2
33. log511
34. log7.385.9
Solve for x:
2
3
1. logx16 = ½
2. log1000x = 
3. logx 7 = -2
4. log1001000 = x
5. logx125 = 6
6. log328 = x
7. log5(2x + 5) = 3
8. log3(x2 +17) = 4
9. log10x =
1
1
log108 + log1081
3
2
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
HONORS ALGEBRA II
x
8
15. 54 = 19
16. 128  33.7
17. .76(52x) = 29.3
18. 4.18.2  2  132
19. 63x – 1 = 28x
20. 42x – 1 = 173x – 1
3x
x
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:
1. e-2 = .135
Express in exponential form:
1. ln .5 = -.693
HONORS ALGEBRA II
2.
e  1.649
2. ln .01 = -4.605
Simplify:
1.
1
ln 9  ln12  2 ln 3
2
2. ln 6 + ln 30 – (ln 5 + 3 ln 2)
1
3. e2 ln 7
4. e 2
ln 3
PART III: CONIC SECTIONS
1. Write an equation of the form x 2  y 2  ax  by  c  0 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 2 3 .
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.
HONORS ALGEBRA II
Sketch the graphs of the following conic sections. Provide all “critical” points (i.e: center,
vertices, foci)
8. 16  x  1  9  y  1  144
11. 4 x 2  y 2  36
9. y  x 2  4x  5
12. y  
10. x 2  y 2  9
13. x 2  y 2  6 x  3y  9
2
2
1 2
x  2x
3