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Algebra 2/Trig Q3 BM review 2008-09 1
Garden Grove Unified School District
Algebra 2/Trigonometry Quarter 3 Benchmark 2008-09
(Scientific calculators are permitted)
1. Std 11.1 What is the logarithmic form for
3x
= 27?
2. Std 11.1 What is x if
log381= x ?
3. Std 11.1 Write an expanded log expression equivalent to
log5
2! 3.
4. Std 11.1 What is x if
2 logx = 4 log2 ?
5. Std 12.0 Which is the graph of
y = 2x?
6. Std 12.0 What is
p2
3 ! p3
5 written in simplified exponent form?
7. Std 12.0 There are 1,000 bacteria in a certain culture. The bacteria double every hour. Write an
inequality that shows how many hours, h, that it will take for the colony to grow to more than 100,000.
8. Std 12.0 Using
f (x) = ax as the basic graph, write a function that shows the following tranformations:
a) a reflection of the graph in the x-axis
b) a reflection of the graph in the y-axis
c) a shifting of the graph 2 units to the right
d) a shifting of the graph up 3 units
A
B C
D
x
y
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Algebra 2/Trig Q3 BM review 2008-09 2
9. Std 14.0 Write an expanded log expression equivalent to
lnA3
B
CD2
Ê
Ë Á
ˆ
¯ ˜ .
10. Std 14.0 Solve for x:
1
3log216 + 2 log3 = logx
11. Std 14.0 What is the value of
log381+ log2 32 + log10 0.01
12. Std 14.0 What is the approximate value of
alog (xy) if
alog x = 0.7782 and
alog y = 0.3010?
13. Std 15.0 Under what conditions does
22x-1
= 32 ?
14. Std 15.0 If x is a real number, for what values of x is the equation
x2
+ 7x +12
x2
- 9
=x + 4
x - 3 true?
15. Std 15.0 If x and y are real numbers and
-2xy2 = y -2x , which of the following is true?
A. Neither x nor y are negative numbers
B. Only x is a negative number
C. Only y is a negative number
D. Both x and y are negative numbers
16. Std 15.0 Which of the following statements regarding the graph of
y = blog (x - h) + k is false?
Explain.
a) The line x = h is a vertical asymptote
b) The domain is all real numbers and the range are value that are greater than k
c) If b > 1, the graph moves up to the right
d) If 0 < b< 1, the graph moves down to the right
17. Std 2.0 If (a,b) is the solution of
5a + 3b = 10
2a + b = 4
Ï Ì Ó
what is a + b?
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Algebra 2/Trig Q3 BM review 2008-09 3
18. Std 2.0 The graph represents the graphical solution for what system of equations? Write the system in
standard form.
19. Std 2.0 Which of the following shaded regions represents the solution of
2x - y ! 2
3x + 5y £ 15
Ï Ì Ó
?
20. Std 2.0 Solve:
2x - y = 5
-4x + 2y = -10
Ï Ì Ó
21. Std 18.0 A new hybrid car was just introduced at the Auto Show. A buyer can choose from four
colors, three interiors, five engine sizes, and three sound systems. How many combination of
arrangements are possible?
22. Std 18.0 Armon, the store clerk receives a shipment of 4 classical CDs, 8 Rock-n-Roll CDs and 3
Country Western CDs. If he lines them upright on a shelf, how many arrangements could be make?
(Leave in factorial form)
23. Std 18.0 Six people are to be seated around a circular table. How many ways can they be seated
relative to each other?
24. Std 18.0 Sahra is ordering a large pizza with 3 different toppings. The restaurant offers 12 different
toppings,. How many different combinations could Sahra select from?
y
x
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Algebra 2/Trig Q3 BM review 2008-09 4
25. Std 19.0 The numbers from, 1 to 8 are put on slips of paper and placed in a box. Three numbers are
drawn at random. What is the probability that each number is greater than 6 or less than 2?
26. Std 19.0 Anita has 6 red and 3 yellow M&Ms in a bag. She randomly selects two M&Ms, one at a
time, and eats the first M&M before drawing the second M&M. What is the probability that both M&Ms
are red?
27. Std 19.0 A four-person student advisory committee is to be randomly selected from five senior boys
and six senior girls. What is the probability that the committee will be all senior boys?
28. Std 19.0 At Loan’s party, each of her ten friends brought her a gift. If she randomly opens the gifts,
what is the probability that the first two gifts opened where from Renae and Stephanie, in that order?
(Note: no 2 girls had the same name.)
29. Std 20.0 What is the 3rd
term in the expansion of
(x + y2)3?
30. Std 20.0 What is the simplified form of the expansion of
(3x - 2y)4 ?
31. Std 20.0 What is the middle term in the expansion of
(2x - 4y)6 ?
32. Std 20.0 In the expansion of
(x + y)6, what is the coefficient of the
x4y2 term?
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Algebra 2/Trig Q3 BM review 2008-09 5
Garden Grove Unified School District
Algebra 2/Trigonometry Quarter 3 Benchmark 2008-09
Answer Key
1.
3log 27 = x
2. x = 4
3. log 5 – log 2 – log 3
4. x = 4
5. B
6.
p19
15
7.
100(2)h> 100,000
8. a)
f (x) = -ax b)
f (x) = a-x c)
f (x) = ax-2 d)
f (x) = ax+ 3
9.
3ln A +1
2ln B- ln C - 2 ln D
10. x = 54
11. 7
12.
ª1.0792
13. x = 3
14. all values of x except
±3
15. B
16. B
17. 2
18.
3x + 2y = 4
x - y = 3
Ï Ì Ó
19. C
20. infinite number of solutions
21. 180
22. 15!
23. 5! or 120
24. 220
25.
1
56
26.
5
12
27.
1
66
28.
1
90
29.
3xy4
30.
81x4 - 216x3y + 216x2y2 - 96xy3 + 16y4
31.
-10240x3y3
32. 15
