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WorksheetsAdvanced Algebra Q3 Review
Total questions: 160
Worksheet time: 13hrs 11mins
x2/3
∛x⁷
∜x5
∛(2x)2
361/2
271/3
Rewrite: 4-3
431
4−31
43
−431
Rewrite: -8-3
−8−31
83
831
−831
Simplify
-1
321
−321
1
351 is the same as
3−5
35
15
53
(54)−2
54
(45)2
(54)1
2516
7−25−2
4910
4925
2549
1410
Write with positive exponents:
a-2
a2
a21
2a
Simplify
b37a5
7a5b3
a−57b3
a57b3
Rewrite using a positive exponent.
2w-13
-w13
w132
w−132
2w13
Simplify. Hint: do product rule first, then negative rule!
42x5
x542
x−542
42x51
When dividing powers with the same base, you _______________ the exponents.
Add
Subtract
Multiply
Divide
x6 / x2
x4
x12
x3
x8
Simplify:
(3x7)(x2y5)(2x3y)
1x2y4
6x2y4
6x12y6
5x12y6
yx31⋅xy23
x34y25
x32y21
x31y23
x32y34
Simplify . Your answer should contain only positive exponents. (a21b21)−1
a21b211
a21b21
−a21b211
−a21b21
Simplify . Your answer should contain only positive exponents. 2x34y−472x21y31
x65y1225
y1225x65
x652y1225
x65y1217
Simplify . Your answer should contain only positive exponents. (6b)3−4
634b341
b346
6b34
b34634
Simplify . Your answer should contain only positive exponents. y−1•2y−313y−45
23y121
23y1219
2y1213
2y12193
A=1200(.85)6
5−3x−2=53x
- 31
31
-3
3
9x−2=1
No Solution
2
-2
All Real Numbers
Jacob borrows $500 from Abraham and agrees to have the loan compounded annually for 5 years with an interest rate of 2.5%. How much will the total amount be that Jacob owes?
$565.70
$262609.38
$65.70
$630.20
Interest Rate: 3.75%
Time: 25 years
Compounded Monthly
State the future account balance.
Convert 16 = 2x to a Log
Log2(x) = 16
Log2(16) = x
Log16(x) = 2
Logx(16) = 2
Convert Log3(x) = 4 to an exponent
3x = 4
34 = x
x3 = 4
4x = 3
log636 = 2
Convert to logarithmic form: 29=512
log9512=2
log2512=9
log29=512
log92=512
log4(3x-1)=log4(2x+3)
4
3
1
8
A
B
C
D
ln (5x + 6) = 5
154.413
30.883
147.213
28.483
Rewrite ex = 9 using a logarithm
ln x = 9
ln 9 = x
logx e = 9
log9 x = e
3e2x + 10 = 25
{-3.940}
{1.228}
{0.451}
{0.805}
What is the asymptote of y = 2x ?
y = 0
x = 0
What is the asymptote of y = 2x - 3
y = 0
y = -3
x = 0
x = -3
A=1200(.85)6
A=10(1.01)3
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.
Consider the equation 70(0.8)x + 2. What is the equation of the asymptote?
y = 70
y = 0.8
y = 2
y = 0.2
f(x)=5(3)x+4 What is the y intercept of the function f?
5
4
9
15
What is the range of the graph
y >2
y = 2
y < 2
y < 0
Which graph matches the function y = -4(1/2)x - 2
Which is the correct equation for the given graph?
y=2x-2-1
y=2x+2-1
y=2x-2+1
y=2x+2+1
Which is the correct equation for the given graph?
y=(1/2)x-2-1
y=(1/2)x+2-1
y=(1/2)x-2+1
y=(1/2)x+2+1
−3(3)x+2
−3(31)x+2
−3(3)x−2
−3(31)x−2
−3(4)x+2
−3(41)x+2
3(4)x+2
3(41)x+2
y=−(41)x−2
y=4x−2
y=−4x−2
y=(41)x−2
Which equation matches the graph?
y = 4x - 6 - 3
y = 4x + 6 - 3
y = 4x - 6 + 3
y = 4x + 6 + 3
As x → -∞ , f(x) →
-4
-3
∞
-∞
As x → ∞ , f(x) →
-4
-3
∞
-∞
43b - 3 = 1/16
343(−2x)=495
16
-7/2
-5/3
5/3
62x=(61)(x−1)
-3
-1
-1/3
1/3
Solve the equation for x
1.771
0.5646
1.6203
1.8456
Solve the equation for x
1.6023
0.7122
0.6477
1.544
Solve the equation for x
1.585
3.169
0.792
1.084
Solve for x
1.631
2.262
1.734
1.465
Solve for x
1.893
2.807
3.169
2.971
Solve for x
-0.4605
1.5395
3.5395
-0.4731
Solve for x
-0.659
-0.528
-2.159
-0.478
0.1487
0.2568
0.1699
0.1135
Solve for x
0.562
1.237
1.431
0.431
Solve for x.
8ex+1 = 40
0.61
2.6
No Solution
-1.61
Solve for x.
ex-10 + 9 = 51
13.7
-13.7
No Solution
-6.26
Rewrite 1.6(x+2) = 14.1
log1.614.1 = x+2
log1.6(x+2) = 14.1
log14.1(x+2) = 1.6
log(x+2)1.6 = 14.1
Solve the equation. e10v+6=38
0.35
0.15
0.19
0.18
Solve the equation. −8(2n+5)=−29.3
-4.44
No solution
-3.13
=3.70
Use the properties of logs to write the expression as a single log.
log(12x2)−log(6x)
log(72x2)
log(12x2−6x)
log(2x)
log(18x)
Use the properties of logs to write the expression as a single log.
log(5x)+log(4)
log(20x)
log(9x)
log(x)
log(5x+4)
log3(2)+log3(5x)−log3(7)=
log3(70x)
log3(10x−7)
log3(710x)
log3(75x2)
log4(3x-1)=log4(2x+3)
4
3
1
8
log2(x+3)=4
16
13
3
10
log8(4x+4)=2
15
12
10
3
Evaluate the following logarithm:
log327
3
2
-3
1/3
Evaluate the following logarithm:
log55
1
0
-1
1/2
Evaluate the following logarithm:
log416
1
-2
2
1/2
Evaluate the following logarithm:
log42
-1/2
-2
2
1/2
Evaluate the following logarithm:
log121
1
0
-1
1/2
Evaluate the following logarithm:
log3(1/3)
-2
-1/2
-1
1/2
Evaluate the following logarithm:
log4(1/64)
3
-1/3
-3
1/3
Evaluate the following logarithm:
log273
1/3
-3
-1/2
1/2
What is the value of
ln(−2)0.693
-0.693
1.349
Does not exist
Use calculator to find
ln(10)2.109
2.303
2.507
2.706
1
2
3
4
What is the growth rate?
6%
.06%
1.35%
.6%
What is the rate of growth as a constant (One number) in the equation?
1.04
7
49
1
Dr. Quander decided to buy a new car, which cost $32,000. He took a 3 year loan from the bank at a rate of 3.1%, compounded monthly, in order to cover the cost of a car. Which equation accurately represents how much Dr. Quander will pay for the car over the course of the 3-year loan?
A(3)=32000(1+123.1)12⋅3
A(3)=32000(1+120.031)3
A(3)=32000(1+120.031)12⋅3
A(3)=32000(1+120.31)12⋅3
Ms. Peralta bought a new car, which cost her $27,000. Which equation represents the value of the car after 5 years, if the car depreciates at a rate of 20% per year?
A(5)=27000(1+0.20)5
A(5)=27000(1−0.20)5
A(5)=27000(1−5)0.20
A(5)=27000(1−0.80)5
A population of a city is 422,000 and increases by 12% each year. Use an exponential function to find the population of the city after 8 years.
1,044,856 people
1,938,0494 people
2,940,093 people
3,048,309 people
