Algebra, Functions, and Data Analysis
3rd 9-weeks Test Review
Test Date: April 1, 2011
Directions: Find the common ratio or difference
1.
2.
3.
4.
Geometric: 27, 729, 19683, 531441
Arithmetic: 58, 85, 112, 139
Finish the Fibonacci sequence 1, 1, 2, …, (up to 10 terms).
How many handshakes would be counted if there was a group of 10 people?
Directions: Use the given formulas to answer the following questions.
The formula to calculate your body mass index is: BMI =
5.
6.
7.
8.
703𝑤
ℎ2
, where w is your weight in lbs
and h is your height in inches. A BMI between 18.5 and 24.9 is considered ideal.
Calculate the BMI for a person 60 inches tall and weighing 157lbs.
Solve: 2 out of 5 = 4 out of ___
4x + 3(5x – 7) + 2 = 3(2x + 5) – 8
Solve the system: 2x + y = 1
–x + y = -5
Use this equation , x2 + x – 12 = 0, to answer question 9-15
9. Solve the equation using the factoring method.
10. Solve the equation using the quadratic equation.
Use the properties of exponents to determine the following:
11. (-5)2
13. (x3y2z4)5
2
2
12. (-3xy )(-x y)
14. (abc)3(a2b3c)2
Show all work for the following growth and decay questions.
15. A suit with an original price tag of $300 was marked down by 60%. What is the corresponding
decay factor?
a. How much is the suit on sale?
b. You have a coupon good for an additional 20% off. What is the decay factor associated
with this percent decrease?
c. What is the final cost?
16. Merrill Lynch announced this week that 3,400 workers will be laid off. What is the percent
decrease of their 65,000 world wide employees?
17. What is the corresponding decay factor in question 16?
18. The birth rate in Japan has declined precipitously during the last half of the century. In 1947,
the average number of children born to a Japanese woman was 4.54. In 1997, the number fell
to 1.39 children. What percent decrease does this represent?
19. Write a model equation of a population growing annually by 3.7% and their initial population
was 125, 000.
20. Write a model equation of a population declining annually by 4.5% and had an initial population
of 135, 000.
21. If pizza price increase is model by the equation y = 5(1.25)t; what will the pizza price be after 12
years?
Evaluate each Expression
22. log3 81
23. ln e4
24. ln
1
𝑒6
25. log8 815
Rewrite each equation in logarithmic form.
26. eb = 8103
27. 2x = 64
Rewrite each equation in exponential form.
28. log 1000 = x
29. -3 = log2 j
Write each expression as a sum or difference of two or more logarithms.
30. log4 (4 *6)
3 𝑥
31. ln[ ]
5
32. log392
33. log5 [(√𝑥)( 3√𝑦)]
Write each expression as the logarithm of a single expression.
34. 2log 4 + 3log 3
36. ½ logx + ½ logy
35. 2log(x + 5) – 2log(x)
Use the change of base formula and a calculator to determine the decimal approximation.
37. log2 42
Solve each equation.
39. 4 + 2logx = 12
40. log4 (3x + 5) =4
38. log9 86