INTEGRATED 3 Final Exam 2011 Topic List
INTEGRATED 3 Final Exam 2011 Topic List:
1. Similar triangles (questions multiple parts)
a) Know the triangle shortcuts for similarity ~ ( AA, SAS, SSS)
b) Know how to find the scale factor after you know 2 triangles are similar
c) Know how to use the scale factor in order to find the lengths of missing sides
d) Use similar triangles to find geometric concepts (area, perimeter)
2. Congruent Triangles and properties (Questions multiple parts)
a) Know how to use law of sines and cosines to solve for sides or angles of triangles
b) Know the triangle congruence shortcuts (ASA, SSS, SAS, AAS)
c) Know how to prove 2 triangles are congruent.
d) Use definitions of midpoint, and properties of parallel lines cut by a transversal to prove triangles are congruent.
e) Properties of quadrilaterals
3. Properties of circles ( Questions multiple parts)
a) Know how to use chords and Pythagorean theorem to find lengths inside the circle
b) Know properties of tangent lines and angles formed when tangent lines meet the radius
c) Know properties of central angles, inscribed angles and intercepted arcs.
4. Trig( Questions multiple parts)
a) Know how to find coterminal angles in radians and degrees
b) Know how to find the compliment and supplement in radians and degrees
c) Know how to find a trig ratio given an angle in radians and in degrees
d) Know how to solve for an angle in radians and degrees when given a trig ratio
5. Stats ( Questions multiple parts)
a) Know how to estimate the mean and standard deviation using a graph
b) Know how to find the z score given a value, standard deviation and mean
d) Know how to use the z score to find percentages
e) Know how to determine if a situation is binomial
f) Know how to determine if a binomial distribution is approximately normal
g) Know the percentages that lie within 1, 2, and 3 standard deviations from the mean
h) Know how to find the expected # of successes
i) Know how to use the probability formula, PDF and CDF programs to find the probability of a certain amount of successes in a binomial distribution.
j) Know how to calculate mean and standard deviation in a binomial distribution and how to use it to determine if a value is statistically significant
6. Recursion ( Questions multiple parts)
a) Write a Now-Next rule and recursive notation to model population, balances, or interest
b) Identify and write a rule for an arithmetic sequence. Find a specific term.
c) Identify and write a geometric sequence. Find a specific term.
FINAL EXAM REVIEW
A. Solve for the missing sides and angles of the Triangle
1. m<A=41o, m<C=52o and a=6
2. a=18, b=25, c=12
3. m<B=2o, m<C= 119o, and b=9
4. m<A=57, a=12, and b=40
5. m<A=135o, b=6, c=7
B. Similar Triangles
6. Prove the two triangles are similar.
Given: BC ║ AD
Prove: Δ BCE ~ Δ DAE
7. Given: lengths marked and <C and <F are right angles
Prove : Δ BCA ~ Δ EFD
8. Prove the two triangles are similar if BE ║ CD
9. If Δ ABE ~ Δ ACD and AB = 20, BC = 5, BE = 6. Find DC.
10. Use new measurements AB = 14, m<EAB = 25o, and m<AEB=110o, find BE
C. Congruent Triangles
11. Prove the triangles are congruent
12.
13.
14. Determine if each pair of triangles are congruent, similar, or neither. If they are congruent of similar, write a congruence or similarity relation showing the correspondence between vertices and cite an appropriate congruence or similarity theorem to support your conclusion.
D. Circles
15. Find the missing angles and arcs.
16. In the OM, chords BR=CR and BM and MC are radii. Find the central angle, inscribed angle, and two arcs.
17. In the OP, arc AB is 160o. Find the following missing parts
18. The length of the diameter of circle O is 26 inches. BC is a chord 10 in long. How far away from the center is the chord? Draw a diagram to help.
E. Quadrilaterals
19. List the quadrilaterals that have the following properties. Choose from parallelogram, rectangle, rhombus, square, trapezoid, isosceles trapezoid, kite
a.Diagonals are perpendicular
bBoth pair of opposite angles are equal
c.Diagonal bisect opposite angles
d.All sides are equal
e.All angles are equal
f.Regular quadrilateral
g.Diagonals are congruent
F. Trigonometry
For the following angles give a) 2 coterminal angles 1 positive and 1 negative and b) the complement and supplement.
20. 35o
21. 87o
22. 210o
23. -40o
24.
25.
26. 5pi/6
27. pi/4
Find the following trig ratios
28. tan
29. sec 210o
30. sin 45o
31. cos
32. tan
33. sin (-135)
34. cot 60o
35. cos
Solve each trig equation for both [0,360o) and [0, 2
36. cosx =
37. sinx = -1
38. tanx = -
39. cscx = 2
40. tanx = 1
41. cosx = -
G. Statistics
42. The weights of 19-day-old pigs are approximately normally distributed with a mean weight of 11.9 pounds and standard deviation of 2.7 pounds.
a. Find the standardized value for a 19-day-old pig that weighs 15 pounds. Write a sentence explaining what the standardized value means.
b. Mason has a 19-day-old pig that weighs only 7.85 pounds. What is the pig’s percentile for weight? Write a sentence explaining what the percentile means.
c. Graciela has a big 19-day-old pig. When she looks at a chart, she realizes that only 10% of 19-day-old pigs are bigger than her pig. Approximately how much does Graciela’s pig weigh?
d. What percentage of pigs weigh between 10 and 13 pounds?
43. In 2003, the United States National Assessment of Adult Literacy found that 22% of adults did not have a basic level of quantitative literacy. The mayor of Pritchette wants to see if this percentage is plausible for his town. Suppose that he takes a random sample of 600 adults and finds that only 120 of them do not have a basic level of quantitative literacy.
a. Is this result statistically significant? Explain your reasoning using all steps and work to support your conclusion.
b. What should the mayor conclude about the level of quantitative literacy in the town
of Pritchette?
44. Approximate the mean and standard deviation from the following histogram.
45. As a summer job, Juliette works for the Empire Pencil Company. She runs a machine that makes pencils, which are supposed to have a mean length of 8 inches. But like all processes, the pencils do not come out exactly 8 inches long each time. The machine is supposed to be set so that the distribution of the lengths of the pencils is normal and the standard deviation of the lengths of the pencils is 0.05 inches.
a. Sketch the distribution of the lengths of pencils when the machine is under control. Mark on
the horizontal scale the mean and one, two, and three standard deviations from the mean.
b. If the machine is set correctly, what percentage of the pencils will be more than 8.1 inches long? Less than 7.85 inches long?
46. The scores on the math section of the SAT Reasoning Test are normally distributed with a mean of 520 and standard deviation of 115. Taylor’s score placed her in the 90th percentile. What was Taylor’s score?
47. According to The Condition of Education 2007, 84.5% of the 2004 high school graduates completed at least one foreign language class. You randomly select 200 people in the United States who graduated from high school in 2004.
a. How many do you expect to have completed at least one foreign language class?
b. Is the binomial distribution of the number of people in the sample who completed at least one foreign language class approximately normal?
c. What is the standard deviation of this distribution?
d. Find the probability that in your sample you would have 160 or fewer people who completed at least one foreign language class.(Use standardized score and then complete using the CDF program on your calculator)
e. Would you be surprised to get a sample with only 150 people who completed at least one foreign language class?
H) Recursion
48. The population of fish in a lake at the end of each month can be modeled by the recursive function
Pn = .92Pn-1 +1200. If P0 = 4000 and none of the conditions change from year to year, what will be the approximate long-term population of fish in the lake?
a. What is P4?
b. Write the recursive formula if there is a 75% decrease in population and if P0 = 700
49. Suppose that the nth term in a sequence is given by the recursive formula Un = Un-1 +5 , U0 = 18. Write the rule in function notation and find U9
Function:
U9
50. The function rule is f(n) = 6n – 5. Write the rule in recursive notation.
51. Eva has a credit card balance of $2,528. Since this balance is more than one month old, the credit card company adds an interest charge each month until it is paid in full. The annual interest rate on this balance is 21%. Suppose that Eva makes monthly payments of $200 and does not make any additional charges to this card.
a. What is the monthly interest rate for this balance?
b. Write a recursive formula that can be used to find the credit card balance at the end of each month.
c. Complete the table below indicating the balance after each of the following number of months.
d. How many months will it take her to reach a zero balance?
52. Suppose that Mark takes a part-time sales job from a company that says his initial monthly income will be $10, and his monthly income will double every month.
a. What kind of sequence (arithmetic or geometric) is formed by Mark’s monthly salaries for the first year?
b. Write the equation.
c. If Mark starts his job in January, what will his monthly salary be in December of that same year?
d. Suppose that in January, Katie takes a different part-time job and is told that her starting salary will be $250 per month for the first month. Her salary will then increase by $25 per month.
Is this arithmetic, geometric, or neither
How much money total will Katie earn in October?
e. If Mark and Katie both start their jobs at the same time, how many months will it take before Mark’s monthly salary is greater than Katie’s monthly salary?
53. Consider the function .
a. Iterate the function starting with . Write the results of your interation in the table below.
b. Write a NOW-NEXT rule to model the sequence.
c.Write a recursive formula using and that will produce the same sequence of values as the function iteration in Part a.
54. Suppose that approximately 5% of trees in a forest die each year due to weather and disease-related conditions. In a particular region of a forest, there are currently 5,000 trees. The forestry company has plans to cut down 200 trees each year.
a. Write a recursive formula that represents this situation. Be sure to specify the initial value.
b.How many trees will be in this section of the forest after 5 years?
c. How many years will it be before there are fewer than 1,000 trees left in this section of the forest?
55. Consider the two sequences below.
a.
i. Determine if the sequence is arithmetic or geometric. Explain how you know.
ii. Find a recursive formula and an function formula for this sequence.
Recursive Formula:
Function Formula:
iii. Find A20
b.
i. Determine if the sequence is arithmetic or geometric. Explain how you know.
ii. Find a recursive formula and an function formula for this sequence.
Recursive Formula:
Function Formula:
iii. Find the term, n, so that the An = 81
56. Suppose that James opens a savings account with an initial deposit of $2,000. The account will earn 6% interest each year, and James will deposit an additional $600 each year. Assume that James does not take any money out of the account.
a. Write a recursive formula that shows how the amount of money in the account changes from month to month. Find monthly rate first. Be sure to include an initial value.
b. How much money will be in the account after 6 months?
c. How many months will it take for James to have at least $20,000 in the account?