Arrowhead High School
Chapter 1 (Terms & Concepts to Know)
Capture-Recapture Method
ALL DISPLAYS
Bar Graphs
Circle Graph
Scatter Plot
Line Plot
Histogram
Stem-and-Leaf Plot
Box-and-Whisker Plot
Know what they are and how to find…
Range
Outliers
Mean
Median
Mode
Lower Quartile
Upper Quartile
Summations ∑
Interquartile Range
Standard Deviation
Variance
Chapter 1 Final Exam Review Questions
1) Takis recorded the rainfall in millimeters at his home each day for a week. The data collected was: 16, 0, 0, 11, 8, 11, 3.
a. Find the range
b. Find the median amount of rain in a day.
c. Find the mean to the nearest millimeter.
d. Find the standard deviation to the nearest whole number.
2) Multiple Choice. Which of the following is a correct formula for finding the standard deviation of the data set c1, c2, c3, …, c12?
a. [pic] b. [pic] c. [pic] d. [pic]
3) To study the snake population in a desert area, a team captured and tagged 23 snakes from various parts of the desert. They released the snakes, and a week later they captured a random sample of 17 snakes. If 5 snakes in the second group were tagged, estimate the number of snakes in the desert area.
4) Consider the following stem-and-leaf plot of heights (in centimeters) for two different groups of tree seedlings. The mean of each group is 53 cm.
Group X Group Y
3 7 8
5 3 2 8 4 5 8 6 0 1
7 5 1 3 1 0 5 9 8 9
6 8 0 6 5 8 7 0 4
a. Find the median height for each group.
b. Without calculating, tell which group’s heights have the greater standard deviation.
5) The number of pets currently owned by 37 seventh-grade students at a school are given.
0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 3 4 4 4 4 5 5 5 6 7 11
a. Find the median.
b. Find the lower quartile (Q1) and upper quartile (Q3).
c. Find the interquartile range.
d. Use 1.5 X IQR criterion to determine which, if any, values are outliers.
6) The plot represents normal Fahrenheit temperatures of the 50 states, using data for one city in each state. The normal was calculated from temperature records for the thirty-year period 1951-1980. The endpoints of each box plot represent the lowest and highest normal temperatures.
Normal Maximum and Minimum Temperatures of the 50 States
Use the box plot above to answer the questions below.
a. In July, what was the lowest normal maximum temperature?
b. True or False. In January, more than half of the states have a normal minimum
temperature between 15oF and 25oF.
7) Make a box plot for the five-number summary given below. Be sure to indicate your scale.
Min. Q1 Median Q3 Max.
52 182 238 284 436
Chapter 2 (Terms & Concepts to Know)
f(x) notation
What constitutes a function? (VLT or no repetition in the x-coordinate)
Line of best fit
Correlation coefficient
Discontinuous functions
Step functions
Rounding up or rounding down
Finding quadratic models
Formula for the height of an object in flight
Chapter 2 Final Exam Review Questions
8) The points (2, 1), (6, 2.44) and (9, 3.52) lie on a line. Write an equation in slope-intercept form of the line.
9) Find an equation for the quadratic function whose graph contains the points (2, 4), (5, 1) and (10, 6).
10) Multiple Choice. Each number below is the correlation coefficient between two variables. Which indicates a weak negative relation?
a. 0.08 b. -0.84 c. 0.96 d. -0.18
11) Use the data in the table below to answer the following questions. An equation for the line of best fit through those points is T = 4.8Y – 208, where T is the turkey population and Y is the number of years after 1900. (Source: U.S. Agriculture Department)
Turkeys on U.S. Farms, 1950-1990
Year (after 1900) |50 |60 |65 |70 |75 |80 |85 |90 | |Turkeys (Millions) |44.1 |84.5 |105.9 |116.1 |124.1 |165.2 |185.4 |260.3 | |a. For the year 1980, find the observed y-value, the predicted y-value, and the error of prediction.
b. Estimate the number in 1962.
12) An architect charges $100 per hour for the first hour of a project and $65 for each additional hour or fraction thereof. Give a formula for the total charges C in t hours of work, using the greatest integer function.
13) Allen launched a model rocket from the top of a hill next to a level meadow. The height h of the rocket in feet above the meadow can be estimated by h = 140 + 100t – 16t2, where t is the time in seconds after the launch.
a. How high is the hill?
b. According to the model, how high will the rocket be 3 seconds after the launch?
c. About how long after the launch will the rocket land on the meadow?
14) Identify the domain and range of the relation shown below.
15) State whether the graph represents a function.
Chapter 3 (Terms & Concepts to Know)
Parent functions
Translation Theorem (Rules, Equations, Graphs)
Translations of data sets
Symmetries of Graphs
Odd
Even
Scale Change Theorem (Rules, Equations, Graphs)
Scale changes of data sets
Composition of functions (including domain)
Inverse functions
Chapter 3 Final Exam Review Questions
16) Let f(x) = 2 – x2 and g(x) = 6x + 8.
a. Evaluate (f ◦ g)(-2).
b. Evaluate (g ◦ f)(-2).
c. Find an expression for (g ◦ f)(x).
d. Give the domain of g ◦ f.
17) The scale change (x, y) (4x, -y) is applied to the graph of y = 2x3. Write an equation for the image.
18) State a rule for the translation that maps f(x) = x2 to g(x) = (x – 5)2 – 7.
19) If d1 = 5, d2 = -2, d3 = -3, d4 = 8, d5 = 3, evaluate
a. [pic] b. [pic] c. [pic] d. [pic]
20) Statistics were calculated from data on the weights of 26 steel castings. The median weight was 311 kg and the standard deviation was 18.9 kg. Some statistics need to be converted to pounds. For the weights in pounds (1 lb = 0.454 kg), give
a. the median.
b. the variance.
21) Suppose that (-6,-5) is a point on the graph of a function f. Give another point on the graph of f if f is
a. even.
b. odd.
22) Is the function graphed at the right even, odd, or neither?
23) Is the function graphed at the right even, odd, or neither?
24) Is the function graphed below even, odd, or neither?
25) If g(x) = __3__, prove that g is an even function algebraically.
x2 + 1
Chapter 4 (Terms & Concepts to Know)
Roots (both fractional numerator of 1 and numerator other than 1)
Properties of powers (exponents)
Exponential growth and decay
Special situations (Doubling time, half-life, etc.)
Logs (changing between log and exponential forms)
Properties of logs
A = Pert
Solving exponential equations
Chapter 4 Final Exam Review Questions
26) Simplify 323/5 without using a calculator.
27) Simplify 7√x21y7 when x > 0 and y > 0, without using a calculator.
28) Simplify (8/125)-2/3 without using a calculator.
29) Solve for x to the nearest thousandth: 7x = 2.843.
30) Evaluate without a calculator: log464.
31) Use a calculator to evaluate log351 to the nearest thousandth.
32) For the function f, where f(x) = log4x, state
a. the domain.
b. the range.
c. an equation for any asymptote(s).
33) Iceland had a population of 251,000 at the end of 1990. Assume the population grows at a constant rate of 1.1%.
a. Write an equation which gives the population P of Iceland in terms of t, where t is the number of years after 1990.
b. Use your model to estimate the year the population will reach 275,000.
34) Match the equations with their graphs.
a. z(x) = log2x b. p(x) = -ln x c. k(x) = (0.7)x d. f(x) = 2x
i. ii.
iii. iv.
Chapter 5 (Terms & Concepts to Know)
Degrees to radians to revolutions
Arc Length
Area of Sectors
SOHCAHTOA
Tangent-Slope Theorem
UNIT CIRCLE!!!!!!! (where are cosine, sine and tangent + or -, exact values)
Properties and graphs of sine, cosine, tangent
Pythagorean Identity
Opposites
Supplements
Complements
Law of Cosines
Law of Sines
Chapter 5 Final Exam Review Questions
35) Give the value of sin 54o to the nearest thousandth.
36) Give the value of sin 0.7 to the nearest thousandth.
37) Give the exact value of cos (4∏/3).
38) Give the exact value of tan (3∏/4). C
39) For ΔABC, find m ................
................
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