2nd Semester Final Exam Review Graphing Calculator Allowed Name___________________________

High School Algebra

Part 1 – This part will be multiple choice on the Final Exam

1. Factor the following polynomial: 16 x4−20

2. Factor the following polynomial: x2−9 x+18

3. Factor the following polynomial: 4a2+a−5

4. Factor the following polynomial: x2−49

5. Factor the following polynomial: 4 a4−16

6. Factor the following polynomial: x2+9

7. Factor the following polynomial: x3+3x2+2 x+6

8. Using the following description of an unknown quadratic function, write a mathematical model (standard form).

A satellite antenna is facing toward the sky and is in the shape of a parabola. The antenna is positioned so that it has vertex at (2, -2) and x-intercepts at (0, 0) and (5, 0).

9. Perform the indicated operation on the given polynomials: (5x - 11) + (4x + 9)

10. Perform the indicated operation on the given polynomials: (3 x+7 )−(−9 x−17)

11. Perform the indicated operation on the given polynomials: ( x−1 )(2 x+8)

12. Perform the indicated operation on the given polynomials: (3a+6 )(−2a+4)

13. Perform the indicated operation on the given polynomials: (5b+12 )(10a−6)

14. Perform the indicated operation on the given polynomials: (−3 x ) (4 x−2 ) ( x+10 )

15. Solve the following equation: x2+41=77

16. Solve the following equation: −3 x2+21=0

17. Solve the following equation: 5 x2=5 x

18. Solve the following equation: x2−40=3 x

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19. Write the given equation in vertex form by completing the square: x2+7x−13= y

20. Simplify √−121

21. Perform the indicated operation: (−10+6 i )+¿)

22. Use the Quadratic Formula to solve the following function: 9a2+30a+25=0

23. Simplifyx7 y−2 z3

y−6 x z0

Part 2 – This part will be multiple choice on the Final Exam

24. What is the average rate of change over the interval from x=4 to x=7 given the graph below?

3 3.5 4 4.5 5 5.5 6 6.5 7 7.502468

10121416

24

8

14

25. Given the following table of values representing the distance traveled by a girl rolling down a hill. Time, t, is measured in seconds while the girl’s distance is measured in meters. What is the average rate of change of the distance over the interval from t=10 seconds to t=20 seconds?

t [sec] f(t) [m]3 | P a g e

5 110 315 920 2725 8130 243

In the next 6 questions, mark either a) true if the statement is a characteristic or mark b) false if the statement is NOT a characteristic of the following quadratic inequality:

y<5 ( x−3 )2−4

26. Vertex is a maximum 27. Vertex at (-3,4) 28. (3,0) is a solutiona) true a) true a) trueb) false b) false b) false

29. Shaded above 30. Graphed with solid line 31. (-2,-5) is a solutiona) true a) true a) trueb) false b) false b) false

32. Given the quadratic function, f ( x )=−x2+8 x−15 which has a zero at x=5, which of the following represents an accurately constructed graph of f (x)?

33. Given the same function as the previous question, f ( x )=−x2+8 x−15, determine a correct x-intercept and approximate extrema (estimate the maximum or minimum).

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-2 -1 0 1 2 3 4 5 6 7 8

-40

-30

-20

-10

0

10

20

30

40

50

60

ABCD

Use the following scenario to answer the next 3 questions:

In a given year, 28.5 million adults browsed the Internet personal advertisements and 17.4 million posted online personal ads. The bar graph shown below shows the amount spent, in millions of dollars, on online dating. Below are three mathematical models for the data shown as a graph. In each formula, D represents the amount spent on online dating in millions of dollars after x years.

0 1 2$0.00

$50.00$100.00$150.00$200.00$250.00$300.00$350.00$400.00$450.00$500.00

$220.00

$400.00$473.00

Dollars (in millions) spent on Dating during 3 consecutive years

Model I: D=−54 x2+234 x+220Model II: D=127 x+239Model III: D=236¿

34. Which mathematical model is the best fit to the graph in the last year shown in the graph?

35. What type of function is each model (linear, quadratic, exponential, cubic, etc.)?

36. Write a statement that can be supported using the given graph and models.

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Use the following scenario to answer the next 2 questions:This histogram shows the number of runs scored by 336 professional baseball players in 1996.

37. Describe the distribution (shape, center, and spread).

38. Estimate the balancing point.

Use the following scenario to answer the next 3 questions:Weather data were recorded for a sample of 25 American cities in one year. Variables measured included January high temperature (in degrees Fahrenheit), January low temperature (in degrees Fahrenheit), annual precipitation (in inches), and annual snow accumulation. The relationships for three pairs of variables are shown in the graphs below (Jan. Low Temperature—Graph A; Precipitation—Graph B; Annual Snow Accumulation—Graph C).

Graph A Graph B Graph C

39.

Which graph has the weakest relationship?

40. Which graph has a linear relationship?

41. If the least squares regression line for a set of data was y=32x+4 where y = May High Temperatures and x

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= May Low Temperatures, explain the meaning of 32 .

Use the following scenario to answer the next 4 questions:

The box plots below display the distributions of maximum speed for 145 roller coasters in the United States, separated by whether they are wooden coasters or steel coasters.

1201101009080706050403020

Wooden

Steel

Speed

Type

42. Which type of coaster, if any, has fewer observations?

43. Which type of coaster, if any, has a smaller percentage of coasters that go faster than 70 mph?

44. Which type of coaster, if any, has a higher percentage of coasters that go slower than 60 mph?

45. Which type of coaster, if any, has a data distribution with a smaller number of outliers?

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