Algebra MATH 107Midterm Exam This exam is worth 100 points. Questions 1 - 10 are each worth 4 points; do not show your work. Questions 11 – 20 are each worth 6 points; show your work to earn full c

College Algebra MATH 107
Midterm Exam

This exam is worth 100 points. Questions 1 - 10 are each worth 4 points; do not show your work. Questions 11 – 20 are each worth 6 points; show your work to earn full credit.

Post only your Answer Sheet in the assignment folder. Write your answers on the answer sheet provided with this exam. Do not post this exam in the assignment folder.

Questions 1 – 10: Select the letter of the one alternative that best completes the statement or answers the question. Check that the answers are all letters (A, B, C, D, or E) and not a value.

1.) Determine the terms and degree of the polynomial. 4m5n4 – m4n6 – 8mn4 + 4

1. Terms: 4m5n4, - m4n6, - 8mn4, 4; degree: 6

2. Terms: 4m5n4, m4n6, 8mn4, 4; degree: 9

3. Terms: 4m5n4, - m4n6, - 8mn4, 4; degree: 10

4. Terms: 4m5n4, m4n6, 8mn4, 4; degree: 10

5. None of these

2.) Factor completely. 8a4b – 50b3

1. 1. 2b(2a2 + 5b)(2a2 - 5b)

   2. 2b(2a + 5b)2

   3. 2b(2a - 5b)2

   4. (4a + 10b)(2ab - 5b2)

   5. None of these

3.) Find the distance between the pair of points (-4, 8) and (-9, 15).
Give an exact answer and an approximation to two decimal places.

1. 1. , 8.60

   2. , 12.17

   3. , 3.46

   4. , 4.90

   5. None of these

4.) How can the graph of be obtained from the graph of ?

1. 1. Shift it horizontally -7 units to the left. Reflect it across the x-axis.

   2. Shift it horizontally 7 units to the left. Reflect it across the y-axis.

   3. Shift it horizontally 7 units to the right. Reflect it across the x-axis.

   4. Shift it horizontally 7 units to the left. Reflect it across the x-axis.

   5. None of these

5.) Given that , find .

1. 

2. 

3. 

4. 

5. None of these

6.) The points (, -2) and (8, 3) are the points at which a particular diameter of a circle intersects the circle. What are the coordinates of the center of the circle?

1. 1. 

   2. 

   3. 

   4. 

   5. None of these

7.) A graph of a function g is shown to the right. Find g(0).

A. 1

B. 0

C. 3.6536

D. -4.5

E. None of these

8.) Find a linear function, h,
given h(-6) = -32 and h(7) = 20.

1. 1. h(x) = -4x - 8

   2. h(x) = -4x + 8

   3. h(x) = 8x - 4

   4. h(x) = 4x - 48

   5. None of these

9.) For the piecewise function, find f(8).

1. 8

2. 37

3. -52

4. 7

5. None of these

10.) Determine the intervals on which the function (to the right) is increasing, decreasing, and constant.

1. 1. Increasing on (-∞, 4); Decreasing on (-4, ∞);
      Constant on (4, ∞)

   2. Increasing on (4, ∞); Decreasing on (-4, ∞);
      Constant on (-4, 4)

   3. Increasing on (4, ∞); Decreasing on (-∞, -4);
      Constant on (-4, 4)

   4. Increasing on (-∞, 4); Decreasing on (-∞, -4);
      Constant on (4, ∞)

   5. None of these

Questions 11 – 20: Leave answers in exact form unless otherwise directed to approximate the results. Write all fractions in lowest form. Round decimals to hundredths unless otherwise directed to round. Write answers using positive exponents. Simplify all radicals.

Short answers. You must show your work to earn full credit.

11.) The paired data below consist of the test scores of 6 randomly selected students and the number of hours they studied for a test. Below is a linear function that predicts a student's score as a function of the number of hours he or she studied. Use the regression line to predict a student’s score if the student studied for 7 hours.

Equation of the regression line: y = 67.30 + 1.07x

(Don’t forget: show your work/rounding/check the units.)

12.) A cross-country skier reaches the 10-km mark of a race 40 min after reaching the 3-km mark. Find and interpret the speed (average rate of change) of the skier in km per hr.

13.) Find the domain of the function . Write answer in set notation.

14.) The temperature T in degrees Fahrenheit t hours after 6 AM is given by
T(t) = - ½t2 + 8t + 3 for 0 ≤ t ≤ 12. Find T(12) and interpret the value.

15.) In order to earn an A in College Algebra, Lela must obtain an average score of at least 90. The course has five exams. On her first four exams, Lela scored 94, 83, 88, and 92. What possible scores does Lela need on the final exam to earn an A in College Algebra?

16.) Construct and simplify the difference quotient for f(x) = 7x + 9.

17.) Solve for n. n2 = 10n + 5

18.) Factor completely.

19.) Calculate.

20.) Simplify.