Algebra 2 Midterm Exam
Name: _________________________
Score: ______ / ______
Answer the questions below. Make sure to show your work when applicable
| _____1. | Simplify.
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___2. Find a quadratic function to model the values in the table. Predict the value of y for x = 6.
| X | y |
| 1 | 2 |
| 0 | 2 |
| 3 | -10 |
| A. y = -2×2 + 2x -2; –58 | |
| B. y = 2×2 – 2x -2; 60 | |
| C. y = 2×2 – 2x -2; 58 | |
| D. y = -2×2 + 2x +2; –58 |
| _____3. | A manufacturer of shipping boxes has a box shaped like a cube. The side length is 5a + 4b. What is the volume of the box in terms of a and b?
A. B. C. D.
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___4. If a function, f(x) is shifted to the left four units, what function represents the transformation?
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5. Solve the problem by writing an inequality. A club decides to sell T-shirts for $12 as a fund-raiser. It costs $20 plus $8 per T-shirt to make the T-shirts. Write and solve an equation to find how many T-shirts the club needs to make and sell in order to profit at least $100.
A.
B.
C.
D.
Short Answer: Type your answer in the space below each question. Show your work when applicable.
6. The velocity of sound in air is given by the equation , where v is the velocity in meters per second and t is the temperature in degrees Celsius. Find the temperature when the velocity is 329 meters per second by graphing the equation. Round the answer to the nearest degree
7. The volume in cubic feet of a box can be expressed as , or as the product of three linear factors with integer coefficients. The width of the box is 2 – x. Factor the polynomial to find linear expressions for the height and the length
8. What is the solution to the equation
9. Solve the equation. Check for extraneous solutions. Type your answers in the blanks.
x = _____ or _____
10. Write an expression for the volume of a cylinder with a height 7in. greater than the radius.
11. What is the value of log81 3?
a. 3
b.¼
c. 4
d. 1/3
12. In an experiment, a petri dish with a colony of bacteria is exposed to cold temperatures and then warmed again.
| Time (hours) | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| Population (1000s) | 5.1 | 3.03 | 1.72 | 1.17 | 1.38 | 2.35 | 4.08 |
| a. | Find a quadratic model for the data in the table. Type your answer below.
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| b. Use the model to estimate the population of bacteria at 9 hours. Type your answer below. | |
____. 13. Evaluate the expression for the given value of the variable(s).
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______14. Find a quadratic model for the set of values. (–2, –20), (0, –4), (4, –20)
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15. Simplify the expression. Type your answer in the blank.
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16. Suppose you cut a small square from a square of fabric as shown in the diagram. Write an expression for the remaining shaded area. Factor the expression. Type your answer below.
17. Solve for x. State any restrictions on the variables.
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18. Is the relation {(3, 5), (–4, 5), (–5, 0), (1, 1), (4, 0)} a function? Explain. Type your answer below.
____19.
a. c.
b. d.
_____20. Consider the leading term of the polynomial function. What is the end behavior of the graph?
-3×5 + 9×4 + 5×3 + 3
a. The leading term is -3×5. Since n is odd and a is negative the end behavior is up and up
b. The leading term is -3×5. Since n is odd and a is negative the end behavior is down and down
c. The leading term is -3×5. Since n is odd and a is negative the end behavior is up and down
d. The leading term is -3×5. Since n is odd and a is negative the end behavior is down and up
