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Algebra II Test
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Algebra II Test
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25 Questions

1. The formula for estimating the number, N, of a certain product sold is N = 7400 In(7t + 3), where t is the number of years after the product is introduced. What is the expected number of sales 7 years after the product is introduced? Round to the nearest whole number.

2. Simplify.

(-3x + 8)/(x² - 49) - (-2x + 1)/(x² - 49)

3. For the function, use synthetic division and substitution to determine whether the given value is a zero of the function.

P(x) = 3x⁴ - 10x³ - 41x² + 68x + 60

4. The two hyperbolas in the graph are conjugates, meaning they share the same asymptotes. Given the following equation of the hyperbola represented by the thin curve, find the equation of its conjugate, which is represented by the thick curve. (Evernote)

x²/9 - y²/25 = 1

5. Identify the conic section produced by the intersection of the plane and the cones in the following diagram.

6. Write a proportion that models the statement 10 is to 5 as 16 is to 8.

7. Solve the equation for x. Write the exact solution and the approximate solution to the nearest hundredth, when appropriate.

In(8x - 6) = 3

8. Find the minimum and maximum values, quartiles, range, and interquartile range for the data set.

29, 14, 40, 12, 16, 46, 22, 23, 19, 31, 7, 9

9. How many different arrangements can be made using all of the letters in the word GAME?

10. Use the Law of Cosines to solve for 'A' to the nearest tenth of a degree. (Evernote)

11. Write an equation in slope-intercept form of the line that passes through (- 5, 4) and is parallel to the graph of y = -4x + 1.

12. Find tan 382°.

13. Solve the system of equations by substitution.

{3x + 4y = 32
{3x + y = 17

14. Find the real zeros of the function. Give approximate values to the nearest hundredth , if necessary.

f(x) = x⁴ - x³ - 16x² + 10x + 60

15. Evaluate the expression. (3/8)⁻²

16. Show that the function is a quadratic function by writing it in the form f(x) = ax² + bx + c and indentifying a, b and c.

f(x) = (5x - 4) (5x + 3)

17. Find the sum of the infinite geometric series, if it exists.
(Evernote)

∑3(-½)^(k-1)

18. Solve log₃(x+4) - log₃(x-4) = log₃5 for x

19. Find
[1 17 14][11 3]
[19 7]
[9 5]

20. Using the given information, which data set is the correct choice? (Evernote)

21. If f(x) = 9 - x² and g(x) = 3 - x, which is the rule of function (f × g)(x)?

22. Solve for x.

x-7=1

23. Classify the polynomial by degree and number of terms. Describe the shape of its graph. 3x³

24. Which equation describes a parabola?

25. A hat contains 22 names, 10 of which are female. If five names are randomly drawn from the hat, what is the probability that at least four female names are drawn?

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