ALEKS Worksheet #1 - 05/15/2014 6:46 PM -Copyright © 2014 UC Regents and ALEKS Corporation. P. 1/4

Worksheet

Student Utd 05-15-13-37 - Worksheet #1 - 05/15/2014 6:46 PM

Preparation for Calculus / Learning – F 2014 (Placement)

Review Questions:

1. Graph the rational function

.

To graph the function, draw the asymptotes (ifany) and plot at least two points on each piece ofthe graph.

2.

Graph the function .

3. The one-to-one functions and are defined as follows.

Find the following.

ALEKS Worksheet #1 - 05/15/2014 6:46 PM -Copyright © 2014 UC Regents and ALEKS Corporation. P. 2/4

4. The mass of a radioactive substance follows a

continuous exponential decay model, with a

decay rate parameter of per day. Find the

half-life of this substance (that is, the time it takes for one-half the original amount in a given sampleof this substance to decay).

Note: This is a continuous exponential decay

model.

Do not round any intermediate computations, andround your answer to the nearest hundredth.

5. Graph the following function.

6. Solve for .

Write the exact answer using base-10 logarithms.

7. Suppose that the function is defined on the

interval as follows.

Graph the function .

8. Find all solutions to the equation.

Write your answer in radians in terms of .

Example: , or

,

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9.

For the real-valued functions and

, find the composition and

specify its domain using interval notation.

Domain of :

10.

Graph the function .

11. Graph the circle.

12. Simplify the expression.

Write your answer without using negative exponents.Assume that all variables are positive real numbers.

13. Let be an angle in quadrant such that

.

Find the exact values of and .

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Figure 1

Figure 2

14. A manufacturer cuts squares from the corners of a rectangular piece

of sheet metal that measures centimeters by centimeters (see

Figure 1). The manufacturer then folds the metal upward to make an

open-topped box (see Figure 2). Letting represent the side-lengths

(in centimeters) of the squares, use a graphing calculator to find the

value of that maximizes the volume enclosed by this box. Then

give the maximum volume. Round your responses to two decimalplaces.

15. Solve for .

16. Suppose that is invested at an interest

rate of per year, compounded

continuously. After how many years will the initial investment be doubled?

Do not round any intermediate computations,and round your answer to the nearest hundredth.