MCS Dept

Exam

If you are planning to take calculus at Skidmore (immediately or eventually), please fill out the following information and take the exam below. The department will use this information and your responses on the exam solely to help place you in the course which is best for you.

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1
How much calculus, if any, have you studied prior to arriving at Skidmore?
 
2
Did you take the AP Exam in Calculus?
3
If yes, which exam?
Score

Part 1

If you have studied no calculus, then please take Part 1 of the exam. If you have studied calculus, please take both Parts 1 and 2. DO NOT USE TEXTBOOKS. DO NOT CONSULT WITH ANYONE, AND DO NOT USE A CALCULATOR (even if your course allowed or required you to use calculators).

4
If f(x) = x2, then f(x+3) =

5
If α is an angle in a right triangle and sin(α) = 12/13, then cos(α) =

6 Write tan2(α) sec(α) in terms of sin(α) and cos(α)

7
If f(t) = 2cos( π t)+1, then f(3) =

8
If x+y = 6 and 4x-3y = 10, then x is

9

Simplify:  


10
Simplify:

11
Combine into a single fraction:

12
The equation of the line through the points (2,4) and (5,13) is

13
The graph of the equation x2 + 4y2 = 4 represents

14
Solve for x :  x2 = x + 6

15
If y = log2(1/16), then y =

16
If f(t) = Ce3t and f(0) = 100, then C is

17
Solve for x :   e4x– 7 = 0 (ln means log with base e )

Part 2

If you have studied no calculus, do not continue. Go to the bottom and press the submit button.
18
Evaluate:

19
Evaluate:

20
Evaluate:

21
Evaluate:

22
The equation of the line tangent to the curve y = 2x3 at the point where x = 1 is

23
The minimum value of y = x4– 2x2 + 5 is

24
Find the area in the first quadrant below the curve y = x2 + 1 to the left of the line x = 1.

25
Evaluate ∫ x cos(x2 + 1)dx

26
Evaluate:    (ln means log with base e )

27 Evaluate:

28 The infinite series is

29 The radius of convergence of the power series is

30 The first three terms of the Taylor series about 0 (i.e. Maclaurin series) of are

   
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