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Pre-Calculus Exam Review: Voltage Decay, Cooling Law, Polynomials, Rational Functions, Log, Exercises of Calculus

Kalinga Institute of Industrial TechnologyCalculus

A pre-calculus exam review covering various topics including voltage decay, newton's law of cooling, graphing parabolas, polynomials, rational functions, logarithmic equations, motor vehicle thefts trends, and graphing ellipses and hyperbolas.

Typology: Exercises

2012/2013

Uploaded on 02/06/2013

sasthi
sasthi ๐Ÿ‡ฎ๐Ÿ‡ณ

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Pre-Calc. 1st Semester Exam Review Name:________________________
1. The voltage of a certain conductor decreases over time according to the law of
uninhibited decay (
0kt
A Ae=
). The initial voltage of the conductor is 40 volts,
and 2 seconds later, the voltage is 10 volts.
a) Find k and determine the function that models the number of volts in the
conductor.
b) Determine the voltage after 5 seconds have elapsed.
c) Determine the time at which the voltage reaches .5 volts.
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Partial preview of the text

Download Pre-Calculus Exam Review: Voltage Decay, Cooling Law, Polynomials, Rational Functions, Log and more Exercises Calculus in PDF only on Docsity!

Pre-Calc. 1st^ _Semester Exam Review Name:_________________________

  1. The voltage of a certain conductor decreases over time according to the law of

uninhibited decay ( A = A e 0^ kt ). The initial voltage of the conductor is 40 volts, and 2 seconds later, the voltage is 10 volts.

a) Find k and determine the function that models the number of volts in the conductor.

b) Determine the voltage after 5 seconds have elapsed.

c) Determine the time at which the voltage reaches .5 volts.

  1. Water that has been removed from a stove to cool in a room obeys Newtonโ€™s Law of Cooling. At the moment that the water is removed from the stove, its temperature reads 212ยฐF (boiling). It is placed in a room which is maintained at a constant temperature of 68ยฐF. Ten minutes after the water is removed from the heat source, the temperature of the water reads 170ยฐF.

a) Determine the function models the temperature of the water at any time t.

b) Determine the temperature of the water 40 minutes after it was removed from the stove.

5. f ( x ) = 2 x^2 โˆ’ 12 x + 11

V( , ) Equation of axis of symmetry:

Circle one of the following: open up or open down

Circle one of the following: wide skinny or normal

In problem 6, graph the polynomial function and identify the requested characteristics.

6. f ( x ) = ( x โˆ’ 1 ) ( 4 x โˆ’ 2 ) ( 2 x + 3 )

a. Determine the domain of the function

b. Determine the x- and y- intercepts. Identify whether the function touches or crosses the x-axis at the x-intercepts.

c. Determine the end behavior

d. Graph the function using the information determined above

e. Check your graph using a graphing utility

f x x^ x x

= โˆ’^ โˆ’

a. Determine the domain of the function b. Write the function in lowest terms

c. Find the x- and y- intercepts d. Find the vertical asymptotes

e. Find the horizontal or oblique asymptotes

In problems 9-11, solve the given logarithmic equations. Be sure to exclude any extraneous solutions.

9. log 4 ( x + 3 ) + log 4 ( 2 โˆ’ x )= 1

10. log a x + log a ( x โˆ’ 2 ) = log a ( x + 4 )

11. log 2 ( x + 3 ) โˆ’ log 2 ( x โˆ’ 4 ) = 3

In problems 13 & 14, graph each ellipse. Identify the center, vertices of both axes, and foci.

x + y โˆ’

  • =

Center _______________________

Major Endpoints________________________

Minor Endpoints_________________

Foci______________________

  1. 25( x + 2)^2 + 4( y โˆ’ 3)^2 = 100

Center _______________________

Major Endpoints________________________

Minor Endpoints__________________

Foci_______________________

In problems 15 & 16, graph each hyperbola. Identify the center, vertices, and foci.

( 2) 2 ( 1)^2

x โˆ’ y + โˆ’ =

Center _______________________

Vertices_________________________________

Foci____________________________

Asymptotes _____________________

16. (^) 16( y + 2) 2 โˆ’ 9( x โˆ’ 1) 2 = โˆ’ 144

Center _______________________

Vertices____________________________

Foci____________________________

Asymptotes _____________________

  1. Use the graph of the function f given below to answer the following questions.

(a) f (0)= (b) f ( 6)โˆ’ =

(c) f (8)= (d) Is f ( 4)โˆ’ positive or negative?

(e) Is f^ (6)positive or negative? (f) For what numbers x is f ( ) x = 0?

(g) On what intervals for x is f ( ) x < 0? (h) What is the domain of f?

(i) What is the range of f? (j) What are the x -intercepts?

(k) What is the y -intercept? (l) For what values of x does f ( ) x = 1?

(m) On what intervals is f decreasing? (n) At what x does f have a local minimum?

(o) At what x does f have a local maximum?

  1. Write the equation of a line that is parallel to 2 ๐‘ฅ + 3๐‘ฆ = 2 and passes through the point (1,-3).
  2. Find the equation of a line perpendicular to a line that has a slope of 3 2

and that

contains the point (3,-1).

  1. Solve for x : (^) โˆš 2 ๐‘ฅ + 3 = (^) โˆš๐‘ฅ + 2 + 2