Download Exam 2 with Answer Key - College Algebra I | MATH 112 and more Exams Algebra in PDF only on Docsity!
Exam Two, Sections 1.4, 2.1, 2.2, 2.3 and 2.4Math 112^ –^ College Algebra I
Tuesday, March 3, 2009
Name: Answer Key
- Beth owns a 1996 VW Passet TDI, Turbo Diesel Injection. The graph at the right shows the number of gallons of diesel fuel left starting with a full tank of gas then in the fuel tank after traveling x miles. a. (2pts) will the fuel tank hold. How many gallons of fuel
18.5 gallons
b. (3pts) Give answer in reduced fraction form and include units. Find the slope of the line.
8. 4505 " 1 " 8. 05 = " 415 gallons per mile
c. (3pts) Write a function !
G that gives an equation of the line.
!
G ( x ) = " 451 x + 1 8. 5
d. (3pts) Interpret the x - intercept in context of the problem.
Beth can travel about 830 miles on one tank of fuel.
Amount of diesel fuel left in the fuel tank, after traveling x miles
02
46
(^108) 1214
1618
20
(^0 100 200 300 400) Miles 500 600 700 800 900
Gallons !
- Beth is looking to replace her VW. She sees an advertisement for a^ Spring 2009Exam 2B-^2 Smart forfour Car that says that it can get 475 miles on a tank of gas. She finds that the car’s fuel capacity is 12.5 gallons. Beth also knows that the numbe of gas used. r of miles traveled is directly proportional to the gallons a. (3pts) Find the constant of proportionality. Show work to get credit for the problem.
m 475 = kg = k ( 12. 5 )
38 = k b. (2pts) Interpret the value found in part a, in context of the problem.
The smart car gets 38 miles per gallon.
- (2 pts each) For each statement below circle T if the statement is true and F if the statement is false. a. T F The equation of the vertical line that passes through the point !
(^) ( 5 ," (^2) )is !
x = 5. b. T F The equation !
(^4) ( x " (^6) ) = 4 x " 28 is an example of an identity. c. T F The function !
f (^) ( x ) = 5 x " 2 is a linear function. d. T F The data in the following table represents a constant linear function. x y - 52 05 25 45 e. T F The slope of a constant function is zero. f. T F The average rate of change of a linear function is constant. g. T F The data in the following table is exacly linear. x y - 52 05 25 45
Spring 2009Exam 2B-^4
- (4pts) Write a formula for a linear function f whose graph has slope 2 and passes through !
f ( x ) = 2 ( x + 5 ) + 3 or
f ( x ) = 2x + 13
- (5pts) Solve the linear equation symbolically. Give an exact answer.
!
4 x " 23 ( 15 " 2 x ) = 23 + ( x " 4 )
4x " 10 +^43 x =^23 + x " 4 3^ # $ % 4x " 10 +^43 x^ & ' ( = 3^ # $ %^23 + x " 4^ & ' ( 12x 16x "" 3030 += 43 xx =" 102 + 3x " 12 13x x = 20 = 20
- (5pts) Solve the linear inequality. Write the solution set in interval notation.^13
!
" 3 x + 7 # 7 ( x " 4 )
" " 3x 10 x + # (^7) (^) "# 357 x " 28 x $^72^ & ' ( "% ,^72 ) * +
- (4pts) g each equation or inequality. are shown in the figure at the right. SolveThe graphs of two linear functions f and
a. !
f ( x ) = g ( x )
x = 1
b. !
f ( x ) > g ( x )
x > 1 or
(^ 1, ")
f ( x )
g ( x )
- Lauren Prochaska, a BGSU basketball player, was the 2008 MAC Freshman of the Year. She broke^ Spring 2009Exam 2B-^5 BGSU’s record for most points scored by a freshman, by scoring 502 points last year. Below is a table that shows how many total points she has scored so far this year and the number of games she has played. Number of Games Total number of points scored ( x ) (^) ( y ) 433 1328 20212 28616 34620 44024 a. (4pts) answer. Find the least-squares regression line that models these data. Use 4 decimal places in your
y = 18.6831x – 16.
b. (2pts) Interpret the slope of the line in part a, in context of the problem.
Lauren scores about 19 points per game.
c. (3pts) she have more points at the end of the regular season then she did as a Assuming Lauren continues to score points at the same rate for the rest of the season, will freshman? During the regular season they will play 29 games. Explain your answer.
!
18.6831 ( (^) (^29) ) " 16. 9496 = 524. 86
Lauren should have 525 points at the end of the
regular season, which is more points than she scored last
season.
or
18.6831 18.6831xx " = 16.9496 518.949 = 6502 x^ =^ 27.
Lauren only needs 28 games to score more points this
year than she scored last year.
d. (2pts) Did your calculation in part c involve interpolation or extrapolation? Explain your answer.
The calculation in part c involved extrapolation because t played were not within the range of games played in the table.he 29 games
