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Math 1120 Final Exam Review: Exam Preparation, Exams of Mathematics

University of Missouri (MU) - ColumbiaMathematics

Review materials for the math 1120 final exam, including problems on logarithms, functions, systems of equations, and graphing inequalities. Students are encouraged to use this document to prepare for the exam by practicing solving problems and understanding concepts.

Typology: Exams

Pre 2010

Uploaded on 08/19/2009

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Math๎˜ƒ1120๎˜ƒFinal๎˜ƒExam๎˜ƒReview๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒDonna๎˜ƒStohr,๎˜ƒThe๎˜ƒLearning๎˜ƒCenter๎˜ƒ
May๎˜ƒ8,๎˜ƒ๎˜ƒ9โ€11am๎˜ƒand๎˜ƒ1โ€3pm๎˜ƒ
๎˜ƒ
1๎˜ƒ
๎˜ƒ
1. ๎˜ƒ24
3
7
77
x
x=๎˜ƒ
2.
()
6
log 2 4 1 1x+โˆ’=๎˜ƒ
3.
(
)
()()
2
ln 4 ln 2 ln 3
x
xxโˆ’โˆ’ += โˆ’๎˜ƒ
4. Solve๎˜ƒand๎˜ƒleave๎˜ƒyour๎˜ƒanswer๎˜ƒin๎˜ƒterm๎˜ƒof๎˜ƒ๎˜ƒln:๎˜ƒ๎˜ƒ
51
219
xโˆ’
=
๎˜ƒ
๎˜ƒ
5. This๎˜ƒtable๎˜ƒshows๎˜ƒthe๎˜ƒair๎˜ƒpressure๎˜ƒin๎˜ƒy๎˜ƒinches๎˜ƒof๎˜ƒmercury๎˜ƒx๎˜ƒmiles๎˜ƒfrom๎˜ƒthe๎˜ƒeye๎˜ƒof๎˜ƒa๎˜ƒhurricane.๎˜ƒ
x(mi)๎˜ƒ2๎˜ƒ ๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ4๎˜ƒ8๎˜ƒ15๎˜ƒ30๎˜ƒ100๎˜ƒ
y(in.๎˜ƒof๎˜ƒmercury)๎˜ƒ27.3๎˜ƒ27.7๎˜ƒ28.04 28.3๎˜ƒ28.7๎˜ƒ29.3๎˜ƒ
a) Make๎˜ƒa๎˜ƒscatterplot๎˜ƒof๎˜ƒthe๎˜ƒdata.๎˜ƒ
b) Find๎˜ƒa๎˜ƒfunction๎˜ƒ๎˜ƒf๎˜ƒ๎˜ƒthat๎˜ƒmodels๎˜ƒthe๎˜ƒdata.๎˜ƒ
c) Estimate๎˜ƒthe๎˜ƒair๎˜ƒpressure๎˜ƒat๎˜ƒ50๎˜ƒmiles.๎˜ƒ
๎˜ƒ
6. ๎˜ƒBetween๎˜ƒ1950๎˜ƒand1980๎˜ƒthe๎˜ƒuse๎˜ƒof๎˜ƒchemical๎˜ƒfertilizers๎˜ƒincreased.๎˜ƒ๎˜ƒThe๎˜ƒtable๎˜ƒlists๎˜ƒworldwide๎˜ƒ
average๎˜ƒusage๎˜ƒ๎˜ƒy๎˜ƒ๎˜ƒin๎˜ƒkilograms๎˜ƒper๎˜ƒhectare๎˜ƒof๎˜ƒcropland๎˜ƒduring๎˜ƒyear๎˜ƒ๎˜ƒx๎˜ƒ,๎˜ƒ๎˜ƒwhere๎˜ƒ0x=๎˜ƒcorresponds๎˜ƒ
to๎˜ƒ1950.๎˜ƒ๎˜ƒ(๎˜ƒ
()
1 hectare 2.47 acresโ‰ˆ๎˜ƒ๎˜ƒ
x๎˜ƒ0๎˜ƒ13๎˜ƒ22๎˜ƒ29๎˜ƒ
y๎˜ƒ12.4๎˜ƒ27.9๎˜ƒ54.3๎˜ƒ77.1๎˜ƒ
a) Graph๎˜ƒthe๎˜ƒdata.๎˜ƒ๎˜ƒAre๎˜ƒthe๎˜ƒdata๎˜ƒlinear?๎˜ƒ
b) Find๎˜ƒa๎˜ƒfunction๎˜ƒ๎˜ƒf๎˜ƒ๎˜ƒthat๎˜ƒmodels๎˜ƒthe๎˜ƒdata.๎˜ƒ
a) Predict๎˜ƒthe๎˜ƒchemical๎˜ƒfertilizer๎˜ƒusage๎˜ƒin๎˜ƒ1989.๎˜ƒ๎˜ƒThe๎˜ƒactual๎˜ƒvalue๎˜ƒwas๎˜ƒ98.7๎˜ƒkilograms๎˜ƒper๎˜ƒ
hectare.๎˜ƒ๎˜ƒWhat๎˜ƒdoes๎˜ƒthis๎˜ƒindicate๎˜ƒabout๎˜ƒusage๎˜ƒof๎˜ƒfertilizer๎˜ƒduring๎˜ƒthe๎˜ƒ1980s?๎˜ƒ
๎˜ƒ
7. Solve๎˜ƒthe๎˜ƒsystem:๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ
135
244
31 5
42 4
xy
xy
โˆ’=
โˆ’=โˆ’
๎˜ƒ๎˜ƒ
๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ
8. ๎˜ƒ๎˜ƒSolve๎˜ƒthe๎˜ƒsystem: 3315
4
x
y
xy
+=
โˆ’โˆ’ =โˆ’
๎˜ƒ
๎˜ƒ
9. ๎˜ƒSolve๎˜ƒthe๎˜ƒsystem:๎˜ƒ๎˜ƒ๎˜ƒ๎˜ƒ
61512
410 8
x
y
xy
โˆ’=
โˆ’+ =โˆ’
๎˜ƒ
๎˜ƒ
pf3

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Download Math 1120 Final Exam Review: Exam Preparation and more Exams Mathematics in PDF only on Docsity!

May 8, 9 โ€11am and 1 โ€3pm

2 4 3

x x

2. log 6 ( 2 x + 4 )โˆ’ 1 = 1

3. ln ( x^2 โˆ’ 4 ) โˆ’ ln ( x + 2 ) = ln 3( โˆ’ x )

Solve and leave your answer in term of ln:

25 x โˆ’^1 = 19

  1. This table shows the air pressure in y inches of mercury x miles from the eye of a hurricane.

x(mi) 2 4 8 15 30 100 y(in. of mercury) 27.3 27.7 28.04 28.3 28.7 29. a) Make a scatterplot of the data. b) Find a function f that models the data. c) Estimate the air pressure at 50 miles.

  1. Between 1950 and1980 the use of chemical fertilizers increased. The table lists worldwide average usage y in kilograms per hectare of cropland during year x , where x = 0 corresponds

to 1950. ( ( 1 hectare โ‰ˆ2.47 acres)

x 0 13 22 29 y 12.4 27.9 54.3 77. a) Graph the data. Are the data linear? b) Find a function f that models the data. a) Predict the chemical fertilizer usage in 1989. The actual value was 98.7 kilograms per hectare. What does this indicate about usage of fertilizer during the 1980s?

  1. Solve the system:

x y

x y

  1. Solve the system:

x y x y

  1. Solve the system:

x y x y

May 8, 9 โ€11am and 1 โ€3pm

  1. Solve by showing shaded regions on a graph:

x y x y

  1. Solve by showing shaded regions on a graph:

x y x y

  1. Find the maximum value of P = 3 x + 5 y subject to the following constraints: 3 8 3 8 0, 0

x y x y x y

13. The total number of cigarettes sold overseas in 1990 and 2000 was 10.9 trillion

cigarettes. The number sold in 2000 was 100 billion more than the number sold in 1990.

How many cigarettes were sold each year?

Key:

  1. x=1,3 2. x=16 3. x= 5/2 4. ln19^1 5ln 2 5

x = + 5. a) see graph below

b) f (^) ( x (^) ) = 26.97 + 0.506ln x c) About 28.95 in. of mercury 6. a) see graph below

b) f (^) ( x (^) ) = 12.42 1.066( ) x c) f (^) ( 39 ) โ‰ˆ 150 Chemical fertilizer use increased but at a slower rate than predicted by f. 7. (^) ( โˆ’5, โˆ’ (^5) ) 8. Inconsistent system, no solution

  1. Infinite solutions 10. See graph below. 11. See graph below 12. Maximum 6, graph below 13. 1990: 5.4 trillion 2000: 5.5 trillion