MATH 225 Final Exam Practice Problems.

Exam

Name



SHORTg ANSWER.g Writeg theg wordg org phraseg thatg bestg completesg eachg statementg org answersg theg question.

Providegthegmissingginformation.
1) Ingagrectangulargcoordinategsystem,gthegpointgwheregthegx-gandgy- 1) g

axesgmeetgisgcalledgthe .

2) Thegx-gandgy- 2) g

axesgdividegthegcoordinategplanegintogfourgregionsgcalled
.

3) Thegdistancegbetweengtwogdistinctgpointsg(x1,gy1)gandg(x2,gy2)gisggivengbygth 3) g

egformula .

4) Thegmidpointgofgtheglinegsegmentgwithgendpointsg(x1,gy1)gandg(x2,gy2)gisggivengb 4) g

ygthegformula .

5) A 5) g

togangequationgingthegvariablesgxgandgygisgangorderedgpairg(x,g
y)gthatgmakesgthegequationgagtruegstatement.

6) Angx-interceptgofgaggraphghasgagy-coordinate . 6)g


7) Agy-interceptgofgaggraphghasgangx-coordinategof . 7)g


8) Givengangequationgingthegvariablesgxgandgy,gfindgthegy- 8) g

interceptgbygsubstitutinggforgxgandgsolvinggfor .




1

,MULTIPLEg CHOICE.g Chooseg theg oneg alternativeg thatg bestg completesg theg statementg org answersg theg ques
tion.

Plotgthegpointgongagrectangulargcoordinategsystem. 9) g
9) A(2,g-5)
y y
A 6 6
5 5
4 4
3 A 3
2 2
1 1

-6g -5g -4g -3g -2g -1- 1g g 2g g 3g 5g g 6g -6g -5g -4g -3g -2g -1- 1g g 2 g g 3g g 4g 6g x
1 g4 x 1 g5

-2 -2
-3 -3
-4 -4
-5 -5
A) -6 B) -6
y y
6 6
5 5
4 4
3 3
2 2
1 1

-6g -5g -4g -3g -2g -1- 1g g 2 g g 3g 5g 6 g -6g -5g -4g -3g -2g -1- 1g g 2 g g 3g g 4g 6g x
g4 xgA g5
1 1
-2 -2
-3 -3
A
-4 -4
-5 -5
C) D)
-6 -6

Findgthegexactgdistancegbetweengthegpoints
. 10) g
10) (-9,g4)gandg(-5,g-6)
A) 2 29 B)g 200 C)g 116 D)g 10 2

Findgthegmidpointgofgtheglinegsegmentgwhosegendpointsgaregtheggivengpoints.
11) (5.3,g4.7)gandg(7.2,g-9.7) 11) g

A) (6.25,g7.2) B)g (5,g-1.25) C)g (6.25,g-2.5) D)g(-0.95,g7.2)


Findgthegexactgdistancegbetweengthegpoints
. 12) g
12) (g 5,g- 3)gandg(4g 5,g-7g 3) C)g 2 58 D)g 3 17
A) 6g 7 B)g 2 42




2

,Findgthegmidpointgofgtheglinegsegmentgwhosegendpointsgaregtheggivengpoint
s. 13) g
13) (3,g1)gandg(9,g4)
5 3
A) (12,g5) B) 6, C) -3, D) (-6,g3)
2 2

14) (-24.6,g38.1)gandg(-25.7,g-17.7) 14) g

A) (-25.15,g10.2) B)g (6.75,g-21.7) C)g (0.55,g27.9) D)g(-
25.15,g27.9)

15) (g 7,g- 3)gandg(6g 7,g-5g 3) 15) g


A) (7g 7,g-6g 3) B)g (5g 7,g- 5 7 7 7
4g 3) C) ,g-2 3 D) ,g-3 3
2 2

Determinegifgtheggivengpointsgformgthegverticesgofgagrightgtriangle
. 16) g
16) (-3,g5),g(-1,g3),gandg(-4,g0)
A) No B)g Yes


Determinegwhichgofgtheggivengpointsgaregsolutionsgtogtheggivengequation.
17) 2x2g+gyg=g4 17) g

I.g(3,g-14) II.g(-3,g14) III.g(-3,g-14)
A)g I B)g IgandgII C)g II D)g IgandgIII E)g III


18) |xg-g3|g-gyg=g2 18) g

I.g(1,g0) II. g1g,gg III.g(-5,g10)
3
4g g 4
A) II B)g IgandgIII C)g III D)g IgandgII E)g I


Identifygthegsetgofgvaluesgxgforgwhichgygwillgbegagrealgnumbe
r.
10 19) g

19) yg=g
xg+g7
10
A) {xg|gxg≠g10} B)g g xg|gxg≠ C)g {xg|gxg≠g-7} D)g {xg|gxg≠g7}
7


20) yg= xg- 20) g

8g|gxg≤g8}
A) {x B)g {xg|gxg>g8} C)g {xg|gxg≥g8}
D)g {xg|gxg<g8}




3

, Graphgthegequationgbygplottinggpoints.
21) xg=g|y|g-g5 21) g

A) B)

6 y 12 y
5 11
4 10
3 9
2 8
1 7
6
-10g-9g -8g -7g -6g -5g -4g -3g -2g -1-1
5
1g g 2g 4
x
3
-2
2
-3
1
-4
-5 -1
C) D) 1 2 3 4 5 6 7 8 9 1

6 y 2 y
5 1
4
-1-1
3
2 1g g 2g g 3g g 4g g 5g g 6 g g 7g g 8g g 9g 1
1 0g 11x
-2
-1 1g g 2g g 3g g 4g g 5g g 6g g 7g g 8g g 9g 10g 1 -3
1 12x -4
-2
-3 -5
-4 -6
-5 -7
-6 -8
-9




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