MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01C3791A.E155E800" This document is a Web archive file. If you are seeing this message, this means your browser or editor doesn't support Web archive files. For more information on the Web archive format, go to http://officeupdate.microsoft.com/office/webarchive.htm ------=_NextPart_01C3791A.E155E800 Content-Location: file:///C:/A51BA2D4/2003contest.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" HSMC Problems 2001

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UNCW HIGH SCHOOL

MATH CONTEST

 

Department of Mathemat= ics and Statistics

 

April 2, 2003<= /h4>

 

Scoring

 <= /span>

Each question answered correctly scores 4 points.

Each question left blank scores 1 point.

Each question answered incorrectly scores 0 points.
 
 

 

 

 

 

 

 

 

 

 

 

 


High School Mathematics Contest Spring 2003

 

 

1.<= /o:p>

Determine the formula for the inverse function of

 = ;

 

A)

B)

C)

D)

E)

 

 

2.<= /o:p>

Determine the solution of the inequality.

 

 

A)

 

B)

 

C)

 

D)

 

E)

 

 

3.<= /o:p>

If the wid= th of a particular rectangle is tripled and the length is increased by four, then= the area is quadrupled.  Determi= ne the length of the rectangle.

 

A)

4

B)

6

C)

8

D)

10

E)

12

 

 

4.<= /o:p>

Determine = the largest integer m such that <= sub> divides <= sub>.

 

A)

0

B)

2

C)

4

D)

6

E)

8

 

 

5.<= /o:p>

Let <= !--[if gte vml 1]>  and = .  Determi= ne the value that  approache= s as n approaches infinity.

 

A)

B)

C)

4

D)

E)

 

 

6.<= /o:p>

Suppose th= at 1 and 3 are roots of  and that = .  Determi= ne the value of a.=

 

A)

B)

C)

D)

E)

4

 

 

 

 

 

 

7.<= /o:p>

Given that=  and = , determine the value of .

 

A)

-1

B)

C)

0

D)

E)

1

 

 

8.<= /o:p>

Suppose th= at 4 cards colored red, green, blue and yellow are randomly placed into 4 boxes, one= in each box, also colored red, green, blue and yellow.  Determine the probability that at least one card is placed into a box of the same color.<= /p>

 

A)

2/3

B)

5/8

C)

7/12

D)

1/2

E)

7/16

 

 

9.<= /o:p>

Given that= , determine the average of the roots of .

 

A)

-3

B)

-1

C)

0

D)

1

E)

3

 

 

10.=

Suppose th= at f is a function with  and that =  for all integers x and y.  Determine the value of .

 

A)

-7

B)

-5

C)

-3

D)

-2

E)

-1

 

 

11.=

The winner of a contest can choose any 8 of 15 pri= zes.  Determine the number of differen= t sets of prizes that can be chosen.

 

 

A)

8

 

B)

715

 

C)

6435

 

D)

32432400

 

E)

259459200

 

 

12.=

You receive 10 cents on the first day of the year, 12 cents on the second day, 14 cents on the third day, and so on.  Determine how much you will rece= ive on the 365th day.

 = ;

 

A)

$7.38

B)

$7.40

C)

$36.50

D)

$43.78

E)

$43.80

 

 

13.=

The sum of two numbers is 1, and their product is 1.=   Find the sum of their cubes.

 

A)

-2

B)

-1

C)

D)

E)

1

 

 

 

14.=

A line seg= ment drawn from a vertex of a unit square to a point on the square as shown in= the picture forms 2 regions.  Th= e area of the smaller region is one-sixth of the area of the larger region.  Determine the length of that line segment.

B)

C)

D)

E)

 

 

15.=

The counting numbers are listed in the triangular ar= ray of rows as shown below.  Determ= ine the row number in which 2003 appears.

1

2  3  4

5  6  7  8  9

10 11 12 13 14 15 16

17 18 19 20 21 22 23 24 25

 = ;

 

A)

44

B)

45

C)

46

D)

1001

E)

1002

 

 

16.=

A regular pentagon is inscribed in a circle.  Each side of the pentagon is 3.5 inches long.  Determine the = radius of the circle, rounded to the nearest hundredth.

 = ;

 

A)

2.47  &nbs= p; 

B)

2.98

C)

3.5

D)

4.11

E)

6.67

 

 

17.=

Given that , find the value of .

 = ;

 

A)

–3

B)

C)

0

D)

E)

3

 

 

 

18.=

The heat index measures the contribution humidity ma= kes to high temperatures in reducing the body’s ability to cool itself.  Heat escapes from the body partly through the evaporation of sweat.  Humidity in the air slows evaporation, so it feels hotter. From the table below, determine the least amount of humidity for which a temperatu= re under  will feel= over.

 

       &nbs= p;            &= nbsp;       

&nbs= p;

&nbs= p;

Air Temp in degrees Fahrenheit

80

85

90

95

100<= /o:p>

&nbs= p;

&nbs= p;

 

 

 

 

 

H

U

M

I

D

I

T

Y

30%<= /o:p>

40%<= /o:p>

50%<= /o:p>

60%<= /o:p>

70%<= /o:p>

80%<= /o:p>

90%<= /o:p>

100%=

78

79

81

85

85

86

88

91

84

86

88

90

93

97

102

108

90

93

96

100

106

113

122

96

101

107

114

124

136

104

110

120

132

144

 

       &nbs= p;            &= nbsp;       How hot it seems

 

 = ;

 

A)

30

B)

40

C)

50

D)

60

E)

70

 

 

19.=

Determine the number of ways a set of identical= tiles can cover a  rectangle= .

 

A)

8

B)

13

C)

21

D)

34

E)

49

 

 

20.=

Given that= the point  is on the= graph of, determine the corresponding point on the graph of the transformed function.

 

A)

(-2,-11)

B)

(12,-13)

C)

(12,-7)

D)

(4,-13)

E)

(0,-13)

 

 

21.=

The weight M of an= object on Mars varies directly as its weight E on Earth.  A person who weighs 95 pounds on= Earth weighs 38 pounds on Mars.  H= ow much would a 160 pound person weigh on Mars?

 = ;

 

A)

50

B)

64

C)

103

D)

120

E)

217

 

 

 

 

 

 

 

22.=

At Sweetie’s= Snacks, caramel corn worth $2.50 per pound is mixed with chocolate covered almond= s worth $7.50 per pound in order to get 20 pounds of a mixture worth $4.50 per po= und. Determine the number of pounds of almonds that are used.

 = ;

 

A)

3

B)

5

C)

8

D)

12

E)

16

 

 

23.=

Write as an expression containing a single radical.

 

A)

 

B)

 

C)

 

D)

 

E)

 

 

24.=

Three solutions of the equation  are = and . Determine the sum

 

A)

-1

B)

0

C)

3

D)

12

E)

14

 

 

25.=

Determine whether the graph of  is symmet= ric to the x-axis, the y-axis and/or the origin.

 

A)

x-axis a= nd the origin

 

B)

y-axis a= nd the origin

 

C)

the origin

 

D)

x –= ;axis and y-axis<= /p>

 

E)

x-axis, = y-axis and the origin

 

 

26.=

At the beginning of the year, $3500 was deposited in= a savings account earning interest compounded once a year.  One year later, another $4000 was deposited in another account earning interest also compounded once a year= .  The interest rate was the same f= or both accounts.  At the end o= f the second year, there was a total of $8518.35 in the accounts.  Determine the annual interest ra= te.

 

A)

6%

B)

7%

C)

8%

D)

9%

E)

10%

 

 

 

27.=

Simplify the expression .

 = ;

 

A)

B)

C)

D)

E)

 

 

28.=

A parallelogram has sides of length 15.4 and 9.8.  Its area is 72.9.  Find the measure of the smaller = angle.  Round your answer to the ne= arest tenth of a degree.

 

A)

12.2  &nbs= p; 

B)

25.7

C)

28.9

D)

61.1

E)

64.2

 

 

29.=

A vertical antenna is mounted atop a 50 foot pole.  From a point on the level ground= 75 feet from the base of the pole, the antenna subtends an angle of 10.5 degrees.  Determine the leng= th of the antenna.  Round your ans= wer to the nearest foot.

 is equal = to the area of , find the length of .