Pre-Algebra State Test 2008

7/31/2019 Pre-Algebra State Test 2008

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Pre-Algebra

2008

Sponsored by the Indiana Council of Teachers of Mathematics

Indiana State Mathematics Contest

This test was prepared by faculty at

Department of Mathematics and Computer Sciences

Indiana State University

ICTM Website

http://www.indianamath.org/

Do not open this test booklet until you have been advised by the test proctor.

Next years ICTM math contest date: April 25, 2009


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2008 Indiana State Mathematics Contest Pre-Algebra ICTM

Indiana State University Page 1 of 10 4/26/2008

1. One and twenty-eight hundredths is equal to

A. 1.128

B. 1.028

C. 1.28

D. 128.00

E. None of these

2. The median number in the data set { 0.3, 0.9, 0.18, 0.27, 0.081 } is:

A. 0.30

B. 0.9

C. 0.18

D. 0.27

E. 0.081

3. If0.01 0.5 1

, , and ,0.05 0.1 0.5

a b c= = = then:

A. a b c> >

B. b c a> >

C. c a b> >

D. a c b> >

E. None of the Above

4. In ,PQR angle Pcontains 60degrees and the bisectors of angles Qand Rmeet at T.

The number of degrees in angle QTRis:

A. 150

B. 120

C. 60

D. 90

E. None of these


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9. The average of a set of integers is 6. The sum of the integers is 18. The number ofintegers in the set is:

A. 3

B. 108

C. 12

D. 6

E. None of these

10. A class of 20 students averaged 66% on an examination; another class of 30students averaged 56% on the same examination. The average percentage for all 50students was:

A. 63

B. 62

C. 61

D. 60

E. 50

11. If A and Bare nonzero digits, the number of digits (not necessarily different) in thesum of 9876 32 1A B+ + is:

A. 4

B. 6

C. 7

D. 8

E. None of these

12. The approximate number of seconds in one year is:

A. 80,000

B. 500,000

C. 1,500,000

D. 3,000,000

E. 30,000,000


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13. Five students wrote a mathematics test. The average mark was 68. If the marks offour boys were 75, 62, 84, and 53, the mark of the fifth boy was:

A. 66

B. 68

C. 76

D. 56

E. None of these

14. How many positive factors of 36 are also multiples of 4?

A. 2

B. 3

C. 4

D. 5

E. 6

15. 90 + 91 + 92 + 93 + 94 + 95 + 96 + 97 + 98 + 99 = ?

A. 845

B. 895C. 945

D. 1025

E. 1045

16. A ream of paper containing 500 sheets is 5 cm thick. Approximately how manysheets of this type of paper would there be in a stack 7.5 cm high?

A. 256

B. 550

C. 667

D. 750

E. None of these


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17. If 2a = , the largest number in the set 224

3 ,4 , , ,1a a aa

is:

A. 3a

B. 4a

C.24

a

D. 2a

E. 1

18. A square and a triangle have equal perimeters. The lengths of the three sides of thetriangle are 6.2 cm, 8.3 cm, and 9.5 cm. The area of the square is, in cm2:

A. 24

B. 36

C. 68

D. 64

E. 144

19. If you walk for 45 minutes at a rate of 4 mph and then run for 30 minutes at a rate of10 mph, how many miles have you gone at the end of one hour and 15 minutes?

A. 3.5 miles

B. 7 miles

C. 9 miles

D. 480 miles

E. None of these

20. The difference between a 6.5% sales tax and a 6% sales tax on an item priced at$200 before tax is:

A. $0.10

B. $1.00

C. $5.00

D. $10.00

E. None of these


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21. The ratio of boys to girls in a class is 2:3. If there are 30 students in the class, howmany more girls than boys are in the class?

A. 18

B. 12

C. 9

D. 6

E. None of these

22. If the radius of a circle is decreased by 10%, then the circumference of the circle isdecreased by:

A. 1%

B. 10%

C. 20%

D. 21%

E. 40%

23. A contest began at noon one day and ended 1000 minutes later. At what time did thecontest end?

A. 10:00 p.m.

B. Midnight

C. 2:30 a.m.

D. 4:40 a.m.

E. None of these

24. If ,2

A BA B

+ = then ( )30 50 80 is:

A. 60

B. 80

C. 120

D. 160

E. None of these


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25. The three numbers 1, 2, and 3 can be used to form a three-digit number such as 231.The number of these three-digit numbers that are divisible by 3 is:

A. 2

B. 1

C. 6

D. 4

E. 0

26. The smallest product one could obtain by multiplying two numbers in the set

{ }7, 5, 1,1, 3

is:

A. -35

B. -21

C. -15

D. -1

E. None of these

27. The difference between the lowest common multiple and greatest common divisor ofthe numbers 5, 10, and 35 is:

A. 1745

B. 35

C. 65

D. 5

E. None of these

28. Rearranging the digits of the number 579 produces different numbers. The sum of allsuch numbers, including 579, is:

A. 4662

B. 4065

C. 3705

D. 3687

E. None of these


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29. If1 2

2 3 5x=

+, then

1

2 1x=

+

A. 2

B.3

2

C.2

3

D.1

2

E.8

5

30. If , , and 9 ,a a a d + (where 0d > ) are the angles of a right-angled triangle, then the

ratio a:dis:

A. 4:1

B. 8:1

C. 20:21

D. 9:1

E. None of these

31. The side, front, and bottom face of a rectangular cube have areas of22 , 2y, and ,x xy cm respectively. The volume of the cube, in cm3, is:

A. xy

B. 2xy

C. x2y2

D. 4xy

E. None of these

32. The area of a circle is 29 cm . The diameter of this circle is, in cm:

A. 3

B. 6

C. 9

D. 3/2

E. None of these


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33. If the area of a square is 36, then the circumference of its inscribed circle is:

A. 36

B. 6

C. 9

D. 12

E. None of these

34. If the radius of the circle is increased by 100%, the area is increased by:

A. 100%

B. 200%

C. 300%

D. 400%

E. None of these

35. Two circles have diameters PSand QR. If PS = 2QR, then the ratio of their areas is:

A. 9:1

B. 4:1

C. 3:1

D. 2:1

E. None of these

36. If the distance between consecutive fence posts is 5 meters, the number of postsneeded to build a fence around a triangular region with sides 20m, 20m, and 30m is:

A. 15

B. 12

C. 14

D. 16

E. None of these


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37. A number which is a multiple of 15, but not a multiple of 18 is:

A. 180

B. 320

C. 360

D. 420

E. 540

38. The smallest value of kso that 75kis a perfect square is:

A. 3

B. 6

C. 9

D. 10

E. 5

39. Henry has $240 more than my cousin Joe, who has $150 more than my friend Ann.Together the three people have $990. The amount Ann has, in dollars, is:

A. $150

B. $200

C. $390

D. $450

E. $600

40. A sequence is 1, 2, 5, 10, 17, . A possible eighth number in this sequence is:

A. 24

B. 26C. 37

D. 50

E. 65

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Pre-Algebra State Test 2008