the university interscholastic league number sense test hs

The University Interscholastic LeagueNumber Sense Test HS Invitational A 2010ì ì

Final ______ ______

Contestant's Number ___________ ______ ______2nd

______ ______1stRead directions carefully DO NOT UNFOLD THIS SHEET Score Initialsbefore beginning test UNTIL TOLD TO BEGIN

Directions: Do not turn this page until the person conducting this test gives the signal to begin. This is a ten-minute test. There are80 problems. Solve accurately and quickly as many as you can in the order in which they appear. ALL PROBLEMS ARE TO BESOLVED MENTALLY. Make no calculations with paper and pencil. Write only the answer in the space provided at the end ofeach problem. Problems marked with a ( * ) require approximate integral answers; any answer to a starred problem that is withinfive percent of the exact answer will be scored correct; all other problems require exact answers.

The person conducting this contest should explain these di rections to the contestants.

STOP -- WAIT FOR SIGNAL!

(1) 210 21 2010 = _______________________ q

(2) = ________________________________3 48 9‚

(3) $20.10 3 = $ __________________________ƒ

(4) 2.01 2 21 = ________________ (decimal)q 110

(5) .3 = ________________________________49 ƒ

(6) 44 % __________________ (proper fraction) =

(7) 9 6 3 6 9 = _______________________‚ ƒ q

(8) 34 43 = ________________________________‚

(9) 63 15 82 15 = ______________________‚ q ‚

*(10) 753 936 842 = ________________________q

(11) 17 = ___________________________________2

(12) If 8 ounces of M&M's costs $1.10 then 112 pounds of M&M's will cost $_______________

(13) The GCD of 48 and 57 is ___________________

(14) (58 79 66) 4 has a remainder of _______ ƒ

(15) 2 bushels is equivalent to ____________ pecks12

(16) The median of 1, 5, 2, 3, 3, 2, 1, & 4 is ________

(17) The greatest prime number less than 99 is ____

(18) 11 = ___________________________________3

(19) MMX V = _____________ (Arabic Numeral)ƒ

*(20) 1243 3421 = _________________________È ‚

(21) 66% of 44 is 22% of ______________________

(22) Which of the following is both a composite number and an evil number, 4, 9, or 11? _____

(23) 235 14 = _______________________________‚

(24) 48 has _____________ positive integral divisors

(25) 10 plus x is the same as tripling x. x = _______

(26) Let k = 7 5 . Truncate k to two decimalÈ È places. __________________________(decimal)

(27) .333... .1666... .08333... = ______________q

(28) (26 24 22) 7 has a remainder of _______‚ q ƒ

(29) 25836k is divisible by 6. Find k 0. _________

*(30) 30456 141 = ___________________________ƒ

(31) If set A has 6 elements, A B has 3, and A B has 9, then set B has ______________ elements.

(32) 2 1 3 4 7 ... 47 = _____________

(33) 6 1 5 2 4 3 = _________¸ ¸ ¸ ¸ ¸ ¸q q q q q

(34) = _____________È È È125 20 x . Find x.

(35) The discriminant of 6x 7x 2 = 0 is _____ 2

(36) Picture A is 8" by 10" and B is 9" by 12". The ratio of A's perimeter to B's perimeter is _____

(37) Find k if 67 59 = 16k. k = ____________ 2 2q

(38) 5 5 20 4 = ________________________‚ x ‚ x

(39) 7 7 = ________________ (mixed number)4 59 9‚

*(40) 400 log 800 = _____________________________

(41) (13) (8)(21) = _________________________2 q

(42) 38 11 33 24 = ______________________‚ ‚

(43) If x y = 1 and xy = 2 then x y = _____ q 3 3

(44) The x-intercept of the line 3x 4y = 5 isq (h, k). Find h. ____________________________

(45) The product of the roots of x 2x 9x 8 = 0 is ____________ 4 3 2 q q 2x

(46) 7 2220 59 = __________________________q

(47) The arithmetic mean of 17, 22, and 25 is ______

(48) Given 1690 26 = 65. Find 1690 5 . ______ƒ ƒ 15

(49) 25 °C = °F__________________________

*(50) 833 2.5 = _________________________‚ ƒ 512

(51) The odds of drawing an ace from a standard 52 card deck is _____________________________

(52) The legs of a right are 8 and 15. The length˜ of the altitude to the hypotenuse is __________

(53) A convex octagon has ______ distinct diagonals

(54) 123 45 = __________________________ 6 6 6 q

(55) (2 5i) (2 5i) = (a bi). Find a. __________q q

(56) If log 7x 4) = 5 then x = _______________2(

(57) The set {e,m,p,t,y} has ____ 3 element subsetsq

(58) 8 intersecting lines create at most ____ regions

(59) 7 6 5 4 ... 1 = ____________ 2 2 2 2q q

*(60) 8 4 2 = ______________________ 3 6 10ƒ ‚

(61) (66 )(77 ) 8 has a remainder of __________9 9 ƒ

(62) If log log 8 = 1 then x = ______________5 5x q

(63) If A is of B and B is 60% of C then A is what23

fractional part of C? _______ (proper fraction)

(64) How many ways can Larry, Mo, and Curly sit in a row of five chairs? ____________________

(65) The greatest integer function g(x) = 3 2x[ ]q

has a value of ___________________ for g(1)

(66) 2 3 4 x(mod 5) & 0 x 4. x = ___x x x z Ÿ Ÿ

(67) 12544 = ______________________________È (68) 2 sin 105 ° 105 ° = _____________________ cos

(69) 3 4 7 11 18 29 ... 123 = ______

*(70) The area of 40x 45y = 1800 is ___________2 2

(71) If f(x) = , then f ( 1) = ____________5 23

x 4x

q

w

q

(72) 1(1 ) 2(2 ) 3(3 ) ... 6(6 ) = __________x x x x

(73) Let f(x) = 3 4x be a real valued function,È q where x {Reals}. The domain of f(x) is− { x| x _________________________________}Ÿ

(74) x dx = __________________________' 0

1 È

(75) If h(x) is the slant asymptote of

f(x) = ____________x x 1x

2q q3

3 , then h(1) = __

(76) If f(x) = x x x, then f ( 3) = ________4 2 q q ww

(77) If csc = 1.2 then sin = __________________) )

(78) = _________________________lim x 0Ä

Š ‹sin 3xx

(79) f(x) = 5x 6 and g(x) = 3x 4. f(g(2)) = _____q q

*(80) 6666 feet/second = ______________ miles/hour

University Interscholastic League - Number Sense Answer Key HS Invitation A 2010ì ì*number) x y means an integer between x and y inclusiveNOTE: If an answer is of the type like it cannot be written as a repeating decimal2

3

(1) 1779q

(2) 16

(3) $6.70

(4) 20.91

(5) , 140 1327 27

(6) 1125

(7) 21

(8) 1462

(9) 285q

*(10) 627 691q

(11) 289

(12) $3.30

(13) 3

(14) 3

(15) 10

(16) 2.5, 25 12 2,

(17) 97

(18) 1331

(19) 402

*(20) 114581 126642q

(21) 132

(22) 9

(23) 3290

(24) 10

(25) 5

(26) 4.88

(27) .25, 14

(28) 0

(29) 6

*(30) 206 226q

(31) 6

(32) 122

(33) 9

(34) 245

(35) 1

(36) 67

(37) 63

(38) 1080

(39) 562081

*(40) 1104 1219q

(41) 1

(42) 1210

(43) 5

(44) 15 23 3,

(45) 8

(46) q 271180

(47) 2164 13 3,

(48) 325

(49) 77

*(50) 4749 5247q

(51) 112

(52) , 7120 117 17

(53) 20

(54) 34

(55) 21q

(56) 4

(57) 10

(58) 37

(59) 28

*(60) 122 134q

(61) 0

(62) 40

(63) 25

(64) 60

(65) 4q

(66) 2

(67) 112

(68) .5, q q 12

(69) 318

*(70) 127 139q

(71) 23

(72) 5039

(73) .75, 34

(74) 23

(75) 1

(76) 110

(77) 56

(78) 3

(79) 4

*(80) 4318 4772q

10A-1 = 2.50

= 2.50x100 10A-2 = -0.0222

= -2.22x10-2 10A-3 = -36900

= -3.69x104 10A-4 = -4.40

= -4.40x100 10A-5 = 0.0212

= 2.12x10-2 10A-6 = 7.27

= 7.27x100

10A-7 = 9.08

= 9.08x100

10A-8 = 51.1

= 5.11x101

10A-9 = 2.86

= 2.86x100

10A-10 = 159

= 1.59x102

10A-11 = -746

= -7.46x102 10A-12 = 669000

= 6.69x105 10A-13 = -0.386

= -3.86x10-1 10A-14 = -0.498

= -4.98x10-1

10A-15 = -8.97x10-5 10A-16 = 0.420

= 4.20x10-1

10A-17 = $20.12

10A-18 = 350 integer

10A-19 = 0.968

= 9.68x10-1

10A-20 = 5230

= 5.23x103

10A-21 = 0.00411

= 4.11x10-3 10A-22 = 0.119

= 1.19x10-1 10A-23 = 5.25

= 5.25x100 10A-24 = -0.275

= -2.75x10-1

10A-25 = 4.32x108 10A-26 = 8030

= 8.03x103

10A-27 = 72.2

= 7.22x101

10A-28 = 1000 (2SD)

= 1.0x103

10A-29 = 0.176

= 1.76x10-1

10A-30 = 82.1

= 8.21x101

10A-31 = 2460

= 2.46x103 10A-32 = 0.487

= 4.87x10-1 10A-33 = 284

= 2.84x102 10A-34 = 2.15

= 2.15x100 10A-35 = 9.42

= 9.42x100 10A-36 = 18,200,000

= 1.82x107

10A-37 = -3.79

= -3.79x100

10A-38 = -0.222

= -2.22x10-1

10A-39 = 5.47

= 5.47x100

10A-40 = 0.583

= 5.83x10-1

10A-41 = -126000

= -1.26x105

10A-42 = -7.29x106 10A-43 = -0.189

= -1.89x10-1 10A-44 = 16.8

= 1.68x101 10A-45 = -6.96

= -6.96x100 10A-46 = 8.13

= 8.13x100

10A-47 = 629

= 6.29x102

10A-48 = 7.30

= 7.30x100

10A-49 = 6.21

= 6.21x100

10A-50 = 2.81

= 2.81x100

10A-51 = 7.75

= 7.75x100 10A-52 = 2480

= 2.48x103 10A-53 = -15100

= -1.51x104 10A-54 = 0.00400

= 4.00x10-3

10A-55 = 3.86x10-5 10A-56 = -0.922

= -9.22x10-1

10A-57 = 18.5

= 1.85x101

10A-58 = 27.6

= 2.76x101

10A-59 = 18.9

= 1.89x101

10A-60 = 57.5

= 5.75x101

10A-61 = 8.97

= 8.97x100 10A-62 = 0.159

= 1.59x10-1 10A-63 = 0.00236

= 2.36x10-3 10A-64 = 1.56

= 1.56x100 10A-65 = 129

= 1.29x102 10A-66 = 2.07

= 2.07x100

10A-67 = 25.4

= 2.54x101

10A-68 = 324

= 3.24x102

10A-69 = 0.950

= 9.50x10-1

10A-70 = 0.507

= 5.07x10-1

UNIVERSITY INTERSCHOLASTIC LEAGUE

do not turn this page until

you are instructed to do so!

MathematicsInvitational A • 2010

WRITE ALL ANSWERS WITH

CAPITAL LETTERS

1. Evaluate: 30 24 18 12 6q ƒ ‚

(A) 6 (B) 10 (C) 20 (D) (E) 350 35.888...

2. Reid Moore went to the Ye Olde Book store to buy 3 copies of the same book for gifts. The regular price of the book is $19.95. Because he is buying 3 copies he gets 25% off of the regular price of the second copy and 40% off the regular price of the third copy. What would the total cost of the 3 books be before taxes? (to the nearest cent)

(A) $ 26.93 (B) $ 32.92 (C) $ 38.91 (D) $ 40.40 (E) $ 46.88

3. Using the partial ruler shown below, find the distance from A to B.

(A) 1 (B) 1 (C) 1 (D) 1 (E) 11 1 3 7 1

8 4 8 16 2 " " " " "

4. Which of the following is not a solution to 8x ?¸ ¸q q 6 4 2

(A) 2 (B) (C) D) 1 (E) 2q q 1 2 3 45 5 5 5 (

5. The function f(x) = x x 12 crosses the x-axis at two points. Find the distance between the 2 q q two points.

(A) 8 (B) 7 (C) 6 (D) (E) 14

6. A male zebra fish has 8 stripes. A female zebra fish has 7 stripes. What is the ratio of male fish to female fish, if the total number of stripes on all of the zebra fish in an aquarium totals 87?

(A) (B) (C) D) (E) 1 2 7 8 33 3 8 7 1 (

7. A box contains four rods whose lengths are 2", 3", 5", and 7". How many different triangles can be made using only three rods at a time.

(A) 0 (B) 1 (C) 2 (D) 3 (E) 4

8. A right cylinder water tank is 6 feet high and has an inside radius of 3 feet. The amount of water in the tank is 75% of its maximum capacity. How much water is in the tank? (nearest gallon)

(A) 1270 gal (B) 635 gal (C) 734 (D) 317 gal (E) 952 gal gal

9. The region bounded by two radii of a circle and their intercepted arc is called a:

(A) slice of pi (B) semicircle (C) secant (D) sector (E) segment

UIL Math A 2010 - page 1

10. Noah Sense has 28 coins consisting of pennies, nickels, and quarters. He has four times as many nickels as pennies and half as many quarters as nickels. How much money does he have?

(A) $ .86 (B) $ 2.36 (C) $ 2.84 (D) $ 1.88 (E) $ .78

11. One-centimeter cubes are glued together to form the object in the figure shown. The two-dimensional perspective of the top view of this figure has a perimeter of:

(A) 30 cm (B) 18 cm (C) 16 cm (D) 15 cm (E) 12 cm

12. If 8 = 16 , then 4 = ?(k 1) (3k) (k )q q1

(A) (B) (C) (D) 4 (E) 1256 21 164 3

È3

13. Babe, Dizzy, and Yogi are playing "toss and catch" with a baseball. The bearing from Babe to Dizzy is 254 °. The bearing from Yogi to Dizzy is 344 °. The bearing from Yogi to Babe is 32 °. The distance from Yogi to Dizzy is 20 feet. How far is it from Yogi to Babe? (nearest inch)

(A) 29 11 (B) 28 3 (C) 26 11 (D) 22 3 (E) 18 1 ' " ' " ' " ' " ' "

14. Determine the frequency of y = 2 3 cos 10x. (nearest tenth)q

(A) 0.1 (B) 0.6 (C) 1.6 (D) 5 (E) 15.7

15. The equation y = ______________ will produce this graph.

(A) 2 3sin (x (B) 3 2cos (x ) (C) 2 3sin (x q q q 1) 1 1)

(D) 2 3cos (x (E) 2 3sin (xq q 1) 1)


16. Which of the following is a reference angle for 456 ° ?

(A) 6 ° (B) 16 ° (C) 44 ° (D) 84 ° (E) 89 °

17. Find the determinant of the 2 x 2 matrix .’ “ 5 7 2 3

qq

(A) 29 (B) 15 (C) 14 (D) 1 (E) 1q

18. Given the arithmetic sequence 15, a, b, c, 47, ..., find a b c.

(A) 24 (B) 32 (C) 78 (D) 93 (E) 108

19. In the binomial expansion of (3x 1) , the coefficient of the fourth term is:q 5

(A) (B) (C) (D) 30 (E) 270q q q 90 45 10

20. Find an equation of the line tangent to the curve y = x x at the point ( 1 , ). 3 2q q 2 1

(A) y = x (B) y = 6x (C) y = (D) y = 3 (E) y = 2 xq q q q 4 2x3

21. Which of the following polar equations will produce this graph on a polar grid?

2

2

4

(A) r = 2sin (B) r = 4 + sin (C) r = 2 sin ) ) )q q 2 2 2

(D) r = 2 (E) r = 2 q 4cos 2cos) )

22. The area (in square units) of the region bounded by y = q q x 4x and y = 0 is:2

(A) 9 (B) 9 (C) 10 (D) 10 (E) 101 5 1 2 34 6 2 3 4

23. A box contains circular poker chips that are congruent in shape but not color. There are red ones, white ones, and blue ones. Drew Goode randomly draws out a chip. He gets 5 points if it is a blue one, The probability of1 point for a white one, and he loses 3 points for a red one. drawing out a red one is 25%, a blue one is 60%, and a white one is 15%. What is his mathematical expectation on any one draw?

(A) 5.0 (B) 3.9 (C) 3.0 (D) 2.4 (E) 2.1


24. What are the odds that a factor of 2010 is a prime number?

(A) (B) (C) (D) (E) 1 1 1 22 3 4 5 1

25. 1 is: The number of integers that satisfy the inequality 4 n 115 5 30Ÿ Ÿ

(A) 3 (B) 4 (C) 5 (D) 6 (E) 7

26. Simplify: (n 1) (n 1)(n 2)

x q q xq x

(A) (B) (C) (D) (E) n 1 n 2n 2n 1 n 2n 1 2 3 2 32(n 1)n 2 n(n 1)

2 q q q q

27. The formula is the base of the natural logarithm and is the/ B 3 B / 33B = cos sin , where imaginary unit, is named after:

(A) Rene Descartes (B) Claudius Ptolemy (C) Theano of Crotona

(D) Leonard Euler (E) Eratosthenes of Cyrene

28. The odd numbers from 1 to 17 are to be placed in this magic square in which the rows and columns have the same sum. Find the value of x.

x

1

135

(A) 3 (B) 7 (C) 9 (D) 11 (E) 15

29. P = {p,l,u,s}, Q = {m,i,n,u,s}, and R = {t,i,m,e,s}. How many elements are in (P Q) (P R)?

(A) 10 (B) 6 (C) 5 (D) 4 (E) 2

30. The number 12010 in base 3 is equivalent to the number wxyz in base 5, where w, x, y, and z are digits. Find w x y z.

(A) 10 (B) 9 (C) 8 (D) 6 (E) 3

31. Simplify: a b a b 5 4 4 5 3 3ƒ ‚ ‚ ƒ ‚q q q a b

(A) a b (B) a b (C) a b (D) a b (E) a b q q q q 2 6 4 2 2 12 4 2 2 6

32. Simplify: 9 64 12 2x x x x x x 2 2

2q q q

ƒ

(A) (B) (C) (D) (E) 4 3 4 34 3 4( 3) 4x x x

x x x q


33. The distance from Abilene to Dallas by way of I30 is 185 miles. Ima Slow is leaving Abilene on I30 at 9:00 a.m. driving toward Dallas at 55 mph. Ura Quick is leaving Dallas on I30 at 9:00 a.m. driving toward Abilene at 70 mph. What time will they meet? (nearest minute)

(A) 10:48 a.m. (B) 10:41 a.m. (C) 10:29 a.m. (D) 10:19 a.m. (E) 10:10 a.m.

34. A and B are complementary angles. A and C are supplementary angles. Find m C ifn n n n n m A = 2x 5 and m B = x 2.n n q

(A) 121° (B) 149° (C) 135° (D) 123° (E) 147°

35. If are the first 3 terms of an arithmetic sequencea = 2 a = 4.5 and a = 7 , then a = ?1 2 3 9 , ,

(A) (B) 19.5 (C) (D) 22 (E) 24.517 21

36. The graph of 4x 9y 18y = 2 is a(n): 2 2 q 16x

(A) parabola (B) line (C) hyperbola (D) ellipse (E) circle

37. The eccentricity of the hyperbola 4x y = 4 is:2 2q

(A) (B) (C) (D) (E) È È5 15È È È17 3

2 2 25

38. If cos 0 and tan 0 which quadrant will terminate in?) ) )

(A) QI or QII (B) QI only (C) QII only (D) QIII only (E) QII or QIII

39. Let V = 15 and V = 9, where the direction angles of V and V are 20 ° and 80 °,¼ ¼ ¼ ¼1 2 1 2

respectively. Find V V . (nearest tenth)¼ ¼1 2

(A) 23.6 (B) 17.5 (C) 20.7 (D) 12.0 (E) 21.0

40. Find AD if AB = 90 cm. and AC = 50 cm. (nearest cm)

A

C

BD

(A) 67 cm (B) 19 cm (C) 28 cm (D) 60 cm (E) 45 cm

41. ' (q x sin x) dx = ________ C, where C is some arbitrary constant.

(A) cos x (B) x cos x sin x (C) sin x cos x (D) x cos x (E) x sin x cos x2 q q q q


42. If f (x) = 6 and f ( ) = and f(1) = 2, then f( ) = _____. ww w q q q 1 8 2

(A)20 (B) 17 (C) 8 (D) (E) q q 7 14

43. Find the instantaneous rate of change of the reciprocal of a number with respect to the number when the number is 4.

(A) (B) (C) (D) (E) q q q 1 1 1 1 116 4 2 4 16

44. How many different letter arrangements can be made by rearranging the letters in the word 'LETTER'?

(A) 180 (B) 21 (C) 120 (D) 24 (E) 360

45. Willie Lawkit can't remember the combination to the padlock shown. He knows that the first number is greater than 30, the second number is a positive Fibonacci number, and the third number is a factor of 30. How many combinations can he try to open the lock?

(A) 25 (B) 378 (C) 576 (D) 72 (E) 480

46. The operation " " is defined by: a b = a b . What is the value of (0 1 (2 3) ?˜ ˜ ˜ ˜ ˜ b aq )

(A) (B) 0 (C) 1 (D) 2 (E) 4q 1

47. 3(x 4) = 5 and 3(4 x) = 5 is an example of the ___________ property.

(A) reflexive (B) commutative (C) identity (D) associative (E) distributive

48. Slim Sails rents kayaks and life vests for white water rafting. The kayak rental fee last year was $40 and the life vest rental fee last year was $12. This year, the kayak rental fee increased 15% and the life vest fee decreased 25%. What is the overall percent increase in rental fees for the kayak and vest from last year to this year? (nearest tenth)

(A) 10.0% (B) 9.1% (C) 8.3% (D) 6.5% (E) 5.8%

49. If (2 x) = 2(x 3) then (2x equals:q q q 3 3)

(A) 12 (B) 9 (C) 21 (D) (E) 1.8q q 3.4

50. The area of a right isosceles triangle is 12.5 cm . Its perimeter is: (nearest tenth). 2

(A) 18.7 cm (B) 11.4 cm (C) 21.2 cm (D) 11.7 cm (E) 17.1 cm


51. Find the slope of a line perpendicular to the line drawn in the graph below.

(A) 2 (B) 1.5 (C) .5 (D) .5 (E) 2q q q __ __ __ __ 52. AB, AC, BD, and CD are chords of circle O and point E lies on circle O. Which of following is a true statement?

A

B

C

D

PE

w w w (A) ABD = (B) BPC = (C) ACD = 2m m m m m mn ‚ n ‚ n ‚1 1

2 2AED CB AED

(D) APD = ABP DCP (E) ABP BDCm m m m mn n n n n

53. A regular polygon has sides and diagonals. If the polygon had one more side, 1, it wouldS D S have 10 diagonals. The polygon is a:D

(A) octagon (B) nonagon (C) decagon (D) undecagon (E) dodecagon

54. Let f(x) = 2 x and g(x) = 3x 5 If h(x) is the inverse function of , then h( 4) = ?q q 5 . f(x)g(x)

(A) (B) (C) (D) (E) q q 422 18 7 177 17 22 18

55. sin sec cos csc is equivalent to:) ) ) )

(A) (B) (C) 1 (D) E) sec 1csc tan seccot csc tan

2 2) ) )) ) ) tan

2 2) ) ( q


56. Willie Ketchit drops a golfball from a height of 10 meters. Each time it hits the ground it rebounds to a height of 50% of the distance it fell. Find the total distance the golfball travels when it reaches the ground the third time. (nearest tenth)

(A) (B) 32.5 m (C) 30.0 m (D) 28.5 m (E) 25.0 m 35.0 m

57. The polynomial 2x x x 5 has at most ____ negative zeros. 4 2q 8

(A) 4 (B) 3 (C) 2 (D) 1 (E) 0

58. Coach Winters has 4 seniors, 5 juniors, 3 sophomores, and 4 freshmen on her math team. How many ways can she form practice groups of four members consisting of one member from each of the grade levels?

(A) 16 (B) 81 (C) 108 (D) 240 (E) 256

59. Romeo, Juliet, and three classmates are randomly assigned seats in a row of five chairs. What is the probability that Romeo and Juliet will be seated next to each other?

(A) 20% (B) 25% (C) 30% (D) 35% (E) 40%

60. Matt and Nick constructed two buildings using identical cubes. Matt's building weighs 200 g, and Nick's building weighs 600 g. How many of the cubes in Nick's building are hidden and cannot be seen in the figure?

Matt'sNick's

(A) 1 (B) 2 (C) 3 (D) 4 (E) 5


University Interscholastic League MATHEMATICS CONTEST

HS Invitation A 2010ì ìAnswer Key

1. C 21. C 41. B 2. E 22. D 42. B

3. D 23. D 43. A

4. C 24. B 44. A

5. B 25. B 45. C

6. A 26. E 46. B

7. B 27. D 47. B

8. E 28. B 48. E

9. D 29. B 49. C

10. C 30. D 50. E

11. B 31. A 51. C

12. B 32. A 52. A

13. A 33. C 53. D

14. B 34. D 54. A

15. A 35. D 55. D

16. D 36. D 56. E

17. E 37. A 57. C

18. D 38. D 58. D

19. A 39. E 59. E

20. A 40. C 60. D

GENERAL DIRECTIONS:

• DO NOT OPEN EXAM UNTIL TOLD TO DO SO. • Ninety minutes should be ample time to complete this contest, but since it is not a race, contestants

may take up to two hours. If you are in the process of actually writing an answer when the signal to stop is given, you may inish writing that answer.

• Papers may not be turned in until 30 minutes have elapsed. If you inish the test in less than 30 minutes, remain at your seat and retain your paper until told to do otherwise. You may use this time to check your answers.

• All answers must be written on the answer sheet provided. Indicate your answers in the appropriate blanks provided on the answer sheet.

• You may place as many notations as you desire anywhere on the test paper except on the answer sheet, which is reserved for answers only.

• You may use additional scratch paper provided by the contest director. • All questions have ONE and only ONE correct (BEST) answer. There is a penalty for all incorrect

answers. • If a question is omitted, no points are given or subtracted. • On the back of this page is printed a copy of the periodic table of the elements. You may wish to

refer to this table in answering the questions, and if needed, you may use the atomic weights and atomic numbers from the table. Other scientiic relationships are listed also.

• Silent hand-held calculators that do not need external wall plugs may be used. Graphing calculators that do not have built-in or stored functionality that provides additional scientiic information are allowed. Small hand-held computers are not permitted. Calculators that accept memory cards or memory sticks are not permitted. Each contestant may bring one spare calculator. All memory must be cleared.

• Answers within 5% of the exact answer will be considered correct.

SCORING:

All questions will receive 6 points if answered correctly; no points will be given or subtracted if unanswered; 2 points will be deducted for an incorrect answer.

SCIENCEInvitational A • 2010

UNIVERSITY INTERSCHOLASTIC LEAGUE

Making a World of Difference

Periodic Table of the Elements

See Reverse Page for Other Useful Information

OTHER USEFUL INFORMATION

Avogadro’s Number, NA = 6.022 ! 1023 mol-1

Absolute zero = 0 K = –273.15°C

Atmospheric pressure, 1 atm = 1.013 ! 105 N/m2 = 101.3 kPa = 760.0 Torr = 760.0 mmHg

Standard temperature and pressure (STP) is 0°C and 1 atm

Gram molecular volume at STP = 22.4 L

Mechanical equivalence of heat, 1 kcal = 1 Cal = 1,000 cal = 4,186 J

Gas constant, R = 1.987 cal/mol•K = 0.08206 atm•L/mol•K = 8.314 J/mol•K

Dulong and Petit’s constant = 6.0 amu•cal/gram•K

Faraday’s constant, 1 F = 96,485 C/mol

Acceleration of gravity at Earth’s surface, g = 9.80 m/s2

Gravitational constant, G = 6.67 ! 10-11 N•m2/kg2

Horsepower, 1 hp = 746 W = 550 ft•lbs/s

Boltzmann’s constant, kB = 1.38 ! 10–23 J/K

Stefan-Boltmann constant, " = 5.67 ! 10-8 W/m2•K4

Elementary charge, e = 1.602 ! 10–19 C

Coulomb’s law constant, k = 1/4#$o = 8.988 ! 109 N•m2/C2

Permittivity of free space, $o = 8.85 ! 10–12 C2/N•m2

Permeability of free space, µo = 4! ! 10–7 T•m/A

Electron volt, 1 eV = 1.602 ! 10–19 J

Vacuum speed of light, c = 3.00 ! 108 m/s

Planck’s constant, h = 6.626 ! 10–34 J·s = 4.136 ! 10-15 eV•s

Planck’s reduced constant, ! % h/2! = 1.054 ! 10–34 J·s = 6.582 ! 10-16 eV•s

Atomic mass unit, 1 amu = 1 u = 1.66 ! 10–27 kg = 931.5 MeV/c2

Electron rest mass, me = 9.11 ! 10–31 kg = 0.000549 u = 0.511 MeV/c2

Proton Mass = 1.6726 ! 10-27 kg = 1.00728 u = 938.3 MeV/c2

Neutron Mass = 1.6749 ! 10-27 kg = 1.008665 u = 939.6 MeV/c2

Some standard values for water:

Mass density, & = 1.00 g/cm3 = 1,000 kg/m3

Heat capacity or Specific heat, c = 1.00 cal/gram•C° = 1.00 kcal/kg•C° = 4186 J/ kg•C°

Latent heats, LF = 79.7 kcal/kg = 3.33 ! 105 J/kg & LV = 539 kcal/kg = 22.6 ! 105 J/kg

Index of refraction, n = 1.33

HS Science • Invitational A • 2010

University Interscholastic League • page 1

Biology Questions (1 – 20)

1. Which of the following is distinctively

associated with organic compounds?

A) carbon

B) hydrogen

C) nitrogen

D) oxygen

E) sulfur

2.Which of the following structures is absent in

bacterial cells?

A) plasma membrane

B) nucleoid

C) cytoplasm

D) nucleus

E) DNA

3. Movement of a molecule against a

concentration gradient is

A) simple diffusion.

B) facilitated diffusion.

C) osmosis.

D) active transport.

E) bulk flow.

4. Organisms that derive their chemical energy

from the process of chemosynthesis are also

classified as

A) autotrophs.

B) parasites.

C) heterotrophs.

D) saprophytes.

E) mutualists.

5. Which of the following is NOT associated with

meiosis?

A) reduction of number of chromosomes.

B) somatic cells

C) sexual reproduction

D) sperm and egg

E) germ cells

6. Various forms of a gene at a given locus are called

A) chiasmata.

B) alleles.

C) autosomes.

D) loci.

E) chromatids.

7. When a virus takes over the machinery of a cell, it

forces the cell to manufacture more

A) mitochondria for energy for the virus.

B) liposomes to isolate themselves from water.

C) food particles.

D) viral particles.

E) Golgi bodies so that the cell will secrete the

excess viruses.

8. The first organisms on Earth that did not require

water for reproduction were the

A) ferns.

B) lycophytes.

C) cycads.

D) flowering plants.

E) gymnosperms.

9. Which of the following does NOT include

parasites?

A) arthropods

B) cnidarians

C) flatworms

D) nematodes

E) roundworms

10. Which of the following cells of plants are alive

when functioning?

A) tracheids

B) cork

C) sclereids

D) parenchyma

E) vessel elements

11. Which of the following is a micronutrient for

plants?

A) sulfur

B) calcium

C) phosphorus

D) manganese

E) magnesium



12. Alternation of generations in plants refers to

A) expression of recessive traits.

B) presence of a diploid and a haploid

generation in the life cycle of plants.

C) presence of the different sexes in two

different plants.

D) occurrence of a sexually reproducing

diploid stage followed by an asexually

reproducing haploid stage during the life

cycle of higher plants.

E) juvenile and adult forms of plants.

13. Which of the following substances is released

by motor neurons to initiate a muscle

contraction?

A) acetylcholine

B) dopamine

C) serotinin

D) noradrenalin

E) adrenalin

14. Which of the following is NOT a function of

the lymphatic system?

A) fighting infection

B) transporting dissolved gases

C) reclaiming fluids

D) harboring white blood cells

E) transporting fats

15. Body cells have "self" markers located

A) in their nuclei.

B) in the endoplasmic reticulum.

C) in the mitochondria.

D) on the plasma membrane.

E) inside the Golgi bodies.

16. Filtration of blood occurs in which section of

the mammalian nephron?

A) glomerulus

B) loop of Henle

C) proximal tubule

D) distal tubule

E) collecting duct

17. Which of the following events of development

occurs last?

A) cleavage

B) gamete formation

C) gastrulation

D) organ formation

E) tissue specialization

18. The forelimbs of early mammals were similar in all

features except

A) embryonic origin.

B) position on the body.

C) number.

D) function.

E) composition.

19. Which of the following is NOT a part of a

community?

A) bacteria

B) populations

C) animals

D) soil

E) plants

20. Which of the following is NOT dependent on the

others as a food supply?

A) carnivores

B) herbivores

C) detritivores

D) producers

E) decomposers

Chemistry Questions (21 – 40)

21. Which of the following changes is a chemical

change?

A) boiling water

B) leaves changing colors in the fall

C) cutting grass

D) crushing a leaf in your hand

E) dropping a ball

22. The number of calories needed to raise the temperature

of 50 g of water from 20°C to 40°C is ___.

A) 200

B) 100

C) 500

D) 1000

E) 800



23. The symbol for the element zinc is _____ .

A) Zn

B) Zc

C) Znc

D) Zi

E) Z

24. The molecular weight of ethylchloride is _____ .

A) 64.5 grams/mole

B) 48.5 grams/mole

C) 28.0 grams/mole

D) 34.0 grams/mole

E) 69.5 grams/mole

25. What is the empirical formula for a compound

that is 87.5% nitrogen and 12.5% hydrogen by

mass?

A) N2H5

B) N3H2

C) NH3

D) N2H3

E) NH2

26. How many mL of a 0.320 molar solution of

sucrose in water are needed to have 0.160

moles of sucrose?

A) 557.3 mL

B) 500 mL

C) 219 mL

D) 438 mL

E) 598.5 mL

27. The combustion of hydrazine, N2H4, produces

NO and water. If the chemical reaction for this

process is properly balanced, what is the sum of

the coefficients for the PRODUCTS? Use the

smallest set of integers to balance the equation.

A) 8

B) 7

C) 4

D) 2

E) 10

28. When silver nitrate(aq) and calcium chloride(aq)

are mixed, the precipitate that forms is:

A) CaNO3

B) Ca(NO3)2

C) AgCl

D) AgNO3

E) AgCl2

29. How many protons are present in one copper(II) ion ?

A) 30

B) 27

C) 29

D) 28

E) 26

30. In the Aufbau order of occupancy of electronic

energy levels, the level occupied just after 4p is ___ .

A) 5s

B) 4d

C) 3f

D) 5p

E) 6p

31. In addition to the s type electrons, Gallium will

have _____ electrons in the 4p energy sublevel.

A) 3

B) 13

C) 1

D) 2

E) 4

32. Which of the following is a poor conductor of

electricity?

A) potassium

B) mercury

C) molten sodium chloride

D) copper

E) sulfur

33. Water molecules bind to each other mainly by

A) breaking an O-H bond in neighboring water

molecules.

B) oxygen lone pair interactions with hydrogen

atoms of a neighboring molecule.

C) electrons being paired between them.

D) ejecting electrons from oxygen.

E) formation of hydronium and hydroxide ions.



34. Consider the following reaction:

H2(g) + CO2 (g) ! H2O(g) + CO(g)

!Hf for CO2(g) = –22.5 kJ/mole

!Hf for CO(g) = –6.3 kJ/mole

!Hf for H2O(g) = –13.8 kJ/mole

A) !H of the reaction is positive.

B) !H of the reaction is negative.

C) !H of the reaction is zero.

D) The reaction is exergonic.

E) Can’t answer because !Hf for H2(g) is not

given.

35. A catalyst ____ .

A) lowers !S for the process

B) increases the amount of products present at

equilibrium

C) increases the rate at which equilibrium is

reached but decreases the equilibrium

constant

D) increases the rate at which equilibrium is

reached without changing the equilibrium

constant

E) increases !H for the process

36. Which solution has the greatest concentration

of hydroxide ions?

A) 1.0 M NaCl

B) 1.0 M NaOH

C) 0.1 M Ca(OH)2

D) 1.0 M HCl

E) 1.0 M Fe(OH)3

37. A sample of pure water is neutral because it

contains _____ .

A) some hydronium ions

B) some hydroxide ions

C) equal amounts of hydroxide and hydronium

ions

D) only H2O molecules

E) non-polar molecules

38. In the following reaction, which species is reduced?

Ni + 2 H+ + 2 Cl

– ! NiCl2 + H2

A) Ni

B) H2

C) NiCl2

D) H+

E) Cl–

39. For the reaction

? Al + ? CuSO4 " ? Al2(SO4}3 + ? Cu,

a maximum of ____ grams of Al2(SO4)3 could be

formed from 8.167 grams of Al and 7.147 grams of

CuSO4 .

A) 2.0

B) 3.6

C) 7.1

D) 11.2

E) 5.1

40. When 0.05956 moles of ammonium sulfate, are

dissolved in enough water to make 116 milliliters

of solution, how many ammonium ions are present?

A) 7.2 " 1022

B) 2.9 " 1022

C) 1.1 " 1024

D) 5.7 " 1021

E) 1.1 " 1022

Physics Questions (41 – 60)

41. According to Feynman which of the following

statements contains the most information to be

passed on if all of scientific knowledge was to be

destroyed.

A) Conservation of Energy

B) Newton’s Second Law of Motion

C) The Atomic Hypothesis

D) Ohm’s Law

E) Einstein’s Equation



42. According to Feynman what happens to water

when it evaporates?

A) It cools because the faster moving

molecules escape from the water surface.

B) It cools because the slower moving


C) It stays the same temperature.

D) It warms because the faster moving


E) It warms because the slower moving


43. This Texas physicist is interested in structural

phase transitions and the effects of entropy on

these transformations. He/she received his/her

Ph.D. from the University of Cincinnati.

A) Tikhon Bykov

B) Margaret Cheung

C) David Hough

D) Mahdi Sanati

E) B. F. L. Ward

44. How much heat is required to bring 1.50 kg of

water at 20°C to 1.50 kg of steam at 100°C?

A) 1.00 " 106 J

B) 1.13 " 106 J

C) 3.39 " 106 J

D) 3.89 " 106 J

E) 4.02 " 106 J

45. What is the change in entropy of the system

when 1.25 " 103 J of heat is added to the system

that is maintained at a constant 75.0°C?

A) + 290 J/K

B) + 16.7 J/K

C) + 3.59 J/K

D) # 3.59 J/K

E) # 16.7 J/K

46. A spelunker drops a stone from rest into a well.

The speed of sound is 343 m/s in air, and the sound

of the stone striking the bottom is heard 2.15 s after

the stone is dropped. How deep is the well? You

may neglect air resistance and assume that the

speed of sound is constant.

A) 10.1 m

B) 11.4 m

C) 20.2 m

D) 21.4 m

E) 22.7 m

47. A person drops from rest off a tall cliff. In falling a

distance h, she attains a speed v. Assuming free-

fall conditions, how much farther must she fall in

order to attain a speed of 2v?

A) 1/4 h

B) h

C) 2h

D) 3h

E) 4h

48. A fire hose ejects a stream of water at an angle of

35.0° above the horizontal. The water leaves the

nozzle with a speed of 25.0 m/s. How far from a

building should the fire hose be to hit the highest

possible fire? You may neglect any dissipative

effects.

A) 21.0 m

B) 30.0 m

C) 42.8 m

D) 59.9 m

E) 63.7 m

49. A 1380 kg car is moving due east with an initial

speed of 27.0 m/s. After 8.00 s the car has slowed

down to 17.0 m/s. Find the magnitude and

direction of the net force that produces the

deceleration.

A) 1730 N, due east

B) 1730 N, due west

C) 4660 N, due west

D) 7590 N, due east

E) 7590 N, due west



50. A coin is placed on a horizontal turntable that is

rotating at 33.3 rpm. If the coefficient of static

friction between the coin and the turntable is

0.100, how far from the center of the turntable

can the coin be placed without having it slip

off?

A) 0.0884 cm

B) 2.81 cm

C) 8.06 cm

D) 28.1 cm

E) 80.6 cm

51. For a force to be conservative, what is the

condition upon the work done by the force as

you go from point A to point B?

A) The work done by the force is zero.

B) The work done by the force is positive.

C) The work done by the force is negative.

D) The work done by the force can have any

value, but depends upon the path taken

from A to B.

E) The work done by the force can have any

value, but is independent of the path taken

from A to B.

52. A boy shoots a 51 g pebble straight up with a

slingshot whose spring constant is 320 N/m.

The slingshot is initially stretched by 0.20 m.

How high above the starting point does the

pebble fly? You may neglect any dissipative

effects.

A) 1.3 m

B) 6.4 m

C) 13 m

D) 64 m

E) 130 m

53. An insect has a completely inelastic collision with

the windshield of a truck that is traveling along a

highway. Which of the following is true about the

collision?

A) The magnitudes of the force and change in

momentum are smaller for the bug than the

truck.

B) The magnitude of the force is smaller for the

bug than the truck, but the magnitude of the

change in momentum is the same for the bug

and the truck.

C) The magnitude of the change in momentum is

smaller for the bug than the truck, but the

magnitude of the force is the same for the bug

and the truck.

D) The magnitudes of the force and change in

momentum are the same for the bug and the

truck.

E) The magnitude of the force is larger for the bug

than the truck, but the magnitude of the change

in momentum is the same for the bug and the

truck.

54. A skater is initially spinning at a rate of 10.0 rad/s

with a rotational inertia of 2.50 kg•m2 when her

arms are extended. What is her angular velocity

after she pulls her arms in and reduces her

rotational inertia to 1.60 kg•m2? You may neglect

any frictional torques during the spin.

A) 0.400 rad/s

B) 6.40 rad/s

C) 15.6 rad/s

D) 64.0 rad/s

E) 154 rad/s

55. A trapped ideal gas has an initial volume V0. If

during a process both the temperature and the

pressure are tripled, then what is the new volume of

the gas?

A) 1/9 V0

B) 1/3 V0

C) V0

D) 3 V0

E) 9 V0



56. An insulator is charged and brought near an

electrically isolated metal conductor that is

initially uncharged. Which of the following is

true about the electrical force between the two

objects?

A) They exert no electric force on one another.

B) They attract one another.

C) They repel one another.

D) If the insulator is positively charged then

they attract, but if it is negatively charged

then they repel.

E) If the insulator is positively charged then

they repel, but if it is negatively charged

then they attract.

57. What is the radius of a circular loop of wire

such that the magnetic field at its center is

1.8 " 10–4 T when the loop carries a current of

12 A?

A) 1.3 cm

B) 4.2 cm

C) 12 cm

D) 16 cm

E) 21 cm

58. Two parallel wires in a horizontal plane are

oriented such that wire 1 is up from wire 2 in

the plane. The two wires carry currents I1 and

I2 to the right. The wires each have length L

and are separated by a distance d. What is the

magnitude and direction of the magnetic field

due to wire 1 at the middle of wire 2? You may

assume that L >> d.

A) (µ0I1)/(2$d) into the horizontal plane

B) (µ0I1)/(2$d) out of the horizontal plane

C) (µ0I1I2)/(2$L) up in the horizontal plane

D) (µ0I2)/(2$d) into the horizontal plane

E) (µ0I2)/(2$d) out of the horizontal plane

59. A slide projector uses a slide of width 5.08 cm and

produces a real image that is 2.00 m wide on a

screen that is 3.50 m away. What is the focal

length of the projector lens?

A) # 9.21 cm

B) # 8.67 cm

C) + 8.67 cm

D) + 9.21 cm

E) + 3.41 m

60. For a radioactive decay, N(t) = N0 e–%t, what are the

appropriate S.I. units for the decay constant, %?

A) Becquerel/s (Bq/s)

B) curie/s (Ci/s)

C) Gray (Gy)

D) sievert (Sv)

E) 1/s

UIL HIGH SCHOOL SCIENCE CONTEST

ANSWER KEY

INVITATIONAL A • 2010

1. A

2. D

3. D

4. A

5. B

6. B

7. D

8. E

9. B

10. D

11. D

12. B

13. A

14. B

15. D

16. A

17. E

18. D

19. D

20. D

21. B

22. D

23. A

24. A

25. E

26. B

27. C

28. C

29. C

30. A

31. C

32. E

33. B

34. A

35. D

36. B

37. C

38. D

39. E

40. A

41. C

42. A

43. D

44. D

45. C

46. D

47. D

48. B

49. B

50. C

51. E

52. C

53. D

54. C

55. C

56. B

57. B

58. A

59. C

60. E

PHYSICS KEY for Science Contest • Invitational A • 2010

41. (C) “If in some cataclysm, all of scientific knowledge were to be destroyed, and only one sentence passed

on to the next generations of creatures, what statement would contain the most information in the

fewest words? I believe that it is the atomic hypothesis (or the atomic fact, or whatever you wish to

call it) that all things are made of atoms – little particles that move around in perpetual motion,

attracting each other when they are a little distance apart, but repelling upon being squeezed into one

another.”

42. (A) The water cools because the faster moving molecules escape from the water surface.

43. (D) Dr. Mahdi Sanati, Assistant Professor of Physics at Texas Tech University, is interested in structural

phase transitions and the effects of entropy on these transformations.

44. (D) Q = mc!T + mLv = 1.5(4186)(100-20) + 1.5(22.6"105) = 3.89"10

6 J

45. (C) !S = Q/T = +1.25"103/(75+273.15) = +3.59 J/K

46. (D) From h = !gt2 & h = vsoundt # ttotal = (2h/g)

! + h/vsound which can be solved to get

(1/vsound)2h

2 – (2t/vsound + 2/g)h + t

2 =0 to get h = 21.4 m

47. (D) using v2 = v0

2 + 2a!y, v

2 = 0

2 + 2gh & (2v)

2 = v

2 + 2gd # d = 3v

2/2g = 3(2gh)/2g = 3h. Note: the

questions asks how much further and not how far from the top of the cliff.

48. (B) t = (vy $ voy)/a = (0 $ 14.34)/9.8 = 1.463 s & x = v0xt = 20.98(1.463) = 30.0 m

49. (B) %F = ma = 1380(17 – 27)/8 = -1730N or 1730 N, due west.

50. (C) From the free-body diagram:

%Fcentrip = macentrip # Ffrs = µsFN = µsmg = mR&2 # R = µsg/&

2 = 0.0806 m

51. (E) The work done by a conservative force is independent of the path taken from point A to point B.

52. (C) By conservation of energy: mgh = !kx2 # h = kx

2/(2mg) = 12.8 m

53. (D) The force on the bug by the truck and the force on the truck by the bug are third law pairs and thus are

equal in magnitude and opposite in direction. Since the collision time is the same for both the bug

and the truck then by the impulse-momentum theorem the magnitude of the change in momentum is

the same for each, or equivalently since momentum is conserved in the collision.

54. (C) By conservation of angular momentum: I0&0 = I& # & = (2.5/1.6)10 = 15.6 rad/s

55. (C) By the ideal gas law: V = nRT/P = nR(3T0)/(3P0) = nRT0/ P0 = V0

56. (B) No matter what the charge is on the insulator it will induce a separation of charge on the conductor

and attract each other.

57. (B) From B = (µ0I)/(2R) # R = (µ0I)/(2B) = 0.0419 m

58. (A) For a long straight wire: B = (µ0I)/(2'R) = (µ0I1)/(2'd) and by the right hand rule it goes into the

horizontal plane.

59. (C) From the lateral magnification equation:

M = hi/ho = - di/do # do = - 3.5 m (0.0508 m/-2.00 m) = 0.0889 m and

thus the focal length is: f = (1/do + 1/di)-1

= 0.08669 m

60. (E) The S.I. units of the decay constant, (, are 1/s.

UIL COMPUTER SCIENCE INVITATIONAL A 2010 • PAGE 1

University Interscholastic League

Computer Science Competition

Number 119 (Invitational A - 2010)

General Directions (Please read carefully!):

1) DO NOT OPEN EXAM UNTIL TOLD TO DO SO.

2) NO CALCULATOR OF ANY KIND MAY BE USED.

3) There are 40 questions on this contest exam. You have 45 minutes to complete this contest. If you are in the

process of actually writing an answer when the signal to stop is given, you may finish writing that answer.

4) Papers may not be turned in until 45 minutes have elapsed. If you finish the test before the end of the allotted time,

remain at your seat and retain your paper until told to do otherwise. Use this time to check your answers.

5) All answers must be written on the answer sheet/Scantron card provided. Indicate your answers in the appropriate

blanks provided on the answer sheet or on the Scantron card. Clean erasures are necessary for accurate Scantron

grading.

6) You may place as many notations as you desire anywhere on the test paper, but not on the answer sheet or

Scantron card which are reserved for answers only.

7) You may use additional scratch paper provided by the contest director.

8) All questions have ONE and only ONE correct (BEST) answer. There is a penalty for all incorrect answers. All

provided code segments are intended to be syntactically correct, unless otherwise stated. Ignore any

typographical errors and assume any undefined variables are defined as used.

9) A reference to commonly used Java classes is provided at the end of the test, and you may use this reference sheet

during the contest. You may detach the reference sheets from the test booklet, but DO NOT DO SO UNTIL THE

CONTEST BEGINS.

10) Assume that any necessary import statements for standard Java packages and classes (e.g. .util, ArrayList,

etc.) are included in any programs or code segments that refer to methods from these classes and packages.

Scoring:

1) All questions will receive 6 points if answered correctly; no points will be given or subtracted if unanswered; 2

points will be deducted for an incorrect answer.


QUESTION 1

What is the sum of 10012 and 112?

A. 11002 B. 11112 C. 10102 D. 1112 E. 10112

QUESTION 2

int x = 3000 / 10 / 100 * 2;

System.out.print(x);

What is output by the code to the right?

A. 2 B. 1 C. 0

D. 6 E. 1.5

QUESTION 3

int count = 0;

for(int i = 0; i < 20; i++)

count++;

System.out.print(count);


A. 19 B. 10 C. 20

D. 0 E. 1

QUESTION 4

String nm = "Yourdon";

String part = "";

part = part + nm.charAt(1) + nm.charAt(3);

System.out.println(part);


A. Yu B. oo C. yu

D. or E. Yourdon

QUESTION 5

int[] nums = {5, 1, 7, 5, 5, 3, 5};

System.out.print(nums[5]);


A. 0 B. 4 C. 3

D. null E. 5

QUESTION 6

int w = 10;

double c = w / 4 + 2.5;

System.out.print(c);


A. 1 B. 42.5 C. 5

D. 4.5 E. 5.0

QUESTION 7

Which answer is logically equivalent to the following boolean expression, where p and q are boolean variables?

!(p || !q)

A. !q B. !p && q C. !p || q D. !p && !q E. p


QUESTION 8 int x = 12;

int y = 12;

if( x < y )

System.out.print(1);

if( x <= y )


else



A. 2 B. 12 C. 1

D. 123 E. 13

QUESTION 9

public class City{

private String name;

private int pop;

public City(String nm){

<*1>;

}

public City(String nm, int p){

name = nm;

pop = p;

}

public String toString(){

return name + " " + pop;

}

}

//////////////////////////////////////////

// client code

City c1 = new City("Waco", 100000);

System.out.println( c1 );

What replaces <*1> in the code to the right to call the

constructor in the City class with two parameters using

nm as the first argument and 0 as the second?

A. super(nm, 0)

B. this(nm, 0)

C. this.City(nm, 0)

D. super.City(nm, 0)

E. City(nm, 0)

Assume <*1> is filled in correctly.

QUESTION 10

What is output by the client code to the right?

A. waco 100,000

B. c1

C. Waco 0

D. WACO

E. Waco 100000

QUESTION 11

int bx = 10;

int ax = ~bx;

System.out.print(bx + " " + ax);


A. -11 -11 B. 10 10 C. 10 -1

D. 10 -2 E. 10 -11

QUESTION 12

double res = Math.pow(5, 2);

System.out.print(res);


A. 32 B. 32.0 C. 25

D. 25.0 E. 10.0

QUESTION 13

String letters = "P\tT";

System.out.print(letters);


A. P T B. Pt C. PTT

D. P\tT E. PtT


QUESTION 14

double value = 19.591;

System.out.printf("%7.5f", value);


A. 19.5910000 B. 20.0

C. 7.5 D. 19.5910

E. 19.59100

QUESTION 15 public int process(int x){

int y = x;

x++;

y--;

return x * y;

}

What is returned by the method call process(3)?

A. 9 B. 8 C. 0

D. 3 E. 5

QUESTION 16

for(int r = 0; r < 10; r++)

for(int c = 0; c < 5; c++)

System.out.print('*');

How many '*'s are output by the code to the right?

A. 20 B. 50 C. 6

D. 15 E. 30

QUESTION 17

String garbage = ":car:-)bat:-(a!!d";

String arg1 = "[^a-zA-Z]+";

String[] parts = garbage.split(arg1);

System.out.print( parts[1] + parts[3] );


A. cara B. bata C. :-):-(

D. ::-) E. batd

QUESTION 18 int[] vals = {-2, 0, 7, 10, 12, 3, 2};

int total = 0;

for(int i = 0; i < vals.length; i++){

total += vals[i];

if(total >= 10)

break;

}

System.out.print(total);


A. 4 B. 17 C. 32

D. 34 E. 15

QUESTION 19

int offset = 3;

char ch = 'N';

ch = (char)(ch + offset);

System.out.print(ch);


A. 91 B. 17 C. 'Q'

D. '17' E. Q

QUESTION 20

String start = "ABCDEFG";

String result = "";

for(int i = 1; i < start.length(); i += i)

result += start.charAt(i);

System.out.print(result);


A. ABD B. AAAAAAA

C. BCE D. BCDEFG

E. There is no output due to a

StringIndexOutOfBoundsException.


QUESTION 21

public class Media

public class Paper extends Media

public class SchoolPaper extends Paper

public class TVShow extends Media

Consider the class headers to the right. Assume all of the

classes to the right have a default constructor. Which of the

following statements will cause a syntax error?

I.

II.

III.

Media m1 = new TVShow();

Media m2 = new SchoolPaper();

SchoolPaper p1 = new Paper();

A. I only B. II only C. III only

D. I and II only E. I, II, and III

QUESTION 22

public class Brick{

private boolean hidden;

public void hit(){

hidden = true;

}

public boolean isShowing(){

return !hidden;

}

}

What is output by the following client code?

Brick b1 = new Brick();

Brick b2 = new Brick();

b1.hit();

System.out.print( b1.isShowing() + " ");

System.out.print( b2.isShowing() );

A. false true B. true false

C. false false D. true true

E. There is no output due to a runtime error caused by

the client code.

QUESTION 23 public class ToughBrick extends Brick{

private int reqHits;

private int hits;

public ToughBrick(){

reqHits = 2;

}

public void hit(){

hits++;

if(hits == reqHits)

hidden = true;

}

}

This question makes use of the Brick class from

question 22. What is output by the following client code?

ToughBrick t1 = new ToughBrick();

t1.hit();

System.out.print( t1.isShowing() + " ");

t1.hit();

System.out.print( t1.isShowing() );

A. false true B. true false

C. false false D. true true

E. There is no output due to a syntax error in the

ToughBrick class.

QUESTION 24

Which of the following is not a Java keyword?

A. throw B. switch C. do D. finally E. range

QUESTION 25

int num = -13;

int div = 5;

System.out.print( num % div );

System.out.print( " " + (num / div) );


A. 3 2 B. 3 -2.6 C. -5 -2

D. -3 -2 E. 3 -2


QUESTION 26

The quicksort algorithm sorts values in an array into ascending order based on the following algorithm:

pick the pivot

partition the elements of the array based on the pivot

quicksort the elements less than or equal to the pivot

quicksort the elements greater than the pivot

Given the following initial array:

{5, 8, 12, 10, -5, 7, 13}

Which of the following is a possible ordering of the elements of the array after the first partition assuming the middle element

of the array (the value 10 in this case) is chosen as the first pivot?

A. {-5, 8, 7, 5, 10, 12, 13} B. {13, 5, 12, 10, -5, 7, 8}

C. {10, 5, 8, -5, 7, 12, 13} D. {12, 13, 5, -5, 8, 7, 10}

E. {5, 8, 12, 10, -5, 7, 13}

QUESTION 27

Given an array of N distinct elements in random order, what is the Big O of the traditional implementation of the quicksort

algorithm?

A. O(NlogN) B. O(N2) C. O(N2logN) D. O(N3/2) E. O(N3)

QUESTION 28

double aa = 2.4;

double bb = 1.6;

int x = (int)aa + (int)bb;

System.out.print(x);


A. 3.0 B. 4 C. 4.0

D. 3 E. 5

QUESTION 29

int[] small = {-3, 4, 1, 2};

int index = small[0];

if(index > 0 && index < small.length

&& small[index] > index){

System.out.print( small[index] );

}

System.out.print(index);


A. false0 B. -3

C. true0 D. 4

E. There is no output due to an

ArrayIndexOutOfBoundsException.

QUESTION 30

String st = "XA";

st = st + st + st;

System.out.print(st);


A. "XA" B. XAXAXAXA

C. XAXAXA D. XXXAAA

E. "XAXAXA"


QUESTION 31

// pre: list.length > 0

public double max(double[] list){

double max = 0.0;

for(double d : list)

if( d > max )

max = d;

return max;

}

Method max to the right is suppose to return the max

value in the array named list but it does not always

work as intended. What must be changed to make the

method work as intended?

A. Change the segment if( d > max ) to if( d <= max)

B. Change the segment for(double d : list)

to for(double d : list<Double>)

C. Change the segment for(double d : list)

to for(double d = list[0] : list)

D. Change the statement return max; to return d;

E. Change the statement double max = 0.0; to double max = list[0];

QUESTION 32 Set<Character> chs;

chs = new TreeSet<Character>();

String ta1 = "milner";

for(int i = 0; i < ta1.length(); i++)

chs.add(ta1.charAt(i));

ArrayList<Character> lst;

lst = new ArrayList<Character>();

String ta2 = "manblum";

for(int i = 0; i < ta2.length(); i++)

lst.add(ta2.charAt(i));

System.out.print(chs.retainAll(lst));

System.out.print(chs);


A. true[l, m, n]

B. true[l, m, m, n]

C. false[l, m, m, n]

D. null[l, m, n]

E. true[a, b, u]

QUESTION 33

int b1 = 8;

int b2 = 7;

b2 = b1 | b2 & 17;

System.out.print(b2);


A. true B. 25 C. 9

D. 15 E. false

QUESTION 34 PriorityQueue<Integer> pq;

pq = new PriorityQueue<Integer>();

pq.add(13);

pq.add(7);

pq.add(7);

pq.add(10);

System.out.print( pq.remove() + " ");

System.out.print( pq.remove() );


A. 7 7 B. 10 13 C. 13 10

D. 7 10 E. 13 7


QUESTION 35 String[] initials = {"GM", "OAS", "LA",

"IB", "JLR"};

ArrayList<String> con;

con = new ArrayList<String>();

for(String s : initials)

con.add(s);

Iterator<String> it = con.iterator();

while(it.hasNext())

if(it.next().length() == 2)

System.out.print(it.next());


A. IB

B. OASIB

C. OASJLR

D. GMLAIB

E. There is no output due to a

NoSuchElementException.

QUESTION 36 public int problem(double[][] mat){

int res = 0;

int m = -1;

for(int i = 0; i < mat.length; i++){

int var = 0;

for(int j = 0; j < mat[i].length; j++)

if( mat[i][j] < 0 )

var++;

if( var > m ){

res = i;

m = var;

}

}

return res;

}

Which of the following best describes what method

problem returns?

A. The maximum value in mat.

B. The index of the row in mat closest to 0 that

contains the minimum value in mat.

C. The index of the last row in mat that contains a

negative value.

D. The index of the row in mat closest to 0 that

contains the most negative values.

E. The minimum value in mat.

QUESTION 37

char[] arr = {'a', 'B', 'A', 'a'};

Arrays.sort(arr);

System.out.println( Arrays.toString(arr) );


A. [a, a, A, B] B. [A, B, a, a]

C. [B, A, a, a] D. [A, a, a, B]

E. [a, A, B]

QUESTION 38

String nm = "Wirth";

boolean result = nm instanceof ArrayList;

System.out.println(result);


A. null B. true C. false

D. There is no output due to a syntax error.

E. There is no output due to a runtime error.


QUESTION 39 public class Structure<E>{

private ArrayList<E> con;

public Structure(){

con = new ArrayList<E>();

}

public boolean add(E obj){

boolean result = con.contains(obj);

if( !result )

con.add(obj);

return result;

}

public boolean present(E obj){

return con.contains(obj);

}

public int size(){

return con.size();

}

public boolean remove(E obj){

return con.remove(obj);

}

}

What is output by the following client code?

Structure<String> s;

s = new Structure<String>();

s.add("A");

s.add("B");

s.add("B");

s.add("AB");

s.add("A");

System.out.print(s.size());

A. 3 B. 2 C. 5

D. 10 E. 6

QUESTION 40

What type of data structure does the Structure class

implement?

A. A stack B. A set C. A heap

D. A queue E. A list


No Test Material on this Page.


Standard Classes and Interfaces — Supplemental Reference

class java.lang.Object

o boolean equals(Object other)

o String toString()

o int hashCode()

interface java.lang.Comparable<T>

o int compareTo(T other)

Return value < 0 if this is less than other.

Return value = 0 if this is equal to other.

Return value > 0 if this is greater than other.

class java.lang.Integer implements

Comparable<Integer>

o Integer(int value)

o int intValue()

o boolean equals(Object obj)

o String toString()

o int compareTo(Integer anotherInteger)

o static int parseInt(String s)

class java.lang.Double implements

Comparable<Double>

o Double(double value)

o double doubleValue()


o String toString()

o int compareTo(Double anotherDouble)

o static double parseDouble(String s)

class java.lang.String implements

Comparable<String>

o int compareTo(String anotherString)


o int length()

o String substring(int begin, int end)

Returns the substring starting at index begin

and ending at index (end - 1).

o String substring(int begin)

Returns substring(from, length()).

o int indexOf(String str)

Returns the index within this string of the first occurrence of

str. Returns -1 if str is not found.

o int indexOf(String str, int fromIndex)

Returns the index within this string of the first occurrence of

str, starting the search at the specified index.. Returns -1 if

str is not found.

o charAt(int index)

o int indexOf(int ch)

o int indexOf(int ch, int fromIndex)

o String toLowerCase()

o String toUpperCase()

o String[] split(String regex)

o boolean matches(String regex)

class java.lang.Character

o static boolean isDigit(char ch)

o static boolean isLetter(char ch)

o static boolean isLetterOrDigit(char ch)

o static boolean isLowerCase(char ch)

o static boolean isUpperCase(char ch)

o static char toUpperCase(char ch)

o static char toLowerCase(char ch)

class java.lang.Math

o static int abs(int a)

o static double abs(double a)

o static double pow(double base,

double exponent)

o static double sqrt(double a)

o static double ceil(double a)

o static double floor(double a)

o static double min(double a, double b)

o static double max(double a, double b)

o static int min(int a, in b)

o static int max(int a, int b)

o static long round(double a)

o static double random()

Returns a double value with a positive sign, greater than

or equal to 0.0 and less than 1.0.

interface java.util.List<E>

o boolean add(E e)

o int size()

o Iterator<E> iterator()

o ListIterator<E> listIterator()

class java.util.ArrayList<E> implements List<E>

Methods in addition to the List methods:

o E get(int index)

o E set(int index, E e)

Replaces the element at index with the object e.

o void add(int index, E e)

Inserts the object e at position index, sliding elements at

position index and higher to the right (adds 1 to their

indices) and adjusts size.

o E remove(int index)

Removes element from position index, sliding elements

at position (index + 1) and higher to the left

(subtracts 1 from their indices) and adjusts size.

class java.util.LinkedList<E> implements

List<E>, Queue<E>

Methods in addition to the List methods:

o void addFirst(E e)

o void addLast(E e)

o E getFirst()

o E getLast()

o E removeFirst()

o E removeLast()


class java.util.Stack<E>

o boolean isEmpty()

o E peek()

o E pop()

o E push(E item)

interface java.util.Queue<E>

o boolean add(E e)

o boolean isEmpty()

o E peek()

o E remove()

class java.util.PriorityQueue<E>

o boolean add(E e)

o boolean isEmpty()

o E peek()

o E remove()

interface java.util.Set<E>

o boolean add(E e)

o boolean contains(Object obj)

o boolean remove(Object obj)

o int size()

o Iterator<E> iterator()

o boolean addAll(Collection<?> extends E> c)

o boolean removeAll(Collection<?> c)

o boolean retainAll(Collection<?> c)

class java.util.HashSet<E> implements Set<E>

class java.util.TreeSet<E> implements Set<E>

interface java.util.Map<K,V>

o Object put(K key, V value)

o V get(Object key)

o boolean containsKey(Object key)

o int size()

o Set<K> keySet()

o Set<Map.Entry<K, V>> entrySet()

class java.util.HashMap<K,V> implements Map<K,V>

class java.util.TreeMap<K,V> implements Map<K,V>

interface java.util.Map.Entry<K,V>

o K getKey()

o V getValue()

o V setValue(V value)

interface java.util.Iterator<E>

o boolean hasNext()

o E next()

o void remove()

interface java.util.ListIterator<E> extends

java.util.Iterator<E>

Methods in addition to the Iterator methods:

o void add(E e)

o void set(E e)

class java.lang.Exception

o Exception()

o Exception(String message)

class java.util.Scanner

o Scanner(InputStream source)

o boolean hasNext()

o boolean hasNextInt()

o boolean hasNextDouble()

o String next()

o int nextInt()

o double nextDouble()

o String nextLine()

o Scanner useDelimiter(String pattern)

Computer Science Answer Key

UIL Invitational A - 2010

1. A 11. E 21. C 31. E

2. D 12. D 22. A 32. A

3. C 13. A 23. E 33. C

4. D 14. E 24. E 34. A

5. C 15. B 25. D 35. B

6. D 16. B 26. A 36. D

7. B 17. A 27. A 37. B

8. A 18. E 28. D 38. D

9. B 19. E 29. B 39. A

10. E 20. C 30. C 40. B

Notes:

The clause "Choose the most restrictive correct answer." is necessary because per the formal definition of Big O, an

algorithm that is O(N2) is also O(N3) , O(N4) , and so forth.

17. The first elements of parts is an empty String formed by the start of the String and the first colon.

23. Descendant classes do not have access to the private instance variables of ancestor classes.

31. The change is necessary for cases when all values in the array are less than 0.

38. The syntax error is "Incompatible conditional operand types String and ArrayList". It is

impossible for variable of type String to ever refer to an object that is an ArrayList so the compiler rejects

the expression.

the university interscholastic league number sense test hs

Documents