uil calculator applications - mr. guerrero's chemistry...

DO NOT OPEN THE TEST UNTIL INSTRUCTED TO BEGIN I. Calculator Applications rules and scoring—See UIL Constitution II. How to write the answers

A. For all problems except stated problems as noted below—write three significant digits.

1. Examples (* means correct but not recommended)

Correct: 12.3, 123, 123.*, 1.23x10*, 1.23x100*

1.23x101, 1.23x1001, .0190, 0.0190, 1.90x10-2

Incorrect: 12.30, 123.0, 1.23(10)2, 1.23.102, 1.230x102,

1.23*102, 0.19, 1.9x10-2, 19.0x10-3, 1.90E-02

2. Plus or minus one digit error in the third significant digit is permitted.

B. For stated problems 1. Except for integer, dollar sign, and significant digit

problems, as detailed below, answers to stated problems should be written with three significant digits.

2. Integer problems are indicated by (integer) in the answer blank. Integer problems answers must be exact, no plus or minus one digit, no decimal point or scientific notation.

3. Dollar sign ($) problems should be answered to the exact cent, but plus or minus one cent error is permitted. Answers must be in fixed notation. The decimal point and cents are required for exact-dollar answers.

4. Significant digit problems are indicated by underlined numbers and by (SD) in the answer blank. See the UIL Constitution and Contest Manual for details.

III. Some symbols used on the test A. Angle measure: rad means radians; deg means degrees. B. Inverse trigonometric functions: arcsin for inverse sine, etc.

C. Special numbers: for 3.14159 ...; e for 2.71828 ... D. Logarithms: Log means common (base 10); Ln means natural

(base e); exp(u) means eu.

UIL Calculator Applications

Test 13B (Invitational B)

Name

5x(Last Problem Attempted) + + +

7x(Number Incorrect) - - -

2x(Number Incorrect SDs) - - -

TOTAL SCORE

Tie Breaker: Points scored on Stated and Geometry Problems

+ + +

B-1

13B-1. (4.7 – 2.21) / (–2.68) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 1= ______________

13B-2. 1.44/ 6.68 + 0.164 – 0.216 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2= ______________

13B-3. (–1.42 – 0.215 – 0.387 + 0.128) x (–1.44) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 3= ______________

13B-4. { (–554) (0.795 + 0.96 – 0.23) (–111) } + 70000 - - - - - - - - - - - - - - - - - - - - - - - - 4= ______________

13B-5. { (0.0741 – 0.0401 + 0.0717) / (–0.0879) }

{ (–0.0841) (0.0565) / (0.0952) } - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 5= ______________

13B-6. What is the product of -22, 9.45 and 5/ 41? - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 6= ______________

13B-7. What is x if the result of 3x-7 divided by 37 equals 37? - - - - - - - - - - - - - - - - - - - 7= ______________

13B-8. I n a group of 235 people, at least a two thirds m ajor ity is needed to pass a m ot ion. What m inim um num ber of people m ust vote negat ively to defeat a m ot ion? - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 8= _________integer

13B-9. RHOMBUS

Area = ?

13B-9 = ______________

13B-10. CI RCLE

Area = 7.28

13B-10 = ______________

AC = 191

BD = 308

B-2

13B-11. (–3.34 + 2.65) (1.79 – 1.74 + 2.34)

(–1.9) (5.8) – 24.4 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 11= ______________

13B-12. (–9940) (17.1) – (835 + 411) (–668)

(264 + 266 + 167) (–870) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 12= ______________

13B-13. (–7.44x10–5 – 1.74x10–4) { 84.7 + (6.89) (1.35) }

(1.64) (–0.945 + 0.435) (5.36) (–1.81) - - - - - - - - - - - - - - - - - - - - 13= ______________

13B-14. (19.8 + 12.8) (1.29 + ) (89.9 – 138)

(49.9 + 8.29) (–53.3) { (32.5) / (–51.5) } - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 14= ______________

13B-15. (68800 + 18800 – 20800) (0.933 – 0.639 – 0.75)

(–0.0758) (–0.0557) (0.0759) (8.75 + + 48.3) - - - - - - - - - - - - - - - - - - - - 15= ______________

13B-16. According to the 2010 census, the populat ion of Wichita Falls TX was 104,553. On average, how m any people in Wichita Falls have Meniere’s Disease if the nat ional prevalence of the disease is 0.2% ? - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 16= ______________

13B-17. What is the percent difference in the populat ion density of Texas,

98.07 persons/ m i2, and that of Wyom ing, 5.851 persons/ m i2? - - - - - - - - - - - - - - - - - - 17= ________% (SD)

13B-18. Clyde Barrow, a fam ous Texas out law, was born on March 24, 1909 and died in an am bush on May 23, 1934. How long did he live? - - - - - - - - - - - - - - - - - - - - - - 18= __________years

13B-19. RI GHT TRI ANGLE

13B-19 = ______________

13B-20. RI GHT TRI ANGLE

Perim eter = ?

13B-20 = ______________

B-3

13B-21. 1

–3.33 + 5.15 + 1 – 3.42

+ 1

(0.66) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 21= ______________

13B-22. 2.23 – 0.638–0.293 +

(–3.89)0.952

2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 22= ______________

13B-23. (0.317) (0.602) (–0.526)2/ 0.573 + 1/ 34.4 + 97.4 - - - - - - - - - - - - - - - - - 23= ______________

13B-24. 7.95 + 1.3 + 0.831/ 0.436–4.29 + 3.53

2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 24= ______________

13B-25. (340) (0.209) + (651) / (4.26) + [ ](0.977) (4.96) 2 - - - - - - - - - - - - - - - - - - - 25= ______________

13B-26. The m ost expensive st reet- legal autom obile in 2012 was the Bugat t i Veyron Super Sports Auto which was pr iced at $2,400,000. Suppose this am ount was paid out over a 3 yr period at no interest . I f a car paym ent should not exceed 15% of one’s total incom e, what m inim um annual salary should this car ’s owner m ake? - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 26= $_____________

13B-27. Frank gave Tim an ent ire pizza one day. On the second and subsequent days, Frank gave Tim a fract ion x of the previous day’s am ount . What was x if Tim eventually wound up with a total of 3.8 pizzas? - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 27= ______________

13B-28. I n the m id-2000s, Br ian Mann threw a football 100 yards. Assum e the release angle was 45. What would be the m axim um vert ical height of a throw with the sam e release velocity if the ball were thrown st raight upwards? - - - - - - - - 28= _____________ft

13B-29. FRUSTUM

Total Surface Area = ?

13B-29 = ______________

13B-30. CYLI NDER

Volum e = 0.00472

13B-30 = ______________

B-4

13B-31. –0.0594–0.219 + 0.185 + 4.97 x { }2860 + (–54.1)2 – 2.80x107 - - - - - 31= ______________

13B-32. (–400 + 2040)2

96.7 – 92.5 +

2.19x107

208 + 518 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 32= ______________

13B-33. [ (639 – 399) (0.629/ 0.29) ] 1/ 2

(0.28)2 + (0.254 + 0.309)2 + 0.0519 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 33= ______________

13B-34. [ 1.11x10–4/ (0.271 + 0.712) + 1/ (3020) ] 1/ 2

(9250 + 9430)2 x 9380 – (–5300) - - - - - - - - - - - - - - - - - - - - - - - - - 34= ______________

13B-35.

5650 + 7750

(2240) (12000)+ (5200)2

3740 + 6240 + (5.86 – 5.51)2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 35= ______________

13B-36. Saturn’s m oon Titan has an average density of 1.88 g/ cm 3. I f it is

com posed of half water and half rock, what is the density of Titan’s rock? - - - - - - - 36= _________g/ cm3

13B-37. A 2.5 in diam eter top spins on a table at constant 2000 RPM. The top’s spindle t ip in contact with the table is not stat ionary but t raverses a circle 7 inches in diam eter on the table top with a linear velocity of 3 in/ s. A dizzy, non-crawling ant on the top’s outer surface t ravels 440 ft before the top falls off the edge of the table. How long did the top spin? - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 37= _____________s

13B-38. A golfer dr ives a ball 120 ft using an 8 iron, not count ing the ball roll after landing. What is the im pact velocity of the 8 iron on the ball if an 8 iron launches a ball at an angle of 37 degrees relat ive to the ground? - - - - - - - - - - - - - - - - 38= ___________m ph

13B-39. CI RCLE AND EQUI LATERAL TRI ANGLE

13B-39 = ______________

13B-40. SCALENE TRI ANGLES

13B-40 = ______________

B-5

13B-41. (–0.744) (–0.881)10{ –0.48/ –0.206} - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 41= ______________

13B-42. (50.1)(33.6) [ ]1 – e–(0.931) (0.729) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 42= ______________

13B-43. (–6.89)Log(6.32 – 3.64)

(–2.48) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 43= ______________

13B-44. (7.51x106 + 2.43x107)–(0.305 + 0.326) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 44= ______________

13B-45.(deg) sin 90° x (–8.23)(55.1) + cos { }147° – 123° - - - - - - - - - - - - - - - - - - - - - - - - - 45= ______________

13B-46. The st raight- line distance between Flour Mound and Monahans, 358 m i

apart , is 2.27 in on a m ap. I f Texas’ area on the m ap was 10.8 in2, what is the

area of Texas? - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 46= ___________m i2

13B-47. The Nat ional Hurr icane Center over the years has im proved the accuracy of their predict ion of the landfall of hurr icanes 72 hr out . I n five year increm ents start ing in 1975, the average error of landfall predict ion in m iles was 400, 401, 330, 300 and 225. What was the est im ated error for 2012? - - - - - - - - - - 47= ____________m i

13B-48. For what value of v does 5v5 = 19v4+ 5? - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 48= ______________

13B-49. CUBE WI TH HEMI SPHERI CAL CAVI TY

Total Surface Area = 79.8

13B-49 = ______________

13B-50. FRUSTUM AND CYLI NDER

Total Volum e = 60

13B-50 = ______________

B-6

13B-51. (0.452) 10–(6.89 – 1.94)

0.88 + 0.301 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 51= ______________

13B-52. (–0.0437 – 0.0388) e(0.615) (2.15)

e–(9.37 – 1.73) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 52= ______________

13B-53. Ln(7.89x10–4 + 8.99x10–4)

3.81x10–5 + Ln(9.37x10–4)

2.66x10–4 – 1.93x10–4 - - - - - - - - - - - - 53= ______________

13B-54. 1

(0.744) (–0.842) + (0.881 + 0.263) (0.275 – 0.293) - - - - - - - - - - - - - - - - - - 54= ______________

13B-55.( rad) arctan (2760) (0.586)(3.48) (13.5) + (0.172) (3.61) - - - - - - - - - - - - - - - - - - - - - - - - - - 55= ______________

13B-56. What is the value of y at the m axim um for y = -5x+ lnx? - - - - - - - - - - - - - - - - 56= ______________

13B-57. Farm er Davis has 100 ft of fence and wants to build the largest rectangular enclosure possible. He decides to use one side of his barn for one of

the four rectangular edges. What is the largest area he can get? - - - - - - - - - - - - - - - - 57= ____________ft2

13B-58. Calculate A11 if A = 3B+ 4CD , B = 嵳13 919 3

嵳, C = 嵳3 44 1

嵳, and D = -B. - - - 58= _________integer

13B-59. SOLI D OF REVOLUTI ON (y = -0.5)

Radians Volum e = ?

13B-59 = ______________

13B-60. CONCENTRI C CI RCLES AND SQUARE

R/ r = ?

13B-60 = ______________

Note: 豹 cos2 (πx)dx=x2

+14π

sin(2πx) + Constant

0

B-7

13B-61. (1/ 2)Ln

(3.86) x (1.72) x (8.82)3

(8.82) (9.86)2

2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 61= ______________

13B-62. eLn[ () (33.1) ] + 10Log[ (0.246) (446) ] - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 62= ______________

13B-63. ( rad) 98.2

6(–7.61){ }(0.42) + (0.281)sin(–3.29) 5 - - - - - - - - - - - - - - - - - - - - - - - 63= ______________

13B-64. (0.38) – (0.38)2

2 + (0.38)3

3 – (0.38)4

4 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 64= ______________

13B-65. ( rad) (0.0692) (–0.00412) – Ln{ }(0.238) + (–6.6)e(–4.04)

arcsin{ }(0.406) / (0.956 + 0.374) - - - - - - - 65= ______________

13B-66. The distance x a carbon atom m oves in solid iron equals 謬2Dot exp( -Q

RT) where Do = 0.2 cm2/ s, t = elapsed t im e, Q = 32,000 cal/ m ole,

R = 1.987 cal/ (m oleK) and T = absolute tem perature (K) . Carbon is placed on the surface of iron powder 80 µm in diam eter. Calculate the m inim um tem perature needed to diffuse carbon to the center of the iron part icles in 4 hr. 66= ____________º C

13B-67. A pipe has an outside diam eter of 2.625 in and an inside diam eter of 1.75 in. I f Kelly hacksaws the pipe in two, what fract ion of the pipe cross sect ional area is sawn when the blade breaks through to the inside? - - - - - - - - - - - - 67= ____________%

13B-68. Bulk potatoes are sliced into 0.015 in thick slices to m ake potato chips. A potato loses 75% of it s m ass during frying. Potatoes on average are 6.5 in long, weigh 0.9 lb and cost $0.75/ lb. An 11-oz bag of chips costs $2.99 and has 128 chips. What is the rat io of the cost of chips to the cost of the start ing bulk potatoes needed to m ake those chips (on a m ass basis)?- - - - - - - - - - - - - - - - - - - - - - - - - - 68= _____________

13B-69. SCALENE TRI ANGLES

13B-69 = ______________

13B-70. THREE-QUARTER CI RCLE AND RECTANGLE

Total Area = 1.98

13B-70 = ______________

13B-1 = -0.929

= -9.29x10-1 13B-2 = 0.164

= 1.64x10-1 13B-3 = 2.73

= 2.73x100 13B-4 = 164,000

= 1.64x105 13B-5 = 24.1

= 2.41x101 13B-6 = -25.4

= -2.54x101

13B-7 = 459

= 4.59x102

13B-8 = 79 integer

13B-9 = 29,400

= 2.94x104

13B-10 = 3.04

= 3.04x100

13B-11 = 0.0466

= 4.66x10-2 13B-12 = -1.09

= -1.09x100 13B-13 = -0.00288

= -2.88x10-3 13B-14 = -3.55

= -3.55x100

13B-15 = -1.58x106 13B-16 = 209

= 2.09x102

13B-17 = -94.034

= -9.4034x101 (5SD)

13B-18 = 25.2

= 2.52x101

13B-19 = 0.757

= 7.57x10-1

13B-20 = 395

= 3.95x102

13B-21 = -1.53

= -1.53x100 13B-22 = 70.4

= 7.04x101 13B-23 = 0.220

= 2.20x10-1 13B-24 = 196

= 1.96x102 13B-25 = 107

= 1.07x102 13B-26 = $5,333,333.33

13B-27 = 0.737

= 7.37x10-1

13B-28 = 150

= 1.50x102

13B-29 = 29,900

= 2.99x104

13B-30 = 0.135

= 1.35x10-1

13B-31 = 3330

= 3.33x103

13B-32 = 2.13x106 13B-33 = 51.0

= 5.10x101

13B-34 = 4.98x10-13

13B-35 = 2.15x10-8 13B-36 = 2.76

= 2.76x100

13B-37 = 19.9

= 1.99x101

13B-38 = 43.2

= 4.32x101

13B-39 = 302

= 3.02x102

13B-40 = 0.619

= 6.19x10-1

13B-41 = 140

= 1.40x102 13B-42 = 0.735

= 7.35x10-1 13B-43 = 1.19

= 1.19x100

13B-44 = 1.84x10-5 13B-45 = 0.681

= 6.81x10-1 13B-46 = 269,000

= 2.69x105

13B-47 = 87.7

= 8.77x101

13B-48 = 3.80

= 3.80x100

13B-49 = 3.43

= 3.43x100

13B-50 = 4.14

= 4.14x100

13B-51 = 4.29x10-6 13B-52 = -644

= -6.44x102 13B-53 = -263,000

= -2.63x105 13B-54 = 1.78

= 1.78x100 13B-55 = 2.16

= 2.16x100 13B-56 = -2.61

= -2.61x100

13B-57 = 1250

= 1.25x103

13B-58 = -421 integer

13B-59 = 6.68

= 6.68x100

13B-60 = 1.41

= 1.41x100

13B-61 = 1.67

= 1.67x100 13B-62 = 214

= 2.14x102 13B-63 = -0.0450

= -4.50x10-2 13B-64 = 0.321

= 3.21x10-1 13B-65 = 6.78

= 6.78x100 13B-66 = 544

= 5.44x102

13B-67 = 19.7

= 1.97x101

13B-68 = 15.0

= 1.50x101

13B-69 = 84.2

= 8.42x101

13B-70 = 0.835

= 8.35x10-1

UNIVERSITY INTERSCHOLASTIC LEAGUE

Making a World of Difference

do not turn this page until

you are instructed to do so!

MathematicsInvitational B • 2013

1. Evaluate: 0.1666... 0.08333... 1 1 13 9 15ƒ ‚ q

(A) (B) 0.22777... (C) (D) 0.23888... (E) 7 1 130 18 44

2. A waitress received a $4.50 tip from one customer whose bill was $25.00 and a $6.00 tip from another customer whose bill was $30.00. What was her average tip percentage?

(A) 20% (B) 19% (C) 18% (D) 16% (E) 15%

3. Venn Circle Estates has 25 houses. Three houses have dogs, but not cats. Ten houses have cats and dogs. Eight houses have cats, but no dogs. How many house do not have a cat or a dog?

(A) (B) 1 (C) 2 (D) 3 (E) 40

4. A bag contains 1 white chip, 2 blue chips, and 3 red chips. What is the probability of randomly selecting two chips (without replacement) that are different colors?

% % %(A) 73 (B) 66% (C) 48% (D) 36 (E) 101 2 23 3 3

5. Two thousand thirteen plus thirty-one thousand two is subtracted from one million one hundred twenty-three thousand five hundred eight. The sum of the digits in the difference is?

(A) 32 (B) 27 (C) 26 (D) 20 (E) 13

6. Line contains point (1, 3) and is perpendicular to the line shown. Which of the following points k lies on line ?k

(A) (11, 7) (B) (10, 6) (C) (9, 3) (D) (13, 8) (E) ( , 0)q 7

7 1, 0, 1} is closed under how many of these operations:. The set {q subtraction multiplication ƒaddition division square rootq ‚ È (A) 1 (B) 2 (C) 3 (D) 4 (E) 5

8. Simplify: Š ‹ Š ‹x 9 3x 10x 3x 6x 9 3x 8x 3

2 2

2 2q

q q ƒ

(A) (B) (C) 1 (D) (E) q 1 x 3 x 3 x 6x 9x 3 x 3 x 6x 9 q q q

2

2

UIL Math B 2013 - page 1

9. If S varies directly as the square of and S = when = 0.5, find when S = 36 .r r r1 1 2

(A) 3 (B) 6 (C) 9 (D) (E) 3 213

È 10. If a quadrilateral is inscribed in a circle, then its opposite angles are _____ angles.

(A) right (B) supplementary (C) base (D) congruent (E) complementary

__ __ __ __ w

w 11. AB, AC, BD, and CD are chords of circle O. Find APB if m mAED mBCn = 190° and = 30° .

A

B

C

D

PE

(A) 70 (B) 80 (C) 90 (D) 100 (E) 110 ° ° ° ° °

12. How many vertices does a Platonic solid have if it has 20 faces and 30 edges?

(A) 2 (B) 10 (C) 12 (D) 18 (E) 20

13. Given the height and diameter find the lateral surface area of the cylinder. (nearest sq. cm.)

(A) 754 cm (B) 565 cm (C) 502 cm (D) 377 cm (E) 314 cm2 2 2 2 2

14. Willie Mixit has a 15-ounce solution of alcohol and water that is 75% alcohol. He wants to add some 67% alcohol solution to his solution to make a 72% alcohol solution. How many ounces of the 67% solution must he add?

(A) 3 oz (B) 5 oz (C) 9 oz (D) 10 oz (E) 15 oz

15. Let f(x) = f (3)2 5x2x 5

1q . Find q .

(A) 7 (B) (C) (D) (E) 1 11 1 2 22 13 17 11 5q q 1 3

16. ACE = _________________ 16 16 16‚ 8

(A) 5670 (B) 456C (C) 765 (D) 72F (E) 158C


17. If A B = 15 and A B = 27 then B A = ______. ‚ ¸ ¸ (A) 3 13 (B) 3 13 (C) 2 3 (D) 2 3 (E) 3È È È Èq

18. Let f(x) = ax x 11 where a, b, and c are constants. If f( ) = 4 then f( 3q q q q b 7 7) = ?

(A) 15 (B) 7 (C) (D) (E) q q q 7 18 26

19. How many degrees are there in 6 radians?341

(A) 2,250° (B) 607.5° (C) 1,080° (D) 1,215° (E) 911.5°

20. Given the triangle shown, find the height, h, if m XZY = YZ = 22 cm, and XZ = 16 cm.n 16 ,

X

Z

Y

h

(A) 11 cm (B) 12.375 cm (C) 13.125 cm (D) 13.75 cm (E) 14 cm

21. If the sin = 0.28 and is in QII, then sec is :) ) )

(A) (B) (C) (D) E) q q q q q 0.68 0.96 1 3 3 (1 3 424 7 7

22. In the expansion of (x ) , the sum of the coefficients of the 2nd, 4th, and 6th terms is:q y 6

(A) (B) (C) (D) (E) q q q q q 41 32 27 20 8

23. Let A = and B = . Find the sum of the elements of AB.’ “ ’ “

3 4 2 1

1 3 4 2q

q

(A) 24 (B) 18 (C) 12 (D) 6 (E) 0

24. Simplify: 3log b log 2b log 3b a a aq 2

(A) 2log ( (B) log (2b) (C) log ( (D) 2log ( (E) 3log ( a a a a a3b 3b 2b b4 4 3 2) ) ) )

2

25. Point P has polar coordinates of ( 5, 16 ) and rectangular coordinates of (x , y). Where does point P lie on the Cartesian coordinate plane?

(A) Q1 (B) (C) QIII (D) x-axis (E) y-axisQII

26. If f (x) = 2x x 5 and f(2) = 0, find f( 1). w 3 4 q q

(A) 5.5 (B) 1.5 (C) 1 (D) (E) q q 1 3.5


27. U combinations. The first number of each. R. SAFE combination locks have three number combination is a prime number, the second is a Fibonacci number, and third digit is a triangular number. How many different combinations are possible?

(A) 768 (B) 678 (C) 616 (D) 28 (E) 25

28. Evaluate: 2x 1)'q a

a 2( q dx

(A) (B) 2a a (C) (D) (E) a4a 4a 6a 2a 2a3 3 3

23 3 3q q 2

q q

29 Let x y = 16. Find D y.. 2 2 x

(A) 4 (B) x y (C) (D) (E) q xy x 8

y x y

30. Lotta Scents has 2 quarters, 3 dimes, and 4 nickels. Each of the coins are distinguishable since they all have a different date on them. How many ways can she give her brother Noah Scents $0.50?

(A) 144 (B) 120 (C) 50 (D) (E) 26 25

31. All of the elements of {14, 16, 19, 21, 25} are considered to be __ numbers.

(A) abundant (B) happy (C) lucky (D) odious (E) wasteful

32. The cardinality of the set of real numbers is strictly larger than the cardinality of the set of natural numbers is a major theorem proven by _________________ .

(A) John Napier (B) Georg Cantor (C) Christian Goldbach (D) Freda Porter (E) Euclid

33. The midradius (nearest tenth) of a dodecahedron with edge length of 10 cm is:

(A) 2.6 cm (B) 6.5 cm (C) 8.1 cm (D) 11.6 cm (E) 13.1 cm

34. Using Blaise Pascal's triangle and letting the 1 at the top be row 0, determine which of the following numbers will be in row 11.

(A) 136 (B) 222 (C) 330 (D) 451 (E) 505

35. Find the number of positive integral divisors of 1,620.

(A) 30 (B) 25 (C) 20 (D) 15 (E) 10


36. If R, S, and T represent digits then RST ST2 4 8 q R has a numeric value in base 10 of:

(A) 9R (B) 5R (C) 5R 6S (D) 9R (E) 10R q q q q q 2S 2S 2S 2T 2S

37. wants to score 194 on this mathematics test. He gets 6 points for each correct Matt E. Mattiks answer and loses 2 points for each incorrect answer. Skipped problems are not counted. What is the least number of problems Matt has to work?

(A) 33 (B) 35 (C) 37 (D) 39 (E) 41

38. Find m PQR of the equilateral triangle shown. (nearest degree)n

(A) 112 (B) 73 (C) 80 (D) 107 (E) 100 ° ° ° ° °

39. Three years ago, Ima Old's age was one year more than twice Ura Young's age. Six years from now, Ima will be ten years more than half Ura's age. What is the difference in their ages now?

(A) 4 years (B) 10 years (C) 5 years (D) 3 years (E) 6 years

40. Let P and Q be the roots of 3x 6x 10 .2 q = 0 Find P 5P Q 10P Q 10P Q 5PQ Q .5 4 3 2 2 3 4 5

(A) (B) (C) 19 (D) (E) q q q q q 12 15 21 32

41. If 2x 1 3x5 6y 4 q = , then y equals ________.

(A) (B) (C) (D) (E) q q q 11 10 21 13 2010x 21x 13x 21x 42x

42. If a = 5, a = 4 and a = a (a for n 3, then a equals:1 2 n n 1 n 2 5(n 3) [( ) )] q q

qq

(A) 25 (B) (C) 9 (D) (E) 16 1 3q q

43. The circumcenter, centroid, and orthocenter of a scalene triangle are always:

(A) concurrent (B) on the interior (C) collinear (D) equidistant (E) on the exterior

44. The Tic Toc Shop's circular clock stopped working at 11:20 pm. What was the measure of the smaller angle between the big hand and the little hand at that time?

(A) 72 ° (B) 108 ° (C) 112 ° (D) 140 ° (E) 150 °


45. The length of the latus rectum of 9x y = 36 is:2 2q 4

(A) 2 (B) 4 (C) 5 (D) 9 (E) 182 13 3

46. Find the slope of the tangent line to 9x y = 36 at point P(1 , 5). (nearest tenth)2 2 13 4 qÈ

(A) 1.3 (B) 1.7 (C) 2.3 (D) 3.0 (E) 3.1

47. Captain Saul T. Water leaves port and sails his barge on a bearing of 40° for 20 miles. Then he changes course and sails 12 miles on a bearing of 75°. How far from port is the barge? (nearest tenth)

(A) 27.3 mi (B) 21.9 mi (C) 32.0 mi (D) 35.0 mi (E) 30.6 mi

48. Find (2 i) and express the answer in standard form. 3 4

(A) 61 i (B) i (C) 119 i (D) 0i E) 0 iq q q q q q q 30 313 312 120 1 239 (

49. Let V = 12, V = 15, where the direction angles of V and V are 61 ° and 331 °,¼ ¼ ¼ ¼1 2 1 2 respectively. Find the direction angle of V V . (nearest degree)¼ ¼1 2

(A) 10 ° (B) 13 ° (C) 22 ° (D) 24 ° (E) 27 °

50. Use the Fibonacci characteristic sequence ... p, q, , r, 4 ... to Find p q r.q 3

(A) 5 (B) 14 (C) 1 (D) 1 (E) q q q 4

51. Let f(x) = 3x 2. Find g(f(x)) f(g(x) .q 4 and g(x) = 5x )

(A) 2x 6 (B) 30x 16 (C) 8x 2 (D) 2x 6 (E) q q q q q 20

52. The outer four small circles are tangent to the big circle and to the inner small circle in the center. All five small circles are congruent. Will Amtel shoots an arrow and hits somewhere in the large circle. What are the odds that the arrow hit the shaded section?

(A) (B) 3:2 (C) 5:2 (D) 1:1 (E) 2:15:4

53. Given the function f(x) = 2x x x 6 there is a possibility of how many real zeroes?4 3 2q q q 3 2 x

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


54. Let f(x) = . At which of these intervals is function f continuous?13 2x x È q 2

(A) [ (B) ( (C) [ (D) ( (E) (q q q q q 1, 3] 3, 1] 1, 3) 1, 3) 3, 1)

55. The polar graph of r = 2 4cos is symmetric to the: )

(A) polar axis (B) pole (C) line = (D) line = (E) line = ) ) )1 12 4 1

56. Determine the number of non-negative integer solutions to the equation: p q r = 24.

(A) 2,024 (B) 1,012 (C) 775 (D) (E) 325 276

57. Find DE to the nearest tenth.

(A) 22.4 cm (B) 10 cm (C) 16.4 cm (D) 17.3 cm E) 14.1 cm (

58 The series converges to _____.. ... 1 1 1 1 1 11 3 5 7 9 11q q q

(A) (B) (C) (D) 0 (E) _ 12 2 4

5 1È 1

59. Dee Sprinter ran 4 warm-up laps before practice. The following chart shows his lap speed. What was Dee's average speed? (nearest hundredth) 1 2 3 4Lap Speed 22.5 km/hr 20.6 km/hr 20.0 km/hr 24.0 km/hr

(A) 21.83 km/hr (B) 21.78 km/hr (C) 21.72 km/hr (D) 21.66 km/hr (E) 21.12 km/hr

60. G. I. Amatree drew a circle with center O with BC = 2*AC. After doing some measuring he calculated the area of ABD to be 48 sq. cm. Based on his calculations what would the area of˜ DCO be?˜

A

D

BC

F E

O

(A) 6 sq. cm. (B) 8 sq. cm. (C) 9.6 sq. cm. (D) 12 sq. cm. (E) 14.4 sq. cm.


University Interscholastic League MATHEMATICS CONTEST

HS Invitation B 2013ì ìAnswer Key

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

3. E 23. A 43. C

4. A 24. C 44. D

5. C 25. A 45. D

6. B 26. B 46. A

7. A 27. A 47. E

8. E 28. C 48. C

9. C 29. C 49. A

10. B 30. C 50. E

11. A 31. D 51. B

12. C 32. B 52. A

13. D 33. E 53. A

14. C 34. C 54. D

15. D 35. A 55. A

16. A 36. B 56. D

17. B 37. B 57. D

18. D 38. E 58. E

19. D 39. A 59. D

20. A 40. E 60. B



do not turn this page until

you are instructed to do so!

Number SenseInvitational B • 2013

The University Interscholastic LeagueNumber Sense Test HS B 2013ì 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 directions to the contestants.

STOP -- WAIT FOR SIGNAL!

(1) 2013 3102 = ______________________________q

(2) 28 15 = __________________________________‚

(3) 310.2 20.13 = _____________________ (decimal)

(4) 2 3 = __________________________________1 13 2ƒ

(5) 0.875 = ______________________ (proper fraction)

(6) 544536 9 = ________________________________ƒ

(7) 6543 9 2 = ______________________________‚ q

(8) 25 20 15 10 5 = _____________________‚ q ƒ

(9) 2.5 gallons = __________________________ quarts

*(10) 21347 1118 2947 76 = __________________

(11) The GCD of 54, 48, and 32 is __________________

(12) 2013 11 has a remainder of __________________ƒ

(13) CMLXIV = _________________ (Arabic Numeral)

(14) 32 17 15 32 = _________________________‚ ‚

(15) 3 7 11 15 ... 31 = __________________

(16) 15 = ____________________ (mixed number)1519 ‚

(17) The largest prime factor of 285 is _______________

(18) = _____________________________7 7 712 24 36 q q

(19) Which is smaller, 0.45 or ? ______________q q 49

*(20) 8 15 1947 = _____________________________‚ ‚

(21) If 9 s cost $6.30 then a dozen s cost $ _______æ æ

(22) 37 67 = ________________________________2 2

(23) 9 6 3 1 = _____________________¹ ¹¸ ¸q q

(24) (21 34 7) 11 has a remainder of _________ ‚ ƒ

(25) 9.111... 3.333... = __________________________q

(26) 253 14 = _________________________________‚

(27) (8) (4) (2) = ______________________ - - -1 2 3ƒ ‚

(28) The sum of x and 5 gives the same result as the product of x and 5. Find x. ____________________

(29) 3 7 10 17 ... 71 115 = ____________

*(30) 88 42 64 42 = _________________________‚ q ‚

(31) 15 15 15 = _____________________________‚ ‚

(32) 15 45 = ________________________________2 2

(33) If x y = 5 and x y = 3 then x q q q q2 2 y = __

(34) f(x) = 9x 6x 1. f(7) = ____________________ 2

(35) If 2x 3x 11x 6 = 0 and P, Q, and R are 3 2 q q the real roots, then PQ QR PR is __________

(36) 134 base 7 is equivalent to ______________ base 10

(37) 5 4 4 3 3 2 = ___________________‚ x q ‚ x q ‚ x

(38) The next term of the arithmetic sequence, ... , , , ... is ______________________________2 7 5

3 6 3

(39) If 150 54 = x, then x = _______________È È Èq

*(40) 201213 748 = ______________________________ƒ

(41) If x y = 5 and xy = 2 then x y = ___________ 3 3

(42) 101 102 103 = ______________________ 2 3 4 10

(43) = __________________________________ 5 318 47 q

(44) 18% of 466 = ______________________________23

(45) An interior angle of a regular decagon has a measure of __________________________ degrees

(46) The sum of the product of the roots taken two at a time of 2x 3x 4 5 = 0 is __________3 2q q x

(47) 28 4 = _______________________________14

2 2( )q

(48) The y-intercept of the line going through (2, 3) and (5, 9) is (x, y). y = ________________________

(49) If is written as the mixed number x x

x x

q

q

7 4

4 7

A then B = _______________________________BC

*(50) 44 = ______________________________________2

(51) 17424 = _________________________________È (52) If two dice are rolled, the probability that the sum of the faces is greater than 10 is ________________

(53) 87 62 = ________________________________2 2

(54) C C = ________________________________5 3 4 2

(55) (6 5i)(5 6i) = (a bi). Find a b. __________q q

(56) sin ( sin ( ____________5 53 31 1) ) ‚ = __________

(57) Let log (x ) = , where x 0. Find x. _________93 3

2

(58) 90 miles per hour = _____________ feet per second

(59) 215 152 = ________________________________‚

*(60) 10 10 10 = ________________________e ‚ ‚1 9

(61) 6 12 18 24 ... 48 = _________________

(62) (333 ) (222 4 has a remainder of _________5 5 ƒ)

(63) A box contains black pens, red pens, blue pens, and green pens. How many different sets of 3 pens can be packaged? ____________________________

(64) The diameter of the circumscribed circle around a 7,24,25-right tria ngle is _______________________

(65) The det is = ________Š ‹” • ” •1 2 1 23 4 3 4

q

q q q

(66) 18 = _____________________ mixed number‚ 1920

(67) sin arctan ( ) ____________ˆ ‰724 = _____________

(68) 2 = ________________________________3 88 3 q

(69) If f(x) = x 5x 10x 10x 5x 1,5 4 3 2 then f( 2) = ________________________________q

*(70) 94 96 102 104 = _______________________‚ ‚ ‚

(71) 101 808 = ________________________________‚

(72) 6 4 5 3 2 1 = __________________x ƒ x x ƒ x q x ƒ x

(73) g(x) = 2x 3 and h(x) = 2 3x. g(h(4)) = _______ q

(74) The slope of the line tangent to f(x) = 2x x 12 q q at the point ( 1, 2) is ________________________q

(75) If f(x) = 2x 3x 3x 2, then f ( 1) = _____3 2 q q qww

(76) (3x x) = _________________________' 1

12

q q dx

(77) = _______________________1 1 1 130 42 56 72

(78) Change .111, base 2, to a base 10 fraction. ________

(79) The next term of 5, 6, 7, 9, 12, 17, ... is __________

*(80) 47.2 miles = _____________________________ feet

University Interscholastic League - Number Sense Answer Key HS Invitation B 2013ì 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) 1,089q

(2) 420

(3) 330.33

(4) 23

(5) 78

(6) 60,504

(7) 58,885

(8) 487

(9) 10

*(10) 24,214 26,762q

(11) 2

(12) 0

(13) 964

(14) 1,024

(15) 136

(16) 111619

(17) 19

(18) 772

(19) .45, q q 920

*(20) 221,958 q 245,322

(21) $8.40

(22) 5,858

(23) 5

(24) 6

(25) , 552 79 9

(26) 3,542

(27) .25, 14

(28) 1.25, , 15 14 4

(29) 294

*(30) 958 1,058q

(31) 3,375

(32) 2,250

(33) 15

(34) 484

(35) 5.5, ,q q112

5q 12

(36) 74

(37) 90

(38) , 213 16 6

(39) 24

*(40) 256 282q

(41) 95

(42) 35

(43) q 13376

(44) 84

(45) 144

(46) 2q

(47) 192

(48) 1q

(49) 121

*(50) 1,840 2,032q

(51) 132

(52) 112

(53) 11,413

(54) 16

(55) 61q

(56) .75, 34

(57) 3

(58) 132

(59) 32,680

*(60) 13,127 14,508q

(61) 216

(62) 3

(63) 20

(64) 25

(65) 16q

(66) 17110

(67) .28, 725

(68) , 125 124 24

(69) 1q

*(70) 90,940,263 q 100,512,921

(71) 81,608

(72) 48

(73) 17q

(74) 5q

(75) 6q

(76) 2

(77) 445

(78) 78

(79) 25

*(80) 236,756 q 261,676

GENERAL DIRECTIONS:

• DONOTOPENEXAMUNTILTOLDTODOSO. • Ninetyminutesshouldbeampletimetocompletethiscontest,butsinceitisnotarace,contestants

maytakeuptotwohours.Ifyouareintheprocessofactuallywritingananswerwhenthesignaltostopisgiven,youmayinishwritingthatanswer.

• Papersmaynotbeturnedinuntil30minuteshaveelapsed.Ifyouinishthetestinlessthan 30minutes,remainatyourseatandretainyourpaperuntiltoldtodootherwise.Youmayusethistimetocheckyouranswers.

• Allanswersmustbewrittenontheanswersheetprovided.Indicateyouranswersintheappropriateblanksprovidedontheanswersheet.

• Youmayplaceasmanynotationsasyoudesireanywhereonthetestpaperexceptontheanswersheet,whichisreservedforanswersonly.

• Youmayuseadditionalscratchpaperprovidedbythecontestdirector. • AllquestionshaveONEandonlyONEcorrect(BEST)answer.Thereisapenaltyforallincorrect

answers. • Ifaquestionisomitted,nopointsaregivenorsubtracted. • Onthebackofthispageisprintedacopyoftheperiodictableoftheelements.Youmaywishto

refertothistableinansweringthequestions,andifneeded,youmayusetheatomicweightsandatomicnumbersfromthetable.Otherscientiicrelationshipsarelistedalso.

• Silenthand-heldcalculatorsthatdonotneedexternalwallplugsmaybeused.Graphingcalculatorsthatdonothavebuilt-inorstoredfunctionalitythatprovidesadditionalscientiicinformation areallowed.Smallhand-heldcomputersarenotpermitted.Calculatorsthatacceptmemorycards ormemorysticksarenotpermitted.Eachcontestantmaybringonesparecalculator. Allmemorymustbecleared.

• Answerswithin5%oftheexactanswerwillbeconsideredcorrect.

SCORING:

Allquestionswillreceive6pointsifansweredcorrectly;nopointswillbegivenorsubtracted ifunanswered;2pointswillbedeductedforanincorrectanswer.

SCIENCEInvitational B • 2013



Periodic Table of the Elements1A

18A

18

1

H1.01

2A

23A

134A

145A

156A

167A

17

2

He4.00

3

Li6.94

4

Be9.01

5

B10.81

6

C12.01

7

N14.01

8

O16.00

9

F19.00

10

Ne20.18

11

Na22.99

12

Mg24.31

3B

34B

45B

56B

67B

78B

88B

98B

101B

112B

12

13

Al26.98

14

Si28.09

15

P30.97

16

S32.07

17

Cl35.45

18

Ar39.95

19

K39.10

20

Ca40.08

21

Sc44.96

22

Ti47.87

23

V50.94

24

Cr52.00

25

Mn54.94

26

Fe55.85

27

Co58.93

28

Ni58.69

29

Cu63.55

30

Zn65.41

31

Ga69.72

32

Ge72.64

33

As74.92

34

Se78.96

35

Br79.90

36

Kr83.80

37

Rb85.47

38

Sr87.62

39

Y88.91

40

Zr91.22

41

Nb92.91

42

Mo95.94

43

Tc(98)

44

Ru101.07

45

Rh102.91

46

Pd106.42

47

Ag107.87

48

Cd112.41

49

In114.82

50

Sn118.71

51

Sb121.76

52

Te127.60

53

I126.90

54

Xe131.29

55

Cs132.91

56

Ba137.33

57

La138.91

72

Hf178.49

73

Ta180.95

74

W183.84

75

Re186.21

76

Os190.23

77

Ir192.22

78

Pt195.08

79

Au196.97

80

Hg200.59

81

Tl204.38

82

Pb207.20

83

Bi208.98

84

Po(209)

85

At(210)

86

Rn(222)

87

Fr(223)

88

Ra(226)

89

Ac(227)

104

Rf(261)

105

Db(262)

106

Sg(266)

107

Bh(264)

108

Hs(277)

109

Mt(268)

110

Ds(281)

111

Rg(272)

112

Cn(285)

58

Ce140.12

59

Pr140.91

60

Nd144.24

61

Pm(145)

62

Sm150.36

63

Eu151.96

64

Gd157.25

65

Tb158.93

66

Dy162.50

67

Ho164.93

68

Er167.26

69

Tm168.93

70

Yb173.04

71

Lu174.97

90

Th232.04

91

Pa231.04

92

U238.03

93

Np(237)

94

Pu(244)

95

Am(243)

96

Cm(247)

97

Bk(247)

98

Cf(251)

99

Es(252)

100

Fm(257)

101

Md(258)

102

No(259)

103

Lr(262)

Some Standard Properties of Water

property symbol value

density ρ1.00 g cm-3

1000 kg m-3

specific heats

ice

water

steam

cice

cwater

csteam

2.09 J g-1 K-1

4.184 J g-1 K-1

2.03 J g-1 K-1

heat of fusion ∆Hfus or Lf 334 J g-1

heat of vaporization ∆Hvap or Lv 2260 J g-1

index of refraction n 1.33

autoionization Kw 1.0 × 10-14

Pressure

1 atm = 760 torr

= 101325 Pa

= 14.7 psi

1 bar = 105 Pa

= 100 kPa

Energy

1 cal = 4.184 J

1 L atm = 101.325 J

1 Cal = 1 kcal

1 hp = 746 W

Various Physical Constants


universal gas

constant

R 8.314 J mol-1 K-1

62.36 L torr mol-1 K-1

0.08206 L atm mol-1 K-1

1.987 cal mol-1 K-1

Planck’s

constant

h 6.626 × 10-34 J s

4.136 × 10-15 eV s

Planck’s reduced constant

h/2π 1.054 × 10-34 J s

6.582 × 10-16 eV s

Boltzmann

constantkB 1.38 × 10-23 J K-1

Stefan-Boltzmann

σ 5.67 × 10-8 W m-2 K-4

speed of light c 3.00 × 108 m s-1

speed of sound (at 20°C)

vair 343 m s-1

acceleration of

gravityg 9.80 m s-2

gravitational

constantG 6.67 × 10-11 N m2 kg-2

Avogadro’s

number

NA 6.022 × 1023 mol-1

elementary

chargee 1.602 × 10-19 C

Faraday F 96485 C mol-1

Coulomb’s

law constantk 8.988 × 109 N m2 C-2

Various Physical Constants


electron rest mass

me 9.11 × 10-31 kg

0.000549 u

0.511 MeV c-2

proton mass mp 1.6726 × 10-27 kg

1.00728 u

938.3 MeV c-2

neutron mass mn 1.6749 × 10-27 kg

1.008665 u

939.6 MeV c-2

atomic mass unit

u 1.6605 × 10-27 kg

931.5 MeV c-2

earth mass 5.972 × 1024 kg

earth radius 6.371 × 106 m

moon mass 7.348 × 1022 kg

sun mass 1.989 × 1030 kg

distance

earth‐moon

3.844 × 109 m

distance

earth‐sun

1.496 × 1011 m

permittivity of free space

ε0 8.85 × 10-12 F m-1

permeability of free space

µ0 4π × 10-7 T m A-1

HS Science • Invitational B • 2013

University Interscholastic League • page 1

Biology Questions (1 – 20)

1. Which of the following is not characteristic of all

living things?

A) They use energy.

B) They contain DNA.

C) They are made up of one or more cells.

D) They can move around.

E) They make proteins.

2. Which of the following is a lipid?

A) an enzyme

B) cholesterol

C) starch

D) DNA

E) ATP

3. If the body cells of an organism have

24 chromosomes, an egg cell will

have ____ chromosomes.

A) 6

B) 12

C) 18

D) 24

E) 48

4. A man and a woman are both heterozygous

carriers of the cystic fibrosis gene. What is the

probably that a child of theirs would have cystic

fibrosis?

A) .0

B) .25

C) .50

D) .75

E) 1.00

5. Which of the following is the largest?

A) chromosome

B) DNA molecule

C) gene

D) genome

E) nucleotide

6. Which of the following cannot be found in

prokaryotic cells?

A) a DNA-containing chromosome

B) ribosomes

C) a nucleus

D) a plasma membrane

E) cytoplasm

7. Most protists live in ____ .

A) the oceans

B) the bodies of other animals

C) fresh water

D) the air

E) soil

8. Which of the following have been on Earth for the

shortest amount of time?

A) algae

B) flowering plants

C) gymnosperms

D) ferns

E) mosses

9. Which of the following types of plant cells is

involved in gas exchange?

A) sieve tube element

B) endodermal cell

C) guard cell

D) vessel element

E) apical meristem cell

10. A fruit is a mature ____ .

A) pistil

B) seed

C) flower

D) zygote

E) ovary

11. Which of the following provides most of the

structural support in non-woody plants?

A) vascular tissue

B) epidermis

C) water

D) cortex

E) root hairs

12. The stomach is not like other organs of the human

digestive system in that it ____ .

A) does not contain any nerve cells

B) chemically breaks down food particles

C) does not contain blood vessels

D) has three muscle layers

E) is lined with mucus



13. By what mechanism does oxygen move from the

air spaces in the lungs into the blood and from the

blood into other body tissues?

A) active transport

B) osmosis

C) facilitated diffusion

D) simple diffusion

E) exocytosis.

14. Which of the following is not a characteristic of

capillaries?

A) narrow inside diameter

B) thick walls

C) nutrients and wastes move across their walls

D) occur in all parts of the body

E) red blood cells barely fit through them

15. Which of the following secretes hormones that

either stimulate or inhibit the secretion of

hormones by other glands?

A) hypothalamus

B) adrenal glands

C) anterior pituitary

D) thyroid gland

E) pancreas

16. Bone tissue is ____ .

A) a source of blood cells

B) dead at maturity

C) a source of proteins

D) incapable of repairing itself

E) All of the above

17. When a fertilized ovum becomes implanted in the

lining of the uterus, it is called a(n) ____ .

A) zygote

B) secondary oocyte

C) embryo

D) fetus

E) gastrula

18. A change in the genetic makeup of a population

is ____ .

A) natural selection

B) artificial selection

C) uniformitarianism

D) evolution

E) adaptive radiation

19. Which of the following makes up a community?

A) a group of organisms of the same species

B) all of the animal species in an area

C) all of the plant species on Earth

D) all of the organisms living in an area and their

nonliving environment

E) all of the organisms living in an area

20. Which of the following biomes experiences the least

amount of temperature variation, greatest rainfall,

and most complex plant and animal communities?

A) grassland

B) tundra

C) coniferous forest

D) temperate deciduous forest

E) tropical rain forest

Chemistry Questions (21 – 40)

21. What is the percentage of calcium in calcium

carbonate?

A) 25.3%

B) 76.9 %

C) 47.6 %

D) 34.5 %

E) 40.0 %

22. Complete the following reaction that occurs in

aqueous solution:

NaCl (aq) + AgNO3 (aq) ⟶ ?

One of the possible products is ____.

A) Na2O (aq)

B) AgCl (s)

C) Ag2O (s)

D) Na3N (s)

E) NOCl (g)

23. 35.0 g of CaCO3 is allowed to react with 22.0 g of

HCl. If the reaction goes to completion, how many

grams of CO2 are produced?

A) 6.64 g

B) 15.4 g

C) 13.3 g

D) 21.3 g

E) 4.26 g



24. Although it’s a rare occurrence, Xe will react to

form compounds when conditions are right.

Consider the following reaction:

Xe (g) + 2 F2 (g) ⟶ XeF4 (s)

180 g of Xe is allowed to react with an excess of

F2. The reaction has a 55% yield. Approximately

how many grams of XeF4 are produced?

A) 284 g

B) 83 g

C) 156 g

D) 142 g

E) 218 g

25. A 50.0 mL sample of an HNO3 solution is titrated

to the endpoint with 27.5 mL of 0.075 M NaOH.

What is the concentration of the HNO3 solution?

A) 0.55 M

B) 0.041 M

C) 0.12 M

D) 0.031 M

E) 0.14 M

26. A sample of 50 mL of 0.52 M NaOH is poured

into 950 mL of water. What is the new

concentration of NaOH in this mixture?

A) 0.052 M

B) 0.035 M

C) 0.0085 M

D) 0.026 M

E) 0.043 M

27. Write the electron dot formula for nitrate. How

many non-bonding pairs of electrons are there on

this structure?

A) 8 pairs

B) 9 pairs

C) 6 pairs

D) 7 pairs

E) 4 pairs

28. What is the maximum number of electrons that

will fill a single 4f orbital?

A) 6

B) 2

C) 14

D) 7

E) 10

29. Consider the piston/cylinder

diagram to the right. 10 identical

weights are loaded on the piston and

are compressing the gas trapped

inside with volume, V. If 6 of the

weights are removed, what will be

the resulting volume of the gas

inside?

A) 5

/3 V

B) 1

/2 V

C) 2

/5 V

D) 4

/2 V

E) 5

/2 V

30. Which of the following atoms will have the largest

radius?

A) Al

B) S

C) N

D) K

E) Br

31. What is the bond angle ∠HCH in CH4?

A) 90°

B) 120°

C) 109.5°

D) 180°

E) 60°

32. How many unpaired electrons are in the ground state

of a sulfur atom?

A) one

B) two

C) three

D) four

E) zero

33. Consider the following reaction:

3 A + 5 B ⟶ 4 C

The heat of reaction (∆Hrxn) as written is −250 kJ.

How much heat will be released when 10 moles of C

is produced by this reaction?

A) 750 kJ

B) 500 kJ

C) 250 kJ

D) 625 kJ

E) 875 kJ



34. What is the pH of a 3.5 × 10–3 M solution of

Sr(OH)2?

A) 11.21

B) 11.54

C) 10.93

D) 11.85

E) 12.12

35. Which of the following properties is an intensive

property?

A) mass

B) temperature

C) width

D) volume

E) number of moles

36. Which of the following is the formula for

copper(II) phosphate?

A) Co2P

B) Cu2(PO4)3

C) Co3(PO3)2

D) Cu2(PO2)4

E) Cu3(PO4)2

37. Balance the following reaction:

Ca3(PO4)2 + SiO2 + C ⟶ CaSiO3 + CO + P4

What is the coefficient for CO?

A) 8

B) 10

C) 20

D) 56

E) 16

38. The pH of a dilute solution of KOH is 8.74. What

is the molar concentration of KOH in this

solution?

A) 7.5 × 10–5 M

B) 1.8 × 10–6 M

C) 5.5 × 10–6 M

D) 9.3 × 10–6 M

E) 1.8 × 10–9 M

39. How many kilojoules of heat is needed to heat

250 grams of water at 25°C to 125°C steam?

A) 656 kJ

B) 175 kJ

C) 604 kJ

D) 587 kJ

E) 724 kJ

40. Consider the following reaction:

A + 2B ⇌ C

At equilibrium all three species are 0.5 M. What is

the value of Kc ?

A) 0.25

B) 2.0

C) 0.50

D) 4.0

E) 1.0

Physics Questions (41 – 60)

41. According to Aczel, what did Einstein describe as

“the happiest thought of my life” to his close friend

Michele Angelo Besso?

A) That light would be deflected by a massive

object.

B) Traveling at the speed of light one would

observe an electromagnetic wave spatially

oscillating, which can NOT be.

C) That a person falling freely will NOT feel his

own weight.

D) That time is relative.

E) That the universe should NOT be static.

42. According to Aczel, which of the following was

NOT one of the steps Einstein worked on toward the

theory of general relativity during the time period

that he was in Prague?

A) the equivalence principle

B) the deflection of light by a massive body

C) gravitational lensing

D) gravitational redshift

E) the use of the mathematics by Ricci and

Levi-Civita

43. According to Aczel, which of Euclid’s postulates did

various mathematicians fail to show was a

consequence of the others?

A) 1st

B) 2nd

C) 5th

D) 13th

E) 15th



44. According to Aczel, while considering a circle

spinning in space Einstein concluded that the ratio

of the circumference to the diameter was no longer

pi and deduced which of the following?

A) that general relativity requires rotations

B) that the special theory of relativity did NOT

apply to rotating frames

C) that a rotating reference frame is non-inertial

D) that there must be an outward force on a

rotating circle

E) that the geometry of space is non-Euclidean

45. A small round rock is thrown straight up with an

initial velocity of 31.0 m/s. What is the maximum

height the rock reaches? You may neglect air

resistance.

A) 1.58 m

B) 49.0 m

C) 82.5 m

D) 98.0 m

E) 147 m

46. A stone is thrown upward at an angle of 45° to the

horizontal from the top of a 67 m tall building.

The stone has an initial speed of 32 m/s. How

long does it take for the stone to reach the ground?

You may neglect air resistance.

A) 1.7 s

B) 2.1 s

C) 4.0 s

D) 4.6 s

E) 6.7 s

47. Which of the following are an example of forces

that are Newton’s third law pairs (or interaction

pairs) for a box that is pulled by a rope at a

constant speed across a horizontal surface?

A) the gravitational force on the box and the

normal force on the box

B) the gravitational force on the box and the

tension force on the box

C) the kinetic friction force on the box and the

tension force on the box

D) the kinetic friction on the box and the tension

force on the rope

E) the tension force on the box and the tension

force on the rope

48. Two blocks of masses m1 and m2 where m1 is greater

than m2 are placed in contact with each other on a

frictionless, horizontal surface. A constant,

horizontal force F is applied to m1. Find the

magnitude of the acceleration of the two blocks.

A) F/m1

B) F/m2

C) Fm1

D) F/(m1 + m2)

E) F(m1 + m2)

49. A little boy of mass 20.0 kg rides on a Ferris wheel.

The Ferris wheel turns in a vertical circle with a

radius of 15.0 m at a constant speed of 4.50 m/s.

Determine the magnitude of the force exerted by the

seat on the child at the top of the ride. Note: a Ferris

wheel does NOT invert at the top of the ride.

A) 1.85 N

B) 27.0 N

C) 169 N

D) 190 N

E) 223 N

50. A ball of mass m is dropped from a height h above

the ground. Using energy methods, determine the

speed of the ball when it is at a height y above the

ground. You may neglect air resistance.

A) 2gh

B) 2gy

C) (2gh)1/2

D) (2gy)1/2

E) [2g(h – y)]1/2

51. A 2200 kg truck is stopped at a stop sign. The

truck is hit from behind by a 1200 kg car moving at

23.0 m/s. If the two vehicles stick together and

move in the same direction that the car was initially

traveling, then what is the speed of the two vehicles

immediately after the collision? You may assume

that the net force on the truck is due to the car and

the net force on the car is due to the truck during the

collision.

A) 8.12 m/s

B) 12.5 m/s

C) 14.9 m/s

D) 23.0 m/s

E) 42.2 m/s



52. A star rotates with a 30-day period. After the

star goes supernova its core, with a radius of

1.3 × 104 km, collapses to a neutron star of radius

3.0 km. What is the period of rotation of the

neutron star? You may treat the core and the

neutron star as uniform spheres.

A) 0.050 s

B) 0.14 s

C) 2.0 s

D) 1.4 × 103 s

E) 1.8 × 103 s

53. A 1500 kg VW bug is lifted by a crane with a

steady speed. The VW is attached to a cable

with a diameter of 12 × 10–3 m. The cable is

initially 12 m in length and stretches 6.0 × 10–3 m

because of the VW’s weight. Determine Young’s

modulus for the cable.

A) 3.8 × 10–12 N/m2

B) 6.5 × 105 N/m2

C) 1.6 × 109 N/m2

D) 2.6 × 1011 N/m2

E) 8.2 × 1011 N/m2

54. A 0.70 kg air track cart is connected to an ideal

spring that has a spring constant (or force constant)

of 18 N/m. The cart-spring system oscillates on a

frictionless, horizontal air track. What is the

maximum speed of the cart if the amplitude of the

oscillation is 5.0 cm? You may neglect air

resistance.

A) 0.25 m/s

B) 1.0 m/s

C) 1.3 m/s

D) 12 m/s

E) 24 m/s

55. A drainage pipe of length 1.67 m makes a howling

noise when the wind blows over its open ends. If

one end is now blocked off, then what is the lowest

natural frequency of the blocked pipe? You may

assume that the speed of sound in air is 343 m/s.

A) 51.3 Hz

B) 85.8 Hz

C) 143 Hz

D) 205 Hz

E) 822 Hz

56. A 1.0 mol sample of an ideal gas is kept at 0.0°C

during an expansion from 2.0 L to 12.5 L. How

much work is done on the gas during the expansion?

A) –5.3 × 103 J

B) –4.2 × 103 J

C) 1.6 × 103 J

D) 4.2 × 103 J

E) 5.7 × 103 J

57. The magnitude of the electric force between two

protons is 2.3 × 10–26 N. How far apart are they?

A) 1.1 × 10–11

m

B) 1.2 × 10–3

m

C) 1.0 × 10–2 m

D) 1.0 × 10–1 m

E) 6.3 × 1016 m

58. A parallel plate capacitor is charged with a battery to

a charge Q0. The battery is removed and a slab of

material with a dielectric constant κ is inserted

between the plates. What happens to the charge on

the plates of the capacitor?

A) remains the same

B) increases

C) decreases

D) increases then decreases

E) decreases then increases

59. An immersion heater must increase the temperature

of 2.65 kg water from 12°C to 55°C in 12 minutes

while operating at 110 V. What is the required

resistance of the heater?

A) 0.33 Ω

B) 14 Ω

C) 18 Ω

D) 48 Ω

E) 2.0 × 103 Ω

60. A light ray of wavelength 589 nm travels through air

is incident on a smooth flat slab of flint glass (with

an index of refraction of 1.66) at an angle of 35.0° to

the normal. Find the angle of refraction.

A) 18.2°

B) 20.2°

C) 29.6°

D) 35.0°

E) 71.8°

UIL HIGH SCHOOL SCIENCE CONTEST

ANSWER KEY

INVITATIONAL B • 2013

1. D

2. B

3. B

4. B

5. D

6. C

7. A

8. B

9. C

10. E

11. C

12. D

13. D

14. B

15. A

16. A

17. C

18. D

19. E

20. E

21. E

22. B

23. C

24. C

25. B

26. D

27. A

28. B

29. E

30. D

31. C

32. B

33. D

34. D

35. B

36. E

37. B

38. C

39. A

40. D

41. C

42. E

43. C

44. E

45. B

46. E

47. E

48. D

49. C

50. E

51. A

52. B

53. D

54. A

55. A

56. B

57. D

58. A

59. C

60. B

21. CaCO3 = 100.09 g/mol (E)

40.08/100.09 x 100% = 40.0 % Ca

22. RXN: NaCl (aq) + AgNO3 (aq) --> NaNO3 (aq) + AgCl (s) (B)

This is a precipitation reaction - a type of metathesis reaction

23. RXN: CaCO3 + 2HCl ---> CaCl2 + H2O + CO2 (C)

CaCO3 = 100.09 g/mol, HCl = 36.458 g/mol, CO2 = 44.01 g/mol

35.0/100.06 = 0.350 mol CaCO3, 22.0/36.458 = 0.603 mol HCl

Convert 0.603 mol HCl into equivalent CaCO3: 0.603(1/2) = 0.302 mol CaCO3 needed

0.350 given is too much - therefore it is in excess and HCl is limiting reactant.

0.603 mol HCl (1/2) = 0.302 mol CO2 made. 0.302(44.01) = 13.3 g of CO2 made

24. Xe = 131.3, XeF4 = 207.3 (C)

(180/131.3)mol of Xe = mol XeF4 = 284 g if 100% yield (it’s not)

0.55(284.188) = 156 g

25. RXN: HNO3 + NaOH ---> H2O + NaNO3 (B)

27.5mL(.075)=2.0625mmol NaOH = 2.0625 mmol of HNO3

2.0625/50.0 = 0.04125 M = 0.41 M

26. 50(.52) = 26mmol NaOH, 50mL+950mL=1000mL (D)

26mmol/1000mL = 0.026 M

27. . . . . : O : N : O : 4 bonding pairs, 8 non-bonding (A) . . . . . . . . there are also 3 resonance structures : O :

28. Maximum number electrons for ANY single atomic orbital is 2 (B)

29. 10 weights means P1 = 10 (proportional to 10), removing 6 leaves 4 so P2 = 4. (E)

Boyle’s Law: P1 V1 = P2 V2, so final volume V2 = (P1/P2)V1 = 10/4 V = 5/2 V

30. potassium, K. Trend is smaller from left to right. Larger top to bottom. (D)

31. C surrounded by 4 H’s with NO lone pairs = tetrahedral w/109.5° bond angles (C)

32. [S] = 1s2 2s2 3s2 3p4 Hund’s rule: fill degenerate orbitals singly before pairing. (B)

So the 3p orbital set will be a pair and two singles.

33. Producing 10 moles of C means the reaction runs 10/4 = 2.5 times (D)

2.5 (-250 kJ) = -625 kJ = 625 kJ heat released

34. [OH-] = (3.5 × 10–3 M)x2 = 7.0 × 10

–3 M (because 2 hydroxides per formula unit) (D)

pOH = -log[OH-] = -log(7.0 × 10–3) = 2.15, pH = 14 - pOH = 14 - 2.15 =11.85

Chemistry Solutions! Invitational B - 2013! 1

35. temperature (doesn’t change with amount of substance) (B)

36. Cu(II) is +2, and phosphate is -3, so Cu3(PO4)2 (E)

37. 2 Ca3(PO4)2 + 6 SiO2+ 10 C ⟶ 6 CaSiO3 + 10 CO + P4 (B)

redox reaction: P(5+) to P(0), C(0) to C(2+), 20 electron transfer reaction

38. [KOH] = [OH-] = 10-pOH , pOH = 14-8.74 = 5.26, 10-5.26 = 5.5 × 10-6 M (C)

39. 3 steps: heat water to 100°C, evaporate to steam, heat steam to 110°C (A)

step1: m·Cs·∆T = 250g(4.184J/g°C)(75°C) = 78450 J

step2: m·∆Hvap = 250g(2260 J/g) = 565000 J

step3: m·Cs,steam·∆T = 250g(2.03J/g°C)25°C = 12685.5 J

total: 78450 + 565000 + 12685.5 = 656137.5 J = 656 kJ

40. Kc = [C] / ([A][B]2) = .5/(.5·.52) = 1/.52 = 1/.25 = 4.0 (D)

Chemistry Solutions! Invitational B - 2013! 2

PHYSICS KEY for Science Contest • Invitational B • 2013

41. (C) ““All of a sudden, a thought occurred to me: if a person falls freely, he will not feel his own weight.”

… To his close friend, Michele Angelo Besso … Einstein described the revelation as “the happiest

thought of my life.””

42. (E) “As early as 1911, Pick may have tried to direct Einstein to the mathematics of Ricci and Levi-Civita,

but Einstein remained oblivious to the good advice and would remain so until after he left Prague.”

43. (C) “By this time, Saccheri was very well-acquainted with Euclid’s fifth and with the historical attempts

to prove it, since he himself had by then demonstrated that Nasiraddin’s proof was false, and that a

1663 attempt, by John Wallis (1616-1703) at Oxford was equally false.”

44. (E) “Thus, Einstein concluded, in a way that surprised even him, the ratio of the circle to the diameter

was no longer pi. He deduced that in the presence of a gravitational force (or field), the geometry of

space is non-Euclidean.”

45. (B) From the kinematic equations (in a particular coordinate system):

Δy = [v2 – v0

2]/(2g) = [0

2 – 31.0

2]/[2(9.80)] = 49.0 m

46. (E) From the kinematic equations (in a particular coordinate system):

y = y0 + v0yt + ½ayt2 ⇒ 0 = 67 + (32 sin45°)t + ½(-9.80)t

2 ⇒ t = 6.7 s

47. (E) Third law pairs of forces have to be the same type and trade the object the force acts on with the

object that exerts the force. Thus only answer E has both forces as tension forces, with one of them

acting on the box (by the rope) and the other acting on the rope (by the box).

48. (D) By Newton’s 2nd

law: asystem = ΣF/mtotal ⇒ asystem = F/(m1 + m2)

49. (C) By Newton’s 2nd

law with in toward the center of the circle as positive:

+mg – FN = mac ⇒ FN = 20.0[9.80 – (4.50)2/15.0] = 169 N

50. (E) With E = KE + PE = ½mv2 + mgy, and with y = 0 at the ground: E0 = 0 + mgh & E = ½mv

2 + mgy,

and since Wnon-conservative = 0 ⇒ E0 = E ⇒ 0 + mgh = ½mv2 + mgy ⇒ v = [2g(h – y)]

1/2

51. (A) This is a completely inelastic collision, thus linear momentum is conserved:

m1v1 + m2v2 = (m1 + m2) v′ ⇒ v′ = [0 + 1200(23.0)]/(2200 + 1200) = 8.12 m/s

52. (B) By conservation of angular momentum: I0ω0 = Iω, and with Isphere = (2/5)mr2 & ω = 2π/T ⇒

[(2/5)mr02](2π/T0) = [(2/5)mr

2](2π/T) ⇒ T = (r/r0)

2 T0 = (3/1.3E+4)

2[(30)(24)(3600)] = 0.14 s

53. (D) For an elastic deformation:

F/A = Y(ΔL/L0) ⇒ Y = (FL0)/(AΔL) = [(1500)(9.80)(12)]/[π(12E-3/2)2(6.0E-3)] = 2.6 × 10

11 N/m

2

54. (A) The cart-spring system undergoes simple harmonic motion,

thus vmax = (k/m)½A = [(18)/(0.70)]

½(0.050) = 0.25 m/s

55. (A) For a half-open/half closed pipe the fundamental frequency is: f = v/(4L) = (343)/[4(1.67)] = 51.3 Hz

56. (B) For an isothermal process the work done by the gas is given as:

Wby = nRT ln(V/V0) = (1.0)(8.314)(273.15) ln(12.5/2.0) = 4.2E+3 J. However the question asks for

the work done on the gas which is the negative of the work done by the gas, thus the answer

is -4.2 × 103 J

57. (D) By Coulomb’s law:

FE = k|q1||q2|/r2 ⇒ r = [ke

2/FE]

½ = [(8.988E+9)(1.602E-19)

2/(2.3E-26)]

½ = 1.0 × 10

-1 m

58. (A) Since the battery is removed before inserting the dielectric the charge is “stranded” on the plates and

thus will remain the same.

59. (C) Equating the relationships for power and using the expression for heat:

P = Q/t = V2/R ⇒ R = V

2t/(mcΔT) = [(110)

2(12)(60)]/[2.65(4186)(55 – 12)] = 18 Ω

60. (B) By Snell’s law: n1 sinθ1 = n2 sinθ2 ⇒ θ2 = sin-1

[(1.00) sin(35.0°)/(1.66)] = 20.2°

UIL COMPUTER SCIENCE INVITATIONAL B - 2013 • PAGE 1

University Interscholastic League

Computer Science Competition

Number 138 (Invitational B - 2013)

General Directions:

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

System.out.println((double) (5/20) + 6);

What is output by the code to the right?

A. 0 B. 6

C. 0.25 D. 6.25

E. 6.0

QUESTION 2

System.out.println(29/3%3*2);


A. 0 B. 14

C. 58 D. 3

E. There is no output

due to a runtime

error.

QUESTION 3

What is the value of 3A916 + 28B16?

A. 63416 B. 69A16 C. 79416 D. 74516 E. 64016

QUESTION 4

int x = 25;

int y = 15;

if(x >= 10) {

if(x <= 50) {

y = x*4;

if(y <= 100) {

x %= 4;

}

else y = 40;

}

}

else y *= x+5;

What are the values of x and y after the code to the right

has been executed?

A. x = 25

y = 40 B. x = 1

y = 100

C. x = 25

y = 450 D. x = 25

y = 30

E. x = 1

y = 60

QUESTION 5

System.out.print("\\//Itsybitsy\nspider\\");


A. \\//Itsybitsy

spider\\

B. \\/Itsybitsy

spider\\

C. \\/Itsybitsy spider\\

D. \//Itsybitsy spider\

E. \//Itsybitsy

spider\


QUESTION 6

Assume x, y and z have type int and have been initialized. Then the expression

(x <= y+z) && !((y > z) || (z > x))

will always be true if:

A. x==y and z>0

B. x==y and y==z and z>=0

C. x<y and z>=0

D. y<=z or z<=x

E. x>0 and y<0 and z>0

QUESTION 7

for(int i = 0; i < 9; i++){

for(int j = 0; j < i; j++) {

System.out.println(j);

}

}

How many times is the method

System.out.println() called when the code to the

right is executed?

A. 81 B. 0 C. 36

D. 45 E. 64

QUESTION 8 int x=15;

int y=0;

while(x>=10) {

y+=3;

while(y<x) {

y = 2*x;

}

x-=5;

}

System.out.print(x + " " + y);


A. 10 24 B. 5 33 C. 10 30

D. 5 27 E. 5 30

QUESTION 9

What is the output when the following statement is executed?

System.out.print("LateReplacement". replace('e', 'a').substring(4, 10));

A. aRapla B. eReple C. Replec D. Raplac E. Lataa


QUESTION 10

// Loop 1

for(int i = 1; i < max; i++)

System.out.print(i);

// Loop 2

int i = 1;

while(i < max){

System.out.print(i);

i++;

}

Assume that max is of type int. Which statement is

true?

A. Loop 1 and Loop 2 produce the same output for

all values of max.

B. Loop 1 and Loop 2 never produce the same

output.

C. Loop 1 and Loop 2 only produce the same

output when max is 1.

D. Loop 1 and Loop 2 produce the same output only

when max is greater than 1.

E. Loop 1 and Loop 2 produce the same output only

when max is less than 1.

QUESTION 11

public static String myst(int a, String x){

String y = a+x;

for(int i = 0; i < a; i++) {

y = a+y;

}

return y;

}

What value is returned by the method call

myst(2, "a")?

A. "222a" B. "22a" C. "aaa"

D. "aaaa" E. "222"

QUESTION 12

double y = 3.5; int n = 3; double x = 2.5;

System.out.print(y+n*x + (int)((y+n)*2));


A. 43.5 B. 24.0 C. 48.25

D. 48 E. 48.0

QUESTION 13

Assume boolean variables p, q and r have all been initialized. Which of the following expressions are false only when p, q

and r are all false?

A. !(!p && !q) || !r

B. (p || !q) && !(q && r)

C. (p || q) || !(!r && !p)

D. (p && r) || q

E. !(p != q) && (q != r)


QUESTION 14

What is the output when the following statement is executed? The character b represents a blank space in the output.

System.out.printf("Hello%5s%n%07.2f!", "Fred", 18.44);

A. HelloFred

bb18.44!

B. HellobFred

0018.44!

C. HellobFredbb18.44!

D. HellobFred

bb18.44!

E. HellobFred

18.44bb!

QUESTION 15

public class Fifteen {

public int myst(String[] r) {

int n = 0;

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

n = n + r[i].length();

}

return n;

}

}

// Client code

Fifteen x = new Fifteen();

String[] t = {"Hello", "World", "hi"};

int m = x.myst(t); // line 0

System.out.print(m); // line 1

What is output by the client code to the right?

A. 0 B. 3

C. 5 D. 12

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

Replace the line labeled line 0 as indicated below before

answering Question 16. QUESTION 16

What is output by the code to the right if the statement

labeled line 0 in the client code is replaced with the

following statement: int m = myst(t);

A. 0 B. 3 C. 5

D. 12 E. There is no output due to a

compilation error.

QUESTION 17 int n = 5;

int sum = 0;

do

{

sum = sum + n;

n = n + 5;

} while(n < 35);

System.out.print(n + " " + sum);

What is the output when the code to the right is executed?

A. 35 140 B. 35 75

C. 40 140 D. 30 75

E. 35 105


QUESTION 18

Which of the following expressions is false? Assume String s and int n have been initialized as follows:

int n = 27;

String s = "27";

I. n == (int) (n + 0.7)

II. String.valueOf(n).equals(s)

III. Integer.parseInt(s) == n

IV. '2' == s.charAt(0)

A. I

B. II

C. III

D. IV

E. All of the expressions I through IV are true.

QUESTION 19

public class Account {

private double balance;

private String status;

public Account(double initial, String s){

status = s;

<*1>;

}

public double getBalance() {

return balance;

}

}

// Client code

Account a = new Account(0, "overdrawn");

System.out.print(a.getBalance()); // line 1

What statement can replace <*1> in the code to the right

so that the Account class compiles correctly and so that

line 1 in the client code prints 0.0?

I. this(initial)

II. balance = initial

III. this.balance = initial

A. I only

B. II only

C. III only

D. I and II

E. II and III


QUESTION 20 public static int met(int[] a) {

int max, maxPos;

for(int i = 0; i < a.length-1; i++) {

max = a[i];

maxPos = i;

for(int j = i+1; j < a.length; j++) {

if(max < a[j]) {

max = a[j];

maxPos = j;

}

}

int temp = a[i];

a[i] = a[maxPos];

a[maxPos] = temp;

}

return maxPos;

}

If n=a.length in the method met to the right, what is

the big O of the met method? Give the most restrictive

correct answer.

A. O(n) B. O(nlogn)

C. O(n2) D. O(logn)

E. O(1)

QUESTION 21

What algorithm does method met implement?

A. insertion sort B. selection sort

C. binary search D. quick sort

E. radix sort

QUESTION 22

public int s(int n) {

if(n == 0) return 10;

else if(n == 1) return 5;

return 2*s(n-2);

}

What is the value returned by the call s(6)?

A. 0 B. 1 C. 8

D. 40 E. 80

QUESTION 23

int a = 25 ^ (16 >>> 2);

System.out.print(a);


A. 0 B. 8 C. 17

D. 28 E. 29


QUESTION 24

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

for(int i : a)

i += 1;

System.out.print(a[a.length-1]);


A. 1 B. 2 C. 3

D. 4 E. 5

QUESTION 25

int[][] b = {{1, 2, 3, 4}, {0, 1}, {1, 2, 3,

4, 5}};

System.out.print(b[1].length);


A. 1 B. 2 C. 3

D. 4 E. 5

QUESTION 26 List<String> list = new ArrayList<String>();

list.add("hey");

list.add("hello");

list.add("hi");

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

String obj = it.next();

it.remove();

it.remove();

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


A. hey

B. hello

C. hi

D. Output will vary from one run to the next.

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

QUESTION 27

Set<String> s = new TreeSet<String>();

s.add("Chinay");

s.add("Elvis");

s.add("Beyonce");

s.add("Abba");

for(String x : s){

System.out.print(x + " ");

}

Which object in set s is printed last?

A. "Chinay" B. "Elvis"

C. "Abba" D. "Beyonce"

E. It varies from one run to the next.


QUESTION 28

public class One {

private String s;

private double x;

public One(String st, double y){

s = st;

x = y;

}

public String getS() {

return s;

}

public double getX() {

return x;

}

public String display(){

return s + " " + x;

}

}

public class Two extends One {

private int k;

public Two(String st, double y, int a){

<*1>

}

public String display(){

<*2>

}

}

In the code to the right, which of the following code segments

could replace <*1> to correctly implement the Two class

constructor?

I. s = st;

x = y;

k = a;

II. super(st, y);

k = a;

III. k = a;

super(st, y);

A. I only B. II only

C. III only D. I and III

E. II and III

Assume <*1> is filled in correctly.

QUESTION 29

Which of the following is a correct substitution for <*2> so

that the display() method in the Two class returns a String

containing the values of all 3 instance fields?

I. return super.display() + " " + k;

II. return s + " " + x + " " + k;

III. return super.s + " " + super.x + "

" + this.k;

IV. return super.getS() + " " +

super.getX() + " " + k;

A. I only B. II only C. III

only

D. IV only E. I and IV


QUESTION 30

What is the output by the code to the right?

A. 41Hi32 B

.

5Hi5 System.out.print(4+1+"Hi"+3+2);

C. 5Hi32 D

.

41Hi5

E. There is no output due to a compilation

error.

QUESTION 31 int[] a = {1, 2, 3, 4};

int[] b = {3, 4, 5, 6};

b = a;

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

b[i]++;

System.out.print(b[2] + " " + a[2]);


A. 5 3 B. 6 3 C

.

4 4

D. 5 2 E. 3 3

QUESTION 32

public static void main(String[] args) <*1> {

File f = new File("appoint.txt");

if(f.canRead()){

Scanner in = new Scanner(f);

}

else System.out.print("File does not exist

or is unreadable");

}

Which expression can replace <*1> so that the

main method compiles without an error?

I. A blank (nothing is needed in place of

<*1>).

II. throw Exception

III. throws IOException

IV. throws Error

A. I only

B. II only

C. III only

D. IV only

E. III and IV

QUESTION 33

public void mu(int[] a) {

for(int i = a.length-1; i>=1; i--){

for(int j = i; j >= 0; j--){

System.out.print(i*j+a[i]*a[j]);

}

}

}

Let n = a.length. What is the big O of the

method to the right? Give the most restrictive

correct answer.

A. O(n2) B. O(n) C. O(nlogn)

D. O(1) E. O(n3)


QUESTION 34

1

21

321

4321

54321

654321

7654321

87654321

987654321

Consider the output to the right. Which of the following code

segments produce it?

I.

String s = "";

for(int i = 1; i <=9; i++) {

s += i;

System.out.println(s);

}

II.

for(int i = 1; i <= 9; i++) {

for(int j = i; j >=1; j--) {

System.out.print(j);

}

System.out.println();

}

III.

String s = "";

for(int i = 1; i <=9; i++) {

s = i + s;


}

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

D. I and

III

E. II and III


QUESTION 35

Scanner scan = new Scanner(new

File("stuff.txt"));

int sum = 0;

while(scan.hasNext()){

if(<*1>) {

int num = scan.nextInt();

sum += num;

}

else scan.next();

}

System.out.print(sum);

The text file "stuff.txt" contains both integer and

string tokens. What expression can replace <*1> so

that the output of the code to the right is the sum of all

of the integer tokens?

I. scan.canRead()

II. scan.hasNextInt()

III. Integer.parseInt(scan.hasNext()

)


C. III Only D. II and III

E. I and III

QUESTION 36

String s = "What? Game: today";

String lim = ":|a|\\?";

String[] t = s.split(lim);

System.out.println(t.length); //line 1

System.out.print(t[1]); // line 2

In the code to the right, what is the output for the

statement labeled line 1?

A. 1 B. 2

C. 3 D. 4

E. 6

QUESTION 37

In the code to the right, what is the output for the

statement labeled line 2?

A. t B. at? C. Wh

D. Ga E. G


QUESTION 38 public interface Stuff {

double one();

String two(int x);

}

public class Stuff2 implements Stuff {

public double one() {

return 3.5;

}

public String two(int x) {

return ""+x+x+x;

}

public void three() {

System.out.print(3);

}

}

For the class and interface to the right, consider the

following client code. Which is correct and produce NO

compilation errors? The output from the client code

should be "555".

I. Stuff t = new Stuff();

System.out.print(t.two(5));

II. Stuff t = new Stuff2();


III. Stuff2 t = new Stuff();



C. III only D. I and II

E. II and III

QUESTION 39

Random ran = new Random();

String[] r = {"hello", "hi", "bye", "yah",

"yay"};

System.out.print(r[ran.nextInt(3)]);

Which of the following strings from r could be the output

from this code? Choose the answer that includes all

possible outputs.

A. yah

B. hello, hi, bye, yah

C. hello, hi, bye

D. hello, hi, bye, yah, yay

E. hello, hi

QUESTION 40

List<String> L = new LinkedList<String>();

//<Assume elements have been added to L>

for(String s : L){

if(s.length() > 10)


}

Consider the code to the right. The maximum number of

Strings that will be printed is:

A. 0 B. 10

C. L.size() D. L.size()-1

D. s.length()


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()

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.ArrayList<E> implements List<E>

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 B - 2013

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

2. A 12. B 22. E 32. C

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

4. B 14. B 24. D 34. E

5. E 15 .D 25. B 35. B

6. B 16. E 26. E 36. E

7. C 17. E 27. B 37. A

8. B 18. E 28. B 38. B

9. D 19. E 29. E 39. C

10. A 20. C 30. C 40. C

Notes:

20 and 33: 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.

32. Note that throws Error does not work. The method throws a FileNotFoundException, and while it will work to

use throws <X> where FileNotFoundException is a descendant of <X> , throws Error is incorrect.

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