UIL Calculator Applicationsmrguerrero.weebly.com/uploads/3/8/0/7/38079917/2012_uil... · 2019. 10....

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 12A (Invitational A)

Name

5x(Last Problem Attempted) + + +

7x(Number Incorrect) - - -

2x(Number Incorrect SDs) - - -

TOTAL SCORE

Tie Breaker: Points scored on Stated and Geometry Problems

+ + +

A-1

12A-1. (4.26/ 4.33) + 0.295 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 1= ______________

12A-2. –3.95/ 4.71 + 0.645 – 0.837 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2= ______________

12A-3. (0.41 – 0.191 – 0.207 + 0.0309) x (–0.826) - - - - - - - - - - - - - - - - - - - - - - - - - - - - 3= ______________

12A-4. (4990 – 3570)

{ (–0.561) / (0.504) } + (485 – 299) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 4= ______________

12A-5. (–0.00183 – 3.45x10–4) (0.94)

{ (0.961) / (–0.807) } – (0.0146 – 0.00777) - - - - - - - - - - - - - - - - - 5= ______________

12A-6. What num ber when added to 3 gives a result of 13? - - - - - - - - - - - - - - - - - - - - - 6= ______________

12A-7. What is 27% of the product of 0.365 and 0.826? - - - - - - - - - - - - - - - - - - - - - - - - - - 7= ______________

12A-8. Calculate x if the negat ive square root of 9x when added to 430 yields 75. - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 8= ______________

12A-9. SEMI CI RCLE

Area = 0.694

12A-9 = ______________

12A-10. PARALLELOGRAM

Perim eter = ?

12A-10 = ______________

A-2

12A-11. (120 + 69) (579 – 566 + 1860)

(938) (–150) – 2.01x106 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 11= ______________

12A-12. (–586 + 66.9 – 162) (878) (444)

( – 2.48) (225 – 487) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 12= ______________

12A-13. 9.84x105 + 4.33x106

() (–0.829) + 1.25 + 2910 – 1780 + 2560

(0.00114) (0.879) - - - - - - - - - - - - - - - - - - - - - - - - 13= ______________

12A-14. –2392.46 +

271 + 192 – 2410.684 – +

(0.00468 + 0.0186)

{ (–4.67x10–4) / (9.62) } - - - - - - - - - - - - - - - - - - 14= ______________

12A-15. 66400 + 98200 – (28000 + 99300) (1.16 – 0.429)

(–719) (0.462) (–0.704) (581 – 2570 + 2650) - - - - - - - - - - - - - - - - - - - 15= ______________

12A-16. A 55–gallon rain barrel is filled from a roof drain. What is the water

gathering area of the roof if the barrel fills during a 0.1 in rain? - - - - - - - - - - - - - - - - - - 16= ____________ft2

12A-17. What is the percent difference in the num ber of Texian com batants reported to have defended the Alam o, 182, and the num ber of Mexican soldiers in Santa Anna’s army, 2400? - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 17= ____________%

12A-18. The product of three consecut ive integers is 328,440. What is their average? - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 18= ________integer

12A-19. RI GHT TRI ANGLE

Area = ? 12A-19 = ______________

12A-20. RI GHT TRI ANGLE

12A-20 = ______________

A-3

12A-21. 1

–2.27 + 4.47 + 1

0.322 – 1.12 + 1

(1.34) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 21= ______________

12A-22.

1.1 – 1.04

6.52 + (0.00885)

0.271

2

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

12A-23. 0.946 + 0.514 + (0.0507) / (0.0522)

–0.969 + 0.475 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 23= ______________

12A-24. (0.225) (7.55) + (16.6) / (9.45) + [ ](0.135) (9.43) 2 - - - - - - - - - - - - - - - - - 24= ______________

12A-25. [ ]–44.5 + 591 2 x [ ]127 + 169 2 x 0.0545/ 0.00427 - - - - - - - - - - - - - - 25= ______________

12A-26. Frank’s hom e water bill was $12.50 for 4000 gal usage. He paid $1.29 for a 20-oz bot t le of water at a convenience store. What would Frank’s water bill have been if hom e water cost the sam e as convenience store water? - - - - - - - - - - - - - 26= $_____________

12A-27. Quincy bikes 4 m i to school in 15 m in and walks to school in 65 m in. She biked a distance d one day towards school and had a flat t ire. She walked the rest of the way. What is d if her total t im e to school was 33 m in? - - - - - - - - - - - - 27= ____________m i

12A-28. Daria has 25 coins totaling $2.41. She has twice as m any dim es as pennies, and one less nickel than quarters. How m any nickels and dim es does she have? - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 28= ________integer

12A-29. CYLI NDER

Volum e = 90.9

12A-29 = ______________

12A-30. HEMI SPHERE

Total Surface Area = ?

12A-30 = ______________

A-4

12A-31. (–4.91x106 + 5.91x106)2

61.8 – 30.9 +

6.10x1014

9.36x106 + 1.10x107 - - - - - - - - - - - - - - 31= ______________

12A-32. 1/ (730 – 227)

(154) (5.88 + 4.86)2 + (–1.10x10–5)2(8.92x106) - - - - - - - - - - - - - 32= ______________

12A-33. (5.72x105)2(1.96x10–12 + 1.31x10–12)

0.0217 + (–0.765) (0.0693) + 1

1–30.2 +

1(12.1)

- - - - - - - - 33= ______________

12A-34. (7.58x10–4) / { }(0.0088) / 0.00381

0.0423 + (0.109) (4.84) + { }0.0103 + 0.07961/ 2 - 34= ______________

12A-35.

5.22 + 11.4

(7060) (11400)+ (8970)2

9.45 + 11.2 + (1.95 – 1.92)2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 35= ______________

12A-36. The m ass of the earth is 5.9742 × 1024 kg. What is the percent error

in calculat ing the m ass based on an average density of 5.613 g/ cm 3? - - - - - - - - - - - 36= _________% (SD)

12A-37. The probability of winning the Texas lot tery is one chance in 50,063,860. The probability of winning the Texas lot tery 1000 t im es in a row is one chance in how m any? - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 37= ______________

12A-38. Rodney m ade punch by adding 20 tablespoons of concent rate to a gallon bot t le and then topped off the bot t le with water. Later, he learned that it should have been 20 teaspoons of concent rate. How m uch punch should be poured out of the bot t le so that the concent rat ion is correct when the bot t le is topped off with water? - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 38= __________cups

12A-39. SCALENE TRI ANGLE AND CI RCLES

12A-39 = ______________

12A-40. SCALENE TRI ANGLE

12A-40 = ______________

A-5

12A-41. 10–(0.453 – 4.46)

7540 + 2420 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 41= ______________

12A-42. (3.58x10–6)

(3.44x10–6) [ ]1 – e–(0.442) (0.949) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 42= ______________

12A-43. (2.16x10–6 – 3.99x10–6) Ln{ (–5.28x10–6) (–6.31x10–5) } - - - - - - - - - - 43= ______________

12A-44. (713 + 4450)1/ 3 + 1/ { (443)–0.45} - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 44= ______________

12A-45.(deg) cos{ (73.8°) / (1.09) }

sin{ 159° – 755°} - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 45= ______________

12A-46. Lara bought a set of scaled hex drivers. I f the driver for a 5-m m screw weighed 15 g, how m uch does the dr iver for a 2-m m screw weigh? - - - - - - - - - - - - - - 46= _____________g

12A-47. Pat needs to dr ive across the United States, 3300 m i. Her daily log of total m iles t raveled the first 5 days was 420 m i, 925 m i, 1170 m i, 1700 m i and 2100 m i. Est im ate how long the ent ire t r ip will take. - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 47= ____________dy

12A-48. ( rad) For what negat ive, nonzero value of d does sin(sin(d) ) =

100d-d3? - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 48= ______________

12A-49. SPHERE AND HEMI SPHERE

Volum e(Sphere) = 9.56 Volum e(Hem isphere)

12A-49 = ______________

12A-50. CUBE AND SQUARE PYRAMI D

Total Volum e = 38,700

12A-50 = ______________

A-6

12A-51. 10+ (0.298) + 10–(0.533) + [ ]10(0.576/ 0.662) – 10(0.803) 1/ 2 - - 51= ______________

12A-52. 84.8 + e(3.25 + 1.4)

1.55 – e–(0.114 – 0.766) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 52= ______________

12A-53. Log{ }0.23 + (0.426) (0.57) – Log{ }(75.8) / (0.079)

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 53= ______________

12A-54. (7.64)0.848 – ()–0.917

668 + 111 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 54= ______________

12A-55.( rad) arctan

(1780) (0.325)

(7.6) (39.9) + (0.775) (1.04) - - - - - - - - - - - - - - - - - - - - - - - - 55= ______________

12A-56. Calculate the slope of the curve f(x) = 5[ 4] 7–5x at x = 0.9. - - - - - - - - - - - - 56= ______________

12A-57. The area dest royed by a forest fire can be considered to be a circle whose radius grows at a constant rate. When the fire consum ed 100 acres, it was 1 m i from a farm house and the burn rate was 10 acres/ hr. How long will it take the fire to reach the farm house? - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 57= ___________hrs

12A-58. Calculate S3 if S = RV , R = 已–2 18 418 –5 74 7 10

已 and V = 保 9–48

保. - - - - - - - - - - - - - - - - - 58= _________integer 12A-59.

Hatched Area = 500

12A-59= ______________

12A-60. RECTANGLE

AB = BC = 0.539 BD = ?

12A-60= ______________

A-7

12A-61. (1/ 2)Ln

(5.93) x (1.85) x ()3

(2.04) (7.67)2

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

12A-62. ( rad) sin(3.25)cos(3.38) – cos(3.25)sin(3.38) - - - - - - - - - - - - - - - - - - - - - - - - - 62= ______________

12A-63. ( rad) 1

(2160) (0.111) Ln{ }(3.36) + (–1.98)sin(1.71) - - - - - - - - - - - - - - - - 63= ______________

12A-64. 1 + (0.689)4

2 – (0.689)6

6 + (0.689)8

24 – (0.689)10

120 - - - - - - - - - - - - - - - - - - - - - 64= ______________

12A-65.( rad) arctan{ }e–(0.225) (0.409) (–0.251) / (–0.696)

(5.86) (1.13) (1.04) (1.55) - - - - - - - - - - - - - - - - 65= ______________

12A-66. A screen t ransm its 55% of incident light and reflects the rest . What fract ion of incident light passes through two screens stacked together? - - - - - - - - - - 66= ____________%

12A-67. Marin runs a m ile in 6 m in 56 sec. She and Mary, who runs a m ile in 8 m in 15 sec, start at the south end of a 1/ 4 m i circular t rack. Marin takes off running on the t rack, and at the sam e t im e, Mary takes off in a st raight line off the t rack, m eet ing up with Marin before she finishes one lap. Considering due east to be 0 rad, at what posit ive angle does Mary need to run? - - - - - - - - - - - - - - - - - 67= ___________rad

12A-68. One point (a,b) on the line y = –8x+ 4 is equidistant from the points (6,10) and (–8, –5) . What is a? - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 68= ______________

12A-69. CONCENTRI C CI RCLES

Hatched Area = 0.0120

12A-69 = ______________

12A-70. RECTANGLE AND CI RCLE

M = Midpoint , end of slant line

12A-70 = ______________

UIL COMPUTER SCIENCE INVITATIONAL A - 2012 • PAGE 1

University Interscholastic League

Computer Science Competition

Number 131 (Invitational A - 2012)

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

What does ABC16 minus 1FF16 equal?

A. 85316 B. 95316 C. 8BD16 D. 8CD16 E. 9CD16

QUESTION 2

int x = 3;

int y = 10 / x + x * 4;

System.out.print(y);

What is output by the code to the right?

A. 4 B. 6.67 C. 15

D. 15.3333 E. 24

QUESTION 3

int val = 0;

int limit = 25;

for(int i = 1; i < limit; i += 2)

val++;

System.out.print(val);


A. 5 B. 12 C. 13

D. 25 E. 50

QUESTION 4

String name = "Bo";

name = name + name + 2;

System.out.print(name);


A. BoBo2 B. BoBoBo C. BoBob

D. BoBoB E. 'BoBo2'

QUESTION 5

double[] list = new double[6];

System.out.print(list[4]);


A. 0 B. 0.0

C. 1.0 D. 4

E. The output will vary from one execution of the code

to the next.

QUESTION 6

int x1 = 2;

int y1 = x1 * x1 * x1 * x1;

System.out.print(y1);


A. 1 B. 2 C. 8

D. 12 E. 16

QUESTION 7

boolean p = true, q = false;

System.out.print(p || q );

System.out.print(" " + (p && q));


A. false false B. true false

C. false true D. true true

E. 0 1


QUESTION 8

String n2 = "126547";

if(n2.indexOf('a') != -1)

System.out.print(1);

else


if(n2.length() > 6)


else



A. 24 B. 23 C. 13

D. 14 E. 1

QUESTION 9

public class School {

private String mascot;

public School(String mascot) {

= mascot;

}

public String toString() {

return "go " + mascot;

}

}

// client code

School sc = new School("Longhorns");

System.out.print(sc.toString());

What replaces in the code to the right so that the

output of the client code to the right is

go Longhorns?

A. mascot

B. School.mascot

C. String mascot

D. toString()

E. this.mascot

Assume is filled in correctly.

QUESTION 10

Given class School to the right, what is output by the

following client code?

School sc2 = new School();

System.out.print(sc2);

A. go null

B. go

C. "go mascot"

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

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

QUESTION 11

int m = 47;

int n = 70;

System.out.print(m | n);


A. true B. false C. 6

D. 111 E. 117

QUESTION 12

int tot = 0;

for(int i = 0; i < 10; i++) {

int temp = (int) (Math.random() * 11);

tot += temp - 5;

}

System.out.print(tot);

What is the largest value that can be output by the code to

the right?

A. 50 B. 55 C. 100

D. 110 E. 150


QUESTION 13

System.out.print("cat");

System.out.print("dog");

System.out.println("ape");


A. cat

dog

ape

B. cat dog

ape

C. cat

dog ape

D. apecatdog

E. catdogape

QUESTION 14

double a4 = 14.267299;

System.out.printf("%7.4f", a4);


A. a4 B. 14.26730 C. 14.2673

D. 14.2672 E. 14.267299

QUESTION 15

public int eval(int y, int x) {

y += x;

x++;

return y * x;

}

What is returned by the method call eval(5, 3) ?

A. 12 B. 32 C. 36

D. 40 E. 4096

QUESTION 16

String stars = "";

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

stars += "*";

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

stars += "*";

System.out.println(stars.length());


A. 20 B. 22

C. 45 D. 200

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

QUESTION 17

Which of the following Java expressions is equivalent to the formula to the

right? a, b, and c are variables of type double.

A. (-b + Math.sqrt(b ^^ 2 - 4 * a * c)) / (2 * a)

B. (-b +- Math.sqrt(b ** 2 - 4 * a * c)) / (2 * a)

C. (-b + (b * b - 4 * a * c) ^ 0.5) / (2 * a)

D. -(b + Math.sqrt(b * b - 4 * a * c)) / 2a

E. (-b + Math.sqrt(b * b - 4 * a * c)) / (2 * a)

QUESTION 18

String garbage = "1000\\100\"\t+5";

System.out.print(garbage.length());


A. 10 B. 12 C. 14

D. 15 E. 17


QUESTION 19

final int rate;

int sts = 7;

int profit = 5;

rate = sts * profit;

System.out.print(rate);


A. 5 B. 7 C. 35



QUESTION 20

Which answer is logically equivalent to the following boolean expression, where x, y, and z are int variables?

(x != y) || !(y >= z)

A. (x != y) && !(y >= z) B. (x == y) && (y == z) C. !((x == y) || (y >= z))

D. (x != z) && (y == z) E. !((x == y) && (y >= z))

QUESTION 21

public static int Total(String st) {

int res;

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

res += st.charAt(i);

return res;

}

Method Total to the right will not compile due to a

syntax error. Which of the following best explains the

syntax error in method Total?

A. Total is not a legal method name.

B. The keyword static must be removed from the

method header.

C. The variable res is not initialized.

D. A char may not be added to a variable of type

int.

E. The for loop must have a set of braces, {}.

QUESTION 22

String[] names = new String[4];

System.out.print(names[2].length());


A. 0 B. null

C. The code runs, but there is no output.



QUESTION 23

double a5 = 3.89293;

a5 /= 2;

System.out.print( (int) a5 );


A. 0 B. 1.0 C. 1

D. 1.946465 E. 2

QUESTION 24

Which of the following could replace so that the following line of code compiles without syntax error?

int = 15;

A. x5 B. 5_x C. _5 D. x-5 E. More than one of A through D is correct.


QUESTION 25 ArrayList grades;

grades = new ArrayList();

grades.add('A');

grades.add('A');

grades.add(1, 'B');

grades.add(0, 'C');

grades.remove(1);

System.out.println(grades);


A. [C, A, B] B. [A, B]

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

E. ['C', 'A', 'B']

QUESTION 26

public String get(String st) {

String r = "";

for(int i = 0; i < st.length(); i *= 2)

r = r + st.charAt(i) + r;

return r;

}

Method get to the right contains a logic error. Which of

the following will occur when the method call

get("aaaa") is made?

A. The program will crash due to a

StackOverError.

B. Nothing. An infinite loops occurs.

C. The program will crash due to a

NullPointerException.

D. The program will crash due to an

OutOfMemoryError.

E. The program will crash due to an

IndexOutOfBoundsException.

QUESTION 27

int v1 = 15;

int v2 = 30;

System.out.print((v1 >= v2) + " ");

System.out.print(v1 > 0 && v2 % v1 == 0);


A. false true B. true false

C. false false D. true true

E. false true true

QUESTION 28

public int check(int[] a, int[] b) {

int diff = 0;

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

if( )

diff++;

return diff;

}

// client code

int[] h1 = {5, -2, 4, 10, 45};

int[] h2 = {5, 2, -4, 10, 45};

System.out.print(check(h1, h2));

What replaces in method check to the right so

that diff is incremented if the element at index i in

a does not equal the element at index i in b?

A. a[i] != b[i]

B. !(a[i].equals(b[i]))

C. a.get(i) != b.get(i)

D. a[i].compareTo(b[i]) != 0

E. More than one of A through D is correct.


QUESTION 29

What is output by the client code to the right?

A. 0 B. 2 C. 3

D. 12 E. 14


QUESTION 30

int bw = 10;

bw = bw >> 6;

System.out.print(bw);


A. 10000000 B. 640

C. 0.15625 D. 0


QUESTION 31

An array with 1,000,000 distinct ints in random order is passed to a method that uses the heapsort algorithm, it takes 4

seconds for the method to complete. What is the expected time for the method to complete when sorting an array with

4,000,000 distinct ints in random order?

A. 1 second B. 4 seconds C. 8 seconds D. 17.6 seconds E. 64 seconds

QUESTION 32

public void sort(ArrayList vs) {

for(int i = 0; i < vs.size(); i++)

for(int j = 1; j < vs.size(); j++)

if( )

;

}

Which of the following replaces in the code to the

right so that the body of the if statement is executed if

the element at position j - 1 in vs is greater than the

element at position j?

A. vs.get(j-1).compareTo(vs.get(j)) > 0

B. vs[j-1].compareTo(vs[j]) > 0

C. vs.get(j-1).compareTo(vs.get(j))

D. vs.get(j-1) vs.get(j)

E. None of answers A through D are correct.


QUESTION 33

Which of the following replaces in the code to

swap the elements at positions j - 1 and j in vs?

A. vs.set(j, vs.get(j - 1))

B. vs.set(j - 1, vs.remove(j))

C. vs.set(j, vs.set(j-1, vs.get(j)))

D. vs.set(j - 1, vs.get(j + 1))



QUESTION 34

Which sorting algorithm does method sort implement?

A. radix sort B. insertion sort

C. selection sort D. quick sort



QUESTION 35

public int add(String s) {

if(s.length() > 20)

return s.length();

else

return add(s + s) + add(s + s + s);

}

What is returned by the method call add("aaaa")?

A. 32 B. 80 C. 164

D. 200 E. 228

QUESTION 36

public int handle(int[][] t) {

int res = 0;

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

int t1, t2;

t1 = t2 = 0;

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

t1 += t[i][j];

t2 += t[j][i];

}

if(t1 == t2)

res += t1;

else

res -= t2;

}

return res;

}

What is returned by method handle if t is the matrix

shown below?

1 4 0 2 1 6

0 -1 5 4 0 -4

2 2 7 1 13 2

10 5 13 13 4 20

1 4 2 1 3 2

0 -6 -5 3 -4 5

A. -88 B. -42 C. -11

D. -10 E. 8

QUESTION 37 Stack st = new Stack();

int[] data = {13, 17, -20, 50, -10};

for(int i : data)

if(i % 5 == 0) {

st.push(i);

st.push(i > 0 ? i : -10);

}

while(!st.isEmpty())

System.out.print(st.pop() + " ");


A. 13 17 B. -10 -10 50 50 -10 -20

C. 17 13 D. 50 50

E. -20 -10 50 50 -10 -10

GO ON TO THE NEXT PAGE.


QUESTION 38

public class Structure {

private ArrayList con;

public Structure() {

con = new ArrayList();

}

public void add(E obj) {

if(!con.contains(obj))

con.add(0, obj);

}

public boolean present(E obj) {

return con.contains(obj);

}

public String toString() {

return con.toString();

}

public boolean remove(E obj) {

return con.remove(obj);

}

}

What is output by the following client code?

String sch = "texasutamtechstate";

Structure st1;

st1 = new Structure();

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

st1.add(sch.charAt(i));

String temp1 = st1.toString();

String[] res;

res = temp1.split("[\\s,\\[\\]]+");

for(String s3 : res)

System.out.print(s3);

A. texasutamtechstate

B. texasumch

C. hcmusaxet

D. The program runs without error, but there is no

output.

E. The output will vary from one run of the program to

the next.

QUESTION 39

Given a Structure that contains N Integers what is

the order (Big O) of the add method for a value that is not

already present in the Structure? Pick the most

restrictive correct answer.

A. O(1) B. O(N) C. O(NlogN)

D. O(logN) E. O(N2)

QUESTION 40

What type of data structure does the Structure class

implement?

A. a graph B. a set

C. a stack D. an array based list

E. a linked 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

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

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

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

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

o boolean add(E e)

o int size()

o Iterator iterator()

o ListIterator 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 implements List

class java.util.LinkedList implements

List, Queue

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

o boolean isEmpty()

o E peek()

o E pop()

o E push(E item)

interface java.util.Queue

o boolean add(E e)

o boolean isEmpty()

o E peek()

o E remove()

class java.util.PriorityQueue

o boolean add(E e)

o boolean isEmpty()

o E peek()

o E remove()

interface java.util.Set

o boolean add(E e)

o boolean contains(Object obj)

o boolean remove(Object obj)

o int size()

o Iterator iterator()

o boolean addAll(Collection c)

o boolean retainAll(Collection c)

class java.util.HashSet implements Set

class java.util.TreeSet implements Set

interface java.util.Map

o Object put(K key, V value)

o V get(Object key)

o boolean containsKey(Object key)

o int size()

o Set keySet()

o Set entrySet()

class java.util.HashMap implements Map

class java.util.TreeMap implements Map

interface java.util.Map.Entry

o K getKey()

o V getValue()

o V setValue(V value)

interface java.util.Iterator

o boolean hasNext()

o E next()

o void remove()

interface java.util.ListIterator extends

java.util.Iterator

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)

UNIVERSITY INTERSCHOLASTIC LEAGUE

Making a World of Difference

do not turn this page until

you are instructed to do so!

MathematicsInvitational A • 2012

WRITE ALL ANSWERS WITH

CAPITAL LETTERS

1. Evaluate: 64 8 4ƒ ‚32 (16) 12 ˆ ‰q 2

(A) (B) (C) 0 (D) (E) 32q q 30 16 6

2. 1.2 thousand is subtracted from the sum of 3.4 million and 5.6 billion. How many zeros will the answer contain when written out using digits instead of words?

(A) 0 (B) 1 (C) 3 (D) 5 (E) 7

3. I. M. Broke borrows $1000.00 from his uncle Sam to buy college textbooks. He will pay back the $1000.00 plus the amount of simple interest in 8 equal monthly payments. What will his monthly payments be if the interest rate is 3%?

(A) $113.33 (B) $120.00 (C) $125.21 (D) $127.50 (E) $128.75

4. The statement 5(4 hich of the following properties?q q 3) = 5(4) 5(3) is an example of w

(A) Associative (B) Commutative (C) Distributive (D) Mult. Inverse (E) Subtraction

5. Find an equation of the line shown using the two points shown.

(A) 4x 3y = 6 (B) 3x y = 8 (C) 4x 3y = 2 (D) 3x y = 2 (E) 3x 4y = 8 q q q q 4 4

6. If 6 x = (ax b)(cx d) then a b c d = _____.q q 7x 20 2

(A) 14 (B) 10 (C) 4 (D) (E) 1q q 720

7. P and Q are complementary. Q and R are supplementary. If m P = 3x 8 andn n n n n m Q = 2x then m R = ?n nq 3

(A) 121° (B) 131° (C) 149° (D) 159° (E) 163°

8. Which of the transformations will map triangle 3 to triangle 6?

(A) glide reflection (B) half-turn (C) reflection (D) rotation (E) translation

UIL Math A 2012 - page 1

9. Dim, Nit, and Half looked at their father's circular clock. The time shown was 4:44 . TheyPM asked their father, Mr. Wit, to find the measure of the smaller angle between the big hand and the little hand. What should Mr. Wit find the measure to be?

(A) 142 ° (B) 112 ° (C) ° (D) ° (E) 122 ° 102 132

10. If x varies directly as 2y x = 9 when y = 2, find y when x = 15.q 1, and

(A) 23 (B) 1 (C) 13 (D) 3 (E) 31 1 32 2 17

11. Given the sequence 3, 9, 18, 30, 45, 63, 84, k, 135, 165, ... find k.

(A) 93 (B) 102 (C) 108 (D) 111 (E) 117

12. Three window washers can wash 6 windows in 60 minutes. How many windows could 5 window washers wash in 90 minutes if they work at the same rate as the 3 window washers?

(A) 9 (B) 12 (C) 15 (D) 16 (E) 20

13. Determine the range of f(x) = 4cos(3x 2 . 1) 1q

(A) [ (B) [ 1 (C) [ 5 (D) [ E) [2q q q 5, 3] , 5] , 5] 1, 4] , 3](

14. Willie B. Quik flies his jet on a bearing of 25° at a speed of 540 mph. How far north of his starting point will Willie be after an hour and a half? (nearest mile)

(A) 608 mi (B) 684 mi (C) 734 mi (D) 755 mi (E) 810 mi

15. Determine the period of y = 1 2 cos 4 .q 3 x’ 1( ) “ (A) 2 (B) (C) (D) (E) 1 1 1 2 13 3 3

16. How many solutions are there for the equation 4x 3y = 72 such that both x and y are non-negative integers?

(A) (B) 7 (C) 8 (D) 9 (E) 126 __ __ __ __ 17. The trapezoid shown exists such that BC = 8 cm, AD = 12 cm, BC EF AD, and EF and them m two diagonals intersect at a common point. Find EF. (nearest tenth)

A D

B C

E F

(A) 8.2 cm (B) 9.8 cm (C) 9.6 cm (D) 10.2 cm (E) 10.0 cm


18. Simplify 6 3 to the form a b( )( ) È Èq q q 18 8 i. (A) 6 3 2 (B) 12 6 2 (C) 30 3 2 (D) 6 6 2 (E) 30 3 2 È È È È Èi i i i iq q 19. Let f(x) = x x 2x x . Find the coefficient of the quadratic term of f (x). 5 4 3 2q q q 2 3x 3

w w

(A) (B) (C) 0 (D) 12 (E) 20q q 24 6

20 A particle is moving in a straight line according to the function f(t) = t 3t 9t 4.. 3 2 q For which of the following values of t will the particle be moving to the left?

(A) 3.5 (B) (C) 1 (D) (E) 0.53 .5 1

21. How many distinguishable permutations can be made from the letters of the word 'DIVISION' ?

(A) 6720 (B) 120 (C) 40320 (D) 720 (E) 5040

22. The IB2 Smart club has 15 members of which 4 are geniuses, 5 are computer geeks, and 6 are puzzle solvers. The club needs a 5-member committee consisting of 2 geniuses, a geek, and 2 solvers. How many 5-member committees can be formed from the club membership?

(A) 3003 (B) 450 (C) 180 (D) 120 (E) 26

23. Coach Garza asks each of his 4 number sense team members what their date of birth is. He calculates what day of the week each of them was born on. What is the probability that all 4 of them were born on a different day of the week? (nearest whole percent)

(A) 14% (B) 28 (C) 35% (D) 43% (E) 57%%

24. The four shapes below are made up of 1 cm squares. If the pattern continues, fine the perimeter of the shape consisting of 14 squares.

(A) 26 (B) 30 (C) 32 (D) 36 (E) 38

25. Simplify: (n 1) (n) (n 2) (n 1) x xq x q x‚

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

26. Let P = {p,r,i,m,e}, N = {n,u,m,b,e,r}, and M = {m,a,k,e,r}. The number of distinct elements in (M N) P is ________.

(A) 3 (B) 5 (C) 7 (D) 8 (E) 9


27. In the algebraic expression, 5xy 6(x y) q q , there are how many terms?x y7

(A) 8 (B) 6 (C) 5 (D) 4 (E) 3

28. Which of the following side lengths form an obtuse isosceles triangle?

(A) 7, 7, 10 (B) 16, 30, 34 (C) 9, 10, 10 (D) 3, 6, 10 (E) 15, 15, 21

29. What is the digit in the tens place of (1!) (1!) (2!) (3!) (5!) (8!) ... (34!) ?

(A) 8 (B) 5 (C) 3 (D) 2 (E) 0

30. sin( )q 12 ) equals :

(A) cos( (B) sin( (C) cos( (D) sin( (E) cos( ) ) ) ) ) 1 1) ) ) ) )1 1 12 2 2q

31. If A = and B = then AB = . Find x y.’ “ ’ “ ’ “ 2 1 1 3 4 13 14 y 1 5 5

x

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

32. If f( ) = sin 2 then f ( ) = ______.) ) w 112

(A) (B) (C) (D) (E) 12 3 22 3 3 31 3È È È

33 The following chart shows the percentage growth of the price of a gallon of gasoline each. quarter for one year. What was the average percentage growth for that year? (nearest hundredth) Quarter Percentage Growth 1 increased 10% 2 increased 5% 3 increased 12% 4 decreased 8%

(A) 4.13% (B) 4.35% (C) 4.41% (D) 4.45% (E) 4.75%

34. The set of numbers, {3, 6, 9, 12, 15, 18} are __________ numbers.

(A) Odious (B) Abundant (C) Perfect (D) Deficient (E) Evil

35. What is 6 ( (0.08333...)?1 14 6% of ƒ

(A) B) (C) (D) (E) 2 1 19 3 8 ( 0.25 0.41666...

36. 234 314 123 = _________________ 5 5 5 5

(A) 1231 (B) 2131 (C) 1321 (D) 1141 (E) 2111


37. Dee Kartez drew this quadrilateral on the coordinate plane below. The coordinates of the vertices are integers. What is the area of his quadrilateral?

-5 -4 -3 -2 -1 1 2 3 4 5-5

-4

-3

-2

-1

1

2

3

4

5

x

y

(A) 27 units (B) 26 units (C) 26 units (D) 25 units (E) 25 units2 2 2 21 12 2

2

38. Simplify: Š ‹Š ‹6x 2x 3x 7x 22x x 6 6x 2 2 22 q q q (A) (B) (C) (D) (E) 3x x 3x 1 6x 2x 3x 1 3x 1 2x 3 6 x 6 3x 22x 3x

2 2 2

2 qq q q qq

39. Which of the following is NOT a member of the solution set for 1 3 6 x 13 ? ¸ ¸q 10 (A) (B) (C) (D) 0.5 (E) 1q q 1 0.6 0.1

40. If a = 8, a = 5 and a = a a , then a equals:1 2 n n 1 n 2 8 q qq

(A) 8 (B) 5 (C) 3 (D) 5 (E) 8q q q

41. Let f(x) = 2x 3 and g(x) = 4x 5. Find f g( ) . Ð Ñq a 14

(A) 2a 9 (B) a (C) a 6 (D) 2a 5 (E) 1.5a q q 6

42. kx (k k! ˆk=0

2q q 1)y = ? ‰

(A) 3x 3 (B) x y 1 (C) 3x y 1 (D) 3x y 3 (E) x 2 q q 2 2

43. The directrix of the parabola y = x is: 2 q 5

(A) x = (B) y = (C) x = (D) y = (E) y = 5 19 5 21 54 4 4 4q q

44. Willie When and Mae Beknott each have a bag containing a red chip, a blue chip, and a white chip. If they randomly draw out a chip what are the odds that at least one of them draws out a red chip?

(A) (B) (C) (D) (E) 1 4 5 4 53 9 9 5 4


45. The sequence 3, 0, 2, 3, 2, 5, ... , where P = 3, P = 0, and P = 2, is a recursive sequence0 1 2 for all P n 3. Find P .n where 8

(A) 3 (B) 5 (C) 7 (D) 10 (E) 12

46. Find the perimeter of the figure shown. (nearest tenth).

4530

3dm

(A) 18.4 dm (B) 17.2 dm (C) 16.2 dm (D) 15.4 dm (E) 15.0 dm

47. The volume of the right prism shown is 48 cubic inches. Find x.

(A) 4 (B) 5 (C) (D) (E) 127 8

48. Find the number of positive integral divisors of 900.

(A) 6 (B) 8 (C) 9 (D) 27 (E) 30

49. Les Scents has a bag containing nickels and dimes. If Les spends a dime, 20% of the remaining coins would be dimes. If Les had spent 2 nickels instead of a dime, 25% of the remaining coins would be dimes. How many coins were in his bag originally?

(A) 18 (B) 24 (C) 26 (D) 30 (E) 36

50. A child's ticket at the Cheap Flick movie theater cost $4.00 and an adult ticket cost $6.50. How many adult tickets were sold if a total of $432.50 was collected for 80 tickets?

(A) 30 (B) 35 (C) 40 (D) 45 (E) 50

51. Two elements of the set { 2 , 1 , 3 , 4 , 7, 11 } are randomly selected. What is the probability that their sum is an element of the set?

(A) 25% (B) 26 % (C) 36 % (D) 50% (E) 66 %2 4 23 11 3

52. Evaluate: (log (log (log 4 3 2 64) 9) 8) q

(A) 2 (B) 3 (C) 4 (D) 5 (E) 6


53. Romeo leans a twelve-foot ladder from the ground to Juliet's window. The angle of inclination is 60 °. How high is Juliet's window from the ground? (nearest inch)

(A) 7 2" (B) 11 3" (C) 10 8" (D) 9 4" (E) 10 5"' ' ' ' '

54. Let cot A = , where A is in QII. Find sin A cos A.q 1160

(A) 1 (B) 1 (C) (D) E) 10 11 51 49 6061 60 60 61 61 (

55. x x , and h(x) = x F f( ) Let f(x) = x 2x 3, g(x) = 2x 3 3. ind h g 13 2 2q q q q Š ‹ˆ ‰ (A) (B) (C) 9 (D) (E) 3 6 3 6q q

56 . Let f(x) = 2x 3x 1, g(x) = x 1, and s(x) be the slant (oblique) asymptote of . 2 f(x)g(x) q

Find S( ).q 4

(A) (B) (C) 1 (D) 5 (E) 6q q 5 3

57. Let f(x) = x x 5x 20. The sum of the x-values of the critical points of the function is: 5 4 3q 5

(A) 21 (B) 11 (C) 5 (D) 4 (E) 3

58. Find the area (in square units) of the region bounded by the curves y = 2 x and y = .È x42 (A) 5 (B) 5 (C) 5 (D) 5 (E) 51 1 1 3 26 4 3 4 3 ___ 59. ABC is a right triangle with ACB being the right angle. Point D lies on AC such that˜ n AD = 3" and CD = 5". Find the area of ABD if BC = 6". (nearest square inch)˜

(A) 6 sq. in. (B) 9 sq. in. (C) 12 sq. in. (D) 15 sq. in. E) 24 sq. in. (

60. 11 111 1111 = _________________ 2 4 8 16

(A) 1111 (B) F22 (C) 667 (D) 261 (E) 25D


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answers. • Ifaquestionisomitted,nopointsaregivenorsubtracted. • Onthebackofthispageisprintedacopyoftheperiodictableoftheelements.Youmaywishto

refertothistableinansweringthequestions,andifneeded,youmayusetheatomicweightsandatomicnumbersfromthetable.Otherscientiicrelationshipsarelistedalso.

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Allquestionswillreceive6pointsifansweredcorrectly;nopointswillbegivenorsubtracted ifunanswered;2pointswillbedeductedforanincorrectanswer.

SCIENCEInvitational A • 2012

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#$0 = 8.988 ! 109 N•m2/C2

Permittivity of free space, $0 = 8.85 ! 10–12 C2/N•m2

Permeability of free space, !0 = 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 ! 10

5 J/kg

Index of refraction, n = 1.33

HS Science • Invitational A • 2012

University Interscholastic League • page 1

Biology Questions (1 – 20)

1. Which of the following is the primary function of

the nucleus?

A) production of proteins

B) storage of water

C) production of materials to add to the cell

membrane

D) storage of DNA

E) storage of ribosomes

2. Which of the following molecules would diffuse

most easily through the plasma membrane?

A) glucose

B) O2

C) DNA

D) ATP

E) hemoglobin

3. The basic building blocks of proteins are ___ .

A) monosaccharides

B) fatty acids and glycerol

C) amino acids

D) nucleotides

E) starches

4. Various forms of a gene at a specific locus are

called ___ .

A) homologs

B) alleles

C) loci

D) autosomes

E) chormatids

5. Which of the following is the process by which a

polypeptide is synthesized from mRNA?

A) transcription

B) replication

C) translation

D) transduction

E) None of the above

6. The distinguishing characteristic of prokaryotes is

that they ___ .

A) do not have a nucleus

B) use RNA as their genetic material

C) are pathogens

D) can become dormant in harsh conditions

E) have cell walls

7. Which of the following is NOT a classification

within the plant kingdom?

A) sexually reproducing

B) nonvascular

C) seed-producing

D) flowering

E) conifers

8. Which of the following phyla of animals contains

the largest number of species?

A) Chordata

B) Mollusca

C) Arthropoda

D) Echinodermata

E) Nematoda

9. The area where dividing cells produce new cells for

the growing plant shoot or root tip is called the ___ .

A) radicle

B) cotyledon

C) cap

D) apical meristem

E) epidermis

10. Plants differ from animals in that their growth

is ___ .

A) uncontrolled

B) stunted

C) indeterminate

D) influenced by the environment

E) determinate

11. Which plant hormone is responsible for

phototropism?

A) auxin

B) cytokinin

C) gibberellin

D) abscissic acid

E) ethylene

12. Which of the following organs of the human

digestive system carries out most of the mechanical

digestion of food?

A) mouth

B) esophagus

C) stomach

D) small intestine

E) large intestine



13. For all organisms, gas exchange between the body

and the environment takes place by the process

of ___ .

A) active transport

B) osmosis

C) facilitated diffusion

D) passive transport

E) simple diffusion

14. Which of the following animals has a two-

chambered heart?

A) frog

B) snake

C) cat

D) human

E) fish

15. Which of the following is NOT an endocrine

gland?

A) pituitary gland

B) thyroid gland

C) salivary gland

D) thymus gland

E) adrenal gland

16. The type of muscle found in the wall of the aorta

is ___ .

A) striated

B) smooth

C) cardiac

D) skeletal

E) None of the above

17. An insect and a flowering plant that the insect

pollinates provide an example of which type of

evolution?

A) convergent evolution

B) divergent evolution

C) neutral evolution

D) coevolution

E) maladaptive evolution

18. Which of the following steps in human evolution

appears to have occurred first?

A) development of language

B) large brain

C) use of tools

D) development of culture

E) erect stance

19. A food chain consists of which of the following?

A) producers and consumers, but not herbivores

B) producers and herbivores only

C) the species through which organic molecules

pass

D) those species which produce but do not consume

E) all of the organisms in a particular habitat

20. The greatest reduction of human population in

recorded history was the result of which of the

following?

A) a global ice age

B) two world wars

C) family planning

D) bubonic plague

E) ozone depletion

Chemistry Questions (21 – 40)

21. Which of the following is a chemical change?

A) pulling silver into silver wire

B) dissolving silver nitrate in water to form a

solution

C) melting solid silver to form liquid silver

D) passing electric current through AgNO3(aq) to

plate out silver

E) boiling water

22. What quantity of energy is required to heat a piece

of gold weighing 1.3 g from 25 ° C to 46 °

C? The

specific heat capacity of Au = 0.131 J/(g–° C).

A) –3.6 J

B) 3.6 J

C) .85 J

D) 15 J

E) 1.3 J

23. The symbol for the element lead is

A) Le

B) Ld

C) Hg

D) La

E) Pb

24. What is the formula weight of lithium phosphate?

A) 99.8 g/mol

B) 101.9 g/mol

C) 108.9 g/mol

D) 112.7 g/mol

E) 115.8 g/mol



25. A compound is found to be 26.95 % sulfur,

13.43 % oxygen, and 59.61 % chlorine by mass.

What is the simplest formula of the compound ?

A) SO2Cl

B) SOCl2

C) SO2 Cl2

D) S2 OCl2

E) SOCl

26. How many Na+ ions are in 500. mL of 0.200 M

NaF solution?

A) 6.02 ! 1020

B) 6.02 ! 1021

C) 6.02 ! 1022

D) 3.01 ! 1021

E) 3.01 ! 1022

27. What is the coefficient of Ca(OH)2 when the

following equation is balanced, using the smallest

possible coefficients?

? Ca(OH)2 + ? HNO3 ! ? Ca(NO3)2 + ? H2O

A) 0

B) 1

C) 2

D) 3

E) 4

28. Consider the reaction:

4 Fe(s) + 3 O2 (g) ! 2 Fe 2 O3(s)

If 12.5 g of iron(III) oxide are produced from 8.7 g

of iron, how many grams of oxygen gas are needed

for this reaction?

A) 21.2 g

B) 12.5 g

C) 3.8 g

D) 8.7 g

E) 7.5 g

29. How many protons are present in one iron(III) ion?

A) 27

B) 29

C) 26

D) 25

E) 28

30. The maximum number of electrons that can be held

in one 5d orbital is ____ .

A) 7

B) 5

C) 1

D) 2

E) 10

31. Which of the following pairs of elements would

combine to give the most covalent bonding?

A) Ca and N

B) C and O

C) Fe and Cl

D) Be and I

E) Ca and S

32. The number of shared electrons that should appear in

the dot formula for the chlorate ion is ____ .

A) 10

B) 8

C) 2

D) 6

E) 4

33. Which of the following species exhibits resonance?

A) NO3–

B) none of the choices has more than one possible

bonding scheme

C) H2S

D) H2O

E) CO2

34. In the periodic table, a horizontal row of elements is

called ____ .

A) a lanthanide

B) a group

C) a period

D) an orbital

E) a transition

35. A 3.9 L sample of gas at STP is cooled to –55 ° C at

808 mm Hg pressure. What is the new volume?

A) 2.9 L

B) 3.3 L

C) 4.6 L

D) 5.2 L

E) 6.2 L



36. Calculate "H for this reaction at 25 ° C and 1 atm.

2 Fe2O3(s) + 3 C (graphite) ! 4 Fe (s) + 3 CO2(g)

"#f for CO2(g) = –393.51 kJ/mole

"Hf for Fe2O3(s) = –824.2 kJ/mole

A) – 430.7 kJ

B) There is insufficient information to answer this

question.

C) – 467.9 kJ

D) + 430.7 kJ

E) + 467.9 kJ

37. For a multistep reaction, the rate of the reaction is

primarily determined by

A) "H

B) the slowest reaction step of the sequence

C) the stoichiometric coefficients of the net

reaction

D) the ratio of reactant and product concentrations

E) "S

38. Which of the following is an acid in aqueous

solution ?

A) NaOH

B) NaCl

C) NH3

D) CH4

E) HNO3

39. Basic, aqueous solutions containing

phenolphthalein are ______ .

A) colorless

B) blue

C) green

D) yellow

E) red

40. Consider the metals in the following reactions:

2 Mg + O2 ! 2 MgO

CuO + H2 ! Cu + H2O

Ag+ + Cl

– ! AgCl

A) Magnesium is oxidized, copper and silver are

reduced.

B) Magnesium is reduced, copper and silver are

neither oxidized nor reduced.

C) Magnesium and silver are oxidized, copper is

reduced.

D) Magnesium is oxidized, copper is reduced,

silver is neither oxidized nor reduced.

E) Magnesium and silver are reduced, copper is

oxidized.

Physics Questions (41 – 60)

41. According to Kaku, what is the fundamental reason

why the world’s physicists are so excited by

superstring theory?

A) Because it tells them how to unite the four

fundamental forces into one theory.

B) Because it requires large machines such as the

Superconducting Super Collider.

C) Because it requires ten dimensions instead of

four.

D) Because of the bizarre predictions that it makes.

E) Because the theory has no rival.

42. According to Kaku, how does superstring theory

propose to explain dark matter?

A) Dark matter is due to the weight of the

individual strings.

B) Dark matter is due to the weight of the extra six

dimensions in the theory.

C) Dark matter is created during the process of

fissioning from a ten-dimensional universe.

D) Dark matter remains a mystery in superstring

theory.

E) Superstring theory doesn’t require dark matter.

43. According to Kaku, what first unification in the

history of science is attributed to Newton?

A) The unification of mass and energy.

B) The unification of force and acceleration.

C) The unification of forces and fields.

D) The unification of electricity and magnetism.

E) The unification of the laws of heaven and earth.

44. According to Kaku, why was Einstein unsuccessful

in the last three decades of his life?

A) Because he rejected quantum mechanics.

B) Because he rejected superstring theory.

C) Because he pursued the unification of the

fundamental forces.

D) Because he pursued purely mathematical

concepts devoid of physical content.

E) Because he introduced the cosmological

constant.



45. A bird watcher whose eyes are 1.75 m above the

ground is standing 40.0 m horizontally away from

a tree. The ground is level and the tree is growing

perpendicular to it. The bird watcher’s line of

sight with the top of the treetop makes an angle of

27.0° above the horizontal. How tall is the tree?

A) 18.2 m

B) 19.3 m

C) 20.4 m

D) 22.1 m

E) 37.4 m

46. A truck traveling at 75 km/hr strikes a tree. The

front end of the truck compresses and the driver

comes to a stop after traveling 0.50 m. What is the

magnitude of the constant acceleration of the

driver during the collision?

A) 7.5 ! 101 m/s2

B) 3.0 ! 102 m/s2

C) 4.3 ! 102 m/s2

D) 5.6 ! 103 m/s2

E) 7.3 ! 103 m/s2

47. A helicopter is ascending upward with a speed of

6.0 m/s. As it passes a height of 125 m above the

ground, a box is dropped out a window. How long

does it take the box to reach the ground? You may

neglect air resistance.

A) 4.5 s

B) 5.7 s

C) 6.6 s

D) 9.0 s

E) 430 s

48. A football is kicked from ground level at 35.0°

above the horizontal with a speed of 21.0 m/s.

What is the maximum height of the football above

the horizontal surface of the ground? You may

neglect air resistance.

A) 7.40 m

B) 14.6 m

C) 21.3 m

D) 22.5 m

E) 67.4 m

49. A 7200 kg helicopter accelerates upward at a

constant 0.75 m/s2 while lifting a 1300 kg car. What

is the magnitude of the lift force exerted by the air

on the rotors? You may neglect drag (air resistance).

A) 6.4 ! 103 N

B) 1.4 ! 104 N

C) 6.2 ! 104 N

D) 7.6 ! 104 N

E) 9.0 ! 104 N

50. For a car traveling at a constant speed v around a

curve of radius r, at what angle should the road be

banked so that no friction is required? You may

neglect lift and drag on the car.

A) tan–1[v2rg]

B) tan–1[(v2r)/g]

C) tan–1[(v2g)/r]

D) tan–1[v2/(rg)]

E) tan–1[(rg)/v2]

51. What is the minimum work needed to push a

1200 kg car 300 m along a 20° incline? You may

neglect dissipative forces.

A) 1.2 ! 103 J

B) 3.9 ! 103 J

C) 3.6 ! 105 J

D) 1.2 ! 106 J

E) 3.5 ! 106 J

52. A 15 g bullet traveling horizontally at 200 m/s

penetrates a 2.0 kg block of wood initially at rest and

emerges out the other side traveling horizontally at

150 m/s. If the block is on a horizontal frictionless

surface when hit, how fast does the block move

horizontally after the bullet emerges?

A) 0.38 m/s

B) 0.75 m/s

C) 1.5 m/s

D) 2.6 m/s

E) 5.3 m/s

53. A 75 kg adult sits at the left end of a 12 m board and

on the right end sits his 25 kg child. Where should

the pivot be placed so that the board is balanced?

You may neglect the mass of the board.

A) 3.0 m left of the child

B) 6.0 m left of the child

C) 3.0 m right of the adult

D) 6.0 m right of the adult

E) 9.0 m right of the adult



54. The maximum gauge pressure in a hydraulic lift is

22 atm. What is the mass of the largest crate it can

lift if the diameter of the output line is 24 cm?

A) 3.3 ! 103 kg

B) 1.0 ! 104 kg

C) 8.6 ! 104 kg

D) 1.0 ! 105 kg

E) 1.2 ! 105 kg

55. A 50 dB sound wave strikes the eardrum with an

area of 5.0 ! 10–5 m2. How much energy is

absorbed by the eardrum per second? Given that

I0 = 1 × 10–12

W/m2.

A) 5.0 ! 102 W

B) 2.0 ! 10–2 W

C) 5.0 ! 10–2 W

D) 2.0 ! 10–3 W

E) 5.0 ! 10–12 W

56. What is the magnitude of the net electric field at a

point midway between a $12 µC point charge and

a +6.0 µC point charge that are 12 cm apart?

A) 1.6 ! 105 N/C

B) 2.7 ! 106 N/C

C) 1.5 ! 107 N/C

D) 3.0 ! 107 N/C

E) 4.5 ! 107 N/C

57. What is the capacitance of a pair of circular

parallel plates each with a radius of 7.5 cm

separated by a 2.8 mm thick slice of mica. Given

that the dielectric constant for mica is %mica = 7.0.

A) 5.2 ! 10–9 F

B) 1.2 ! 10–10 F

C) 3.9 ! 10–10 F

D) 1.1 ! 10–12 F

E) 3.1 ! 10–15 F

58. A 0.25 µF capacitor and a 0.50 µF capacitor are

placed in parallel. How much energy does a 60 V

battery expend to charge them?

A) 3.8 ! 10–7 J

B) 2.3 ! 10–5 J

C) 4.7 ! 10–5 J

D) 4.5 ! 10–4 J

E) 1.4 ! 10–3 J

59. Suppose charged particles are emitted from a source

with velocity v. How should the magnetic field be

oriented with respect to the velocity such that the

path of the charged particles is circular?

A) at 45°

B) parallel

C) perpendicular

D) antiparallel

E) at 135°

60. A nearsighted woman has a near point of 13 cm and

a far point of 19 cm. What is the refractive power of

the corrective lens in a pair of glasses (with an eye-

lens distance of 2.0 cm) so that she can see distant

objects clearly?

A) +8.3 D

B) +5.9 D

C) $5.3 D

D) $5.9 D

E) $8.3 D

12A-1 = 1.28

= 1.28x100

12A-2 = –1.03

= –1.03x100

12A-3 = –0.0354

= –3.54x10–2

12A-4 = –1090

= –1.09x103

12A-5 = –0.00511

= –5.11x10–3

12A-6 = 3.58

= 3.58x100

12A-7 = 0.0814

= 8.14x10-2

12A-8 = 14,000

= 1.40x104

12A-9 = 0.665

= 6.65x10-1

12A-10 = 172

= 1.72x102

12A-11 = –0.165

= –1.65x10–1

12A-12 = 1.53x106 12A-13 = –241000

= –2.41x105 12A-14 = –667

= –6.67x102 12A-15 = 0.463

= 4.63x10–1

12A-16 = 882

= 8.82x102

12A-17 = 1220

= 1.22x103

12A-18 = 69 integer

12A-19 = 1.03

= 1.03x100

12A-20 = 0.758

= 7.58x10-1

12A-21 = –0.0523

= –5.23x10–2 12A-22 = 0.00493

= 4.93x10–3 12A-23 = –3.16

= –3.16x100 12A-24 = 4.64

= 4.64x100

12A-25 = 1.28x108

12A-26 = $33024.00

12A-27 = 2.56

= 2.56x100

12A-28 = 15 integer

12A-29 = 4.15

= 4.15x100

12A-30 = 2.54x106

12A-31 = 3.15x1011 12A-32 = 0.00141

= 1.41x10–3 12A-33 = –14.0

= –1.40x101 12A-34 = 0.428

= 4.28x10–1

12A-35 = 5.57x10–9

12A-36 = 1.9

= 1.9x100 (2SD)

12A-37 = 3.34x107699

12A-38 = 10.7

= 1.07x101

12A-39 = 968

= 9.68x102

12A-40 = 0.167

= 1.67x10-1

12A-41 = 1.02

= 1.02x100 12A-42 = 0.357

= 3.57x10–1

12A-43 = 3.99x10–5 12A-44 = 32.8

= 3.28x101 12A-45 = 0.458

= 4.58x10–1

12A-46 = 0.960

= 9.60x10-1

12A-47 = 7.93

= 7.93x100

12A-48 = -10.0

= -1.00x101

12A-49 = 38.9

= 3.89x101

12A-50 = 53.7

= 5.37x101

12A-51 = 3.31

= 3.31x100 12A-52 = –513

= –5.13x102 12A-53 = –2.04

= –2.04x100 12A-54 = 0.00675

= 6.75x10–3

12A-55 = 1.89

= 1.89x100

12A-56 = -1110

= -1.11x103

12A-57 = 89.7

= 8.97x101

12A-58 = 88 integer

12A-59 = 2.91

= 2.91x100

12A-60 = 0.679

= 6.79x10-1

12A-61 = 0.610

= 6.10x10–1 12A-62 = –0.130

= –1.30x10–1 12A-63 = 0.00140

= 1.40x10–3 12A-64 = 1.10

= 1.10x100 12A-65 = 0.0634

= 6.34x10–2

12A-66 = 37.9

= 3.79x101

12A-67 = 1.00

= 1.00x100

12A-68 = 0.344

= 3.44x10-1

12A-69 = 0.0474

= 4.74x10-2

12A-70 = 1.09

= 1.09x100

Computer Science Answer Key

UIL Invitational A 2012

1. C 11. D 21. C 31. D

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

3. B 13. E 23. C 33. C

4. A 14. C 24. E 34. E

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

6. E 16. A 26. D 36. D

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

8. A 18. B 28. A 38. C

9. E 19. C 29. B 39. B

10. D 20. E 30. D 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(N

3) , O(N

4) , and so forth.

10. With the addition of a non-default constructor, the built in default constructor is no longer available.

24. Choices A and C are both correct.

34. The sorting algorithm used is the bubble sort.

University Interscholastic League MATHEMATICS CONTEST

HS Invitation A 2012ì ìAnswer Key

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

3. D 23. C 43. D

4. C 24. B 44. E

5. B 25. B 45. D

6. C 26. B 46. A

7. C 27. E 47. D

8. D 28. A 48. D

9. E 29. B 49. C

10. E 30. A 50. D

11. C 31. C 51. B

12. C 32. E 52. A

13. A 33. D 53. E

14. C 34. E 54. D

15. D 35. E 55. C

16. B 36. A 56. B

17. C 37. B 57. D

18. E 38. A 58. C

19. A 39. D 59. B

20. E 40. D 60. D

University Interscholastic League - Number Sense Answer Key HS Invitation A 2012ì 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 decimal23

(1) 90q

(2) 12.09

(3) 11360

(4) 7

(5) 484

(6) 2,706

(7) 206

(8) 99

(9) 536

*(10) 34,009 37,587q

(11) 1,110

(12) 187.5, , 187375 12 2

(13) 17.5

(14) 11917

(15) 813

(16) 35

(17) 4,069

(18) 2,700

(19) $.74

*(20) 139,947 q 154,677

(21) 0

(22) 33

(23) 77

(24) 80q

(25) 31

(26) 81

(27) 32

(28) 81720

(29) 46

*(30) 59 64q

(31) 833

(32) 14

(33) 1

(34) 5.0625, , 581 116 16

(35) 25

(36) 144

(37) 1,024

(38) 22.4

(39) $16.00

*(40) 1,225 1,352q

(41) 120

(42) 5

(43) 5

(44) 4

(45) 12q

(46) 50

(47) 729

(48) .5, 12

(49) 66

*(50) 6,929 7,657q

(51) 220

(52) 13

(53) 911

(54) 45q

(55) 4,141

(56) 4

(57) 21

(58) 8

(59) 26,320

*(60) 99,728 110,224q

(61) 290 2831 31,

(62) 35

(63) .25, q q 14

(64) 16

(65) .5, 12

(66) 729

(67) 10,094

(68) 4

(69) 2

*(70) 5,852 6,468q

(71) 100

(72) 3

(73) 56,055

(74) 13

(75) 1

(76) 2q

(77) 2

(78) 25

(79) 2323

*(80) 13,680 15,120q

UIL HIGH SCHOOL SCIENCE CONTEST

ANSWER KEY

INVITATIONAL A • 2012

1. D

2. B

3. C

4. B

5. C

6. A

7. A

8. C

9. D

10. C

11. A

12. C

13. E

14. E

15. C

16. B

17. D

18. E

19. C

20. D

21. D

22. B

23. E

24. E

25. B

26. C

27. B

28. C

29. C

30. D

31. B

32. D

33. A

34. C

35. A

36. E

37. B

38. E

39. E

40. D

41. A

42. C

43. E

44. D

45. D

46. C

47. B

48. A

49. E

50. D

51. D

52. A

53. C

54. B

55. E

56. E

57. C

58. E

59. C

60. D

PHYSICS KEY for Science Contest • Invitational A • 2012

41. (A) “But the fundamental reason why the world’s physicists are so excited by this new theory is that it

appears to solve perhaps the most important scientific problem of the century: namely, how to unite

the four forces of nature into one comprehensive theory.”

42. (C) “The superstring theory might possibly change that, for the process of fissioning from a ten-

dimensional universe down to small universes probably created a new form of matter, [dark matter].”

43. (E) “In retrospect, we can appreciate Newton’s discovery of the law of gravitation as the first

“unification” in the history of science, uniting the laws of heaven and earth.”

44. (D) “…Einstein failed to create the unified field theory largely because he abandoned this conceptual

approach, resorting to the safety of obscure mathematics without any clear visual picture.”

45. (D) Draw a right triangle with vertices at the eyes, the treetop and the point on the tree trunk level with

the eyes. By trigonometry the distance from this point on the trunk to the treetop is:

40.0 m tan(27.0°) and the height of the tree is h = 1.75 + 40.0 tan(27.0°) = 22.1 m.

46. (C) From the 1-D kinematic equation: |a| = |[v2!v0

2]/[2("x)]| = |[0

2!(75/3.6)

2]/[2(0.50)]| = 4.3 E+2 m/s

2.

47. (B) From the 1-D kinematic equation: y = y0 +v0y t + ! a t2, in a particular coordinate system

gives 0 = 125 + 0 +1/2 (-9.80) t2 # t = 5.7 s.

48. (A) From the 2-D kinematic equation: "y = [vy2!v0y

2]/[2(ay)] = [0

2!(21.0 sin35.0°)

2]/[2(-9.80)] = 7.40 m

49. (E) From the free-body diagram for both the helicopter and the car together:

Flift ! FG = ma # Flift = (7200 + 1300) $ (9.80 + 0.75) = 9.0 E+4 N.

50. (D) From the free-body diagram of the car on the curve: %Fy = 0 # FN cos& ! mg = 0 # FN = mg/cos & &

%Fc = mac # FN sin & = m v2/r # (mg/cos &) sin & = m v

2/r # tan & = [v

2/(gr)].

51. (D) Wnet = "KE # WA = !WG = +"PEG = mg"y = 1200(9.80)[300 sin20°] = 1.2 E+6 J.

52. (A) By conservation of 1-D linear momentum:

m1v1 + m2v2 = m1v1' + m2v2' # v2' = [0.015(+200)+0!0.015(+150)]/2.0 = 0.38 m/s.

53. (C) Since the board is in rotational equilibrium then the %( = 0, which implies that the pivot is at the

center of mass: xcom = [m1x1 + m2x2]/(m1 + m2) = [75(0) + 25(12)]/(75 + 25) = 3.0 m right of the adult.

54. (B) From the definition of pressure:

P = F/A = mg/A # m = PA/g = 22(1.013 E+5) [)(0.12)2]/9.80 = 1.0 E+4 kg.

55. (E) From the definition of intensity and the decibel scale: I = P/A & # * = 10 dB log(I/I0) # P = IA =

I010(*/10) A = (10

-12)$(10

(50/10))$(5.0 E!5) = 5.0 E !12 W.

56. (E) From a diagram the electric field vectors are seen to both point towards the negative charge and thus

their magnitudes will add:

%E = kq1/r12 + kq2/r2

2 = {(8.998 E+9)/(0.06)

2}$[(12 E!6) + (6.0 E!6)] = 4.5 E+7 N/C.

57. (C) For a parallel plate capacitor: C = +,0A/d = 7.0(8.85 E!12)[)(0.075)2]/(0.0028) = 3.9 E !10 F.

58. (E) Since they are in parallel: Ceq = C1 + C2 = 0.25 E!6 + 0.50 E!6 = 0.75 E!6 F. The work done by the

battery to charge them is equal to the energy stored: W = ! CV2 = ! (0.75 E!6) 60

2 = 1.4 E!3 J.

59. (C) The magnetic field needs to be perpendicular to the velocity so that the force is perpendicular to the

velocity so that the particle will move in a circle.

60. (D) The refractive power for a thin lens is given by:

P = 1/f = 1/do + 1/di = 1/- + 1/[!(0.19 ! 0.02)] = !5.9 D.

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