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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.
TMSCA Calculator Applications
Test 13C (Invitational)
Name
5x(Last Problem Attempted) + + +
7x(Number Incorrect) - - -
2x(Number Incorrect SDs) - - -
TOTAL SCORE
Tie Breaker: Points scored on Stated and Geometry Problems
+ + +
Page 13C-1
13C-1. (2.17 + 2.47) x 5.3 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 1= ______________
13C-2. (0.988 x 0.0704) – (0.0317 – 0.0371) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2= ______________
13C-3. (–0.633) (–0.605) (–0.408)
–0.38 + 0.161 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 3= ______________
13C-4. (2450 – 1280)
{ (–9.58) / (7.69) } + (752 – 571) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 4= ______________
13C-5. { (1.4 – 0.591 + ) / (–7.28) }
{ (–7.83) (2.38) / (2.76) } - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 5= ______________
13C-6. What is the posit ive square root of the difference of 824 and 58.8? - - - - - - 6= ______________
13C-7. What is 2/ 3 of the product of 4 and -65? - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 7= ______________
13C-8. What is the area of a 9 ft by 12 ft carpet? There are 320 rods in a m i. 8= ___________rod2
13C-9. RECTANGLE
Area = ?
13C-9 = ______________
13C-10. PARALLELOGRAM
Area = 144,000
13C-10 = ______________
Page 13C-2
13C-11. (–58.7 + 53.3) (–8.33 + 21.3)(–2.27) (0.574) (6540 – 7910) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 11= ______________
13C-12. (0.0136 + 0.00533 – 0.0104) (–0.141) (–0.283)
(4.53 – ) (–0.524 – 1.6) - - - - - - - - - - - - - - - - - - - - - - 12= ______________
13C-13. 4.59x105 + 5.18x105
(–1.1) (–0.827) + 1.19 + 1600 – 1330 + 2170
(3.66x10–4) () - - - - - - - - - - - - - - - - - - - - - - - - 13= ______________
13C-14. 300 + 162 – 197(0.911) (–0.733) –
(2.01x105) (8.42x10–4 + 6.91x10–4)0.947 + 0.709 – 3.33 - - - - - - - - - - - - 14= ______________
13C-15. (95400 + 87200 – 1.47x105) (0.858 – 0.504 – )
(5.31) (1.65) (–6.94) (3.07 + 2.36 + 2.51) - - - - - - - - - - - - - - - - - - - - 15= ______________
13C-16. How tall would a stack of quarters be if the stack was worth $1 m illion? A quarter is 0.07 in thick. - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 16= ____________m i
13C-17. The populat ion of the world in early 2012 was 6,994,962,555 persons. The US populat ion was 313,034,569. What fract ion of the world does not live in the US? - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 17= ____________%
13C-18. A Broadway theater has 1000 seats. They sell 70% of the seats for perform ance averaging $100/ seat and two thirds of the rem aining seats at half pr ice. I f there are two shows daily, and the theater is closed Tuesdays, what is the total weekly incom e? - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 18= $_____________
13C-19. RI GHT TRI ANGLE
13C-19 = ______________
13C-20. RI GHT TRI ANGLE
13C-20 = ______________
Page 13C-3
13C-21. 0.0174 + 1/ (7.73)1/ (0.165) + 8.85 +
1(99.4) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 21= ______________
13C-22. 1
–2.73 + 3.17 + 1
0.402 – 0.767 + 1
(0.138) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 22= ______________
13C-23. (–0.128) (–296) + (215) / (1.22) + [ ](0.754) (5.41) 2 - - - - - - - - - - - - - - - - 23= ______________
13C-24. 479 + 109 + (2.82x105) / (700)
–772 + 680 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 24= ______________
13C-25. [ ]–47.9 + 2290 2 x [ ]102 + 190 2 x 875/ 222 - - - - - - - - - - - - - - - - - - - - - 25= ______________
13C-26. The local blood bank allows persons to donate a pint of blood every two m onths. What is the shortest t im e interval needed for an individual to donate a total of 15 gallons of blood? - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 26= ____________yr
13C-27. Danny wants to “grow” $500 into $600 in four years. What annual interest rate, com pounded quarter ly, m ust he find? - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 27= ____________%
13C-28. I n what year was nineteenth century post- im pressionist painter Paul Cézanne born? The sum of the digits in his bir th year total 21. The sum of the first two digits equals the last digit , and twice the sum of the first and third digit equals the second digit . - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 28= ________integer
13C-29. FRUSTUM
Volum e = ?
13C-29 = ______________
13C-30. CYLI NDER
Total Surface Area = 138,000
13C-30 = ______________
Page 13C-4
13C-31. (–1.94x10–4 + 6.98x10–4)2
46.5 – 46.4 +
9.75x10–9
8.05x10–5 + 5.23x10–4 - - - - - - - - 31= ______________
13C-32. 6.49
61.7 + 24.7 x
1
(8.21 – 3.39)2 + 1
(7.67 + 7.65)2 - - - - - - - - - - - - 32= ______________
13C-33. [ (0.0688 – 0.0475) (0.655/ 0.143) ] 1/ 2
(0.104)2 + (0.101 + 0.19)2 + 0.0474 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 33= ______________
13C-34. (2.46x105)2(1.58x10–11 + 7.07x10–12)
0.498 + (–0.685) (1.12) + 1
1–3.3 +
1(1.8)
- - - - - - - - - - 34= ______________
13C-35.
0.0425 + 0.0843
(6150) (12500)+ (8770)2
0.133 + 0.155 + (0.702 – 0.353)2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 35= ______________
13C-36. ( rad) The distance d from a beach house to the ocean water line var ies
with the t ide according to d = 100 ft – 30 ft cos岾 2πt
24hr峇 where t is m ilitary t im e:
t = 0 or 24 is m idnight , t = 10 is 10 AM, t = 15 is 3 PM, etc. Som e kids want to spend 5 hr building a sand cast le as far away as possible from the house. I f they start at a receding waterline and finish when the waterline again reached the finished sand cast le, how far from the beach house should they start? - - - - - - 36= _____________ft
13C-37. A bug stands atop a 2 1/ 4 in diam eter pool ball which sits in the m iddle of a 6 in diam eter flat paper disk. The bug stands up on the ball and just barely sees the edge of the paper disk. How tall is the bug? - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 37= _____________in
13C-38. A spring elongates 1 in for every 5 lbs of load. Four gallons of coconut
oil (density equals 0.92 g/ cm 3) are hung on the spring which is at tached to a fram e. However, the container has a leak, losing 10 tablespoons of coconut oil every m inute. How long will it take for the container to r ise 1.875 in? - - - - - - - - - - 38= _____________hr
13C-39. CI RCLE AND EQUI LATERAL TRI ANGLE
13C-39 = ______________
13C-40. PARALLELOGRAM
Parallelogram Area = ?
13C-40 = ______________
AB = 3990
Page 13C-5
13C-41. 10–( – 5.85)
–7.43x105 + 5.41x105 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 41= ______________
13C-42. (–4820)(–3380) [ ]1 – e–(0.71) (0.321) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 42= ______________
13C-43. 3620 – 3880
Log(2400 + 806) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 43= ______________
13C-44. (323 + 805)1/ 3 + 1/ { (309)–0.493} - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 44= ______________
13C-45.(deg) sin
90° x (–6.72x105)
(7.22x105) + cos { }146° – 80.3° - - - - - - - - - - - - - - - - - - 45= ______________
13C-46. A recipe for a dozen 2- in m ild j alapeno cornbread m uffins calls for 2 jalapenos. How m any jalapenos are needed to m ake a gross (144) of 3- in spicy jalapeno cornbread m uffins if spicy dough has 3 t im es as m any jalapenos as m ild dough? - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 46= ______________
13C-47. Frank pract ices throwing horseshoes by tossing shoes at five- ft intervals start ing at 10 ft . His tosses m easured 9.1 ft , 17 ft , 18 ft , 24 ft and 29 ft . What distance should he aim for if he wants to throw a “ r inger” at 40 ft? - - - - - - - - - - - - - - 47= _____________ft
13C-48. What is posit ive d if 100
5+ 4d= 3(d-7)+ 3
d2+ 1? - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 48= ______________
13C-49. HOLLOW CYLI NDER
Total Surface Area = 438
Volum e = ?
13C-49 = ______________
13C-50. HEMI SPHERE AND CONE
Total Volum e = 0.090
13C-50 = ______________
Page 13C-6
13C-51. 10+ (0.46) + 10–(0.661) + [ ]10(0.675/ 0.921) – 10(0.416) 1/ 2
- - - - 51= ______________
13C-52. 41.5 + e(3.91 + 0.736)
0.709 – e–(0.602 – 0.275) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 52= ______________
13C-53. Ln{ }(0.0241) (8.77) (0.875)
–2.78 + (–5.81) Ln(4.34) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 53= ______________
13C-54. (8.77)0.879 – (7.36)–0.343
0.00777 + 0.0013 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 54= ______________
13C-55.( rad) arcsin{ }(–0.00888) (0.00151) / (–1.41x10–5)
1.17x10–6 + (0.00123) (0.00279) - - - - - - - - - - - - - - - - - - - 55= ______________
13C-56. What is the m axim um value of y on the curve y = -x4-3x3+ 16x2+ 27? 56= ______________
13C-57. The space shut t le accelerat ion a during liftoff m ay be taken to be
a = 嶐 2ao
1+c
cm ax
嶐 where ao is the init ial accelerat ion, c is the instantaneous am ount
of fuel and cm ax is the m axim um , init ial am ount of fuel (4.3x106 lbs) . The shut t le accelerates as fuel is consum ed. I f the fuel consum pt ion rate was constant at 2300 lbs/ s, what is ao if the velocity of the shut t le is 17,500 m ph
when the fuel is com pletely consum ed? - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 57= __________ft / s2
13C-58. What is the determ inant of CD if C = 鞭 9 4-4 8
鞭 and D = 鞭-5 66 3
鞭? - - - - - - - - - 58= ________integer
13C-59. SOLI D OF REVOLUTI ON (y = 3)
Volum e = ?
13C-59 = ______________
13C-60. SEMI CI RCLE
13C-60 = ______________
Page 13C-7
13C-61. 106.39 x (109.33) (100.159)
(10–0.678) (100.45) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 61= ______________
13C-62. ( rad) sin(5.47)cos(5.47) 1 – { }sin(0.225 x 7.19) 2 - - - - - - - - - - - - - - - - - - - - - - - - - - - 62= ______________
13C-63. (deg) sin(–11°)cos (109°) + cos(–11°)sin(109°) - - - - - - - - - - - - - - - - - - - - - - - 63= ______________
13C-64. 1 + 0.439 + (0.439)2 + (0.439)4
8 – (0.439)5
15 - - - - - - - - - - - - - - - - - - - - - - - - 64= ______________
13C-65. (–16300)
(7.95) – (6.2)
(–0.113)2 Ln
(–0.0899)2 + (0.00696)
(–8.45) + 146 - - - - - - - - - - - - - - - - - 65= ______________
13C-66. I t takes Abe 42 m in to row his boat 3 m i up r iver. He rows back to where he started in 18 m in. What is the r iver velocity? - - - - - - - - - - - - - - - - - - - - - - - - - - - 66= __________m ph
13C-67. The lines y = 15x, y = 3x+ 6 and y = b intersect to form a t r iangle. Solve for b if the length of the line segm ent associated with y = b equals 22 and b is negat ive. - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 67= ______________
13C-68. A farm er guessed a rectangular field to be 3.48 acres. The subsequent survey produced side dim ensions of 172.05 ft and 612.68 ft . What is the percent error of the farm er ’s guess? - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 68= _________% (SD)
13C-69. CONCENTRI C CI RCLES
Hatched Area = 1990
13C-69 = ______________
13C-70. SQUARE AND RI GHT TRI ANGLE
Tr iangle Area = A
13C-70 = ______________
13C-1 = 24.6
= 2.46x101 13C-2 = 0.0750
= 7.50x10-2 13C-3 = 0.572
= 5.72x10-1 13C-4 = -758
= -7.58x102 13C-5 = 0.0804
= 8.04x10-2 13C-6 = 27.7
= 2.77x101
13C-7 = -545
= -5.45x102
13C-8 = 0.397
= 3.97x10-1
13C-9 = 113,000
= 1.13x105
13C-10 = 227
= 2.27x102
13C-11 = -0.0392
= -3.92x10-2 13C-12 = -0.000115
= -1.15x10-4
13C-13 = 2.59x106 13C-14 = -213
= -2.13x102 13C-15 = 206
= 2.06x102 13C-16 = 4.42
= 4.42x100
13C-17 = 95.5
= 9.55x101
13C-18 = $960,000.00
13C-19 = 0.500
= 5.00x10-1
13C-20 = 68.8
= 6.88x101
13C-21 = 0.0199
= 1.99x10-2 13C-22 = 6.78
= 6.78x100 13C-23 = 67.8
= 6.78x101 13C-24 = -0.342
= -3.42x10-1 13C-25 = 359
= 3.59x102 13C-26 = 19.8
= 1.98x101
13C-27 = 4.58
= 4.58x100
13C-28 = 1839 integer
13C-29 = 12.8
= 1.28x101
13C-30 = 177
= 1.77x102
13C-31 = 1.20x10-6 13C-32 = 0.0395
= 3.95x10-2 13C-33 = 2.19
= 2.19x100 13C-34 = -1.18
= -1.18x100
13C-35 = 3.52x10-9 13C-36 = 124
= 1.24x102
13C-37 = 0.368
= 3.68x10-1
13C-38 = 0.521
= 5.21x10-1
13C-39 = 4.09
= 4.09x100
13C-40 = 4.08x106
13C-41 = -0.00253
= -2.53x10-3 13C-42 = 0.291
= 2.91x10-1 13C-43 = -74.2
= -7.42x101 13C-44 = 27.3
= 2.73x101 13C-45 = -0.583
= -5.83x10-1 13C-46 = 243
= 2.43x102
13C-47 = 42.0
= 4.20x101
13C-48 = 7.90
= 7.90x100
13C-49 = 430
= 4.30x102
13C-50 = 0.272
= 2.72x10-1
13C-51 = 4.78
= 4.78x100 13C-52 = -12,100
= -1.21x104 13C-53 = 0.149
= 1.49x10-1 13C-54 = 688
= 6.88x102 13C-55 = 273,000
= 2.73x105 13C-56 = 220
= 2.20x102
13C-57 = 9.90
= 9.90x100
13C-58 = -4488 integer
13C-59 = 50.3
= 5.03x101
13C-60 = 21.2
= 2.12x101
13C-61 = 1.77x1011 13C-62 = -0.0496
= -4.96x10-2 13C-63 = 0.990
= 9.90x10-1 13C-64 = 1.64
= 1.64x100 13C-65 = 614
= 6.14x102 13C-66 = 2.86
= 2.86x100
13C-67 = -75.0
= -7.50x101
13C-68 = 44
= 4.4x101 (2SD)
13C-69 = 34.3
= 3.43x101
13C-70 = 35.1
= 3.51x101
T M S C A H I G H S C H O O L
M A T H E M A T I C S
T E S T # 6 ©
D E C E M B E R 1 , 2 0 1 2
GENERAL DIRECTIONS 1. About this test: A. You will be given 40 minutes to take this test. B. There are 60 problems on this test. 2. All answers must be written on the answer sheet/Scantron form/Chatsworth card provided. If you are using an answer sheet, be sure to use BLOCK CAPITAL LETTERS . Clean erasures are necessary for accurate grading. 3. If using a scantron answer form, be sure to correctly denote the number of problems not attempted. 4. You may write anywhere on the test itself. You must write only answers on the answer sheet. 5. You may use additional scratch paper provided by the contest director. 6. All problems have ONE and ONLY ONE correct [BEST] answer. There is a penalty for all incorrect answers. 7. Calculators used on this test must be conform to the UIL standards. Graphing calculators are allowed. Calculators need not be cleared. 8. All problems answered correctly are worth SIX points. TWO points will be deducted for all problems answered incorrectly. No points will be added or subtracted for problems not answered. 9. In case of ties, percent accuracy will be used as a tie breaker.
© TMSCA 2012
TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSC A TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA
1. Evaluate: 2 1 3 7 11) 18 ‚ ƒ ‚q 4 ( 29
(A) 1 (B) 30 (C) (D) (E) 581 129 1834 37
2. Willis Cheep goes to the store to buy some items. The store is having aBuy More Pay Less special sale. Customers get 20% off of the first $20.00 worth of purchases, 30% off of the next $30.00 of purchasess, and 50% off of any purchases over $50.00. How much will Willis' final bill be if he purchases $70.00 worth of items?
(A) (B) $35.00 (C) $38.00 (D) $47.00 (E) $62.00$25.00
3. 70 miles per hour = _________________ inches per second.
(A) (B) (C) 102.666... (D) 123.2 (E) 73,9201,232 6,160
4. Which of the following is an equation of the line shown?
(A) 5x (B) 2x (C) 3x (D) 3x (E) 5x q q q q q q 3y 2 5y 3 5y 2 2y 2 2y 3 = = = = =
5. Simplify: Š ‹Š ‹x 2x 8 x x 6xx 4 x x 12
2 3 2
2 2 q q q
q q
(A) x (B) (C) (D) (E) x 2 x 3 q x 4 x x 2 x 3 q q
6. If the distance one travels varies directly with the amount of time travelling and the distance is 60 km when the time is 1 hour 30 minutes, then the time it will take to travel 140 km is? (nearest minute)
(A) 2 hrs 50 min (B) 3 hrs 30 min (C) 3 hrs 45 min (D) 4 hrs 12 min (E) 5 hrs 3 min
7. P and Q are complementary. Q and R are supplementary. If m R = 112° then m P = ?n n n n n n
(A) 22° (B) 32° (C) 58° (D) 68° (E) 90°
8. A right cylinder water tank is 5 feet high and has an inside diameter of of 8 feet. The amount of water in the tank is 60% of its maximum capacity. How many gallons of water is in the tank? (nearest gallon)
(A) 4,512 gal (B) 3,384 gal (C) 2,820 (D) 1,128 gal (E) 705 gal gal
2012-13 TMSCA High School Math Test 6 - page 1
9. Find the lateral surface area of the trapezoidal prism shown.
(A) 4,785 cm (B) 6,050 cm (C) 6,820 cm (D) 7,205 cm (E) 8,596 cm2 2 2 2 2
10. The faces of a regular octahedron are ________________.
(A) hexagons (B) pentagons (C) rectangles (D) squares (E) triangles
11. If = , then equals:2x 1 3x 2 Ax Bx C A B C4x 3 5x 4 P Q RPx Qx R
q q
q 2
2
(A) (B) (C) (D) (E) 2q q q 1 1 13 4 37 7 4
12. Let f(x) = x and g(x) = 2 x and h(x) = 2x 1. Find h g f(q q q 1 2x) . Š ˆ ‹ (A) 4x 7 (B) 4x (C) 5 4x (D) 4x (E) 2x 4 2 q q
13. Three times one number equals 25% of another number. The sum of four times the first number and twelve equals three times the second number. What is the value of the second number?
(A) 0.375 (B) 0.75 (C) 2.666... (D) 3.333... (E) 4.5
14. Determine the period of y = 3cos .( ) 12 4x 1 1 q
(A) (B) (C) (D) 2 (E) 41 14 2 1 1 1
15. A belt joins the two pulleys shown. If the smaller pulley is rotating at 40 rpm, then the larger pulley is rotating at _______ rpm .
16"6"
(A) 2.4 (B) 2.666... (C) 11 (D) 15 E) 18 (
16. Saul T. Water sails his shrimp boat from his dock 100 km on a bearing of 75° to his best shrimp area. When he leaves there he sails 125 km on a bearing of 150° to his second best shrimp area. What bearing will he have to sail to go straight back to his dock? (nearest degree)
(A) 225° (B) 237° (C) 297° (D) 303° (E) 327°
2012-13 TMSCA High School Math Test 6 - page 2
17. Use the Fibonacci characteristic sequence ... p, q, , r, s, ... to Find pq rs.q q q 8, 2
(A) 48* (B) 14 (C) (D) (E) q q q 48 78 87
18. B).Let 1 12 3
4 31 2 A = and B = . Find the sum of the elements of A(A ” • ” •q
q
q
(A) 29 (B) 25 (C) 12 (D) 7 (E) 5
19. George Alexander picked up a pencil and drew this figure on dot paper. The dots are 5 cm apart from each other both vertically and horizontally. Find the area the shaded region.
(A) 9 cm (B) 10.5 cm (C) 52.5 cm (D) 225 cm (E) 262.5 cm2 2 2 2 2
20. Find the area of the shaded region in square units.
(A) 11 (B) 10 (C) 10 (D) 9 (E) 82 1 2 1
3 3 3 3
21. 4x 6 x F f (x )Let f(x) = 5x and g(x) = 3 2. ind g( 1 ) 2 q q q w
(A) 8 6 (B) 21 (C) 7 (D) 21 (E) 11x x 16 24x x 7 24x q q
22. Let f(x) = At what value(s) of x does only the left-hand limit exist?1 if 0 x 1,
1 if 1 x 22 if x 2.
ÚÛÜ
È q x2 Ÿ Ÿ œ
(A) 0 (B) 1 (C) 2 (D) 0 & 1 (E) 1 & 2
23. How many distinguishable arrangements can be made from the letters "INDEPENDENT"?
(A) (B) 2,217,600 (C) 990 (D) 554,400 (E) 23,10040,320
24. Seven boys were nominated for homecoming king and seven girls for queen at UIL High. How many ways can a king, a queen, and their court be chosen if the court consists of two girls?
(A) 29 B) 35 (C) 245 (D) (E) ( 735 1,029
2012-13 TMSCA High School Math Test 6 - page 3
25. Which of the following mathematicians is noted for his work with polynomial equations that allows variables to be integers only?
(A) Erastosthenes (B) Archimedes (C) Diophantus (D) Leibniz (E) Descartes
26 Q. IF PQ is a two-digit number and P = 1 then PQ is a(n) _____ number.2 2
(A) abundant (B) lucky (C) happy (D) perfect (E) prime
27. A regular octahedron has F faces, E edges, and V vertices. Find F + E + V.
(A) 8 (B) 16 (C) 24 (D) 26 (E) 32
28. Professor I. C. Little teaches an optometry class. He has 24 students in the class. 12 students have glasses, 5 have both glasses and contacts, 6 have neither glasses nor contacts. How many students have contacts?
(A) (B) 11 (C) 9 (D) 6 (E) 112
29. baked several trays of cookies. She boxed up 60% of the cookies to take to her class Ima Kooker party. She gave of the cookies she had left to her family for snacks. She ate 3 of the remaining1
2 cookes. If she had 5 cookies left, how many did she bake originally?
(A) (B) 32 (C) 36 (D) 40 (E) 4824
30. The Real value solution set for 5x 2 is?¸ ¸ 3
(A) } (B) (C) 1} { | } { | } { | }x { 1 x} {x x x x {x } {x 1 q q q q q 1 1 1
5 5 5 (D) (E) }{ | } { | }x 1 x x { 1 x} {x q q q1 1
5 5
31. HowMo de Gras landscaping company has three workers that can plant five trees in 4.5 hours. long would it take to plant 25 trees if the company hey all work at hired two more workers and t the same rate as the original three workers? (nearest minute)
(A) 15 hrs 34 min (B) 15 hrs 15 min (C) 15 hrs (D) 13 hrs 30 min (E) 12 hrs 45 min
32. Using Blaise Pascal's triangle, determine the sum of the numbers in the 7 row.th
1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 ...
(A) 91 (B) 64 (C) 52 (D) 41 (E) 30
2012-13 TMSCA High School Math Test 6 - page 4
33. Find T.
T
BA
C
D
5 in 5 in
3 in2 in
(A) 15 in (B) 4 in (C) 17 in (D) 3 2 in (E) 19 inÈ È ÈÈ
34. Chord AB intersects chord CD inside circle O at point P. If PA = 4 cm, PC = 5 cm, PD = 8 cm, then AB = ?
(A) 17 cm (B) 14 cm (C) 10 cm (D) 9 cm (E) 7 cm
35. If a = 1, a = and a = a (a for n 3, then a equals:1 2 n n 2 n 1 612q ( ) ) q qƒ
(A) (B) (C) (D) 2 (E) 8q q q 21 132 4
36. The graph of 4x y 4 = 0 is a(n): 2 2 q 8x 4y
(A) circle (B) concave curve (C) ellipse (D) hyperbola (E) parabola
37. Roland Dyce rolls a pair of dice. What are the odds that the sum of top faces is a prime number?
(A) (B) (C) (D) (E) 5 5 5 5 54 6 7 11 12
38. The equation y = ______________ will produce this graph.
(A) 2cos(3x (B) 3cos(2x (C) 2cos(2x 1 1 1) ) ) q
2 ) )(D) 3sin(3x (E) 2sin(3x q q1 1
39. Simplify: sin(2 )tan( ) cos(2 )) ) )
(A) tan(2 ) (B) sin( )cos( ) (C) 1 (D) sin ( ) E) cos ( )) ) ) ) )2 2 (
2012-13 TMSCA High School Math Test 6 - page 5
40. Let f(x) = 2x 5x 11 1x 2 2
2 and s(x) be the slant asymptote of f. Find the value of s( ).q
(A) (B) (C) 0 (D) 6 (E) 9q q 4.5 2
41. Determine the sum of the infinite geometric series: 3 2.5 ...q q q q q 2.08333... 1.736111...
(A) (B) (C) (D) (E) Sum does not existq q q q 9.319444... 12.8333... 15 18
42. If x 6 x 6 Bx 6 x 6 C qq is written as the mixed number A then B = ?
(A) 12 (B) 24 (C) 36 (D) 66 (E) 144
43. A pencil box contains 78 colored pencils. The odds of drawing a blue pencil from the box is .310
How many blue pencils would have to be added to the box to change the odds to ?13
(A) 1 (B) 2 (C) 3 (D) (E) 6 12
44. Suppose that f(a) = g(a) = 0, that f (a) and g (a) exist, and that g (a) 0. Then = ?w w w
ÄÁ lim
x af(x)g(x)Š ‹
(A) (B) f (a) g (a) (C) 0 (D) f (a) g (a) (E) f (a) f (a)g(a) g (a)
w w w wq Š ‹Š ‹ w
w
45. Line is tangent to the curve y = x 5 6x at (2, 3). Find the slope of Line L.P 2q q
(A) 12 (B) (C) (D) (E) 3q q q 21 12 2
46. 01 12 23 34 45 56 67 78 = _________________ 2 3 4 5 8 9 106 7
(A) 232 (B) 64 (C) 434 (D) 316 (E) 89
47. Find k if GCF( 48, k ) = 12 and LCM( 48, k ) = 336.
(A) 24 (B) 36 (C) 60 (D) 72 (E) 84
48. If the roots of x bx cx d = 0 are c d equals: 3 2 q q 3, 1, and 4, then b
(A) (B) (C) 0 (D) (E) q q 25 1 1 12
49. Find f(3) 4 f(x) = if x 0
if 0 x 31 if x 3
q q
qf( ) f(0 if
x 52 x
x)
ÚÛÜ
Ÿ
(A) (B) (C) 3 (D) (E) 1q q q q 11 9 1
2012-13 TMSCA High School Math Test 6 - page 6
50. A triangle is inscribed in a circle. Find the diameter of the circle. (nearest tenth)
6" 6"
6"
(A) 6.0 " (B) 6.3 " (C) (D) (E) 6.6 " 6.9 " 7.2 "
51. If y = 3 i and y = 2 i where y = a + bi then a b equals: 2 3q q 4 11
(A) (B) (C) 0 (D) 1 (E) 2q q 2 1
52. Find (1 i) and express the answer in standard form. 5
(A) 4 i (B) 4 2 4i (C) 4 4i (D) 4 2 4i E) 4iq q q q 4 4È È (
Ç 53. Find OQ given that PQ tangent to the circle at P and intersects the x-axis at Q and °. (nearest tenth)m POQ = 40n
(A) 8.0" (B) 7.8" (C) 7.3" (D) 6.5" (E) 6.0"
54. Shirley Sheecaan needs to draw 2 pink golf balls from a box containing 6 white ones, 3 yellow ones, 2 orange ones, and 5 pink ones. What is the probability that both of the balls she randomly draws without replacement are pink? (nearest per cent)
(A) 7 (B) 8 (C) 12 (D) 16 (E) 1813 1 1 2 216 3 2 3 11% % % % %
55. The diameter of the largest circle is 12 cm. The diameter of the smallest circle is 4 cm. The diameter of the other circle is 8 cm. Willie Tell shoots an arrow and hits the target. What is the probability that the arrow hit inside the smallest circle? (nearest whole percent)
(A) (B) 13% (C) 8% (D) 7% (E) 1133% %
2012-13 TMSCA High School Math Test 6 - page 7
56. BA9 = _________________ 12 12 12 123
(A) C10 (B) DDC (C) 1110 (D) 1230 (E) 1332
57. Des Kartez plotted the points A (0, 2), B(15, 10), C(15, 2), and D (0, q 18). He connected the four points forming a quadrilateral. What is the area of this quadrilateral?
(A) 30 sq. units (B) 60 sq. units (C) 140 sq. units (D) 210 sq. units (E) 238 sq. units
58. Let f(x) = ax bx cx 9 where a, b, and c are constants. If f(6) = 17 then f( 5 3 q 6) = ?
(A) 8 (B) 1 (C) 0 (D) (E) q q 9 17
59. How many solutions are there for the equation 3x 5y = 2013 such that both x and y are positive integers?
(A) (B) 188 (C) 205 (D) 222 (E) 252134
60 Let y = x . Find D y.. xx
(A) x (ln x 1) (B) x ln x (C) x (D) x ln(x 1) (E) x (ln (x 1))x x x ln
2012-13 TMSCA High School Math Test 6 - page 8
2012-13 TMSCA HS Math Test #6Answer Key
1. B 21. C 41. D 2. D 22. C 42. E
3. A 23. D 43. B
4. E 24. D 44. E
5. A 25. C 45. C
6. B 26. C 46. A
7. A 27. D 47. E
8. D 28. B 48. A
9. C 29. D 49. B
10. E 30. E 50. D
11. C 31. D 51. D
12. A 32. B 52. E
13. E 33. E 53. D
14. E 34. B 54. B
15. D 35. A 55. E
16. C 36. C 56. C
17. D 37. C 57. D
18. B 38. A 58. B
19. E 39. C 59. A
20. B 40. C 60. A
1st Score: __________ Grader: ____________
2nd Score: __________ Grader: ____________
3rd Score: __________ Grader: ____________
Final Score
Name: ___________________________________ School: __________________________________ SS/ID Number: ____________________________ City: ____________________________________ Grade: 9 10 11 12 Classification: 1A 2A 3A 4A 5A
T M S C A H I G H S C H O O L
N U M B E R S E N S E
T E S T # 6 ©
D E C E M B E R 1, 2 0 1 2
GENERAL DIRECTIONS 1. Write only the requested information on this cover sheet. Do not make any additional marks on this cover sheet. 2. You will be given 10 minutes to take this test. 3. There are 80 problems on the test. 4. Write in ink only! It would be advantageous to use non-black ink. 5. Solve as many problems as you can in the order that they appear. 6. Problems that are skipped are considered wrong. 7. Problems that appear after the last attempted problem do not count either for or against you. 8. ALL PROBLEMS ARE TO BE SOLVED MENTALLY! [No scratch work!] 9. Only the answer may be written in the answer blank. 10. Starred [*] problems require approximate INTEGRAL answers that are within 5% of the exact answers. All other problems require exact answers. 11. All problems answered correctly are worth FIVE points. FOUR points will be deducted for all problems answered incorrectly or skipped before the last problem attempted.
© TMSCA 2012
TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA TMSCA
2012-13 TMSCA High School Number Sense Test 6 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) 1206 2012 = _______________________________
(2) 2012 1206 = ______________________________q
(3) 235 14 = _________________________________‚
(4) 1206 12 = ________________________ (decimal)ƒ
(5) 2.5% = ______________________ (proper fraction)
(6) 235 9 has a remainder of ____________________ƒ
(7) 12 6 20 (13 1) = _____________________ƒ ‚ q
(8) 43 55 55 23 = _________________________‚ q ‚
(9) 40% of (.4 = ____________________________ 14)
*(10) 213 4711 1829 47 = ____________________ q
(11) 25 248 = __________________________________‚
(12) The LCM of 72 and 54 is _____________________
(13) Two-thirds of a yard is equivalent to ______ inches
(14) 27 72 = __________________________________‚
(15) 31 25 19 29 23 17 = ________________
(16) The number of positive integral divisors of 100 is ______________________________________
(17) 12 is what % 20? __________________________%
(18) 23 ____________________ (mixed number)‚ 2325 =
(19) 29 = ______________________________________ 2
*(20) 1206 2012 = ______________________________‚
(21) The multiplicative inverse of is ____________q 23
(22) 14 42 = ________________________________ 2 2
(23) 1 3 6 10 15 21 = ______________¸ ¸ ¸ ¸ ¸ ¸q q q
(24) 40% of 40 minus 40 is ________________________
(25) A pentagon has ______________ distinct diagonals
(26) If x y = 5 and y x = 3 then y = _____________ q
(27) 0.125 0.625 = ______________________________ƒ
(28) 0.151515... = ________________________ (fraction)
(29) 136 19 = _________________________________‚
*(30) 21 = ______________________________________4
(31) The next term of the arithmetic sequence, ... , , , ... is ______________________________1 7 5
3 12 6
(32) If 18 's cost $6.90 then 12 's cost $ __________æ æ
(33) The sum of the positive integral divisors of 40 is __
(34) If f(x) = x 8x 16 then f(4) is ______________ 2
(35) 54 35 = ________________________________ 2 2
(36) 3 4 12 3 = ___________________________‚ x ‚ x
(37) 123 base 4 is equivalent to ______________ base 10
(38) If 50 18 = x then x = ______________È È Èq
(39) 2 4 6 10 16 ... 68 110 = _________
*(40) 1206 2012 13 = __________________________‚ ƒ
(41) A triangle has sides of 12, 7, and x. What is the greatest integral value of x? ___________________
(42) 36 4 = ______________________________14
2 2( )q
(43) A A A = A . If A 1, then k = __________3 5‚ ƒ k 4
(44) Find the slope of a line containing the points ( 5, 5) and (3, 3). _________________________q q
(45) 234 56 = ______________________________7 7 7 q
(46) If is written as the mixed number x x
x x
q
q
5 5
5 5
A then B = _______________________________BC
(47) If 9 = 81 then x = _______________________(x 3)q
(48) The product of the roots minus the sum of the roots of 3x 4x 6 = 0 is ___________ 3 2 q q 17x
(49) An interior angle of a regular pentagon has a measure of __________________________ degrees
*(50) (1000) = __________________________È5 q 1
2 ‚
(51) 132 214 = ________________________________‚
(52) 6C4 = _______________________________
(53) 9% of 833 _______________________________13 =
(54) 11 10 9 8 ... 1 = __________q q q q 2 2 2 2 2
(55) If log (x ) = 1.5 then x = _____________________93
(56) If P varies directly with Q and P = 8 when Q = 4, find P when Q = 5. ___________________________
(57) (2 3 3 = a b . Find a b. ___________ q i i i)(2 )
(58) How many distinct 6 letter words, imaginary or real can be made using the letters ? ____d e g r e e , , , , ,
(59) The simplified coefficient of the x y term in2 2
the expansion of (2x y) is ____ ____________q 4 __
*(60) 6 radians = _________________________ degrees14
(61) (233 )(322 ) 3 has a remainder of ____________4 4 ƒ
(62) (sin 135°)(cos 135°)(tan 135°) = ________________
(63) 2 ( = _____________________________q 11 1212 11)
(64) If log 2 = .25 and log x = 1 then x = ___________ b b
(65) If A = and B = then A B = _____” • ” • ¹ ¹4 1 2 33 2 1 4
(66) A bank contains pennies, nickels, and dimes. How many different sets of 3 coins can be formed? ____
(67) g(x) = x 1 and h(x) = 1 x . g(h(2)) = ________2 2 q
(68) The radius of the circumscribed circle around a 5,12,13-right triangle is ______________________
(69) The Greatest Integer Function is written as
f(x) = x . Find 8 2 . ________________[ ] ’ “È Èƒ
*(70) 729 512 343 ... 27 8 1 = __________
(71) 6 3 4 2 = __________________________x ƒ x q x ƒ x
(72) The vertical asymptote of f(x) = is _______ 2x 1 3x 4
q
(73) 101 123 = ________________________________‚
(74) = __________________________lim
x 5255Ä
Š ‹x x 2qq
(75) Given the sequence 4, 9, 25, 49,..., 289, k, 529,... find k. _____________________________________
(76) Change 0.31 base 4 to a base 10 fraction. _________
(77) (x 2 ) dx = ___________________________'
0
2q
(78) Find k, 0 k 8, if 4k 5 6(mod 7). _______Ÿ Ÿ q z
(79) Gx) = x 3x 5x 7. G (1) = _____________ 4 2q q w
*(80) 416.666... x 1430 = ___________________________
2012-13 TMSCA High School Number Sense Test 6 - Answer Key*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) 3,218
(2) 806
(3) 3,290
(4) 100.5
(5) 140
(6) 1
(7) 242
(8) 1,100
(9) .26, 1350
*(10) 6,371 7,041q
(11) 6,200
(12) 216
(13) 24
(14) 1,944
(15) 144
(16) 9
(17) 60
(18) 21425
(19) 841
*(20) 2,305,149 q 2,547,795
(21) 1.5, , 1q q q 3 12 2
(22) 1,960
(23) 8q
(24) 24q
(25) 5
(26) 4
(27) .2, 15
(28) 533
(29) 2,584
*(30) 184,757 q 204,205
(31) , 113 112 12
(32) $4.60
(33) 90
(34) 64
(35) 4,141
(36) 144
(37) 27
(38) 8
(39) 284
*(40) 177,320 q 195,984
(41) 18
(42) 320
(43) 6
(44) 1q
(45) 145
(46) 100
(47) 5
(48) , 310 13 3
(49) 108
*(50) 588 648q
(51) 28,248
(52) 15
(53) 75
(54) 66q
(55) 3
(56) 10
(57) 13
(58) 120
(59) 24
*(60) 341 376q
(61) 2
(62) .5, 12
(63) q 1132
(64) 16
(65) 20
(66) 10
(67) 10
(68) 6.5, , 613 12 2
(69) 2
*(70) 1,924 2,126q
(71) 108
(72) , 1q q4 13 3
(73) 12,423
(74) 10
(75) 361
(76) 1316
(77) 2q
(78) 8
(79) 3
*(80) 566,042 q 625,625
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T M S C A H I G H S C H O O L
S C I E N C E
T E S T # 6 ©
D E C E M B E R 1, 2 0 1 2
GENERAL DIRECTIONS 1. About this test: A. You will be given 120 minutes to take this test. B. There are 60 problems on this test. 2. All answers must be written on the answer sheet/Scantron form/Chatsworth card provided. If you are using an answer sheet, be sure to use CAPITAL PRINTED LETTERS . Clean erasures are necessary for accurate grading. 3. If using a Scantron answer form, be sure to correctly denote the number of problems not attempted. 4. You may write anywhere on the test itself. You must write only answers on the answer sheet. 5. You may use additional scratch paper provided by the contest director. 6. All problems have ONE and ONLY ONE correct [BEST] answer. There is a penalty for all incorrect answers. 7. On the back of this page is a copy of the periodic table of the elements as well as a list of some potentially useful information in answering the questions. 8. A simple scientific calculator with the following formulas is sufficient for the science contest: +, -, %, ^, log x, ex , lnx, yx, sin x, sin-x, cos x, cos-x, tan x, tan-x, with scientific notation and degree/radian capability. The calculator must be silent, hand-held and battery operated. The calculator cannot be a computer, cannot have built-in or stored functionality that provides scientific information and cannot have communication capability. If the calculator has memory, it must be cleared. Each student may bring one spare calculator. GRAPHING CALCULATORS ARE PERMITTED, IF THE CALCULATOR IS TOTALLY CLEARED, WITH ALL MEMORY RESET. 9. All answers within +/- 5% will be considered correct. 10. All problems answered correctly are worth SIX points. TWO points will be deducted for all problems answered incorrectly. No points will be added or subtracted for problems not answered. 11. In case of ties, percent accuracy will be used as a tie breaker.
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Copyright © 2012 TMSCA
2012-2013 TMSCA High School Science Test 6
1. Where do the microtubules of the spindle originate during mitosis? A) centrosome B) centriole C) chromatid D) kinetochore E) centromere 2. Chromosomes become visible during which phase of mitosis? A) metaphase B) prophase C) interphase D) prometaphase E) anaphase 3. With around 25,000 species, this phylum includes mushrooms, puffballs, and stinkhorns. A) Chytridiomycota B) Zygomycota C) Ascomycota D) Basidiomycota E) Phoronida 4. Seeds are produced by all of the following EXCEPT: A) ferns B) angiosperms C) gymnosperms D) flowering plants E) conifers 5. Eukaryotic cells are differentiated from prokaryotic cells because eukaryotic cells A) are much smaller B) have permeable membranes C) have a higher rate of reproduction D) have nuclei E) are much larger 6. Which of these would have the least effect on natural selection in a subspecies of elephant that is geographically isolated from other subspecies of elephant? A) available niches B) existing predators C) chromosome number D) available food resources E) lack of predators 7. A squirrel that produces an alarm call is displaying which of the following? A) dominance B) territoriality C) agnostic behavior D) submissive behavior E) altruistic behavior 8. As livestock graze in a field they stir up insects in which cattle egrets will then consume. This is an example of: A) parasitism B) commensalism C) mutualism D) interspecific competition E) intaspecific competition 9. Which member of this group have no uniform body symmetry? A) Sponges B) Cnidaria C) Platyhelminthes D) Annelida E) Chordata 10. In humans, glucose is kept in balance in the bloodstream by insulin. Which concept does this best illustrate? A) adaptation B) homeostasis C) metabolism D) organization E) glycolosis 11. Plant virus contains A) DNA B) RNA C) DNA & RNA D) TMV E) None of these 12. Genophore is a term coined by Hans Ris to denote A) Lysosomes B) Eukaryotic chromosomes C) Prokaryotic chromosomes D) Chloroplast E) Viroid
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TMSCA 12-13 HSSC Test 6 Page 2 13. Plants create their own food by absorbing and processing sunlight. The ability to produce your own food source is a metabolic process known as A) heterotrophy B) autotrophy C) homotrophy D) ditrophy E) self-metabolization 14. Members of which of the following are the major primary producers in the marine ecosystem? A) Yeasts B) Sponges C) Sporozoans D) Fishes E) Diatoms 15. Which phylum has a closed circulatory system, protosome and many body segments? A) Annelida B) Mollusca C) Arthopoda D) Echinodermata E) Chordata 16. All of the following are proteins EXCEPT: A) hemoglobin B) actin C) immunoglobulin D) chitin E) myosin 17. Which of these birds are found in Texas? 1) Great Horned Owl 2) Scissor-tailed Flycatcher 3) Great Gray Owl 4) Painted Bunting
A) 1,2,4 B) 1,2,3 C) 3,4 D) 1,3 E) 2 18. Which of the following snakes are found in Texas? 1) Trans-pecos Copperhead 2) Rock Rattlesnake 3) Red Diambondback 4) Boomslang
A) 3 B) 1,2,3 C) 1,2 D) 3,4 E) 4 19. Which of these mammals have been introduced to the United States? 1) Brown Rat 2) House Mouse 3) Nutria 4) Barbary Sheep
A) 1,2,3 B) 1,2,3,4 C) 1,2 D) 2 E) 2,3 20. Which of these plants are spermatophytes? 1)Texas Bluebonnet 2)Indian Paintbrush 3)Loblolly Pine 4)Horsetail
A) 1,2 B) 1,2,3 C) 4 D) 1,2,3,4 E) 1,4
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TMSCA 12-13 HSSC Test 6 Page 3 21. An example of a physical change would be A) fermentation of sugar to alcohol B) rusting of iron C) bleaching a clothing stain D) dissolving camphor in acetone E) growth of a plant 22. A solid substance at room temperature is known to contain two elements. It has a low vapor pressure, is soluble in
water, and does not conduct electricity in the solid phase. From this information, you can conclude that A) the substance contains primarily metallic bonding. B) the substance contains primarily covalent bonding. C) the substance contains primarily ionic bonding. D) the substance does not contain metallic bonds but could contain covalent or ionic bonding. E) No conclusions can be made as to the type of bonding based on this information.
23. What is the correct formula for the precipitate formed when aqueous chromium (III) nitrate reacts with aqueous
sodium carbonate? A) CrCO3 B) Cr(CO3)3 C) NaNO3 D) CrNa E) Cr2(CO3)3 24. Which has the largest radius? A) O2- B) F- C) Na+ D) Mg2+ E) all are equal 25. Which of the following is not a polyatomic ion? A) hydride B) phosphate C) hydronium D) nitrite E) all are polyatomic ions 26. A radioactive isotope has a half-life of 35.7 hours. How many grams of the sample will remain if a 2.30 g sample
decays for exactly 7 days? A) 0.00440 B) 0.238 C) 0.0246 D) 0.0881 E) 6.69 x 10-5
27. Three 1.0 L containers are placed at 25 C. Container 1 holds 0.5 mol of O2 gas, container 2 holds 0.5 mol of CO2 gas,
and container 3 holds 0.5 mol of C2H2 gas. Which container will have the highest internal pressure? A) 1 B) 2 C) 3 D) 2 and 3 are equal and higher E) 1, 2, and 3 are all equal
28. How many grams of methane are needed to completely react with 25.0 g of chlorine according to the unbalanced
equation CH4 + Cl2 → CH3Cl + CH2Cl2 + HCl A) 33.3 B) 18.8 C) 2.11 D) 4.23 E) 5.63
29. A crystal that loses its water of hydration spontaneously is said to be A) deliquescent B) anhydrous C) amorphous D) efflorescent E) hygroscopic 30. Consider the unbalanced reaction NaN3 + NaNO3 → Na2O + N2 . If 2.50 g of sodium azide react with
excess sodium nitrate and 0.796 L of nitrogen gas is recovered at STP, what is the percent yield? A) 57.7 B) 25.0 C) 41.7 D) 81.4 E) 72.9
31. For a metal atom to replace a different metallic ion in a solution, the metal atom must be A) a better oxidizing agent than the metallic ion B) a better reducing agent than the metallic ion C) lower in the activity series than the metal in solution D) equal in activity to the metal in solution E) be easily reduced
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TMSCA 12-13 HSSC Test 6 Page 4 32. Which of the following processes is expected to be the fastest? A) ∆G = 0 kJ
B) ∆G = -5300 kJ C) ∆G = 52 kJ D) ∆G = 335 kJ E) speed cannot be determined
33. What is the molar solubility of calcium fluoride if 4.2 g of sodium fluoride is added to 1.0 L of a saturated solution of
calcium fluoride? (Ksp of calcium fluoride is 4.0 x 10-11) A) 1.0 x 10-3 B) 4.0 x 10-10 C) 4.0 x 10-9 D) 1.0 x 10-1 E) 1.0 x 10-11 34. Which shows the compounds in order of increasing bond polarity? A) I2 < CO2 < CN- < H2O < MnO2 B) I2 < H2O < CO2 < MnO2 < CN- C) MnO2 < CO2 < H2O < CN- < I2 D) I2 < H2O < MnO2< CO2 < CN- E) CO2 < MnO2 < I2 < CN- < H2O 35. What is the coefficient for the water when the equation is balanced in acid solution? Fe2+ + Cr2O7
2- → Fe3+ + Cr3+
A) 2 B) 6 C) 7 D) 10 E) 14 36. What is the predicted molecular geometry for xenon tetrafluoride? A) linear B) octahedral C) square planar D) tetrahedral E) see saw 37. What is the pOH of a solution prepared by mixing 19.2 grams of hydrogen iodide with water into a total volume of
500.0 mL? (assume no volume change) A) 13.50 B) 0.52 C) 7.00 D) 0.15 E) 3.50
38. What is the normal boiling point of an unknown liquid if its heat of vaporization is 29.1 kJ/mol and its vapor pressure at 300. K is 69.2 torr?
A) 305 K B) 378 K C) 250 K D) 325 K E) 275 K 39. When 79.85 grams of iron(III) oxide is reacted with an unknown solid element, it is found that 55.85 grams of pure
iron metal is formed along with 50.99 grams of the oxide of the unknown element. Further analysis of the oxide product indicates that there are two atoms of the element for every three atoms of oxygen. What is the unknown element?
A) Scandium B) Boron C) Cobalt D) phosphorus E) aluminum 40. Which of the following compounds can be used to produce oxygen gas through decomposition in the lab? 1) NaOH 2) H2O2 3) KClO3 A) 1, 2, 3 B) 1, 2 C) 2, 3 D) 1, 3 E) 3 only
TMSCA 2012-2013 HSSC Test 6 Page 5 41. According to Amir Aczel, “__________’s law states that the further a galaxy lies from us, the faster it is receding from us.” (A) Perlmutter (B) Hubble (C) Rayleigh (D) Bahcall (E) Daly 42. According to Amir Aczel, when Einstein graduated from the Swiss Federal Institute of Technology, he took a job working at the ___________________________. (A) University of Berlin (B) observatory outside of Zurich (C) center for advanced physics in Hamburg (D) Swiss patent office (E) rocket research center in Munich 43. According to Amir Aczel, “when Einstein discovered the special theory of relativity, the mathematics was there for him: the Lorentz transformation and the mathematics of space time worked out by ___________.” (A) Minkowski (B) Soldner (C) Freundlich (D) Mandl (E) Pick 44. According to Amir Aczel, this mathematician is known as the “Copernicus of Geometry.” His work revolutionized geometry by discarding the parallel postulate. (A) Gauss (B) Bolyai (C) Lobachevsky (D) Euclid (E) Saccheri 45. Carson throws a ball upward with an initial velocity of 20.6 m/s. How long is the ball in the air before it returns to his hand? (A) 3.20 s (B) 3.52 s (C) 3.91 s (D) 4.20 s (E) 4.53 s 46. Nate was speeding along on his new motorcycle on a horizontal stretch of road which came to an abrupt end at the edge of a 66.2-m-tall cliff. He was able to clear the river below and land on level ground 108 m from the base of the cliff. How fast was he traveling when he left the edge of the cliff? (A) 27.8 m/s (B) 29.4 m/s (C) 31.1 m/s (D) 33.0 m/s (E) 35.9 m/s 47. A 3.65-kg block is stacked on top of an 8.45-kg block. The bottom block is accelerating along a horizontal surface at 4.66 m/s2. Assume .s k Find the minimum value of between the two blocks so that
the upper block does not slide off. (A) 0.338 (B) 0.373 (C) 0.401 (D) 0.438 (E) 0.475 48. A weather satellite orbits the Earth in geosynchronous orbit, which means that it stays above the same point on the equator at all times. Find the speed of the satellite if it orbits at an altitude of 35,880 km. (A) 3073 m/s (B) 3247 m/s (C) 3431 m/s (D) 3649 m/s (E) 3887 m/s 49. How much work must be done to accelerate Davis’s 1350-kg truck from 28 m/s to 38 m/s? (A) 394,000 J (B) 421,000 J (C) 446,000 J (D) 473,000 J (E) 499,000 J 50. A billiard ball moving at 2.24 m/s to the east collides with an identical ball that is at rest. The first ball moves off at an angle of 30º N of E and the second ball moves off at an angle of 60º S of E. Find the speed of the second ball after the collision. (A) 1.12 m/s (B) 1.32 m/s (C) 1.53 m/s (D) 1.73 m/s (E) 1.94 m/s
TMSCA 2012-2013 HSSC Test 6 Page 6 51. A 2.44-kg bucket is attached to the end of a cord that is wrapped around a pulley at the top of a deep well. The radius of the pulley is 24.2 cm and its moment of inertia is 0.377 kg·m2. The bucket is released and begins to descend into the well. Find the speed of the bucket 2.64 s after it is released. (A) 5.43 m/s (B) 6.04 m/s (C) 6.62 m/s (D) 7.12 m/s (E) 7.77 m/s 52. A 6.00-m-long ladder leans against a wall. The 16.0-kg ladder makes an angle of 50º with the ground. The coefficient of friction between the ladder and the ground is 0.444. How far up the ladder can Austin climb before it begins to slip? Austin has a mass of 67.4 kg. (A) 2.72 m (B) 3.00 m (C) 3.22 m (D) 3.48 m (E) 3.75 m 53. Mr. Altman found a cube made of an unknown metal. He hung the cube from a spring scale which read 16.3 kg. He then submerged the cube in water and the spring scale read only 14.5 kg. Find the density of this unknown metal. (A) 8530 kg/m3 (B) 9060 kg/m3 (C) 9680 kg/m3 (D) 10,300 kg/m3 (E) 10,900 kg/m3 54. Allison made a simple pendulum using a 2.44-m length of string and a 680-g bob. Find the period of oscillation of her pendulum. (A) 3.48 s (B) 3.13 s (C) 2.84 s (D) 2.51 s (E) 2.18 s 55. Samantha is tuning her piano. One of the strings is 94.7 cm long and has a mass of 8.66 g. How much tension must the string be under if it is to vibrate at 144 Hz? (A) 600 N (B) 640 N (C) 680 N (E) 760 N 56. Matthew wants to find the specific heat of the new alloy he created. A 750-g sample is heated to 585ºC and then it is placed in a 300-g aluminum cup filled with 500 g of water. If the initial temperature of the water and the cup was 12.0ºC and the final equilibrium temperature of the mixture was 67.6ºC, find the specific heat of Matthew’s alloy in J/kg·Cº. The specific heat of aluminum is 900 J/kg·Cº. (A) 263 (B) 282 (C) 301 (D) 320 (E) 339 57. Two parallel plates are separated by 1.83 cm and they are charged such that a 5.66x104 N/C electric field exists between the plates. A positron is placed near the positive plate and it accelerates from rest passing through a tiny hole in the negative plate. Find the speed of the positron just as it passes through the hole. (A) 1.91x107 m/s (B) 1.79x107 m/s (C) 1.57x107 m/s (D) 1.31x107 m/s (E) 1.09x107 m/s 58. Find the capacitance of a capacitor with circular plates of radius 32.0 cm if the air gap between the plates is 1.14 mm. (A) 2.31 nF (B) 2.50 nF (C) 2.73 nF (D) 3.03 nF (E) 3.41 nF 59. Find the equivalent resistance of four 25.0-Ω resistors connected in parallel. (A) 6.25 Ω (B) 25.0 Ω (C) 75.0 Ω (D) 100 Ω (E) 125 Ω 60. Two wires of a 6.00-m-long appliance cord are 2.00 mm apart and carry 12.0 A of dc current. Find the repulsive force between the wires. (A) 0.337 N (B) 0.286 N (C) 0.199 N (D) 0.143 N (E) 0.0864 N
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Answer Key 2012-2013 TMSCA High School Science Test 6 1. E 2. B 3. D 4. A 5. D 6. C 7. E 8. B 9. A 10. B 11. B 12. C 13. B 14. E 15. A 16. D 17. A 18. C 19. B 20. B
21. D 22. D 23. E 24. A 25. A 26. D 27. E 28. D 29. D 30. A 31. B 32. E 33. C 34. A 35. C 36. C 37. A 38. B 39. E 40. C
41. B 42. D 43. A 44. C 45. D 46. B 47. E 48. A 49. C 50. A 51. D 52. C 53. B 54. B 55. C 56. E 57. A 58. B 59. A 60. E
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2012-2013 TMSCA High School Science Test 6 SOLUTIONS
26. 7 days = 168 hours k = ln2/35.7 = 0.0194 岫 岻( 岫 岻岫 岻)
28. 3 CH4 + 4 Cl2 → 2 CH3Cl + CH2Cl2 + 4 HCl 岫 岻 岾 峇 岾 峇 岾 峇
30. 5 NaN3 + NaNO3 → 3 Na2O + 8 N2
岫 岻 岾 峇 岾 峇 岾 峇 岫 岻 岾 峇 岾 峇 0.995/1.72 = 57.8%
33. 4.2g(mol/41.99g) = 0.10 mol NaF CaF2(s) ⇄ Ca2+ + 2F- x 0.10 +2x 岫 岻岫 岻 37. (19.2g)(mol/127.91g) = 0.150 mol HI 0.150 mol/0.5000L = 0.300 M HI = 0.300 M H3O
+ pH = -log(0.300) = 0.523 pOH = 13.477
38. 岾 峇
39. Fe2O3 + 2X → 2 Fe + X2O3 79.85g Fe2O3 = 0.5 mol therefore mass of 2X in equation equals 1mol X 79.85 26.99 55.85 50.99 26.99 = Al 41-44 God’s Equation, Amir Aczel, Four Walls Eight Windows, New York, 1999 41. page 5 42. page 19 43. page 32 44. page 58
45. 20 0 20.6 4.9
4.20 s
t t
t
46.
20 66.2 4.9
3.6756
108 (3.6756)
29.4 m/s
t
t
v
v
47.
4.66
9.8070.475
mg ma
48.
2
2
11 24
6
6.67 10 5.98 10
35880000 6.37 103073 m/s
GMm mv
r r
x xv
xv
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49. 2 2.5(1350)38 .5(1350)28
446,000 J
W
W
50.
1 1 2 2 1 3 2 4
3 4
3 4
3 4
2.24 cos30 cos( 60 )
0 sin30 sin( 60 )
1.94 m/s, 1.12 m/s
mv m v mv m v
v v
v v
v v
51.
2
2.44(9.807)2.6955
.3772.44
(.242)
2.6955(2.64) 7.12 m/s
Fr I
a r
aTr I
rmg T ma
a
v
52.
.444(16 67.4)(9.807) 363.15
363.15(6)sin50 16(9.807)3sin 40 67.4(9.807) sin 40
3.22 m
F
x
x
53.
316.31000 9060 kg/m
16.3 14.5
wc
c
m g gV mg
m
Vm
m m
54. 2.44
2 3.13 s9.807
T 55. 2
144(2).947 272.736
(272.736) (.00866)680 N
.947
v
T
56.
.3(900)(67.6 12) .5(4186)(67.6 12)
.75 (585 67.6)
339 J/kg
c
c C
57.
4 19
1531
15 7
,
5.66 10 1.6 109.94 10
9.11 10
2(9.94 10 )(.0183) 1.91 10 m/s
FE F ma
Q
x xa x
x
v x x
58. 212 (.32)
8.85 10.00114
2.50 nF
C x
C
59. 1 1
4 , 6.25 25
RR 60.
72 10 (12)(12)6.0864 N
.002
xF
