the university interscholastic league number sense …€¦ · the university interscholastic...

The University Interscholastic LeagueNumber Sense Test HS A 2016ì ì

Final ______ ______

Contestant's Number ___________ ______ ______2nd

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

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

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

STOP -- WAIT FOR SIGNAL!

(1) 116 611 = _________________________________

(2) 345 612 = ________________________________q

(3) 116 5 = __________________________________‚

(4) 0.444... = ____________________ (proper fraction)

(5) 36% = _______________________(proper fraction)

(6) 14 = ______________________________________2

(7) 1616 4 = __________________________________ƒ

(8) 9 12 6 3 = ____________________________q ‚ ƒ

(9) 2 = ______________________________ (decimal)18

*(10) 1601 1610 1160 1061 = _________________

(11) 1 2 = ____________________ (mixed number)1 36 4

(12) 65 25 = __________________________________‚

(13) 345 9 = ____________________ (mixed number)ƒ

(14) 15% of 44 = ________________________________

(15) Which is larger, 0.63 or ? ____________________58

(16) MDCVI = ___________________ (Arabic numeral)

(17) The GCD of 35, 56, and 70 is __________________

(18) 2 yards 1 foot 6 inches = ___________ inchesq q

(19) 3 1 = ___________________ (mixed number)4 37 5 q

*(20) 373 464 = ________________________________‚

(21) 12% of 166 ______________________________23 =

(22) The additive inverse of 0.444... is ______________

(23) 12 4 = _________________________________2 2

(24) 2197 = ___________________________________È3

(25) 41 39 = __________________________________‚

(26) 1 4 7 7 1 4 = __________________¸ ¸ ¸ ¸q q q

(27) If 12 pens cost $1.60 then 9 pens cost $ __________

(28) 0.3111... = ___________________ (proper fraction)

(29) Set T = {t,i,m,e,s} and M = {s,q,u,a,r,e}. T M contains how many distinct elements? ___________

*(30) 3 12515 16 = __________________________15 ‚ ƒ

(31) (21 7 14) 6 has a remainder of ___________‚ q ƒ

(32) If 5x 1 = 9, then x 5 = ____________________q q

(33) 1 1 = __________________ (mixed number)2 15 14‚

(34) 1 _______________3 5 7 ... 17 19 =

(35) If x = 11 and y = 8 then x 2xy y = ________2 2q

(36) 67 base 8 in base 10 is ________________________

(37) 14 = ___________________ (mixed number)‚ 1516

(38) The area of a rectangle with a length of 1.25 ft and a width of 3.2 ft is _______________________sq. ft

(39) The product of the first 3 prime numbers is ______

*(40) 12515 = __________________________________È (41) 35% of 40 45% of 50 is _____________________

(42) The leg opposite the 60° angle in a right triangle is 12 3 cm hypotenuse is _____________ cmÈ . The

(43) If x 2 = 3 then x = _________________q q q 1 1 1q

(44) The midpoint of the segment with endpoints ( 1, 2) and (3, 4) is (x, y). Find x y. ________q q

(45) The sum of the roots of (2x 3) = 0 is __________2

(46) Let 16 16 16 = 16 . Find k. ___________ q 2 3 5 k‚ ƒ

(47) 18 22 4 = _______________________________‚

(48) 123 45 ______________________________6 6 6 = q

(49) The sum of the solutions of x 1 = 3 is ________¸ ¸q

*(50) 12 6 = __________________________________3 2‚

(51) The middle term of the 5th row of Pascal's triangle is _________________________________________

(52) Each face of a Platonic octahedron has _____ sides

(53) Find the 7 term of the Fibonacci sequence,th

1, 1, 2, 3, ... . ______________________________

(54) If = , then x = ___________________________4 16 xxx

(55) = _______________________________6 64 2C C q

(56) 12 6 3 = _____________________________2 2 2ƒ ‚

(57) (2 3i) (4 5i) = (a bi). Find ab. ____________q

(58) 221 133 = ________________________________‚

(59) The probability of selecting an even integer between 1 and 11 is ___________ (proper fraction)

*(60) 322.3 37.73 = _____________________________‚

(61) The number of positive integral divisors of 48 is __

(62) 11 15 has a remainder of __________________13 ƒ

(63) The Greatest Integer Function is written as

f(x) = x . Find 1 . ________________[ ] ’ “qÈ5 1

2

(64) If f(x) = (x 3)(x 6x 9), then f(18) = _______q q2

(65) The volume of a rectangular prism with base width 5", base length 12", and height 13" is _______ in3

(66) Let f(x) = 3x x 1. Find f(f(1)). ____________2 q q

(67) Find k if = 15k. __________________ 1 3 6 10º ºq q

(68) 2sin( os( = ____________________________1 14 4)c )

(69) Change 0.123 base 4 to a base 10 fraction. _______

*(70) (28 24 20 16 12 8 4) = ___________2

(71) The product of the 2 triangular number and thend

2 pentagonal number is ____________________nd

(72) 0.242424... = _______________ (proper fraction)5 5

(73) Truncate (2 3 3 2) to the nearest whole. ___È È (74) The first four digits of the decimal for 14

33 is 0. ___

(75) If f(x) = x 2 , then f (4) = _______________È q 1

(76) f(x) = 2x 6x 6x 2. Find f ( 1) = _______3 2 qw

(77) (3x 4) = ___________________________' 1 2

q dx

(78) The largest number in the domain of y = 4 x2 2q is _________________________________________

(79) The minimum value of f(x) = 5(x 3) 2 is ____q 2

*(80) The interest on $6000 for 6 years at 6% compounded semiannually is ____________________________ dollars (integer)

University Interscholastic League - Number Sense Answer Key HS Invitation A 2016ì ì*number) x y means an integer between x and y inclusiveNOTE: If an answer is of the type like it cannot be written as a repeating decimal2

3

(1) 727

(2) 267q

(3) 580

(4) 49

(5) 925

(6) 196

(7) 404

(8) 15q

(9) 2.125

*(10) 5,161 5,703q

(11) 3 1112

(12) 1,625

(13) 38 13

(14) 6.6, , 633 35 5

(15) .63, 63100

(16) 1,606

(17) 7

(18) 54

(19) 1 3435

*(20) 164,419 q 181,725

(21) 20

(22) q 49

(23) 160

(24) 13

(25) 1,599

(26) 2q

(27) $1.20

(28) 1445

(29) 2

*(30) 2,378 2,628q

(31) 1

(32) 3q

(33) 1 12

(34) 100

(35) 9

(36) 55

(37) 13 18

(38) 4

(39) 30

*(40) 107 117q

(41) 36.5, , 3673 12 2

(42) 24

(43) 1.2, , 16 15 5

(44) 2

(45) 3q

(46) 4q

(47) 400

(48) 34

(49) 2

*(50) 59,098 65,318q

(51) 6

(52) 3

(53) 13

(54) 30

(55) 0

(56) 36

(57) 46

(58) 29,393

(59) 59

*(60) 11,553 12,768q

(61) 10

(62) 11

(63) 1q

(64) 3,375

(65) 780

(66) 1

(67) 815

(68) 1

(69) 2764

*(70) 11,917 13,171q

(71) 15

(72) 1222 (not reducible)

(73) 7

(74) 4242

(75) 14

(76) 0

(77) .5, 12

(78) 2

(79) 2

*(80) 2,427 2,682q

The University Interscholastic LeagueNumber Sense Test HS B 2016ì ì

Final ______ ______






(1) 2312 2016 = ______________________________q

(2) 212 316 = ________________________________

(3) 2016 3 = _________________________________ƒ

(4) 231 6 = ___________________________________‚

(5) = _____________________________________ %35

(6) 23 11 = __________________________________‚

(7) 0.375 = _________________________________q 14

(8) 2 1 2 3 (1 2) = ____________________q q ƒ ‚

(9) 3 2 = ___________________ (mixed number)1 12 6 q

*(10) 136 1015 2128 3645 = __________________q

(11) 23 = ______________________________________2

(12) 14% of 16 = ________________________ (decimal)

(13) 1 2 3 4 5 ... 19 20 = ____________

(14) 17 23 = __________________________________‚

(15) 12 = ______________________________________3

(16) 3 2 = ____________________ (mixed number)1 35 4

(17) 3 gallons 2 quarts = ___________________ pintsq

(18) MMXVI IV = ______________ (Arabic numeral)‚

(19) 21231216 8 has a remainder of ______________ƒ

*(20) 31216 396 = ______________________________ƒ

(21) 2 3 4 = ______________________________4 3 2

(22) 2 1 2 3 1 = __________________¸ ¸ ¸ ¸q q q 2

(23) The multiplicative inverse of 1.25 is __________q

(24) 7 = _______________________________________3

(25) Let x = 2. Find 3 4q q x. _____________________

(26) If 15 cost $18.45 then 10 cost $ __________æ æs s

(27) 11 (mixed number)‚ 1417 = ______________________

(28) 3 1 = ___________________ (mixed number)3 25 9‚

(29) Set E = {e,l,p,a,s,o} and A = {a,u,s,t,i,n}. E A contains how many distinct elements? ___________

*(30) 4 6390 15 = ___________________________27 ‚ ƒ

(31) 0.515151... = _________________ (proper fraction)

(32) 12 36 = ________________________________2 2

(33) (37 17) 8 has a remainder of __________27 ‚ ƒ

(34) 27% of 211 ______________________________19 =

(35) If a = 12 and b = 11, then 9a 6ab b = ______2 2q

(36) 15% of 30 minus 45 is ________________________

(37) 312 base 5 in base 10 is _______________________

(38) 73 23 = __________________________________‚

(39) The perimeter of a square is 14". The area of the square is ______________________________ sq. in.

*(40) 44044 = __________________________________È (41) 22 28 9 = _______________________________‚

(42) If 9 x = 10 then x = _______________q q q 1 1 1q

(43) 75% of 80 = 30% of _________________________

(44) A face of a Platonic dodecahedron has ____vertices

(45) Let 21 21 21 = 21 . Find k. ___________7 3 5 k‚ ƒq

(46) The area of a right triangle with a base of 7 cm and a hypotenuse of 25 cm is ________________ sq. cm

(47) ( ( ( = ________________________3 3 34 8 16) ) )2 2 2ƒ ‚

(48) How many subsets containing only 3 elements does the set {p,r,i,m,e} have? ___________________

(49) 312 3 _______________________________ 4 4 4‚ =

*(50) 12 21 = _________________________________3 2‚

(51) Find the units digit of 17 . ____________________ 6

(52) The midpoint of the segment with endpoints (x, y) and (1, 7) is ( 3, 5). Find x y. _____________q q

(53) 7 9 16 25 41 66 107 173 = ______

(54) = ________________________________5 53 2C C

(55) The probability of selecting a multiple of three from the set of positive digits is ________________

(56) The sum of the roots of (x 5) = 0 is ___________3

(57) The sum of coeficients of the x y term and the2 2

xy term of (x y) is _______________________3 4

(58) = ______________________________________63 3xx x

(59) 271 314 = ________________________________‚

*(60) 212312 201.6 = ____________________________ƒ

(61) The Greatest Integer Function is written as f(x) = x . Find sin( ) cos( ) tan( ) . ____[ ] ’ “1 1 1

4 4 4

(62) How many positive integers less than 30 are relatively prime to 30? _______________________

(63) If = 35 k then k = _______________ 1 512 22º ºq

q

(64) If 2log (3x 1) = 3 and x 0 then x = _________4 q

(65) The smallest integral value of x such that 2x 3 4 is _____________________________¸ ¸q Ÿ

(66) Change 0.2111... base 5 to a base 10 fraction. _____

(67) F(x) = 2x 4. G(x) = 1 x. F(G( 2)) = ________3 q q q

(68) sec( ) csc( ) = ___________________________1 13 6

(69) The volume of a rectangular based pyramid with a base width 5", a base length 12", and a height 13" is ______________________________________ in3

*(70) (2 4 6 8 ... 18 20) = _____________2

(71) The first four digits of the decimal for is 0.___31111

(72) Truncate (2 3 5) to the nearest whole. ____È Èq

(73) If f(x) = 1 , then f (2) = ______________q x 34

1 q

(74) f(x) = 2x 6x 6x 2. Find f (3) = _________3 2 ww

(75) The minimum value of f(x) = 4(x 3) 1 is ____q 2

(76) If x 6 2(mod 7), 0 x 6, then x = ________´ Ÿ Ÿ

(77) (2 3x) = ____________________________' 0

1q dx

(78) The sum of the first 3 hexagonal numbers is _____

(79) The range of the function y = 3 x is y ____È q

*(80) The compound interest on $2000 for 4 years at 8% compounded annually is _______ dollars (integer)

University Interscholastic League - Number Sense Answer Key HS Invitation B 2016ì ì*number) x y means an integer between x and y inclusiveNOTE: If an answer is of the type like it cannot be written as a repeating decimal2

3

(1) 296

(2) 528

(3) 672

(4) 1,386

(5) 60

(6) 253

(7) .125, 18

(8) 1q

(9) 1 13

*(10) 2,535 2,801q

(11) 529

(12) 2.24

(13) 210

(14) 391

(15) 1,728

(16) 5 1920

(17) 20

(18) 8,064

(19) 0

*(20) 75 82q

(21) 59

(22) 3

(23) .8, q q45

(24) 343

(25) 11

(26) $12.30

(27) 9 117

(28) 4 25

(29) 10

*(30) 1,735 1,917q

(31) 1733

(32) 1,440

(33) 0

(34) 57

(35) 625

(36) 40.5, ,q q812

40q12

(37) 82

(38) 1,679

(39) 12.25, , 1249 14 4

*(40) 200 220q

(41) 625

(42) 90

(43) 200

(44) 5

(45) 1q

(46) 84

(47) .140625, 964

(48) 10

(49) 2202

*(50) 723,946 q 800,150

(51) 9

(52) 10

(53) 444

(54) 20

(55) 13

(56) 15q

(57) 10

(58) 20

(59) 85,094

*(60) 1,001 1,105q

(61) 2

(62) 8

(63) 47q

(64) 3

(65) 0

(66) 920

(67) 50

(68) 4

(69) 260

*(70) 11,495 12,705q

(71) 2792

(72) 1

(73) 7q

(74) 48

(75) 1

(76) 3

(77) .5, 12

(78) 22

(79) 0

*(80) 685 757q

The University Interscholastic LeagueNumber Sense Test HS District 1 2016ì ì

Final ______ ______






(1) 356 817 = _________________________________

(2) 815 324 = ________________________________q

(3) 325 7 = __________________________________‚

(4) 1947 3 = _________________________________ƒ

(5) 76% = _______________________(proper fraction)

(6) 0.444 = ___________________ % (mixed number)

(7) 8 15 20 16 (6 8) = _________________q ‚ ƒ q

(8) 2 = __________________________________5 58 6 q

(9) 18 = ______________________________________2

*(10) 247 2126 1014 4756 = __________________q

(11) 11 = ______________________________________3

(12) The arithmetic mean of 20, 16, and _________ is 17

(13) 81547 9 has a remainder of _________________ƒ

(14) 21% of 21 = ________________________ (decimal)

(15) Which is larger, or 0.83? ____________________56

(16) 2 3 = ____________________ (mixed number)2 17 4

(17) 1 quart 2 pint 3 cup = _________ fluid ounces

(18) If 12 's cost $20.20 then 3 's cost $ ___________æ æ

(19) CDLIV = ___________________ (Arabic numeral)

*(20) 42116 595 = ______________________________ƒ

(21) The multiplicative inverse of 1.333... is _________

(22) 25 75 = ________________________________2 2

(23) 3 2 4 1 6 = _____________________q q q¸ ¸ ¸ ¸ (24) Let x = 4. Find 3x 2q q . _____________________

(25) The sum of three consecutive integers is 132. The largest of the three is integers is ________________

(26) 0.2333... = ___________________ (proper fraction)

(27) Let = . Find x. __________________________4x 25 3

(28) 2 1 = ___________________ (mixed number)2 35 4‚

(29) 24% of 433 = ______________________________13

*(30) 32126 15 = _______________________________ƒ

(31) 235 111 = ________________________________‚

(32) If 6x 4 = 2, then x 8 = ____________________q q

(33) The set A = {A,U,S,T,I,N} contains how many proper subsets? _____________________________

(34) 21 (mixed number)‚ 2325 = _____________________

(35) Truncate ___È7 to the tenths place. _________

(36) 37 43 = __________________________________‚

(37) 36 base 9 in base 10 is ________________________

(38) The area of a square is 196 cm . The perimeter of2

the square is _____________________________ cm

(39) (25 45) 6 has a remainder of ___________35 ‚ ƒ

*(40) 32126 = __________________________________È (41) 27 33 9 = _______________________________‚

(42) The leg opposite the 30° angle in a right triangle is 30 cm hypotenuse is _________________ cm. The

(43) 28 78 = ________________________________2 2

(44) Find the slope of the line through the points ( 2, 3) and (5, 8). _______________________q q q

(45) The product of the roots of (2x 3) = 0 is ______q 3

(46) How many triangles meet at each vertex of a Platonic icosahedron? ________________________

(47) 1110 3 = ______________________________4 4 4ƒ

(48) The sum of the integral values of x such that 3 x 2 5 is ___________________________q Ÿ¸ ¸ (49) 4 3 = ____________________ (mixed number)3 2

5 3ƒ

*(50) 6 7 8 = _______________________________‚ ‚2 3

(51) The midpoint of the segment with endpoints ( 3, 2) and ( 8, 5) is (x, y). x y = ________q q q

(52) Let a b (ab) a = a b . m n = _____4 3 2 1‚ ƒ q q m n

(53) Let = . Find x. ______________________64

( 1xx x

xx x

)

(54) The odds of selecting a vowel from the letters in the word "fraction" is ___________________________

(55) = _______________________________6 4 35C C‚

(56) The sum of the coefficients of the x y term and the3

xy term of (x y) is _______________________3 4

(57) 5 9 14 23 37 ... 157 254 = _______

(58) 321 326 = ________________________________‚

(59) = ____________________ˆ ˆ ˆ1 1 16 12 24‰ ‰ ‰2 2 2

ƒ ‚

*(60) 8151947 326 = ____________________________ƒ

(61) The sum of the reciprocals of all of the positive divisors of 10 is _____________________________

(62) Let f(x) = 3x 1 and g(x) = 2x 1.2 q Find f(g( 1)) = _____________________________q


f(x) = x . Find . _______________[ ] ’ “1È5 1

2

(64) If log (4x 3) = 2 then x = __________________53q

(65) 9 13 has a remainder of ___________________11 ƒ


(67) The sum of the positive integral divisors of 42 is___

(68) 2sin( )cos( ) = ________________________ˆ ‰5 56 61 1 2

(69) How many lines are determined by five points, no three of which are collinear? __________________

*(70) (3 10 17 24 ... 52 59) = __________2


(72) The product of the 4 triangular number and theth

3 pentagonal number is ____________________.rd

(73) Let f(x) = 2x 3x 2x 3. Find f ( 2) = ___3 2 qww

(74) If f(x) = , then f (4) = ________________2x 35

q 1

(75) (2 3i) (4 5i) = (a bi). Find (a b). _______q q

(76) (x 1) = ___________________________'q 2

2 q dx

(77) The smallest element of the domain of y = 9 x2 2q is _________________________________________

(78) Round 7 7 to the nearest tenth. _____________È (79) The range of the function y = 2x 3 is y ____¸ ¸ q

*(80) The simple interest on $4,500.00 at 4.5% for 4.5 years is ___________________ dollars (integer)

University Interscholastic League - Number Sense Answer Key HS District 1 2016ì ì*number) x y means an integer between x and y inclusiveNOTE: If an answer is of the type like it cannot be written as a repeating decimal2

3

(1) 1,173

(2) 491

(3) 2,275

(4) 649

(5) 1925

(6) 44 25

(7) 183

(8) 1 1924

(9) 324

*(10) 5,810 6,420q

(11) 1,331

(12) 15

(13) 7

(14) 4.41

(15) 56

(16) 5 1528

(17) 88

(18) $5.05

(19) 454

*(20) 68 74q

(21) .75, 34

(22) 6,250

(23) 6

(24) 14q

(25) 45

(26) 730

(27) 56

(28) 4 15

(29) 104

*(30) 2,035 2,248q

(31) 26,085

(32) 7q

(33) 63

(34) 19 825

(35) 2.6, 213 35 5,

(36) 1,591

(37) 33

(38) 56

(39) 4

*(40) 171 188q

(41) 900

(42) 60

(43) 6,868

(44) q 57

(45) 327 38 8,

(46) 5

(47) 130

(48) 10

(49) 1 1455

*(50) 143,002 q 158,054

(51) 4q

(52) 4

(53) 29

(54) .6, 35

(55) 150

(56) 8

(57) 656

(58) 104,646

(59) 1144

*(60) 23,756 26,256q

(61) 1 45

(62) 28

(63) 4

(64) 343

(65) 3

(66) 1415

(67) 96

(68) .75, 34

(69) 10

*(70) 73,949 q 81,733

(71) 0690

(72) 120

(73) 18q

(74) 8.5, 817 12 2,

(75) 29q

(76) 4

(77) 3q

(78) 18.5, 1837 12 2,

(79) 3q

*(80) 866 956q

The University Interscholastic LeagueNumber Sense Test HS District 2 2016ì ì

Final ______ ______






(1) 1865 1492 = ______________________________q

(2) 9.05 8 = _________________________ (decimal)‚

(3) 357 1944 = _______________________________

(4) 1948 11 = __________________ (mixed number)ƒ

(5) 64% = _______________________(proper fraction)

(6) 1 = ______________________________ (decimal)116

(7) 26 = ______________________________________2

(8) 6102723 9 has a remainder of _______________ƒ

(9) 2 = ___________________________________4 29 3 q

*(10) 572 2016 1812 897 = ___________________q q

(11) 4 3 = ____________________ (mixed number)2 43 9

(12) 72 25 = __________________________________‚

(13) 1965 3 has a remainder of __________________ƒ

(14) 3 yards 2 feet 8 inches = ____________ inchesq

(15) 1 2 3 4 5 ... 24 25 = ____________

(16) MXCVI = ___________________ (Arabic numeral)

(17) The GCD of 24, 54, and 72 is __________________

(18) 15% of $14.00 = $ ____________________________

(19) If 9 's cost $15.45 then 12 's cost $ ____________♦ ♦

*(20) 796854 395 = _____________________________ƒ

(21) 2 3 5 = ______________________________5 3 2

(22) The additive inverse of is _________________q 38

(23) The sum of the prime numbers greater than 10 and less than 20 is _______________________________

(24) 2 3 5 8 1 3 = __________________q q q q¸ ¸ ¸ ¸ (25) 27 33 = __________________________________‚

(26) 1728 = _________________________________È3

(27) 109 % of 66 = _____________________________111

(28) The number of proper divisors of 12 is __________

(29) Set A = {a,c,u,t,e}, O = {o,b,t,u,s,e}, and R = {r,i,g,h,t}. O (A R) contains how many distinct elements? ____________________________

*(30) 4 3198 13 = ___________________________78 ‚ ƒ

(31) If x = 39 and y = 13 then x 2xy y = _______2 2q

(32) The LCM of 54 and 24 is _____________________

(33) 0.181818... = _________________ (proper fraction)

(34) 4 4 = ___________________ (mixed number)3 25 5‚

(35) 35% of 30 minus 25 is ________________________

(36) (60 38 16) 7 has a remainder of __________‚ q ƒ

(37) 135 base 6 in base 10 is _______________________

(38) 54 35 = __________________________________‚

(39) 37 43 9 = _______________________________‚

*(40) 61027 = __________________________________È (41) 65% of 65 45% of 45 is _____________________q

(42) Let A A A = A . If A 1,k 2 3 5‚ ƒq q

then k = ____________________________________

(43) 22 26 4 = _______________________________‚

(44) The sum of the roots of 3x 2x = 5 minus the2 q product of the roots of 3x 2x = 5 is ___________2 q

(45) The perimeter of a right triangle with a base of 7" and a hypotenuse of 25" is ______________ inches

(46) 2016 7 = ______________________________8 8 8‚

(47) How many pentagons meet at each vertex of a Platonic dodecahedron? ______________________

(48) How many subsets containing 3 or 4 elements does the set {n,u,m,b,e,r} have? ____________________

(49) 1 4 = _________________________________3 27 3ƒ

*(50) 24 6 = __________________________________2 3‚

(51) The midpoint of the segment with endpoints (6, 1) and ( 5, 4) is (x, y). Find x y. _______________q

(52) 7 12 19 31 50 81 131 212 = _____

(53) = _______________________________6 4 35C P _‚

(54) If = , then x = ______________________75 (

(xx x

xx 2x 1

))

(55) The probability of selecting an abundant number from the set of positive digits is ________________

(56) ( 2 5i) (7 3i) = (a bi). Find a b. _______q

(57) 314 319 = ________________________________‚

(58) If 3 x 2 = 1 then x = ____________q q q 1 1 1

(59) The number of positive integral divisors of 64 is___

*(60) 123581 321 = _____________________________ƒ


(62) The Greatest Integer Function is written as f(x) = x . Find 2 3 5 . __________[ ] ’ “È È È (63) If = 6k, then k = _____(mixed number)1 15

6 28º ºq

(64) cos( ( sin( ( = ___________5 5 5 56 6 6 61 1 1 1)cos ) )sin ) q

(65) If 2log (x 5) = 3 then x 0 is _______________4 q

(66) Change 0.1222... base 3 to a base 3 fraction. ______

(67) The volume of a rectangular pyramid with a base width of 2.4", a base length of 2.5", and a height 7" is ___________________________________ in3

(68) F(x) = x 4x x 6. F(F( 1)) = __________3 2q q


*(70) 1 2 3 4 ... 11 12 = ____________2 2 2 2 2 2

(71) The 3 hexagonal number plus the 3 pentagonalrd rd

number plus the 3 triangular number is _______rd

(72) Let f(x) = x 4x x 6. Find f ( 2). ______3 2q qww


(74) If 6x 4 2(mod 8), 2 x 7, then x = _______q ´ Ÿ Ÿ

(75) If f(x) = 2x 1 , then f (4) = ______________È3 q q 1

(76) Truncate ( ) to the nearest whole. ____È5 1

2 ‚1

(77) (3x 5) = ___________________________' 0

2q dx

(78) The range of the function y = is y ______e ( )q x

(79) The dot product of the vectors (2, 1) andq ( 3, 4) is __________________________________q

*(80) The interest on $2000 for 4 years at 6% compounded semiannually is ____ dollars (integer)

University Interscholastic League - Number Sense Answer Key HS District 2 2016ì ì*number) x y means an integer between x and y inclusiveNOTE: If an answer is of the type like it cannot be written as a repeating decimal2

3

(1) 373

(2) 72.4

(3) 2,301

(4) 177 111

(5) 1625

(6) 1.0625

(7) 676

(8) 3

(9) 16 79 9, 1

*(10) 555 502q qq

(11) 8 19

(12) 1,800

(13) 0

(14) 124

(15) 325

(16) 1,096

(17) 6

(18) $2.10

(19) $20.60

*(20) 1,917 2,118q

(21) 84

(22) .375, 38

(23) 60

(24) 4

(25) 891

(26) 12

(27) 72

(28) 5

(29) 3

*(30) 1,140 1,259q

(31) 676

(32) 216

(33) 211

(34) 20 625

(35) 14.5, q q 292 ,

q 14 12

(36) 3

(37) 59

(38) 1,890

(39) 1,600

*(40) 235 259q

(41) 22

(42) 4

(43) 576

(44) 27 13 3,

(45) 56

(46) 16142

(47) 3

(48) 35

(49) 1549

*(50) 118,196 q 130,636

(51) 3

(52) 543

(53) 900

(54) 40

(55) 0

(56) 0

(57) 100,166

(58) 6

(59) 7

*(60) 366 404q

(61) 1.6, 18 35 5,

(62) 5

(63) 19q 23

(64) .5, 12

(65) 13

(66) 210 (not reducible)

(67) 14

(68) 6

(69) 0511

*(70) 618 682q

(71) 33

(72) 20q

(73) 0

(74) 5

(75) 32.5, 3265 12 2,

(76) 5

(77) 4q

(78) 0

(79) 10q

*(80) 507 560q

The University Interscholastic LeagueNumber Sense Test HS Regional 2016ì ì

Final ______ ______






(1) 6102 524 423 = __________________________q q

(2) 234 5 = __________________________________‚

(3) 1947 3 = _________________________________ƒ

(4) 0.1875 = ____________________ (proper fraction)

(5) 55% = _______________________(proper fraction)

(6) 31 = ______________________________________2

(7) 5 2 3 5 (2 4) 2 1 6 = ________q ‚ ƒ q ‚0

(8) 13 = ______________________________________3

(9) 1111967 9 has a remainder of ________________ƒ

*(10) 246 1357 2134 711 = __________________q q

(11) 4 3 = ___________________ (mixed number)1 14 3

(12) 135 12 = _________________________________‚

(13) 42325 8 has a remainder of _________________ƒ

(14) 125% of 88 = _______________________________

(15) 5 3 = ___________________ (mixed number)2 25 3 q

(16) If 8 's cost $6.40 then 5 's cost $ _____________ú ú

(17) 37 14 14 33 = _________________________‚ ‚

(18) CXXV XLIV = ____________ (Arabic numeral)‚

(19) 4 gallons 2 quarts 2 pints = __________ cupsq q

*(20) 815 1947 = _______________________________‚

(21) 2 4 8 = ____________________________ _5 3 2

(22) What number divided by four gives the same result as that number minus twelve? ____________

(23) Let x = 1. Find 3x 9q q2 6x . _______________

(24) The sum of three consecutive even integers is 144. The smallest of the three integers is _____________

(25) 4 2 = __________________ (mixed number)1 12 10‚

(26) 23 (mixed number)‚ 2629 = _____________________

(27) What is 27% of 444 _______________________49 =

(28) 0.02555... = __________________ (proper fraction)

(29) F = {f,o,r,t,y}, S = {s,i,x,t,y}, and E = {e,i,g,h,t,y}. (F S) E has how many distinct elements? _____

*(30) 4 1423 14 = ___________________________23 ‚ ƒ

(31) 15 45 = ________________________________2 2

(32) If 7x 5 = 3, then 7x 1 = ___________________q

(33) 213 base 4 in base 10 is _______________________

(34) If a = 22 and b = 14, then 4a 4ab b = ______2 2q

(35) = ___________________________________Š ‹916

32

(36) Given the set {1,5,12,22,m,51,70,n,117, 145,... }. Find m _____________________n. ___________

(37) 36 53 = __________________________________‚

(38) 4 4 = ___________________ (mixed number)5 38 8‚

(39) (22 66) 8 has a remainder of __________44 ‚ ƒ

*(40) 523524 = _________________________________È (41) 31 39 16 = _____________________________‚

(42) Let 39 39 39 = 39 . Find k. ___________4 2 k 3‚ ƒ q

(43) The sum of the roots of 9x 6x = 1 is ________2 q q

(44) The area of a right triangle with a base of 40 cm and a hypotenuse of 41 cm is ______________ cm2

(45) The midpoint of the segment with end points ( 1, 3) and (6, 10) is (x, y). Find x y. _______q q

(46) If 3 x = 6 then x = ________________ q q q2 1 1

(47) Which of the following is an odious number, 3, 5, or 7? __________________________________

(48) The sum of the integral values of x such that x 2 4 6 is ___________________________¸ ¸q q Ÿ

(49) The sum of the number of faces, the number of sides, and the number of vertices of a Platonic icosahedron is _______________________________

*(50) 4 3 2 = ______________________________2 4 5‚ ‚

(51) (2 3 ) 5 = (a b ). Find (a b). ___________ƒi i i

(52) Find the 5 term of the geometric sequence,th

81, 27, 9, 3, ... . _______________q q __________

(53) = _______________________________7 55 3C P _‚

(54) If = , then x = _____________________5 46 x

(x x xx x

x 1)

(55) 8 15 23 38 61 ... 160 259 = _____

(56) The sum of the coefficients of the x y term and3 2

the xy term of (x y) is ____________________4 5

(57) 423 425 = ________________________________‚

(58) Find the units digit of 18 . ____________________7

(59) The odds of selecting a pentagonal number from the set of digits is _____________ (proper fraction)

*(60) 4232016 425 = ____________________________ƒ




f(x) = x . Find 3.14 . _____________[ ] ’ “È5 12 q

(64) If log (4x 3) = 2 then x = ____________________8

(65) 524 423 201 =6 6 6 6 ________________________

(66) Change 0.4232323... to a base 10 fraction. ______ 5

(67) How many positive integers less than 20 are relatively prime to 20? _______________________

(68) 1 cos ( ) = ______________________________q 2 531

(69) The first four digits of the decimal for 711 is 0.___

*(70) 2 4 6 8 ... 14 16 = ____________2 2 2 2 2 2

(71) Truncate 5 6 to the nearest tenth. ____________È (72) The largest element of the range of y = 16 x2 2q is _________________________________________

(73) If f(x) = 1, then f ( 4) = ____________23

1x q q q

(74) (3x 4) = ___________________________'q 1 1

q dx

(75) If 3x 2 4(mod 8), 0 x 7, then x = _______q ´ Ÿ Ÿ

(76) The 1 triangular number times the 2 hexagonalst nd

number times the 3 pentagonal number is ______rd

(77) The domain of the function Ln( is x _____È ex)

(78) How many subsets containing only 4 elements does the set {r,e,g,i,o,n} have? _________________

(79) 44 22 11 = ___________________________2 2 2ƒ ‚

*(80) The interest on $5000 for 2.5 years at a simple interest rate of 1.5% is _________ dollars (integer)

University Interscholastic League - Number Sense Answer Key HS Regional 2016ì ì*number) x y means an integer between x and y inclusiveNOTE: If an answer is of the type like it cannot be written as a repeating decimal2

3

(1) 5,155

(2) 1,170

(3) 649

(4) 316

(5) 1120

(6) 961

(7) 21.5, , 2143 12 2

(8) 2,197

(9) 8

*(10) 297 327q

(11) 7 712

(12) 1,620

(13) 5

(14) 110

(15) 1 1115

(16) $4.00

(17) 980

(18) 5,500

(19) 52

*(20) 1,507,465 q 1,666,145

(21) 160

(22) 16

(23) 12q

(24) 46

(25) 9 920

(26) 20 1829

(27) 120

(28) 23900

(29) 3

*(30) 451 498q

(31) 2,250

(32) 9

(33) 39

(34) 900

(35) 2764

(36) 127

(37) 1,908

(38) 20 1564

(39) 6

*(40) 688 759q

(41) 1,225

(42) 1q

(43) 23

(44) 180

(45) 1q

(46) 18

(47) 7

(48) 42

(49) 62

*(50) 39,399 43,545q

(51) .2, 15

(52) 1

(53) 1,260

(54) 3

(55) 663

(56) 15

(57) 179,775

(58) 2

(59) 14

*(60) 9,460 10,455q

(61) , 148 1335 35

(62) 4

(63) 2q

(64) 15.25, , 1561 14 4

(65) 1552

(66) 109120

(67) 8

(68) .75, 34

(69) 6363

*(70) 776 856q

(71) 12.2, , 1261 15 5

(72) 4

(73) , 3q q11 23 3

(74) 8q

(75) 2

(76) 72

(77) 0

(78) 15

(79) 484

*(80) 179 196q

The University Interscholastic LeagueNumber Sense Test HS State 2016ì ì

Final ______ ______






(1) 5232 425 2016 = _________________________

(2) 525 201 6 = ____________________________q q

(3) 345 6 = __________________________________‚

(4) 6102 4 = __________________________________ƒ

(5) 3 = ______________________________ (decimal)58

(6) 4 2 = ____________________ (mixed number)2 33 4

(7) 29 = ______________________________________2

(8) (5 2) 5 20 16 = ______________________ ‚ q ƒ

(9) 1.0625 = _______________________________q 916

*(10) 1492 1776 1963 1044 = _________________q q

(11) The arithmetic mean of 17, 23, and ________ is 26.

(12) 5 2 = ___________________ (mixed number)3 14 6 q

(13) 523525 9 has a remainder of ________________ƒ

(14) 20 inches 1 foot 6 yards = __________ inches

(15) 41 % of 36 is _______________________________23

(16) If 6 TDs cost $7.00 then 21 TDs cost $ ___________

(17) 44 22 26 22 = _________________________‚ ‚

(18) 14 = ______________________________________3

(19) 1 3 5 7 9 ... 31 33 = ____________

*(20) 620 1975 = _______________________________‚

(21) The multiplicative inverse of 2.2 is ___________q

(22) 0.23444... = __________________ (proper fraction)

(23) Let G = {g,e,r,m,a,i,n}, P = {p,r,i,m,e} and N = {n,u,m,b,e,r}. The number of distinct elements of (G N is ____________________________. P)

(24) (20 16 ) 5 has a remainder of __________‚ ƒ 52

(25) 6 6 = ___________________ (mixed number)1 56 6‚

(26) 5 2 3 5 2 5 = __________________ q q q¸ ¸ ¸ ¸ (27) 54 56 = __________________________________‚

(28) 67 base 8 in base 9 is ________________________ 9

(29) Given the set {1,6,15,28,45,m,91,n,153,... }. Find m _____________________ n. ___________

*(30) 3 1875 43.75 = ________________________516 ‚ ƒ

(31) Round 2 5 __È to the tenths place. ___________

(32) If a = 14 and b = 6, then a 6ab 9b = _______2 2

(33) 1833 % of 36 _____________________________13 =

(34) The perimeter of a square is 60 cm. The area of the square is _______________________________ cm2

(35) The sum of the first 4 hexagonal numbers is ______

(36) How many natural numbers less than 10 are considered to be evil numbers? _________________

(37) 523 525 _____________________________6 6 6 =

(38) 4 4 = ___________________ (mixed number)5 38 8ƒ

(39) The sum of the prime factors of 210 is ___________

*(40) 6102325 525 = _____________________________ƒ

(41) 25% of 60 60% of 25 is ____________________q

(42) If (9 )(x ) = 10 then x = ________________q q q 1 1 1

(43) 37 67 = _________________________________2 2

(44) (1 3i) (6 10i) = (a bi). Find a b. ________q

(45) The sum of the solutions of x 2 4 = 0 is ____¸ ¸ q

(46) Find the units digit of 8 . _____________________8

(47) The sum of the number of faces, vertices, and edges of a Platonic octahedron is _______________

(48) 32 35 9 = _______________________________‚

(49) The least value of x such that x 4 2 is ______¸ ¸ Ÿ

*(50) 75 54 33 = ___________________________2 2 2

(51) The product of the coefficient of the x y term of2

(x y) and the xy term of (x y) is ________ 3 3 4

(52) = __________________________________8 75 4x xx x q

(53) 361 215 = ________________________________‚

(54) = ___________________5 5 5 54 3 2 1C C C C q q

(55) The probability of selecting a perfect number from the set of natural numbers less than 101 is _____%

(56) Let a b a b = a b .5 3 1 2 m nab

3‚ ƒq ˆ ‰

Find m n. ________________________________

(57) The sum of the reciprocals of all of the positive integral divisors of 21 is ______________________

(58) The first 4 digits of the decimal for is 0.______39110

(59) 6 10 16 26 ... 288 466 = __________

*(60) 523524525 = ______________________________È (61) 120 has how many positive integral divisors? _____

(62) If log (4x 4) = 4 then x = ___________________4


(64) 46 23 11.5 = _________________________2 2 2ƒ ‚

(65) Let f(x) = 5x 2x 5. Find f(f( 1)). _________2 q q q

(66) cos ( ) sin ( ) = _______________________2 25 56 61 1ƒ

(67) Find k if = 35 k. _______________ 1 5 12 22º ºq q

q

(68) The total surface area of a rectangular prism with a base width of 5", a base length of 12", and a height of 13" is __________________________ in2


*(70) 1 3 5 7 9 ... 17 19 = _______2 2 2 2 2 2 2

(71) If 6 9x 5(mod 7), 0 x 6, then x = _______ ´ Ÿ Ÿ

(72) y = has how many asymptotes? ______x xx

3 22

q 2 5

(73) (523 )(25 ) 7 has a remainder of _____________8 8 ƒ

(74) If f(x) = , then f ( 1) = ______________3 2

1x 54 x

qq

q q

(75) Find k given the geometric sequence {k, 3k, 20 k, ...}. _______________q ___________

(76) (5 2x) = __________________________' 1 1q

dx

(77) The range of the function y = (x 2) is y ___ q 12

(78) = _______________________________limx 2

4 2Ä

xx 2qq

(79) The 3 hexagonal number plus the 4 pentagonalrd th

number plus the 5 triangular number is _______th

*(80) $4000 compounded quarterly at an annual rate of 4% for 4 years is ______________ dollars (integer)

University Interscholastic League - Number Sense Answer Key HS State 2016ì ì*number) x y means an integer between x and y inclusiveNOTE: If an answer is of the type like it cannot be written as a repeating decimal2

3

(1) 7,673

(2) 318

(3) 2,070

(4) 1525.5, ,30512

1525 12

(5) 3.625

(6) 7 512

(7) 841

(8) 33.75, , 33135 34 4

(9) .5, 12

*(10) 604 666q

(11) 38

(12) 3 712

(13) 4

(14) 248

(15) 15

(16) $24.50

(17) 1,540

(18) 2,744

(19) 289

*(20) 1,163,275 q 1,285,725

(21) q 511

(22) 211900

(23) 3

(24) 2

(25) 42 536

(26) 4

(27) 3,024

(28) 61

(29) 186

*(30) 135 149q

(31) 4.5, , 49 12 2

(32) 1,024

(33) 660

(34) 225

(35) 50

(36) 4

(37) 1452

(38) 1 235

(39) 17

*(40) 11,043 12,204q

(41) 0

(42) 10 19 9, 1

(43) 5,858

(44) 28

(45) 4q

(46) 6

(47) 26

(48) 1,129

(49) 6q

*(50) 9,149 10,111q

(51) 12

(52) 126

(53) 77,615

(54) 0

(55) 2

(56) 9

(57) , 132 1121 21

(58) 3545

(59) 1,210

*(60) 21,737 24,024q

(61) 16

(62) 63

(63) 2328

(64) 529

(65) 11

(66) 3

(67) 3q

(68) 562

(69) 1

*(70) 1,264 1,396q

(71) 3

(72) 2

(73) 0

(74) 1

(75) 2

(76) 10

(77) 0

(78) 4

(79) 52

*(80) 4,456 4,924q

the university interscholastic league number sense …€¦ · the university interscholastic...

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