The University Interscholastic League Number Sense Test HS a 2016

The University Interscholastic League Number Sense Test ìì HS A 2016 Final ______Contestant's Number ______2nd ______1st ______Read directions carefully DO NOT UNFOLD THIS SHEET Score Initials before 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 are 80 problems. Solve accurately and quickly as many as you can in the order in which they appear. ALL PROBLEMS ARE TO BE SOLVED MENTALLY. Make no calculations with paper and pencil. Write only the answer in the space provided at the end of each problem. Problems marked with a ( * ) require approximate integral answers; any answer to a starred problem that is within five percent of the exact answer will be scored correct; all other problems require exact answers.

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STOP -- WAIT FOR SIGNAL!

(1) 116 611 = ______43 (19) 375 q 1 = ______(mixed number)

(2) 345 q 612 = ______*(20) 373‚ 464 = ______

(3) 116‚ 5 = ______2 (21) 12% of 1663 = ______(4) 0.444... = ______(proper fraction) (22) The additive inverse of 0.444... is ______(5) 36% = ______(proper fraction) (23) 1222 4 = ______2 (6) 14 = ______3 (24) È 2197 = ______(7) 1616ƒ 4 = ______(25) 41‚ 39 = ______(8) 9 q‚ƒ 12 6 3 = ______(26) 1q 4 7 q 7 q 1 4 = ______¸¸¸¸ (9) 21 = ______(decimal) 8 (27) If 12 pens cost $1.60 then 9 pens cost $ ______*(10) 1601 1610 1160 1061 = ______ (28) 0.3111... = ______(proper fraction) (11) 113 2 = ______(mixed number) 64 (29) Set T = {t,i,m,e,s} and M = {s,q,u,a,r,e}. T M contains how many distinct elements? ______(12) 65‚ 25 = ______*(30) 31 ‚ƒ 12515 16 = ______(13) 345ƒ 9 = ______(mixed number) 5

(14) 15% of 44 = ______(31) (21‚q 7 14) ƒ 6 has a remainder of ______

5 (32) If 5x qq 1 = 9, then x 5 = ______(15) Which is larger, 0.63 or 8 ? ______(33) 121‚ 1 = ______(mixed number) (16) MDCVI = ______(Arabic numeral) 5 14

(17) The GCD of 35, 56, and 70 is ______(34) 1357...1719 = ______22 (18) 2 yards qq 1 foot 6 inches = ______inches (35) If x = 11 and y = 8 then x q 2xy y = ______(36) 67 base 8 in base 10 is ______(59) The probability of selecting an even integer between 1 and 11 is ______(proper fraction) 15 (37) 14‚ 16 = ______(mixed number) *(60) 322.3‚ 37.73 = ______(38) The area of a rectangle with a length of 1.25 ft and a width of 3.2 ft is ______sq. ft (61) The number of positive integral divisors of 48 is __ 13 (39) The product of the first 3 prime numbers is ______(62) 11ƒ 15 has a remainder of ______

(63) The Greatest Integer Function is written as *(40) È 12515 = ______5 1 f(x) = [] x . Find 1 q È . ______(41) 35% of 40 45% of 50 is ______’“2 2 (42) The leg opposite the 60° angle in a right triangle is (64) If f(x) = (x qq 3)(x 6x 9), then f(18) = ______12 3 cm. The hypotenuse is ______cm È (65) The volume of a rectangular prism with base width 5", base length 12", and height 13" is ______in3 (43) If x qqq 111 q 2 = 3 then x = ______2 (44) The midpoint of the segment with endpoints (66) Let f(x) = 3x qq x 1. Find f(f(1)). ______(qq 1, 2) and (3, 4) is (x, y). Find x y. ______qq 1 3 (67) Find k if = 15k. ______6 10 (45) The sum of the roots of (2x 3)2 = 0 is ______ºº (68) 2sin(11 os( = ______(46) Let 16 q 235k‚ƒ 16 16 = 16 . Find k. ______44)c )

(47) 18‚ 22 4 = ______(69) Change 0.123 base 4 to a base 10 fraction. ______

*(70) (28 24 20 16 12 8 4)2 = ______(48) 12366 q 45 = ______6 nd (49) The sum of the solutions of x q 1 = 3 is ______(71) The product of the 2 triangular number and the ¸¸ 2nd pentagonal number is ______*(50) 1232‚ 6 = ______(72) 0.242424...55 = ______(proper fraction) (51) The middle term of the 5th row of Pascal's triangle is ______(73) Truncate (2È 3 3È 2) to the nearest whole. ___ 14 (52) Each face of a Platonic octahedron has _____ sides (74) The first four digits of the decimal for 33 is 0. ___

(53) Find the 7th term of the Fibonacci sequence, q 1 (75) If f(x) = È x 2 , then f (4) = ______1, 1, 2, 3, ... . ______(76) f(x) = 2x32 6x 6x 2. Find fw ( q 1) = ______(54) If 41x = , then x = ______6x x 2 (77) (3x q 4) dx = ______' 1 (55) 66CC42 q = ______(78) The largest number in the domain of y22 = 4 q x 222 (56) 12ƒ‚ 6 3 = ______is ______

(57) (2q 3i) (4 5i) = (a bi). Find ab. ______(79) The minimum value of f(x) = 5(x q 3)2 2 is ____

(58) 221‚ 133 = ______*(80) The interest on $6000 for 6 years at 6% compounded semiannually is ______dollars (integer) University Interscholastic League - Number Sense Answer Key HS ìì Invitation A 2016 *number) x y means an integer between x and y inclusive 2 NOTE: If an answer is of the type like 3 it cannot be written as a repeating decimal

34 (36) 55 5 (1) 727 (19) 1 35 (59) 9 1 (2) q 267 *(20) 164,419 q (37) 13 8 *(60) 11,553 q 12,768 181,725 (3) 580 (38) 4 (61) 10 (21) 20 (4) 4 (39) 30 (62) 11 9 4 (22) q 9 9 *(40) 107 q 117 (63) q 1 (5) 25 (23) 160 (41) 36.5, 73 , 36 1 (6) 196 22 (64) 3,375 (24) 13 (7) 404 (42) 24 (65) 780 (25) 1,599 61 (66) 1 (8) q 15 (43) 1.2, 55 , 1 (26) q 2 8 (9) 2.125 (44) 2 (67) 15 (27) $1.20 *(10) 5,161 q 5,703 (45) q 3 (68) 1 (28) 14 11 45 27 (11) 3 12 (46) q 4 (69) 64 (29) 2 (12) 1,625 (47) 400 *(70) 11,917 q 13,171 *(30) 2,378 q 2,628 1 (48) 34 (71) 15 (13) 38 3 (31) 1 33 3 (49) 2 12 (14) 6.6, , 6 (72) 22 (not reducible) 55 (32) q 3 *(50) 59,098 q 65,318 63 1 (73) 7 (15) .63, 100 (33) 1 2 (51) 6 (16) 1,606 (74) 4242 (34) 100 (52) 3 (17) 7 (75) 14 (35) 9 (53) 13 (18) 54 (76) 0 (54) 30 1 (77) .5, 2 (55) 0 (78) 2 (56) 36

(57) 46 (79) 2

(58) 29,393 *(80) 2,427 q 2,682 The University Interscholastic League Number Sense Test ìì HS B 2016 Final ______Contestant's Number ______2nd ______1st ______Read directions carefully DO NOT UNFOLD THIS SHEET Score Initials before beginning test UNTIL TOLD TO BEGIN

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

STOP -- WAIT FOR SIGNAL!

(1) 2312 q 2016 = ______(19) 21231216ƒ 8 has a remainder of ______

(2) 212 316 = ______*(20) 31216ƒ 396 = ______

(3) 2016ƒ 3 = ______(21) 2432 3 4 = ______

(4) 231‚ 6 = ______(22) 2 1 qqq 2 3 12 = ______¸¸¸¸ 3 (5) 5 = ______% (23) The multiplicative inverse of q 1.25 is ______

(6) 23‚ 11 = ______(24) 73 = ______

1 (25) Let x = qq 2. Find 3 4x. ______(7) 0.375 q 4 = ______

(8) 2 qqƒ‚ 1 2 3 (1 2) = ______(26) If 15 ææs cost $18.45 then 10 s cost $ ______

11 (27) 11‚ 14 = ______(mixed number) (9) 326 q 2 = ______(mixed number) 17 32 *(10) 136q 1015 2128 3645 = ______(28) 359‚ 1 = ______(mixed number)

(11) 232 = ______(29) Set E = {e,l,p,a,s,o} and A = {a,u,s,t,i,n}. E A contains how many distinct elements? ______(12) 14% of 16 = ______(decimal) *(30) 42 ‚ƒ 6390 15 = ______(13) 1 2 3 4 5 ... 19 20 = ______7 (31) 0.515151... = ______(proper fraction) (14) 17‚ 23 = ______(32) 1222 36 = ______(15) 123 = ______

13 (33) (37 27 ‚ƒ 17) 8 has a remainder of ______(16) 354 2 = ______(mixed number) (34) 27% of 2111 = ______(17) 3 gallons q 2 quarts = ______pints 9 (35) If a = 12 and b = 11, then 9a22 q 6ab b = ______(18) MMXVI‚ IV = ______(Arabic numeral) (36) 15% of 30 minus 45 is ______(59) 271‚ 314 = ______

(37) 312 base 5 in base 10 is ______*(60) 212312ƒ 201.6 = ______

(38) 73‚ 23 = ______(61) The Greatest Integer Function is written as 111 f(x) = [] x . Find sin(444 ) cos( ) tan( ) . ____ (39) The perimeter of a square is 14". The area of the ’“ square is ______sq. in. (62) How many positive integers less than 30 are relatively prime to 30? ______*(40) È 44044 = ______1 q 5 (41) 22‚ 28 9 = ______(63) If = 35 q k then k = ______ºº12 22 (42) If 9 qq 11 q x = 10 q 1 then x = ______(64) If 2log4 (3x q 1) = 3 and x 0 then x = ______(43) 75% of 80 = 30% of ______(65) The smallest integral value of x such that 2x qŸ 3 4 is ______(44) A face of a Platonic dodecahedron has ____vertices ¸¸ (66) Change 0.2111... base 5 to a base 10 fraction. _____ (45) Let 21735k‚ƒ 21q 21 = 21 . Find k. ______(67) F(x) = 2x3 qqq 4. G(x) = 1 x. F(G( 2)) = ______(46) The area of a right triangle with a base of 7 cm and a hypotenuse of 25 cm is ______sq. cm 11 (68) sec(36 ) csc( )= ______(47) (33))22ƒ‚ ( ( 3 )2 = ______4 8 16 (69) The volume of a rectangular based pyramid with a base width 5", a base length 12", and a height 13" (48) How many subsets containing only 3 elements is ______in3 does the set {p,r,i,m,e} have? ______*(70) (2 4 6 8 ... 18 20)2 = ______(49) 31244‚ 3 = ______4 (71) The first four digits of the decimal for 31 is 0.___ *(50) 1232‚ 21 = ______111

(51) Find the units digit of 17 6 . ______(72) Truncate (2È 3 q È 5) to the nearest whole. ____

x 3 q 1 (52) The midpoint of the segment with endpoints (x, y) (73) If f(x) = 1 q 4 , then f (2) = ______and (1, qq 7) is ( 3, 5). Find x y. ______(74) f(x) = 2x32 6x 6x 2. Find fww (3) = ______(53) 7 9 16 25 41 66 107 173 = ______(75) The minimum value of f(x) = 4(x q 3)2 1 is ____ (54) 55CC32 = ______(76) If x´ 6 2(mod 7), 0 ŸŸ x 6, then x = ______(55) The probability of selecting a multiple of three from the set of positive digits is ______1 (77) (2 q 3x) dx = ______' 0 (56) The sum of the roots of (x 5)3 = 0 is ______(78) The sum of the first 3 hexagonal numbers is _____ (57) The sum of coeficients of the x2 y2 term and the (79) The range of the function y = 3 x is y ____ xy3 term of (x y)4 is ______È q *(80) The compound interest on $2000 for 4 years at 8% (58) 6x = ______33xx compounded annually is ______dollars (integer) University Interscholastic League - Number Sense Answer Key HS ìì Invitation B 2016 *number) x y means an integer between x and y inclusive 2 NOTE: If an answer is of the type like 3 it cannot be written as a repeating decimal

(19) 0 81 (59) 85,094 (1) 296 (36) qq 40.5, 2 , 1 q 40 (2) 528 *(20) 75 q 82 2 *(60) 1,001 q 1,105 (37) 82 (3) 672 (21) 59 (61) 2 (38) 1,679 (4) 1,386 (22) 3 (62) 8 49 1 4 (39) 12.25, , 12 (63) q 47 (5) 60 (23) qq .8, 5 44

(6) 253 (24) 343 *(40) 200 q 220 (64) 3 1 (41) 625 (65) 0 (7) .125, 8 (25) 11 (42) 90 (66) 9 (8) q 1 (26) $12.30 20 (43) 200 (9) 1 1 1 (67) 50 3 (27) 9 17 (44) 5 (68) 4 *(10) 2,535 q 2,801 2 (28) 4 5 (45) q 1 (11) 529 (69) 260 (29) 10 (46) 84 (12) 2.24 *(70) 11,495 q 12,705 *(30) 1,735 q 1,917 (47) .140625, 9 (71) 2792 (13) 210 17 64 (31) 33 (14) 391 (48) 10 (72) 1 (32) 1,440 (15) 1,728 (49) 2202 (73) q 7 (33) 0 *(50) 723,946 q (16) 5 19 (74) 48 20 (34) 57 800,150 (75) 1 (17) 20 (35) 625 (51) 9 (76) 3 (18) 8,064 (52) 10 (77) .5, 1 (53) 444 2

(54) 20 (78) 22

1 (79) 0 (55) 3 *(80) 685 q 757 (56) q 15

(57) 10

(58) 20 The University Interscholastic League Number Sense Test ìì HS District 1 2016 Final ______Contestant's Number ______2nd ______1st ______Read directions carefully DO NOT UNFOLD THIS SHEET Score Initials before beginning test UNTIL TOLD TO BEGIN

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

STOP -- WAIT FOR SIGNAL!

(1) 356 817 = ______(19) CDLIV = ______(Arabic numeral)

(2) 815 q 324 = ______*(20) 42116ƒ 595 = ______

(3) 325‚ 7 = ______(21) The multiplicative inverse of 1.333... is ______

(4) 1947ƒ 3 = ______(22) 2522 75 = ______

(23) 3 qq 2 4 1 q 6 = ______(5) 76% = ______(proper fraction) ¸¸¸¸ (6) 0.444 = ______% (mixed number) (24) Let x = qq 4. Find 3x 2. ______

(7) 8q‚ƒq 15 20 16 (6 8) = ______(25) The sum of three consecutive integers is 132. The largest of the three is integers is ______55 (8) 286 q = ______(26) 0.2333... = ______(proper fraction) 2 (9) 18 = ______4x 2 (27) Let 53 = . Find x. ______*(10) 247q 2126 1014 4756 = ______23 (28) 254‚ 1 = ______(mixed number) (11) 113 = ______(29) 24% of 4331 = ______(12) The arithmetic mean of 20, 16, and ______is 17 3 *(30) 32126ƒ 15 = ______(13) 81547ƒ 9 has a remainder of ______(31) 235 111 = ______(14) 21% of 21 = ______(decimal) ‚

5 (32) If 6x qq 4 = 2, then x 8 = ______(15) Which is larger, 6 or 0.83? ______(33) The set A = {A,U,S,T,I,N} contains how many 21 (16) 274 3 = ______(mixed number) proper subsets? ______

(17) 1 quart 2 pint 3 cup = ______fluid ounces 23 (34) 21‚ 25 = ______(mixed number) (18) If 12ææ 's cost $20.20 then 3 's cost $ ______(58) 321‚ 326 = ______(35) Truncate È7 to the tenths place. ______222 (36) 37‚ 43 = ______(59) 11ƒ‚ 1 = ______ˆˆ6‰‰‰ 12 ˆ 24 (37) 36 base 9 in base 10 is ______*(60) 8151947ƒ 326 = ______

2 (38) The area of a square is 196 cm . The perimeter of (61) The sum of the reciprocals of all of the positive the square is ______cm divisors of 10 is ______(39) (25 35 ‚ƒ 45) 6 has a remainder of ______(62) Let f(x) = 3x2 q 1 and g(x) = 2x 1. Find f(g(q 1)) = ______*(40) È 32126 = ______(63) The Greatest Integer Function is written as (41) 27‚ 33 9 = ______5 1 f(x) = [] x . Find1 È . ______’“2 (42) The leg opposite the 30° angle in a right triangle is 3 30 cm. The hypotenuse is ______cm (64) If log5 (4x q 3) = 2 then x = ______

(43) 2822 78 = ______(65) 911 ƒ 13 has a remainder of ______

(44) Find the slope of the line through the points (66) Change 0.5333... base 6 to a base 10 fraction. _____ (qq 2, 3) and (5, q 8). ______(67) The sum of the positive integral divisors of 42 is___ (45) The product of the roots of (2x q 3)3 = 0 is ______2 (68) 2sin(5511 )cos( ) = ______(46) How many triangles meet at each vertex of a ˆ‰66 Platonic icosahedron? ______(69) How many lines are determined by five points, no three of which are collinear? ______(47) 11104ƒ 3 4 = ______4 *(70) (3 10 17 24 ... 52 59)2 = ______(48) The sum of the integral values of x such that 3qŸ x 2 5 is ______¸¸ 23 (71) The first four digits of the decimal for 333 is 0.___ (49) 432ƒ 3 = ______(mixed number) 53 (72) The product of the 4th triangular number and the 3rd pentagonal number is ______. *(50) 6‚‚ 723 8 = ______(73) Let f(x) = 2x32 3x 2x 3. Find fww ( q 2) = ___ (51) The midpoint of the segment with endpoints ( 3, 2) and ( 8, 5) is (x, y). x y = ______qq q 2x 3 q 1 (74) If f(x) = 5 , then f (4) = ______(52) Let a43 b‚ƒ (ab) qq 2 a 1 = amn b . m n = _____ (75) (2 qq 3i) (4 5i) = (a bi). Find (a b). ______6x (1x x ) (53) Let 4xx = x . Find x. ______2 (76) (x q 1) dx = ______q 2 (54) The odds of selecting a vowel from the letters in the ' word "fraction" is ______(77) The smallest element of the domain of y22 = 9 q x is ______(55) 6CC43‚ 5 = ______(78) Round 7È 7 to the nearest tenth. ______(56) The sum of the coefficients of the x3 y term and the 3 4 (79) The range of the function y = 2x q 3 is y ____ xy term of (x y) is ______¸¸ (57) 5 9 14 23 37 ... 157 254 = ______*(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 ìì District 1 2016 *number) x y means an integer between x and y inclusive 2 NOTE: If an answer is of the type like 3 it cannot be written as a repeating decimal

(19) 454 13 3 (58) 104,646 (1) 1,173 (35) 2.6, 55, 2 1 (2) 491 *(20) 68 q 74 (36) 1,591 (59) 144 3 (3) 2,275 (21) .75, 4 (37) 33 *(60) 23,756 q 26,256 (4) 649 4 (22) 6,250 (38) 56 (61) 1 5 19 (23) 6 (5) 25 (39) 4 (62) 28

2 (24) q 14 *(40) 171 q 188 (63) 4 (6) 44 5 (25) 45 (41) 900 (7) 183 (64) 343 7 (42) 60 (65) 3 19 (26) 30 (8) 1 24 5 (43) 6,868 (66) 14 (9) 324 (27) 6 15 (44) 5 *(10) 5,810 6,420 1 q 7 (67) 96 q (28) 4 5 27 3 (68) .75, 3 (11) 1,331 (29) 104 (45) 88, 3 4

(12) 15 *(30) 2,035 q 2,248 (46) 5 (69) 10

(13) 7 (31) 26,085 (47) 130 *(70) 73,949 q 81,733 (14) 4.41 (32) q 7 (48) 10 (71) 0690 5 (15) (33) 63 (49) 1 14 6 55 (72) 120 8 (16) 5 15 (34) 19 *(50) 143,002 q 28 25 (73) q 18 158,054 (17) 88 17 1 (51) q 4 (74) 8.5, 22, 8 (18) $5.05 (52) 4 (75) q 29

(53) 29 (76) 4 3 (54) .6, 5 (77) q 3 (55) 150 37 1 (78) 18.5, 22, 18 (56) 8 (79) q 3 (57) 656 *(80) 866 q 956 The University Interscholastic League Number Sense Test ìì HS District 2 2016 Final ______Contestant's Number ______2nd ______1st ______Read directions carefully DO NOT UNFOLD THIS SHEET Score Initials before beginning test UNTIL TOLD TO BEGIN

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

STOP -- WAIT FOR SIGNAL!

(1) 1865 q 1492 = ______(19) If 9♦♦ 's cost $15.45 then 12 's cost $ ______

(2) 9.05 ‚ 8 = ______(decimal) *(20) 796854ƒ 395 = ______

(3) 357 1944 = ______(21) 2532 3 5 = ______

(4) 1948ƒ 11 = ______(mixed number) 3 (22) The additive inverse of q 8 is ______

(5) 64% = ______(proper fraction) (23) The sum of the prime numbers greater than 10 and less than 20 is ______1 (6) 116 = ______(decimal) (24) 2 qq 3 5 8 qq 1 3 = ______¸¸¸¸ (7) 262 = ______(25) 27‚ 33 = ______(8) 6102723ƒ 9 has a remainder of ______3 (26) È 1728 = ______(9) 242 q = ______93 1 (27) 10911 % of 66 = ______*(10) 572 qq 2016 1812 897 = ______(28) The number of proper divisors of 12 is ______24 (11) 439 3 = ______(mixed number) (29) Set A = {a,c,u,t,e}, O = {o,b,t,u,s,e}, and (12) 72‚ 25 = ______R = {r,i,g,h,t}. O (A R) contains how many distinct elements? ______(13) 1965ƒ 3 has a remainder of ______7 *(30) 48 ‚ƒ 3198 13 = ______(14) 3 yardsq 2 feet 8 inches = ______inches (31) If x = 39 and y = 13 then x22 q 2xy y = ______(15) 1 2 3 4 5 ... 24 25 = ______(32) The LCM of 54 and 24 is ______(16) MXCVI = ______(Arabic numeral) (33) 0.181818... = ______(proper fraction) (17) The GCD of 24, 54, and 72 is ______(34) 432‚ 4 = ______(mixed number) (18) 15% of $14.00 = $ ______55 (35) 35% of 30 minus 25 is ______(59) The number of positive integral divisors of 64 is___

(36) (60‚q 38 16) ƒ 7 has a remainder of ______*(60) 123581ƒ 321 = ______

(37) 135 base 6 in base 10 is ______(61) The sum of the reciprocals of all of the positive divisors of 15 is ______(38) 54‚ 35 = ______(62) The Greatest Integer Function is written as (39) 37‚ 43 9 = ______f(x) = [] x . Find 2 3 5 . ______’“È È È *(40) 61027 = ______È 1 15 (63) If = 6k, then k = _____(mixed number) (41) 65% of 65 q 45% of 45 is ______ºº6q 28 5511 55 11 k235qq (42) Let A‚ƒ A A = A . If A 1, (64) cos(66)cos ( ) q sin( 66 )sin ( ) = ______then k = ______(65) If 2log4 (x q 5) = 3 then x 0 is ______(43) 22‚ 26 4 = ______(66) Change 0.1222... base 3 to a base 3 fraction. ______(44) The sum of the roots of 3x2 q 2x = 5 minus the product of the roots of 3x2 q 2x = 5 is ______(67) The volume of a rectangular pyramid with a base width of 2.4", a base length of 2.5", and a height (45) The perimeter of a right triangle with a base of 7" 7" is ______in3 and a hypotenuse of 25" is ______inches (68) F(x) = x32 qq 4x x 6. F(F( 1)) = ______(46) 20168‚ 7 8 = ______8 (69) The first four digits of the decimal for 23 is 0.___ (47) How many pentagons meet at each vertex of a 450 Platonic dodecahedron? ______*(70) 12222 2 3 4 ... 11 2 12 2 = ______

(48) How many subsets containing 3 or 4 elements does (71) The 3rd hexagonal number plus the 3 rd pentagonal the set {n,u,m,b,e,r} have? ______number plus the 3rd triangular number is ______

32 32 ww (49) 173ƒ 4 = ______(72) Let f(x) = x q 4x x 6. Find f ( q 2). ______

*(50) 2423‚ 6 = ______(73) 1210 ƒ 8 has a remainder of ______

(51) The midpoint of the segment with endpoints (6, 1) (74) If 6x q´ 4 2(mod 8), 2 ŸŸ x 7, then x = ______and (q 5, 4) is (x, y). Find x y. ______3 q 1 (75) If f(x) = È 2x q 1 , then f (4) = ______(52) 7 12 19 31 50 81 131 212 = _____ 5 1 (76) Truncate (È ‚ 1 ) to the nearest whole. ____ (53) 6CP43‚ 5 = ______2

(x x 2) 2 (54) If 7x = , then x = ______(77) (3x q 5) dx = ______5(xxx 1) ' 0 (55) The probability of selecting an abundant number (78) The range of the function y = e ()q x is y ______from the set of positive digits is ______(79) The dot product of the vectors (2, q 1) and (56) (q 2 5i) (7 3i) = (a bi). Find a b. ______(q 3, 4) is ______

(57) 314‚ 319 = ______*(80) The interest on $2000 for 4 years at 6% compounded semiannually is ____ dollars (integer) (58) If 3 qq 11 x 2 q 1 = 1 then x = ______University Interscholastic League - Number Sense Answer Key HS ìì District 2 2016 *number) x y means an integer between x and y inclusive 2 NOTE: If an answer is of the type like 3 it cannot be written as a repeating decimal

(19) $20.60 29 (59) 7 (1) 373 (35) qq 14.5, 2 , 1 q 14 (2) 72.4 *(20) 1,917 q 2,118 2 *(60) 366 q 404

(21) 84 (36) 3 83 (3) 2,301 (61) 1.6, 55, 1 3 (37) 59 1 (22) .375, (62) 5 (4) 177 11 8 (38) 1,890 2 16 (23) 60 (63) q 19 (5) 25 3 (39) 1,600 (24) 4 1 (6) 1.0625 (64) .5, 2 *(40) 235 q 259 (25) 891 (7) 676 (65) 13 (41) 22 (26) 12 2 (8) 3 (66) (not reducible) (42) 4 10 16 7 (27) 72 (9) , 1 (67) 14 99 (43) 576 (28) 5 (68) 6 *(10) qq 555 q 502 71 (44) 2 (29) 3 33, 1 (69) 0511 (11) 8 9 *(30) 1,140 q 1,259 (45) 56 *(70) 618 q 682 (12) 1,800 (31) 676 (46) 16142 (71) 33 (13) 0 (32) 216 (47) 3 (72) q 20 (14) 124 (33) 2 (48) 35 11 (73) 0 (15) 325 15 6 (49) (34) 20 49 (74) 5 (16) 1,096 25 *(50) 118,196 q 65 1 (17) 6 130,636 (75) 32.5, 22, 32

(18) $2.10 (51) 3 (76) 5

(52) 543 (77) q 4

(53) 900 (78) 0

(54) 40 (79) q 10 (55) 0 *(80) 507 q 560 (56) 0

(57) 100,166

(58) 6 The University Interscholastic League Number Sense Test ìì HS Regional 2016 Final ______Contestant's Number ______2nd ______1st ______Read directions carefully DO NOT UNFOLD THIS SHEET Score Initials before beginning test UNTIL TOLD TO BEGIN

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

STOP -- WAIT FOR SIGNAL!

(1) 6102 qq 524 423 = ______(19) 4 gallons qq 2 quarts 2 pints = ______cups

(2) 234‚ 5 = ______*(20) 815‚ 1947 = ______

(3) 1947ƒ 3 = ______(21) 2532 4 8 = ______

(4) 0.1875 = ______(proper fraction) (22) What number divided by four gives the same result as that number minus twelve? ______(5) 55% = ______(proper fraction) (23) Let x = qq 1. Find 3x2 6x 9 . ______(6) 312 = ______(24) The sum of three consecutive even integers is 144. (7) 5q‚ƒ 2 3 5 (2 q 4) 20 ‚ 1 6 = ______The smallest of the three integers is ______

3 11 (8) 13 = ______(25) 42‚ 2 10 = ______(mixed number)

(9) 1111967ƒ 9 has a remainder of ______26 (26) 23‚ 29 = ______(mixed number) *(10) 246 qq 1357 2134 711 = ______4 (27) What is 27% of 4449 = ______11 (11) 443 3 = ______(mixed number) (28) 0.02555... = ______(proper fraction) (12) 135‚ 12 = ______(29) F = {f,o,r,t,y}, S = {s,i,x,t,y}, and E = {e,i,g,h,t,y}. (13) 42325ƒ 8 has a remainder of ______(F S) E has how many distinct elements? _____ 2 (14) 125% of 88 = ______*(30) 43 ‚ƒ 1423 14 = ______

22 22 (15) 553 q 3 = ______(mixed number) (31) 15 45 = ______

(16) If 8 úú 's cost $6.40 then 5 's cost $ ______(32) If 7x q 5 = 3, then 7x 1 = ______

(17) 37‚‚ 14 14 33 = ______(33) 213 base 4 in base 10 is ______

(18) CXXV‚ XLIV = ______(Arabic numeral) (34) If a = 22 and b = 14, then 4a22 q 4ab b = ______3 9 2 (35) = ______(58) Find the units digit of 187 . ______Š‹16

(36) Given the set {1,5,12,22,m,51,70,n,117, 145,... }. (59) The odds of selecting a pentagonal number from Find m n. ______the set of digits is ______(proper fraction)

(37) 36‚ 53 = ______*(60) 4232016ƒ 425 = ______(61) The sum of the reciprocals of all of the positive (38) 453 4 = ______(mixed number) 88‚ divisors of 35 is ______(39) (2244 66) 8 has a remainder of ______ ‚ƒ (62) 710 ƒ 13 has a remainder of ______

*(40) È 523524 = ______(63) The Greatest Integer Function is written as 5 1 (41) 31 39 16 = ______f(x) = [] x . Find È q 3.14 . ______‚ ’“2

42k3 q (42) Let 39‚ƒ 39 39 = 39 . Find k. ______(64) If log8 (4x 3) = 2 then x = ______

2 (43) The sum of the roots of 9x qq 6x = 1 is ______(65) 524666 423 201 = ______6

(44) The area of a right triangle with a base of 40 cm (66) Change 0.4232323... 5 to a base 10 fraction. ______and a hypotenuse of 41 cm is ______cm2 (67) How many positive integers less than 20 are (45) The midpoint of the segment with end points relatively prime to 20? ______(qq 1, 3) and (6, 10) is (x, y). Find x y. ______2 51 (68) 1 q cos (3 ) = ______(46) If 3 qqq 211 x = 6 then x = ______(69) The first four digits of the decimal for 7 is 0.___ (47) Which of the following is an odious number, 11 3, 5, or 7? ______*(70) 22222 4 6 8 ... 14 2 16 2 = ______(48) The sum of the integral values of x such that x qqŸ 2 4 6 is ______(71) Truncate 5È 6 to the nearest tenth. ______¸¸ 22 (49) The sum of the number of faces, the number of (72) The largest element of the range of y = 16 q x sides, and the number of vertices of a Platonic is ______icosahedron is ______2 q 1 (73) If f(x) = x 3 qq 1, then f ( 4) = ______*(50) 424‚‚ 3 2 5 = ______1 (74) (3x q 4) dx = ______(51) (2ƒ 3ii ) 5 = (a b i ). Find (a b). ______'q 1 (52) Find the 5th term of the geometric sequence, (75) If 3x q´ 2 4(mod 8), 0 ŸŸ x 7, then x = ______81, qq 27, 9, 3, ... . ______(76) The 1st triangular number times the 2 nd hexagonal number times the 3rd pentagonal number is ______(53) 75CP53‚ = ______x 54xx (x x 1) (77) The domain of the function È Ln(e ) is x _____ (54) If 6xxx = , then x = ______(78) How many subsets containing only 4 elements (55) 8 15 23 38 61 ... 160 259 = _____ does the set {r,e,g,i,o,n} have? ______

(56) The sum of the coefficients of the x32 y term and (79) 442 ƒ‚ 22 2 11 2 = ______the xy4 term of (x y)5 is ______*(80) The interest on $5000 for 2.5 years at a simple (57) 423‚ 425 = ______interest rate of 1.5% is ______dollars (integer) University Interscholastic League - Number Sense Answer Key HS ìì Regional 2016 *number) x y means an integer between x and y inclusive 2 NOTE: If an answer is of the type like 3 it cannot be written as a repeating decimal

(19) 52 27 (58) 2 (1) 5,155 (35) 64 *(20) 1,507,465 q 1 (2) 1,170 (36) 127 (59) 4 1,666,145 (3) 649 (37) 1,908 *(60) 9,460 q 10,455 (21) 160 3 15 (4) (38) 20 (61) 48 , 1 13 16 (22) 16 64 35 35 11 (5) 20 (23) q 12 (39) 6 (62) 4

(6) 961 (24) 46 *(40) 688 q 759 (63) q 2 61 1 (7) 21.5, 43 , 21 1 9 (41) 1,225 (64) 15.25, , 15 22 (25) 9 20 44 (42) q 1 (8) 2,197 18 (65) 1552 (26) 20 29 2 (43) 3 109 (9) 8 (27) 120 (66) 120 (44) 180 *(10) 297 q 327 23 (67) 8 (28) 900 (11) 7 7 (45) q 1 3 12 (29) 3 (68) .75, 4 (46) 18 (12) 1,620 *(30) 451 q 498 (69) 6363 (47) 7 (13) 5 (31) 2,250 *(70) 776 q 856 (48) 42 (14) 110 61 1 (32) 9 (71) 12.2, 55 , 12 11 (49) 62 (15) 1 15 (33) 39 (72) 4 *(50) 39,399 q 43,545 (16) $4.00 (34) 900 11 2 (73) qq 33 , 3 (51) .2, 1 (17) 980 5 (74) q 8 (18) 5,500 (52) 1 (75) 2 (53) 1,260 (76) 72 (54) 3 (77) 0 (55) 663 (78) 15 (56) 15 (79) 484 (57) 179,775 *(80) 179 q 196