The University Interscholastic League Number Sense Test ììHS 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. The person conducting this contest should explain these directions to the contestants. 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) È2197 = ___________________________________ (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) È12515 = __________________________________ 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) = Èx 2 , then f (4) = _______________ 1, 1, 2, 3, ... ______________________________ (76) f(x) = 2x32 6x 6x 2. Find fw ( q 1) = _______ 41x (54) If = , 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 ììInvitation 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 ììHS 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 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. 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 .