The University Interscholastic League
Number Sense Test ì HS SAC ì 2015
Contestant's Number ___________
Read directions carefully
before beginning test
DO NOT UNFOLD THIS SHEET
UNTIL TOLD TO BEGIN
Final ______
______
2nd
______
______
1st
______
______
Score
Initials
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) 915  519 = _________________________________
(18) CCLVIII = __________________ (Arabic Numeral)
(2) 337 q 245 = ________________________________
(19) 2 yards  1 foot = _____________________ inches
(3) 231 ‚ 4 = __________________________________
*(20) 92015 ƒ 498 = ______________________________
(4) 2418 ƒ 6 = __________________________________
(21) 32  92 = __________________________________
(5) 44% = _______________________(proper fraction)
(22) 9  ¸15 q 10¸ q ¸1 q 5¸ = ____________________
(6) 3 45 = ______________________________ (decimal)
(23) If 6 eggs cost 78¢ then 9 eggs cost $ _____________
(7) 0.125 = ______________________ (proper fraction)
(24) 2  4  6  8  ...  18  20 = _______________
(8) 8  12 ‚ 4 ƒ 6 = ____________________________
(25) The sum of the prime numbers less than 10 is ____
(9) 162 = ______________________________________
3
(26) È
729 = ____________________________________
*(10) 2016  201  216  26 = _____________________
(27) 15% of 233 13 = ______________________________
(11) 1 12  2 23 = ____________________ (mixed number)
(28) Let x = q 5. Find 4  3x. _____________________
(12) 64 ‚ 25 = __________________________________
(29) Set m = {m,e,n,t,a,l} and M = {m,a,t,h}. M  m
contains how many distinct elements? ___________
(13) 345 ƒ 9 has a remainder of ___________________
(14) 15% of 38 = ________________________________
6
(15) Which is smaller, 49 or 11
? ____________________
(16)
2 23
q 1 12
*(30) 2 14 ‚ 92015 ƒ 9 = ___________________________
(31) 44 base 5 in base 10 is ________________________
(32) If 5 q 2x = 3, then 2  3x = ___________________
= ___________________ (mixed number)
(17) The GCD of 28, 56, and 63 is __________________
(33) 0.151515... = _________________ (proper fraction)
(34) 2 23 ‚ 1 12 = _________________________________
(58) 151 ‚ 212 = ________________________________
(35) (17 ‚ 22  35) ƒ 4 has a remainder of __________
(59) The probability of selecting a prime number from
the set of digits is __________________________%
(36) 37 ‚ 43 = __________________________________
(37) 12 ‚
13
14
= ________________ (mixed number)
(38) The perimeter of a rectangle with a of length of
4.25" and a width of 3.25" is ____________ inches
(39) If a = 13 and b = 8, then a2  2ab  b2 = ________
*(40) È 91015 = __________________________________
(41) 20% of 30 q 40% of 50 is _____________________
(42) Let 123 ‚ 12q 5 = 12k . Find k. _________________
*(60) 69875 ƒ 142.857 = ___________________________
(61) The sum of the positive integral divisors of 20 is __
(62) ( x3 q 6x q 10) ƒ (x q 2) has a remainder of ____
(63) Find k if º
k
2
3
= 7. k = __________________
q 5º
(64) If log5 (2x  1) = 3 then x = ___________________
(65) The volume of a cone with a diameter of 8" and a
height of 12" is _______________________1 cu. in
(43) 13 ‚ 15  1 = _______________________________
(66) Change 0.22 base 4 to a base 8 decimal. ________8
(44) The midpoint of the segment with endpoints (1, 3)
and (5, 7) is (x, y). Find x  y. _________________
(67) The Greatest Integer Function is written as
f(x) = [x]. Find’sin 30°  cos 30°“. ____________
(45) 2347  567 = ______________________________7
(68) F(x) = 3x2 q 1. G(x) = 3  2x. F(G(q1)) = _______
(46) The leg opposite the 30° angle in a right triangle is
6 inches. The hypotenuse is _____________ inches
(69) sin2 ( 231 )  cos2 ( 231 ) = _______________________
(47) If 5 q 1  x q 1 = 2 q 1 then x = ________________
(48) The product of the roots of (x  3)2 = 0 is ________
*(70) (2  4  6  8  10  12  14)2 = _____________
(71) The sum of the first 3 pentagonal numbers is _____
(49) The least value of x such that ¸x q 1¸ Ÿ 3 is ______
(72) The first four digits of the decimal for 16
90 is 0.___
*(50) 152 ‚ 113 = _________________________________
(51) (5  6i) (5 q 6i) = (a  bi). Find (a  b). ________
(74) The domain of the function È 2 q 3t is t Ÿ ______
(52) The number of Platonic solids is _______________
(75) If f(x) = 1  2x 4q 3 , then f q 1 (5) = ______________
(53) Find the 8th term of the arithmetic sequence,
11, 8, 5, 2, ... . ______________________________
(54)
3x
4x
= _______________________________________
(55) 8 C6 q 8 P2 = ________________________________
(56) How many subsets containing only 4 elements
does the set {p,r,e,c,a,l} have? __________________
(57) The sum of the terms in the 4th row of Pascal's
triangle is __________________________________
(73) 1110 ƒ 9 has a remainder of ___________________
(76) Let f(x) = x3 q 5x2  2x  4. Find f w (3) = _______
(77)
' 12 (2x q 1) dx
= ___________________________
(78) Round 3È 2 to the nearest tenth. _____________
(79) The minimum value of f(x) = 3(x q 2)2  5 is ____
*(80) The interest on $5000 for 5 years at 5.5%
compounded annually is ________________ dollars