The University Interscholastic League
Number Sense Test ì HS SAC ì 2013
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) 213  214 = _________________________________
(18) The mean of 1, 4, 9, 16, and 25 is _______________
(2) 213 ‚ 4 = __________________________________
(19) 201314 ƒ 9 has a remainder of ________________
(3) 412 q 213 = ________________________________
*(20) 2013 ‚ 2014 = ______________________________
(4) 312 ƒ 4 = ___________________________________
(21) 3  6 ‚ 10 q 6 ƒ 3 = ________________________
(5) 34% = ______________________ (proper fraction)
(22) 6 25 ‚ 6 35 = ___________________ (mixed number)
(6) 43 ‚ 21 = ___________________________________
(23) 4.555...  2.777... = _________________________
(7) 2 13  2 14 = ____________________ (mixed number)
(24) 3(q 1) q 3(q 2) = _____________________________
(8) 13 ‚ 20  20 ‚ 14 = _________________________
(25) Set A has 6 elements and set B has 8 elements. If
A  B has 4 elements, then A  B has ___ elements
(9) 20.13 ƒ 0.4 = _______________________ (decimal)
(26) (26  35 q 44) ƒ 8 has a remainder of __________
*(10) 927  1009  2013 = _________________________
(27) The multiplicative inverse of 3.4 is ______________
(11) 1  2 ‚ 3 ƒ 4 q 5 = _________________________
(28) 30 inches/minute = __________________ feet/hour
(12) 63 ‚ 43 = __________________________________
(29) Find k if 26 2 q 21 2 = 5k. k = ________________
(13) 25% of 25 = ________________________________
(14) Which is smaller,
7
8
or
8
9?
_____________________
(15) The GCD of 48 and 84 is _____________________
(16) 12 feet q 3 yards = _____________________ inches
(17) DLV = ______________________ (Arabic Number)
*(30) 14 34 ‚ 2006 ƒ 15 = __________________________
(31) 113 = ______________________________________
(32) 1 q ¹3 q ¸6 q 10¸¹ = _________________________
(33) Find the sales tax on an item costing $90.00 if the
sales tax rate is 8%. $ ________________________
(34) 4 ‚ 3x  5 ‚ 4x = ____________________________
(59) 24  18  13 12  10 18  ... = __________________
(35) If 4 q 3x = 10, then 3x  4 = __________________
*(60) 182 ‚ 222 = ________________________________
(36) 321 base 4 = _________________________ base 10
(37) If a = 15 and b = 16, then a2  2ab  b2 = _______
(38) 14 (242 q 42 ) = _______________________________
(39) È 54  È 24 = È x . Find x. _______________
*(40) 49 x 61 x 73 = ______________________________
(41) 9142013 ƒ 11 has a remainder of ______________
(42) The slope of the line containing the points
(2, 3) and (5, 7) is ____________________________
(43) If 6x = 432 then 6(x1) = ______________________
(44) 101 ‚ 108 = ________________________________
(45) Let 4x q 2y = 1 and 3x  2y = 2. Find x. ________
(46) The leg opposite the 60° angle in a right
triangle is 2È 3 cm. The hypotenuse is ______ cm
(47) If x q y = 2 and x  y = 3 then
x2
q
y2
= _______
(48) 38 q 28
71 = ___________________________________
(49)
52
‚ 25
= ___________________________________
*(50) 82 ‚ 43 ƒ 24 = ______________________________
4
(51) 444 ‚ 37
= _________________________________
(52) 2357  1467 = _____________________________ 7
(53) The area of x2  y2 = 9 is k1. k2 = ___________
(61) 282 q 262  242 q 222 = _____________________
(62) If 4x  3x  2x z x (mod 5), where
0 Ÿ x Ÿ 4, then x = __________________________
(63) The sum of the coefficients of (x  2y)3 is ________
(64) If f(x) = 4x3  3x2 q 2x  1, then f ww (0) = _______
(65) The sum of the first ten terms of the Fibonacci type
sequence 3,7,10,17,27,... is ____________________
(66) Change 0.333... base 6 to a base 6 fraction. _____ 6
(67) How much time has past from 8:30 a.m.
to 3:45 p.m. in one day? _______________ minutes
(68) 13
37 ‚ 111 = _________________________________
(69) log5 8 ƒ log5 4 ‚ log5 2= log5 È k. Find k. _______
*(70) È 956230 = _________________________________
(71) If f(x) = 2x q 3, then f q 1 (4) = _________________
1
(72) 2(sin 1
6 )(cos 3 ) = ___________________________
1
1
1
(73) 16  12
 20
 30
= _________________________
È5  1
2
(74) The Greatest Integer Function is written as
f(x) = [x]. Find’
“. ___________________
(75) A number is randomly drawn from the set
{2,1,3,4,7}. What are the odds that the number
drawn is not a prime number? _________________
(54) If log 4 8 = x then x = _________________________
(76) If det”
(55) 5 C3  5 P2 = _______________________________
(77) The 18th triangular number is _________________
(56) The larger root of 7x2  22x  3 = 0 is _________
(78)
(57) How many 3-element subsets does the set
{n, u, m, b, e, r} have? ________________________
(79) If x  0 and x2 = È x3  x3  x3 then x = _______
(58) (2 q 3i) (2 q 3i) = (a  bi). Find a q b. _________
*(80) 5.5 rods = ____________________________ inches
1
3
q6
= 28, then x = _________________
x •
' 01 (2  3x) dx
= ___________________________