MATH 100 EXAM 1 Millersville University Fall 2007 Ron Umble Instr Name INSTRUCTIONS Turn off and stow all cell phones and pagers Calculators may be used but cell phone may not be used as calculators MULTIPLE CHOICE Choose the one alternative that best completes the statement or answers the question Determine the most probable next term in the sequence 1 486 162 54 18 6 A 1 1 B 2 Use the method of Gauss to find the sum 2 1 2 3 875 A 191 406 25 B 382 812 5 C 3 2 D 3 C 383 250 D 767 376 2 Use the method of successive differences to determine the next term in the sequence 3 14 20 31 47 68 A 89 B 98 C 99 3 D 94 Use problem solving strategies to solve the problem 4 I m thinking of a number between 4 and 10 If I square my number and find the difference of the digits I will end up with the cube root of my number What is my number A 8 B 6 C 4 D 13 Solve the problem 5 If you raise 9 to the 387th power what is the units digit of the result A 6 B 9 C 1 4 5 D 7 In a school survey students showed these preferences for instructional materials Answer the question 6 About how many students would you expect to prefer computers in a school of 650 students A About 130 students B About 36 students C About 117 students D About 234 students 1 6 Complete the magic addition square A magic square has the property that the sum of the numbers in any row column or diagonal is the same 7 7 Use each number 3 4 5 6 7 8 9 10 and 11 once 6 5 10 7 3 8 B A 6 11 5 7 10 3 4 9 8 C 6 5 10 9 11 7 4 3 8 D 6 11 5 7 10 3 9 4 8 6 5 10 9 4 7 11 3 8 Write the set in set builder notation 8 2 4 6 8 A x x is any even natural number B x x is an even natural number less than 10 C x x is any even integer less than 10 D 2 4 6 8 8 Find n A for the set 9 A x x is a month in the year A n A 12 B n A 52 9 C n A 1 D n A 24 Decide whether both or neither can be placed in the blank to make a true statement 10 11 12 13 10 11 12 13 A B Neither C D Both and 10 Find the number of subsets of the set 11 6 7 8 A 6 B 7 11 C 8 D 3 Find the number of proper subsets of the set 12 3 4 5 A 2 B 7 C 6 D 5 12 Let U 1 2 4 5 a b c d e Find the complement of the set 13 Q 2 4 b d A 1 3 5 a c e B 1 5 a c e C 1 5 a e D 1 2 4 5 a b c d e 13 List the elements in the set Let U q r s t u v w x y z A q s u w y B q s y z C v w x y z 14 A B A q s t u v w x y C r t u v w x z 14 B s u w D t v x 2 15 C A A q r s t u v x z C s t B w y D q s u v w x y z 16 A C B A v x C r t u v w s y z B r t v w x D y z 15 16 Find the Cartesian product 17 A 12 9 10 B 14 4 Find A B A 12 14 9 10 10 14 B 12 14 9 4 C 14 12 14 9 14 10 4 12 4 9 4 10 D 12 14 12 4 9 14 9 4 10 14 10 4 17 Find the indicated cardinal number 18 Find n A B given that A 2 and B 1 3 A 2 B 1 18 C 4 3 D 3 For the given sets construct a Venn diagram and place the elements in the proper region 19 Let U 1 2 3 4 5 6 7 8 A 3 6 8 B 4 6 C 1 6 7 8 A B C D 20 U a b c d e f g h i j k l m n o p A a e i o B b c d f g h j k l m C a b c d e f g 19 20 4 A B C D Show that the set is infinite by placing it in a one to one correspondence with a proper subset of itself Be sure to show the pairing of the general terms in the sets 21 5 6 7 8 21 A 5 6 7 8 n 4 B 5 6 7 8 n 4 4 5 6 7 n 3 6 7 8 9 n 5 D 5 6 7 8 n 5 C 5 6 7 8 n 4 6 7 8 9 n 6 4 5 6 7 n 3 Let p represent a true statement while q and r represent false statements Find the truth value of the compound statement 22 p q r 22 A False B True Let p represent 7 8 q represent 2 5 6 and r represent 3 2 Decide whether the statement is true or false 23 p q r 23 A True B False 5 Construct a truth table for the statement 24 r s A r s r s T T F F C r T F T F s F T T T r s T T F F T F T F F F F T 24 B r s r s T T T T F F F T F F F T D r s r s T T F F T F T F F F F F Use De Morgan s laws to write the negation of the statement 25 A day late and a dollar short A A day late or not a dollar short B Not a day late and not a dollar short C Not a day late and a dollar short D Not a day late or not a dollar short Solve the problem 26 Given that p q is false what can you conclude about the truth values of p and q A Exactly one of p and q is false B At least one of p and q is false C Both p and q are false D p and q have the …