Mathematics 3201 Sample Mid-Year Exam #2, Item Breakdown/Solutions

Transcription

1 Mathematics 01 Sample Mid-Year Eam #, Item Breakdown/Solutions PART I: # Ans M A L Guide Outcome # Ans M A L Guide Outcome 1 A X p. LR 19 D X p.9 P A X p.4 LR 0 A X p.88 P B X p.6 LR 1 D X p.88 P 4 C X p.6 LR B X p.84 P5 5 D X /0 LR B X p.9 P 6 A X p.4 LR 4 C X p.84 P6 7 D X p.0 LR 5 D X 9/94 P 8 B X p.5 P4 6 B X p.100 RF1 9 D X 5/58 P4/P5 7 A X p.100 RF1 10 C X p.58 P5 8 C X p.10 RF1 11 D X p.60 P5 9 B X p.104 RF1 1 B X p.64 P5 0 D X p.104 RF1 1 A X p.68 P5 1 A X p.106 RF 14 A X p.68 P5 D X p.106 RF 15 C X p.70 P5/P6 B X p.108 RF 16 B X 70/7 P6 4 C X p.108 RF 17 A X p.7 P6 5 C X p.114 RF 18 C X 80/8 P1 PART II: Item Value LA L Guide Outcome Item Value LA L Guide Outcome 6a X p.4 LR 8b X 80/84/9 P1/P/P6 6b X p.0 LR 8c X p.8 P6 7a X p.64 P5 9ai 1 X p.106 RF 7b X 5/5 P4 9aii X p.106 RF 7c X p.74 P5/P6 9b X p.106 RF 7d X p.64 P4 9c 4 X p.114 RF 8a X 84/86 P5

2 PART II - Total Value: 5 marks Answer ALL items in the space provided. Show ALL workings. Value 6(a). Students were surveyed on what beverage(s) they have ordered at the cafeteria. 10 ordered milk 140 ordered juice 170 ordered water 40 had ordered juice and milk 70 had ordered juice and water 50 had ordered milk and water 0 had ordered all three 0 had not ordered any beverage Draw a Venn diagram to illustrate this information and use it to determine how many students were surveyed. Venn diagram ( marks) M J W 0 = = 40 The # of students surveyed was 40. Page of 7 Mathematics 01 Sample Mid-Year Eam #, , Item Breakdown/Solutions

3 6(b). In a group of 5 people: 18 people own a laptop computer 19 people own a desktop computer 17 people own a tablet computer 5 people own a laptop and a desktop but not a tablet 6 people own a desktop and a tablet but not a laptop people own all three types of computers 4 people do not own either type of computer Determine the number of people who own a laptop and a tablet, but not a desktop. Laptop Desktop Tablet 4 (10 ) + + (8 ) = 5 (1.5 marks) 41 = 5 = 6 = 6 The # of children who own a laptop and a tablet, but not a desktop, is 6. 7(a). In how many ways can a teacher arrange 9 students in a line if Alice, Bob, and Carol must be seated together? 7!! (1.5 marks)= 040 Page of 7 Mathematics 01 Sample Mid-Year Eam #, , Item Breakdown/Solutions

4 7(b). In Newfoundland and Labrador a license plate consists of a letter-letter-letterdigit-digit-digit arrangement such as CRT 1. i) How many arrangements are possible if a license plate must start with C and end in when repetition is allowed? = ii) How many arrangements are possible if a license plate must start with C and end in when repetition is not allowed? = 400 7(c). Algebraically solve for n: nc = 10 n!!(n )! = 10 n(n 1)(n )!!(n )! = 10 n(n 1) = 10 n(n 1) = 40 n n = 40 n n 40 = 0 (n 16)(n + 15) = 0 n = 16 or n = 15 7(d). Given the digits 1,,, 4, and 5, how many two or three digit even numbers can be made if repetition is not allowed? (4 ) 8 two digit even numbers no repetition (4 ) 4 three digit even numbers no repetition (1. 5 marks) two or three digit even numbers no repetition Page 4 of 7 Mathematics 01 Sample Mid-Year Eam #, , Item Breakdown/Solutions

5 8(a). Nine horses are entered in a race and each one is equally likely to win. To the nearest percent, determine the probability that one horse, Mr. Mal, will not finish in the top three. Show your workings. P(Mr. Mal in top three) = 8! + 8! + 8! 9! P(Mr. Mal in top three) = (8!) 9 8! = 9 = (8!) 9! P(Mr. Mal not in top three) = 1 = =67% OR Probability of Mr. Mal ending up in either of the 9 places is 1 9 not in the top, then for each position 9 th through 4 th : =67%. Therefore, if (1. 5 marks) = 8(b). There are 6 blue marbles, red marbles, and 1 green marble in a bag. If you reach in and randomly select marbles from the bag, what are the odds of them both being blue? P( blue marbles) = = 1 Therefore, P(not blue marbles) = 1 1 = Therefore, odds of them both being blue: 1 1: (1.5 marks) OR P(both blue)= 6 C 10C = 6!!4! 10!!8! = = = 1 Therefore, P(not blue marbles) = 1 1 = Therefore, odds of them both being blue: 1 1: (1.5 marks) 8(c). A committee of 4 people is chosen at random from 5 married couples. What is the probability that the committee contains no married couples? There are( 10 C 4 ) ways to choose 4 committee members from 10 people. There are( 5 C 4 ) ways to choose 4 couples and there are( C 1 ) ways to choose 1 personfrom each couple. Therefore, P(committee contains no individuals married to each other) = 5C 4 C 1 C 1 C 1 C 1 ( marks) = 10C 4 5 ( ) = 8 1 Page 5 of 7 Mathematics 01 Sample Mid-Year Eam #, , Item Breakdown/Solutions

6 9(a). Karen simplified an epression as follows: = = 4 +4 (+4)( 4) = 1 4 = Step 1 Step Step Step 4 1 (i) Identify the step in which the error occurred and eplain the mistake. The error occurred in Step 1. She divided + 8 and 8 by instead of factoring out a. (ii) Correct the error and simplify. (+4) (+4)( 4) = 4 = 4 ( 4) = 4 ( 4) = 1 ( 4) ( 4) ( 4) (1.5 marks) 9(b). Simplify: 10( ) , 6,,, 6 = 10( ) = 10( ) ( 6)(+6) 4(+6) ( )(+) = 10( 6) 4(+) = 5( 6) (+) Page 6 of 7 Mathematics 01 Sample Mid-Year Eam #, , Item Breakdown/Solutions

7 4 9(c). A school volleyball team and its chaperones are going to a tournament out of the province that has a total cost of $700. The cost of the trip is to be divided amongst everyone going. At the last minute, two people get sick and cannot attend, increasing the cost per person by $40. If represents the number of people travelling and the situation is modelled by = 40, algebraically determine the number of people who originally planned to attend the tournament. ( ) [ 700 ] ( ) [700] = 40( ) 700 ( ) = = = 0 60 = 0 ( 0)( + 18) = 0 = 0; is an etraneous root 0 people Page 7 of 7 Mathematics 01 Sample Mid-Year Eam #, , Item Breakdown/Solutions