Name: Class: Date: Math 12 - Unit 4 Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A combination lock opens with the correct three-digit code. Each wheel rotates through the digits 1 to 8. How many different three-digit codes are possible? A. 24 B. 64 C. 512 D. 1024 2. Evaluate. (3!) 2 A. 8 B. 9 C. 18 D. 36 3. Evaluate. 10! 9! + 3! A. 13 B. 16 C. 20 D. 23 4. Solve for n, where n I. Ê (n + 1)! ˆ 2 Ë Á n! = 40 A. 10 B. 19 C. 20 D. 39 1
Name: 5. Evaluate. 21P 2 A. 441 B. 420 C. 399 D. 2 097 152 6. Suppose a word is any string of letters. How many two-letter words can you make from the letters in LETHBRIDGE if you do not repeat any letters in the word? A. 72 B. 100 C. 81 D. 90 7. Solve for n. np 4 = 120 A. n = 5 B. n = 6 C. n = 7 D. n = 8 8. Solve for n. n 2P 2 = 30 A. n = 5 B. n = 6 C. n = 7 D. n = 8 9. Evaluate. 15! 10! 3! 2! A. 30 030 B. 30 300 C. 60 060 D. 60 600 2
Name: 10. How many different arrangements can be made using all the letters in ATHABASCA? A. 60 480 B. 10 080 C. 15 120 D. 90 720 11. There are 14 members of a student council. How many ways can 4 of the members be chosen to serve on the dance committee? A. 1001 B. 2002 C. 6006 D. 24 024 12. How many ways can 4 representatives be chosen from a hockey team of 17 players? A. 2380 B. 57 120 C. 31 060 D. 9575 13. Identify the term that best describes the following situation: Determine the number of pizzas with 4 different toppings from a list of 40 toppings. A. permutations B. combinations C. factorial D. none of the above 14. How many ways can the 6 starting positions on a hockey team (1 goalie, 2 defense, 3 forwards) be filled from a team of 2 goalies, 4 defense, and 7 forwards? A. 420 B. 500 C. 858 D. 1716 3
Name: 15. Euchre is played with a deck of 24 cards that is similar to a standard deck of 52 playing cards, but with only the ace, 9, 10, jack, queen, and king for all four suits. How many different five-card hands are there with at least three clubs? A. 375 B. 926 C. 3336 D. 10 626 Short Answer 1. Indicate whether the Fundamental Counting Principle applies to this situation: Counting the number of possibilities when drawing a face card from a standard deck. 2. There are nine different marbles in a bag. Suppose you reach in and draw one at a time, and do this six times. How many ways can you draw the six marbles if you do not replace the marble each time? 3. How many different routes are there from A to B, if you only travel south or east? 4
Name: 4. How many different routes are there from A to B, if you only travel north or east? 5. A physics teacher has three topics for students to research: baryons, mesons, and leptons. How many different ways can her class of 24 students be divided evenly among the 3 topics? 6. A physics teacher has four topics for students to research: reflection, refraction, the visible spectrum, and the speed of light. How many different ways can her class of 24 students be divided evenly among the 4 topics? 7. How many ways can the top four cash prices be awarded in a lottery that sold 150 tickets if each ticket is replaced when drawn? 5
Math 12 - Unit 4 Review Answer Section MULTIPLE CHOICE 1. ANS: C PTS: 1 DIF: Grade 12 REF: Lesson 4.1 OBJ: 4.1 Represent and solve counting problems, using a graphic organizer. 4.2 Generalize the fundamental counting principle, using inductive reasoning. 4.3 Identify and explain assumptions made in solving a counting problem. 4.4 Solve a contextual counting problem, using the fundamental counting principle, and explain the reasoning. TOP: Counting Principles KEY: counting Fundamental Counting Principle 2. ANS: D PTS: 1 DIF: Grade 12 REF: Lesson 4.2 OBJ: 5.1 Represent the number of arrangements of n elements taken n at a time, using factorial notation. 5.2 Determine, with or without technology, the value of a factorial. 5.3 Simplify a numeric or algebraic fraction containing factorials in both the numerator and denominator. 5.4 Solve an equation that involves factorials. TOP: Introducing Permutations and Factorial Notation 3. ANS: B PTS: 1 DIF: Grade 12 REF: Lesson 4.2 OBJ: 5.1 Represent the number of arrangements of n elements taken n at a time, using factorial notation. 5.2 Determine, with or without technology, the value of a factorial. 5.3 Simplify a numeric or algebraic fraction containing factorials in both the numerator and denominator. 5.4 Solve an equation that involves factorials. TOP: Introducing Permutations and Factorial Notation 4. ANS: B PTS: 1 DIF: Grade 12 REF: Lesson 4.2 OBJ: 5.1 Represent the number of arrangements of n elements taken n at a time, using factorial notation. 5.2 Determine, with or without technology, the value of a factorial. 5.3 Simplify a numeric or algebraic fraction containing factorials in both the numerator and denominator. 5.4 Solve an equation that involves factorials. TOP: Introducing Permutations and Factorial Notation 5. ANS: B PTS: 1 DIF: Grade 12 REF: Lesson 4.3 6. ANS: A PTS: 1 DIF: Grade 12 REF: Lesson 4.3 7. ANS: A PTS: 1 DIF: Grade 12 REF: Lesson 4.3 1
8. ANS: D PTS: 1 DIF: Grade 12 REF: Lesson 4.3 9. ANS: A PTS: 1 DIF: Grade 12 REF: Lesson 4.4 OBJ: 5.6 Determine the number of permutations of n elements taken n at a time where some elements are not distinct. 5.7 Explain, using examples, the effect on the total number of permutations of n elements when two or more elements are identical. TOP: Permutations When Objects Are Identical 10. ANS: C PTS: 1 DIF: Grade 12 REF: Lesson 4.4 OBJ: 5.6 Determine the number of permutations of n elements taken n at a time where some elements are not distinct. 5.7 Explain, using examples, the effect on the total number of permutations of n elements when two or more elements are identical. TOP: Permutations When Objects Are Identical 11. ANS: A PTS: 1 DIF: Grade 12 REF: Lesson 4.5 OBJ: 4.3 Identify and explain assumptions made in solving a counting problem. 5.1 Represent the number of arrangements of n elements taken n at a time, using factorial notation. TOP: Exploring Combinations KEY: counting combination factorial notation 12. ANS: A PTS: 1 DIF: Grade 12 REF: Lesson 4.6 OBJ: 6.1 Explain, using examples, why order is or is not important when solving problems that involve permutations or combinations. 6.2 Determine the number of combinations of n elements taken r at a time. 6.3 Generalize strategies for determining the number of combinations of n elements taken r at a time. TOP: Combinations KEY: counting combination 13. ANS: B PTS: 1 DIF: Grade 12 REF: Lesson 4.7 TOP: Solving Counting Problems KEY: counting permutation combination 14. ANS: A PTS: 1 DIF: Grade 12 REF: Lesson 4.7 TOP: Solving Counting Problems KEY: counting permutation combination 2
15. ANS: C PTS: 1 DIF: Grade 12 REF: Lesson 4.7 TOP: Solving Counting Problems KEY: counting combination Fundamental Counting Principle SHORT ANSWER 1. ANS: no PTS: 1 DIF: Grade 12 REF: Lesson 4.1 OBJ: 4.1 Represent and solve counting problems, using a graphic organizer. 4.2 Generalize the fundamental counting principle, using inductive reasoning. 4.3 Identify and explain assumptions made in solving a counting problem. 4.4 Solve a contextual counting problem, using the fundamental counting principle, and explain the reasoning. TOP: Counting Principles KEY: counting Fundamental Counting Principle 2. ANS: 60 480 PTS: 1 DIF: Grade 12 REF: Lesson 4.3 3. ANS: 100 PTS: 1 DIF: Grade 12 REF: Lesson 4.4 OBJ: 5.6 Determine the number of permutations of n elements taken n at a time where some elements are not distinct. 5.7 Explain, using examples, the effect on the total number of permutations of n elements when two or more elements are identical. TOP: Permutations When Objects Are Identical 4. ANS: 525 PTS: 1 DIF: Grade 12 REF: Lesson 4.4 OBJ: 5.6 Determine the number of permutations of n elements taken n at a time where some elements are not distinct. 5.7 Explain, using examples, the effect on the total number of permutations of n elements when two or more elements are identical. TOP: Permutations When Objects Are Identical 3
5. ANS: 9 465 511 770 PTS: 1 DIF: Grade 12 REF: Lesson 4.7 TOP: Solving Counting Problems KEY: counting combination Fundamental Counting Principle 6. ANS: 2 308 743 493 056 PTS: 1 DIF: Grade 12 REF: Lesson 4.7 TOP: Solving Counting Problems KEY: counting combination Fundamental Counting Principle 7. ANS: 506 250 000 PTS: 1 DIF: Grade 12 REF: Lesson 4.7 TOP: Solving Counting Problems KEY: counting Fundamental Counting Principle 4