ExamView - Untitled - MrTrenholm - homemrtrenholm.wikispaces.com/file/view/Quizzes+2011.pdfName: _____ ID: A 3 9. Austin made the following conjecture: As you travel farther south,

Name: ________________________ Class: ___________________ Date: __________ ID: A

1

Sept 9 2011

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

____ 1. Gary works at a bicycle store in Vancouver. For the start of spring, the manager of the store has ordered 50 mountain bikes and 10 racing bikes.

Which conjecture is Gary most likely to make from this evidence?

a. Either type of bike will sell equally well.b. Racing bikes will likely sell better than mountain bikes.c. It will rain all summer and no one will ride bicycles.d. Mountain bikes will likely sell better than racing bikes.

____ 2. Emma works part-time at a bakery shop in Saskatoon. Today, the baker made 20 apple pies, 20 cherry pies, and 20 bumbleberry pies. Which conjecture is Emma most likely to make from this evidence?

a. People are more likely to buy bumbleberry pie than any other pie.b. People are more likely to buy apple pie than any other pie.c. Each type of pie will sell equally as well as the others.d. People are more likely to buy cherry pie than any other pie.

____ 3. Justin gathered the following evidence.

17(22) = 374 14(22) = 308 36(22) = 742 18(22) = 396

Which conjecture, if any, is Justin most likely to make from this evidence?

a. When you multiply a two-digit number by 22, the last and first digits of the product are the digits of the original number.

b. When you multiply a two-digit number by 22, the first and last digits of the product are the digits of the original number.

c. When you multiply a two-digit number by 22, the first and last digits of the product form a number that is twice the original number.

d. None of the above conjectures can be made from this evidence.

Name: ________________________ ID: A

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____ 4. Taylor noticed a pattern when dividing these numbers by 4: 33, 73, 113.

Determine the pattern and make a conjecture.

a. When the cube of an odd number that is 1 less than a multiple of 4 is divided by 4, the decimal part of the result will be .75.

b. When the cube of an odd number that is 1 more than a multiple of 4 is divided by 4, the decimal part of the result will be .25.

c. When the cube of an odd number that is 1 more than a multiple of 4 is divided by 4, the decimal part of the result will be .75.

d. When the cube of an odd number that is 1 less than a multiple of 4 is divided by 4, the decimal part of the result will be .25.

Short Answer

5. Katy gathered the following evidence.

17(22) = 374 36(22) = 742 18(22) = 396

From this evidence, Katy made the following conjecture.

When you multiply a two-digit number by 22, the first and last digits of the product form a number that is twice the original number.

Is her conjecture reasonable? Briefly justify your decision.

6. Kathryn texts this message to her friend Jamie:

1 2 12

dinner L8R?

Jamie responds:GR8! CU FTR WRK.

Make a conjecture about what was said.

7. Austin told his little sister, Celina, that horses, cats, and dogs are all mammals.As a result, Celina made the following conjecture:

All mammals have four legs.

Use a counterexample to show Celina her conjecture is not valid.

8. Bradley made the following conjecture:

All professional hockey players can skate well.

Do you agree or disagree? Briefly justify your decision with a counterexample if possible.

Name: ________________________ ID: A

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9. Austin made the following conjecture:

As you travel farther south, the climate gets hotter.


10. Cheyenne made the following conjecture:

As you travel farther south, toward the equator, the climate gets hotter.


11. Ryan made the following conjecture:

Every even number can be written as the sum of two consecutive integers.


12. Kendra made the following conjecture:

The sum of any three integers is greater than each integer.


ID: A

1

Sept 9 2011Answer Section

MULTIPLE CHOICE

1. ANS: D PTS: 1 DIF: Grade 11 REF: Lesson 1.1OBJ: 1.1: Make conjectures by observing patterns and identifying properties, and justify the reasoning.TOP: conjectures and Inductive Reasoning KEY: conjecture| inductive reasoning

2. ANS: C PTS: 1 DIF: Grade 11 REF: Lesson 1.1OBJ: 1.1: Make conjectures by observing patterns and identifying properties, and justify the reasoning.TOP: conjectures and Inductive Reasoning KEY: conjecture| inductive reasoning

3. ANS: D PTS: 1 DIF: Grade 11 REF: Lesson 1.1OBJ: 1.1: Make conjectures by observing patterns and identifying properties, and justify the reasoning.TOP: conjectures and Inductive Reasoning KEY: conjecture| inductive reasoning

4. ANS: A PTS: 1 DIF: Grade 11 REF: Lesson 1.1OBJ: 1.1: Make conjectures by observing patterns and identifying properties, and justify the reasoning.TOP: conjectures and Inductive Reasoning KEY: conjecture| inductive reasoning

SHORT ANSWER

5. ANS: No, it is not reasonable, because 19(22) = 418, and 48 is not twice 19.

PTS: 1 DIF: Grade 11 REF: Lesson 1.1 OBJ: 1.1: Make conjectures by observing patterns and identifying properties, and justify the reasoning.TOP: conjectures and Inductive Reasoning KEY: conjecture| inductive reasoning

6. ANS: For example: Kathryn: Want to have dinner later?Jamie: Great! See you after work.

PTS: 1 DIF: Grade 11 REF: Lesson 1.1 OBJ: 1.1: Make conjectures by observing patterns and identifying properties, and justify the reasoning.TOP: conjectures and Inductive Reasoning KEY: conjecture| inductive reasoning

7. ANS: For example, dolphins are mammals, and they don’t have any legs.

PTS: 1 DIF: Grade 11 REF: Lesson 1.3 OBJ: 1.4 Provide and explain a counterexample to disprove a given conjecture.TOP: Disproving conjectures: Counterexamples KEY: conjecture| disproving conjectures| counterexamples

ID: A

2

8. ANS: For example, agree: I couldn’t think of a counterexample. A person would have to be able to skate very well to play hockey professionally.


9. ANS: For example, disagree: if you travel toward the south pole, the climate gets colder.


10. ANS: For example, agree: the closer you get to the equator, the warmer the climate gets.


11. ANS: For example, disagree: it is not possible to write “4” as the sum of two consecutive integers.


12. ANS: For example, disagree: –3 + (–4) + 2 = –5, and –5 is less than each integer.



3

September 16


____ 1. All cats are mammals. All mammals are warm-blooded. Tashi is a cat. What can be deduced about Tashi?

1. Tashi is warm-blooded.2. Tashi is a mammal.

a. Choice 1 and Choice 2b. Neither Choice nor Choice 2c. Choice 1 onlyd. Choice 2 only

____ 2. All birds have backbones. Birds are the only animals that have feathers.Rosie is not a bird. What can be deduced about Rosie?

1. Rosie has a backbone.2. Rosie does not have feathers.

a. Neither Choice 1 nor Choice 2b. Choice 1 onlyc. Choice 1 and Choice 2d. Choice 2 only

____ 3. What type of error, if any, occurs in the following deduction?

All swimmers can swim one kilometre without stopping. Joan is a swimmer. Therefore, Joan can swim one kilometre without stopping.

a. a false assumption or generalizationb. an error in reasoningc. an error in calculationd. There is no error in the deduction.

____ 4. What type of error, if any, occurs in the following deduction?

All people who work, do so in an office, at a computer. Bill works, so he works in an office, at a computer.

a. a false assumption or generalizationb. an error in reasoningc. an error in calculationd. There is no error in the deduction.

Name: ________________________ ID: A

2

____ 5. Choose the next figure in this sequence.

Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6

a.

b.

c.

d.

____ 6. Which number should appear in the centre of Figure 4?

Figure 1 Figure 2 Figure 3 Figure 4

a. 41b. 24c. 36d. 11

Short Answer

7. Complete the following deductive argument:

If an integer is divisible by 4, then half the number is an even number. 44 is divisible by 4, therefore, ...

Name: ________________________ ID: A

3

8. Try the following calculator trick with different numbers. Make a conjecture about the trick.

• Start with your age.• Multiply it by 3.• Multiply it by 7.• Multiply it by 37.• Multiply it by 13.

9. Examine the following example of deductive reasoning. Why is it faulty?

Given: TechShop sells computers. Aaron wants to buy new headphones.Deduction: Aaron should not shop at TechShop.

10. What type of error occurs in the following deduction? Briefly justify your answer.

All teens watch TV or play video games for more than seven hours each day. Julie is a teen. Therefore, Julie watches TV or plays video games for more than seven hours each day.

11. What type of error occurs in the following deduction?Briefly justify your answer.

Let x = y. x2 = xy x2 + x2 = x2 + xy 2x2 = x2 + xy 2x2 – 2xy = x2 + xy – 2xy 2x2 – 2xy = x2 – xy 2(x2 – xy) = 1(x2 – xy) 2 = 1

12. Alison created a number trick in which she always ended with the original number. When Alison tried to prove her trick, however, it did not work. In which step does the calculation error occur? What is the error?

n Use n to represent any number.n + 4 Add 4.2n + 4 Multiply by 2.2n + 8 Add 4.n + 4 Divide by 2.n – 1 Subtract 5.

Name: ________________________ ID: A

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13. In a leapfrog puzzle, coloured counters are moved along a space on a board. A counter can move into an empty space. A counter can leapfrog over another counter into an empty space.

Board at start:

Board at end:

What would be the minimum number of moves needed to exchange 9 red counters with 9 blue counters?

14. Emma and Alexander are playing darts.Emma has a score of 48. To win, she must reduce her score to zero and have her last counting dart be a double. Give a strategy that Emma might use to win.

Name: ________________________ ID: A

5

Problem

15. Annabeth wrote the following equations. The results led her to make the conjecture that the sum of three consecutive perfect squares is divisible by 3.

Let n be the first integer.

n2 + (n + 1)2 + (n + 2)2 = n2 + (n2 + 2n + 2) + (n2 + 4n + 4) n2 + (n + 1)2 + (n + 2)2 = 3n2 + 6n + 6 n2 + (n + 1)2 + (n + 2)2 = 3(n2 + 2n + 2)

But in checking her work, Annabeth found the following counterexample, so she knew she had made an error.

1 + 4 + 9 = 14

Determine what Annabeth’s error is. What should her result have been?

16. Kim tried this number trick:• Write down the number of your birth month.• Multiply by 2.• Add the number of days in a week.• Multiply by 50.• Add the last two digits of your birth year.• Subtract the number of days in a year.• Add 15.

Kim’s result was a number in which the tens and ones digits were her birth year and the rest of the digits was her address. She tried to prove why this works, but her final expression did not make sense.

Let n represent any address.2n Multiply by 2.2n + 7 Add the number of days in a week.100n + 350 Multiply by 50.Let y represent the last two numbers of your birth year.100n + 350 + y Add your birth year.100n + 350 + y – 366 Subtract the number of days in a non-leap year.100n + p – 1 Add 15.

Determine the errors in Kim’s proof, and then correct them.

ID: A

1

September 16Answer Section

MULTIPLE CHOICE

1. ANS: A PTS: 1 DIF: Grade 11 REF: Lesson 1.4OBJ: 1.3 Compare, using examples, inductive and deductive reasoning.| 1.5 Prove algebraic and number relationships, such as divisibility rules, number properties, mental mathematics strategies or algebraic number tricks| 1.6 Prove a conjecture, using deductive reasoning (not limited to two column proofs).TOP: Proving conjectures| deductive reasoning KEY: conjecture| proving conjectures| reasoning| deductive reasoning

2. ANS: D PTS: 1 DIF: Grade 11 REF: Lesson 1.4OBJ: 1.3 Compare, using examples, inductive and deductive reasoning.| 1.5 Prove algebraic and number relationships, such as divisibility rules, number properties, mental mathematics strategies or algebraic number tricks| 1.6 Prove a conjecture, using deductive reasoning (not limited to two column proofs).TOP: Proving conjectures| deductive reasoning KEY: conjecture| proving conjectures| reasoning| deductive reasoning

3. ANS: A PTS: 1 DIF: Grade 11 REF: Lesson 1.5OBJ: 1.7 Determine if a given argument is valid, and justify the reasoning. | 1.8 Identify errors in a given proof; e.g., a proof that ends with 2 = 1. TOP: invalid proofs| deductive reasoningKEY: valid proofs| invalid proofs| deductive reasoning

4. ANS: A PTS: 1 DIF: Grade 11 REF: Lesson 1.5OBJ: 1.7 Determine if a given argument is valid, and justify the reasoning. | 1.8 Identify errors in a given proof; e.g., a proof that ends with 2 = 1. TOP: invalid proofs| deductive reasoningKEY: valid proofs| invalid proofs| deductive reasoning

5. ANS: D PTS: 1 DIF: Grade 11 REF: Lesson 1.6OBJ: 1.9 Solve a contextual problem involving inductive or deductive reasoning.TOP: reasoning to solve problems KEY: reasoning| inductive reasoning| deductive reasoning

6. ANS: B PTS: 1 DIF: Grade 11 REF: Lesson 1.6OBJ: 1.9 Solve a contextual problem involving inductive or deductive reasoning.TOP: reasoning to solve problems KEY: reasoning| inductive reasoning| deductive reasoning

SHORT ANSWER

7. ANS: For example, half of 44 is an even number (22).

PTS: 1 DIF: Grade 11 REF: Lesson 1.4 OBJ: 1.3 Compare, using examples, inductive and deductive reasoning.| 1.5 Prove algebraic and number relationships, such as divisibility rules, number properties, mental mathematics strategies or algebraic number tricks| 1.6 Prove a conjecture, using deductive reasoning (not limited to two column proofs).TOP: Proving conjectures| deductive reasoning KEY: conjecture| proving conjectures| reasoning| deductive reasoning

ID: A

2

8. ANS: For example, the answer is always your age repeated three times.


9. ANS: For example, TechShop may sell other products, we only know that they do sell computers.


10. ANS: There is a faulty assumption or generalization: many teens do not spend seven hours watching TV or playing video games.

PTS: 1 DIF: Grade 11 REF: Lesson 1.5 OBJ: 1.7 Determine if a given argument is valid, and justify the reasoning. | 1.8 Identify errors in a given proof; e.g., a proof that ends with 2 = 1. TOP: Invalid proofs| deductive reasoning KEY: valid proofs| invalid proofs| deductive reasoning

11. ANS: There is an error in reasoning: in the second last step, there is division by 0, which makes the equation meaningless.

PTS: 1 DIF: Grade 11 REF: Lesson 1.5 OBJ: 1.7 Determine if a given argument is valid, and justify the reasoning. | 1.8 Identify errors in a given proof; e.g., a proof that ends with 2 = 1. TOP: invalid proofs| deductive reasoningKEY: valid proofs| invalid proofs| deductive reasoning

12. ANS: In step 2, the “4” in “n + 4” was not multiplied by 2.In step 3, the expression on the left should be 2n + 8.


13. ANS: 99

PTS: 1 DIF: Grade 11 REF: Lesson 1.7 OBJ: 2.1 Determine, explain and verify a strategy to solve a puzzle or to win a game. | 2.2 Identify and correct errors in a solution to a puzzle or in a strategy for winning a game.| 2.3 Create a variation on a puzzle or a game, and describe a strategy for solving the puzzle or winning the game.TOP: analyzing puzzles and games KEY: reasoning| solving puzzles

ID: A

3

14. ANS: For example, score: 20, 20, double 4, in order.

PTS: 1 DIF: Grade 11 REF: Lesson 1.7 OBJ: 2.1 Determine, explain and verify a strategy to solve a puzzle or to win a game. | 2.2 Identify and correct errors in a solution to a puzzle or in a strategy for winning a game.| 2.3 Create a variation on a puzzle or a game, and describe a strategy for solving the puzzle or winning the game.TOP: analyzing puzzles and games KEY: reasoning| solving puzzles

PROBLEM

15. ANS: For example, in the first line, Annabeth miscalculated (n + 1)2 as (n2 + 2n + 2). It should be (n2 + 2n + 1).

The proof should be: n2 + (n + 1)2 + (n + 2)2 = n2 + (n2 + 2n + 1) + (n2 + 4n + 4) n2 + (n + 1)2 + (n + 2)2 = 3n2 + 6n + 5 n2 + (n + 1)2 + (n + 2)2 = 3(n2 + 2n) + 5

This proof shows that the sum of three consecutive perfect squares is not divisible by 3.


16. ANS: Kim subtracted the number of days in a leap year, not a non-leap year.Here is the correct proof:

2n Multiply by 2.2n + 7 Add the number of days in a week.100n + 350 Multiply by 50.Let y represent the last two numbers of your birth year.100n + 350 + y Add your birth year.100n + 350 + y – 365 Subtract the number of days in a non-leap year.100n + p Add 15.



1

Sept 23 2011


____ 1. Which pairs of angles are equal in this diagram?

a. a = b, c = d, and e = fb. a = e, c = g, and b = fc. a = c, e = g, and f = hd. a = e, b = d, and c = g

____ 2. In which diagram(s) is AB parallel to CD?

1.

2.

a. Choice 1 onlyb. Choice 2 onlyc. Choice 1 and Choice 2d. Neither Choice 1 nor Choice 2

Name: ________________________ ID: A

2

____ 3. Which statement about the angles in this diagram is false?

a. b = 50°b. c = 50°c. e = 130°d. f = 62°

____ 4. Which statement about the angles in this diagram is false?

a. a = eb. c = e c. d = bd. b = f

____ 5. Which angle property proves PYD = 90°?

a. corresponding anglesb. alternate interior anglesc. alternate exterior anglesd. supplementary angles

Name: ________________________ ID: A

3

____ 6. Which are the correct measures for YXZ and XZY?

a. YXZ = 63°, XZY = 91°b. YXZ = 53°, XZY = 91°c. YXZ = 63°, XZY = 81°d. YXZ = 53°, XZY = 81°

Short Answer

7. Determine the measure of ABF.

8. Determine the values of a, b, and c.

Name: ________________________ ID: A

4

9. Determine the values of a, b, and c.

10. Determine the measure of PQT.

11. Determine the measure of NMO.

Name: ________________________ ID: A

5

12. Given QP || MR, determine the measure of MOQ.

13. Given QP || MR, determine the measure of OPN.

Problem

14. Given UWX = WYZ, prove: TV || WX

15. Prove that the sum of the three interior angles of a triangle is 180°. Use a labelled diagram.

ID: A

1

Sept 23 2011Answer Section

MULTIPLE CHOICE

1. ANS: B PTS: 1 DIF: Grade 11 REF: Lesson 2.1OBJ: 1.1 Generalize, using inductive reasoning, the relationships between pairs of angles formed by transversals and parallel lines, with or without technology. | 1.5 Verify, with examples, that if lines are not parallel the angle properties do not apply. TOP: Parallel lines KEY: parallel lines| transversals

2. ANS: D PTS: 1 DIF: Grade 11 REF: Lesson 2.1OBJ: 1.1 Generalize, using inductive reasoning, the relationships between pairs of angles formed by transversals and parallel lines, with or without technology. | 1.5 Verify, with examples, that if lines are not parallel the angle properties do not apply. TOP: Parallel lines KEY: parallel lines| transversals

3. ANS: A PTS: 1 DIF: Grade 11 REF: Lesson 2.2OBJ: 1.2 Prove, using deductive reasoning, properties of angles formed by transversals and parallel lines, including the sum of the angles in a triangle. | 1.4 Identify and correct errors in a given proof of a property involving angles. | 2.1 Determine the measures of angles in a diagram that involves parallel lines, angles and triangles, and justify the reasoning. | 2.2 Identify and correct errors in a given solution to a problem that involves the measures of angles. | 2.3 Solve a contextual problem that involves angles or triangles. | 2.4 Construct parallel lines, using only a compass or a protractor, and explain the strategy used. | 2.5 Determine if lines are parallel, given the measure of an angle at each intersection formed by the lines and a transversal.TOP: Angles formed by parallel lines KEY: parallel lines| transversals| angles

4. ANS: B PTS: 1 DIF: Grade 11 REF: Lesson 2.2OBJ: 1.2 Prove, using deductive reasoning, properties of angles formed by transversals and parallel lines, including the sum of the angles in a triangle. | 1.4 Identify and correct errors in a given proof of a property involving angles. | 2.1 Determine the measures of angles in a diagram that involves parallel lines, angles and triangles, and justify the reasoning. | 2.2 Identify and correct errors in a given solution to a problem that involves the measures of angles. | 2.3 Solve a contextual problem that involves angles or triangles. | 2.4 Construct parallel lines, using only a compass or a protractor, and explain the strategy used. | 2.5 Determine if lines are parallel, given the measure of an angle at each intersection formed by the lines and a transversal.TOP: Angles formed by parallel lines KEY: parallel lines| transversals| angles

5. ANS: A PTS: 1 DIF: Grade 11 REF: Lesson 2.2OBJ: 1.2 Prove, using deductive reasoning, properties of angles formed by transversals and parallel lines, including the sum of the angles in a triangle. | 1.4 Identify and correct errors in a given proof of a property involving angles. | 2.1 Determine the measures of angles in a diagram that involves parallel lines, angles and triangles, and justify the reasoning. | 2.2 Identify and correct errors in a given solution to a problem that involves the measures of angles. | 2.3 Solve a contextual problem that involves angles or triangles. | 2.4 Construct parallel lines, using only a compass or a protractor, and explain the strategy used. | 2.5 Determine if lines are parallel, given the measure of an angle at each intersection formed by the lines and a transversal.TOP: Angles formed by parallel lines KEY: parallel lines| transversals| angles

6. ANS: C PTS: 1 DIF: Grade 11 REF: Lesson 2.3OBJ: 1.2 Prove, using deductive reasoning, properties of angles formed by transversals and parallel lines, including the sum of the angles in a triangle.| 2.1 Determine the measures of angles in a diagram that involves parallel lines, angles and triangles, and justify the reasoning. TOP: Angles in trianglesKEY: angles| triangles

ID: A

2

SHORT ANSWER

7. ANS: ABF = 66°

PTS: 1 DIF: Grade 11 REF: Lesson 2.2 OBJ: 1.2 Prove, using deductive reasoning, properties of angles formed by transversals and parallel lines, including the sum of the angles in a triangle. | 1.4 Identify and correct errors in a given proof of a property involving angles. | 2.1 Determine the measures of angles in a diagram that involves parallel lines, angles and triangles, and justify the reasoning. | 2.2 Identify and correct errors in a given solution to a problem that involves the measures of angles. | 2.3 Solve a contextual problem that involves angles or triangles. | 2.4 Construct parallel lines, using only a compass or a protractor, and explain the strategy used. | 2.5 Determine if lines are parallel, given the measure of an angle at each intersection formed by the lines and a transversal.TOP: Angles formed by parallel lines KEY: parallel lines| transversals| angles

8. ANS: a = 18°, b = 54°, c = 27°


9. ANS: a = 32°, b = 84°, c = 12°


10. ANS: PQT = 36°


ID: A

3

11. ANS: NMO = 82°

PTS: 1 DIF: Grade 11 REF: Lesson 2.3 OBJ: 1.2 Prove, using deductive reasoning, properties of angles formed by transversals and parallel lines, including the sum of the angles in a triangle.| 2.1 Determine the measures of angles in a diagram that involves parallel lines, angles and triangles, and justify the reasoning. TOP: Angles in trianglesKEY: angles| triangles

12. ANS: MOQ = 82°


13. ANS: OPN = 105°


PROBLEM

14. ANS: TUY = 37° and UWX = 37°, by the transitive property. So, TV || WX by equal alternate interior angles.


ID: A

4

15. ANS: For example:

By alternate interior angles, PDR = DRE and QDE = RED.A straight line contains 180°, so PDR + RDE + QDE = 180°.Substitute DRE for PDR and RED for QDE: DRE + RDE + RED = 180°Therefore, the sum of the three interior angles of an acute triangle is 180°.



3

October 3 2011


____ 1. Which are the correct measures of the indicated angles?

a. w = 77°, x =77°, y = 103°b. w = 77°, x =103°, y = 103°c. w = 103°, x =77°, y = 77°d. w = 103°, x =103°, y = 77°



Name: ________________________ ID: A

2



____ 4. Solve for the unknown side length. Round your answer to one decimal place.

qsin30

10.0sin80

a. 5.0b. 5.1c. 20.3d. 0.5

____ 5. What information do you need to know about an acute triangle to use the sine law?

a. two angles and any sideb. two sides and any anglec. all the anglesd. all the sides

Name: ________________________ ID: A

3

____ 6. Determine the length of k to the nearest centimetre.

a. 29 cmb. 28 cmc. 27 cmd. 30 cm

Short Answer

7. Solve for the unknown angle measure. Round your answer to the nearest degree.

1.1sinZ

1.7sin72

Problem

8. Kim tried this number trick:• Write down the number of your birth month.• Multiply by 2.• Add the number of days in a week.• Multiply by 50.• Add the last two digits of your birth year.• Subtract the number of days in a year.• Add 15.

Kim’s result was a number in which the tens and ones digits were her birth year and the rest of the digits was her address. She tried to prove why this works, but her final expression did not make sense.

Let n represent any address.2n Multiply by 2.2n + 7 Add the number of days in a week.100n + 350 Multiply by 50.Let y represent the last two numbers of your birth year.100n + 350 + y Add your birth year.100n + 350 + y – 366 Subtract the number of days in a non-leap year.100n + p – 1 Add 15.

Determine the errors in Kim’s proof, and then correct them.

ID: A

1

October 3 2011Answer Section

MULTIPLE CHOICE

1. ANS: C PTS: 1 DIF: Grade 11 REF: Lesson 2.2OBJ: 1.2 Prove, using deductive reasoning, properties of angles formed by transversals and parallel lines, including the sum of the angles in a triangle. | 1.4 Identify and correct errors in a given proof of a property involving angles. | 2.1 Determine the measures of angles in a diagram that involves parallel lines, angles and triangles, and justify the reasoning. | 2.2 Identify and correct errors in a given solution to a problem that involves the measures of angles. | 2.3 Solve a contextual problem that involves angles or triangles. | 2.4 Construct parallel lines, using only a compass or a protractor, and explain the strategy used. | 2.5 Determine if lines are parallel, given the measure of an angle at each intersection formed by the lines and a transversal.TOP: Angles formed by parallel lines KEY: parallel lines| transversals| angles

2. ANS: C PTS: 1 DIF: Grade 11 REF: Lesson 2.3OBJ: 1.2 Prove, using deductive reasoning, properties of angles formed by transversals and parallel lines, including the sum of the angles in a triangle.| 2.1 Determine the measures of angles in a diagram that involves parallel lines, angles and triangles, and justify the reasoning. TOP: Angles in trianglesKEY: angles| triangles

3. ANS: A PTS: 1 DIF: Grade 11 REF: Lesson 2.3OBJ: 1.2 Prove, using deductive reasoning, properties of angles formed by transversals and parallel lines, including the sum of the angles in a triangle.| 2.1 Determine the measures of angles in a diagram that involves parallel lines, angles and triangles, and justify the reasoning. TOP: Angles in trianglesKEY: angles| triangles

4. ANS: B PTS: 1 DIF: Grade 11 REF: Lesson 3.1OBJ: 3.5 Solve a problem involving the sine law that requires the manipulation of a formula.TOP: Side-angle relationships in acute triangles KEY: primary trigonometric ratios

5. ANS: A PTS: 1 DIF: Grade 11 REF: Lesson 3.2OBJ: 3.2 Explain the steps in a given proof of the sine law or cosine law.TOP: Proving and applying the sine law KEY: sine law

6. ANS: D PTS: 1 DIF: Grade 11 REF: Lesson 3.2OBJ: 3.5 Solve a problem involving the sine law that requires the manipulation of a formula.TOP: Proving and applying the sine law KEY: sine law

SHORT ANSWER

7. ANS: 38°

PTS: 1 DIF: Grade 11 REF: Lesson 3.1 OBJ: 3.5 Solve a problem involving the sine law that requires the manipulation of a formula.TOP: Side-angle relationships in acute triangles KEY: primary trigonometric ratios

ID: A

2

PROBLEM

8. ANS: Kim subtracted the number of days in a leap year, not a non-leap year.Here is the correct proof:

2n Multiply by 2.2n + 7 Add the number of days in a week.100n + 350 Multiply by 50.Let y represent the last two numbers of your birth year.100n + 350 + y Add your birth year.100n + 350 + y – 365 Subtract the number of days in a non-leap year.100n + p Add 15.



1

Oct 7 2011

Short Answer

1. Solve for the unknown side length. Round your answer to one decimal place.

vsin84

15.0sin40

2. In RST, the values of s and T are known. What additional information do you need to know if you want to use the sine law to solve the triangle?

3. Determine the length of c to the nearest tenth of a centimetre.

4. Determine the measure of to the nearest degree.

5. In QRS, r = 4.1 cm, s = 2.7 cm, and R = 88°. Determine the measure of Q to the nearest degree.

Name: ________________________ ID: A

2

6. Determine the length of w to the nearest tenth of a centimetre.

7. Determine the length of s to the nearest tenth of a centimetre.

8. In STU, s = 78.5 cm, u = 90.0 cm, and T = 67°. Determine the measure of t to the nearest tenth of a centimetre.

9. How would you determine the indicated side length, if it is possible? Explain briefly.

Problem

10. A radio tower is supported by two wires on opposite sides. On the ground, the ends of the wire are 280 m apart. One wire makes a 60° angle with the ground.The other makes a 66° angle with the ground.

Draw a diagram of the situation. Then, determine the length of each wire to the nearest metre. Show your work.

Name: ________________________ ID: A

3

11. Two Jasper National Park rangers in their fire towers spot a fire.Determine the distances, to the nearest tenth of a kilometre, from each tower to the fire. Show your work.

ID: A

1

Oct 7 2011Answer Section

SHORT ANSWER

1. ANS: 23.2


2. ANS: For example, knowing either the value of t or S would allow me to solve for the other. Then I could determine the value of R and solve for r.

PTS: 1 DIF: Grade 11 REF: Lesson 3.2 OBJ: 3.1 Draw a diagram to represent a problem that involves the cosine law or the sine law. | 3.2 Explain the steps in a given proof of the sine law or cosine law. TOP: Proving and applying the sine lawKEY: sine law

3. ANS: c = 42.7 cm

PTS: 1 DIF: Grade 11 REF: Lesson 3.2 OBJ: 3.5 Solve a problem involving the sine law that requires the manipulation of a formula.TOP: Proving and applying the sine law KEY: sine law

4. ANS: = 69°


5. ANS: Q = 51°


6. ANS: w = 27.3 cm

PTS: 1 DIF: Grade 11 REF: Lesson 3.3 OBJ: 3.3 Solve a problem involving the cosine law that requires the manipulation of a formula.TOP: Proving and applying the cosine law KEY: cosine law

ID: A

2

7. ANS: s = 45.9 cm


8. ANS: t = 93.5 cm


9. ANS: The measures of two sides and the contained angle are given, so use the cosine law to solve for x.

PTS: 1 DIF: Grade 11 REF: Lesson 3.4 OBJ: 3.3 Solve a problem involving the cosine law that requires the manipulation of a formula.TOP: Solving problems using acute triangles KEY: cosine law

PROBLEM

10. ANS: Let the x and y be the length of the wires.The third angle is 180° – 66° – 60° = 54°.

Use the sine law to determine the length of each wire:x

sin66 280

sin54

x 280sin66sin54

316.177. . .

y

sin60 280

sin54

x 280sin60sin54

299.730. . .The wires are 316 m and 300 m long.

PTS: 1 DIF: Grade 11 REF: Lesson 3.2 OBJ: 3.1 Draw a diagram to represent a problem that involves the cosine law or the sine law. | 3.5 Solve a problem involving the sine law that requires the manipulation of a formula. | 3.6 Solve a contextual problem that involves the cosine law or sine law. TOP: Proving and applying the sine lawKEY: sine law| primary trigonometric ratios

ID: A

3

11. ANS: Let C represent the measure of the remaining unknown angle. A + B + C = 180° 64° + 48° + C = 180° C = 68°Let b represent the distance from tower A to the fire.

bsinB

csinC

bsin48

4.2sin68

b sin48 4.2sin68

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

b 3.366. . .The distance from tower A to the fire is 3.4 km.Let a represent the distance from tower B to the fire.

asinA

csinC

asin64

4.2sin68

a sin64 4.2sin68

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

a 4.071. . .The distance from tower B to the fire is 4.1 km.

PTS: 1 DIF: Grade 11 REF: Lesson 3.2 OBJ: 3.5 Solve a problem involving the sine law that requires the manipulation of a formula. | 3.6 Solve a contextual problem that involves the cosine law or sine law. TOP: Proving and applying the sine lawKEY: sine law


1

Oct 7 Redo

Short Answer

1. Solve for the unknown angle measure. Round your answer to the nearest degree.

1.1sinZ

1.7sin72

2. In LMN, the values of m, L, and N are known. How can you use the sine law to solve for n?

3. Determine the length of e to the nearest tenth of a centimetre.

4. Determine the length of d to the nearest tenth of a centimetre.

5. In QRS, r = 4.1 cm, s = 2.7 cm, and R = 88°. Determine the measure of S to the nearest degree.

Name: ________________________ ID: A

2

6. Determine the length of d to the nearest tenth of a centimetre.

7. Determine the length of s to the nearest tenth of a centimetre.

8. Determine the measure of to the nearest degree.

9. In GHI, g = 30.0 cm, i = 19.3 cm, and H = 53°. Determine the measure of h to the nearest tenth of a centimetre.

10. How would you determine the indicated angle measure, if it is possible? Explain briefly.

ID: A

1

Oct 7 RedoAnswer Section

SHORT ANSWER

1. ANS: 38°


2. ANS: For example, determine the measure of M using the fact that the sum of the angles in a triangle add up to

180°. Then calculate m = sinNm

sinM.

PTS: 1 DIF: Grade 11 REF: Lesson 3.2 OBJ: 3.1 Draw a diagram to represent a problem that involves the cosine law or the sine law. | 3.2 Explain the steps in a given proof of the sine law or cosine law. TOP: Proving and applying the sine lawKEY: sine law

3. ANS: e = 7.2 cm


4. ANS: d = 6.2 cm

PTS: 1 DIF: Grade 11 REF: Lesson 3.2 OBJ: 3.5 Solve a problem involving the sine law that requires the manipulation of a formula. TOP: Proving and applying the sine law KEY: sine law

5. ANS: S = 41°


6. ANS: d = 10.0 cm


ID: A

2

7. ANS: s = 45.9 cm


8. ANS: = 57°


9. ANS: h = 24.0 cm


10. ANS: The measures of two sides and an angle opposite one of the sides are given, so use the sine law to solve for .

PTS: 1 DIF: Grade 11 REF: Lesson 3.4 OBJ: 3.5 Solve a problem involving the sine law that requires the manipulation of a formula.TOP: Solving problems using acute triangles KEY: sine law


1

November 4

Short Answer

1. Environment Canada compiled data on the number of lightning strikes per square kilometre in Ontario towns from 1999 to 2008.3.60 2.11 0.96 0.653.47 2.04 0.90 0.652.53 1.90 0.85 0.652.38 1.90 0.72 0.632.25 1.33 0.70 0.382.25 1.13 0.66 0.19

Complete the frequency table.

Lightning Strikes (per square kilometre) Frequency0.00–0.991.00–1.992.00–2.993.00–3.99

2. At the end of a bowling tournament, three friends analyzed their scores.Lucia’s mean bowling score is 144 with a standard deviation of 12.Zheng’s mean bowling score is 88 with a standard deviation of 6.Kevin’s mean bowling score is 108 with a standard deviation of 5.

Who is the more consistent bowler?

3. Khamid and Gerbrand are laying interlocking bricks. Their supervisor records how many bricks they lay each hour.Hour 1 2 3 4 5 6Khamid 212 193 204 195 182 216Gerbrand 230 195 214 207 218 191

Which worker is more consistent?

Name: ________________________ ID: A

2

Problem

4. The manager of a customer support line currently has 250 unionized employees. Their contract states that the mean number of calls that an employee should handle per day is 45, with a maximum standard deviation of 7 calls. The manager tracked the number of calls that each employee handles. Does the manager need to hire more employees if the calls continue in this pattern?

Daily Calls Frequency26–30 331–35 1536–40 4441–45 7646–50 6351–55 3956–60 861–65 2

xInterval Frequency Midpoint f*m (m - x) (m - x)2 (m - x)

2f

ID: A

1

November 4Answer Section

SHORT ANSWER

1. ANS:

Lightning Strikes (per square kilometre) Frequency0.00–0.99 121.00–1.99 42.00–2.99 63.00–3.99 2

PTS: 1 DIF: Grade 11 REF: Lesson 5.2 TOP: Frequency tables, histograms, and frequency polygons KEY: frequency distribution

2. ANS: Kevin

PTS: 1 DIF: Grade 11 REF: Lesson 5.3 OBJ: 1.3 Explain, using examples, the properties of a normal curve, including the mean, median, mode, standard deviation, symmetry and area under the curve. TOP: Standard deviationKEY: mean | standard deviation

3. ANS: Khamid has the lower standard deviation.

PTS: 1 DIF: Grade 11 REF: Lesson 5.3 OBJ: 1.2 Calculate, using technology, the population standard deviation of a data set. | 1.3 Explain, using examples, the properties of a normal curve, including the mean, median, mode, standard deviation, symmetry and area under the curve. TOP: Standard deviation KEY: standard deviation

ID: A

2

PROBLEM

4. ANS: Determine the midpoint of each interval.

Midpoint of Interval (min) Frequency

28 333 1538 4443 7648 6353 3958 863 2

Using technology, the mean is 44.8 calls and the standard deviation is about 8.8 calls.

The manager needs to hire more employees because the standard deviation is greater than 7 calls.

PTS: 1 DIF: Grade 11 REF: Lesson 5.3 OBJ: 1.2 Calculate, using technology, the population standard deviation of a data set. | 1.6 Explain, using examples that represent multiple perspectives, the application of standard deviation for making decisions in situations such as warranties, insurance or opinion polls. | 1.7 Solve a contextual problem that involves the interpretation of standard deviation. TOP: Standard deviation KEY: mean | standard deviation


1

Nov 18 2011

Short Answer

1. Determine the z-score for the given value.µ = 360, = 20, x = 315

2. Determine the z-score for the given value.µ = 55, = 1, x = 54.6

3. Determine the percent of data to the left of the z-score: z = –2.20.

4. Determine the percent of data to the right of the z-score: z = –0.19.

5. Determine the percent of data between the following z-scores:z = –0.68 and z = 1.74.

6. A poll was conducted about an upcoming election. The results are considered accurate within ±2.8 percent points, 19 times out of 20.State the confidence level.

7. A poll was conducted about an upcoming election. The result that 18% of people intend to vote for one of the candidates is considered accurate within ±4.5 percent points, 9 times out of 10.State the confidence interval.

8. A poll was conducted about an upcoming election. The result that 52% of people intend to vote for one of the candidates is considered accurate within ±8.0 percent points, 19 times out of 20.State the confidence interval.

Problem

9. A tile company produces floor tiles that has an average thickness of 55 mm, with a standard deviation of 0.6 mm. For premium-quality floors, the tiles must have a thickness between 54 mm and 55 mm. What percent, to the nearest whole number, of the total production can be sold for premium-quality floors?

10. In a population, 50% of the adults are taller than 172 cm and 10% are taller than 190 cm. Determine the mean height and standard deviation for this population.


1

Nov 24 2011

Short Answer

1. Is the point (–2, 2) in the solution set for the linear inequality 10y – 12x > 5?

2. Is the point (–2, 2) in the solution set for the linear inequality 4y – 2x 0?

3. Which side of the boundary line is the solution set for the linear inequality 5y + 3x 0?

4. How would you graph the solution set for the linear inequality 10y – 2x –20?

5. Graph the solution set for the linear inequality x + y 1.

Problem

6. Gordon’s favourite activities are going to the movies and skating with friends. He budgets himself no more than $180 a month for entertainment and transportation. Movie admission is $12 per movie, and skating costs $10 each time. A student bus pass for the month costs $50.a) Define the variables and write a linear inequality to represent the situation.b) Graph the linear inequality. Use your graph to determine:i) a combination of activities that Gordon can afford with no money left overii) a combination of activities that will exceed his budget

7. Trang’s favourite activities are going to the movies and skating with friends. He budgets himself no more than $120 a month for entertainment and transportation. Movie admission is $10 per movie, and skating costs $8 each time. A student bus pass for the month costs $30.a) Define the variables and write a linear inequality to represent the situation.b) Graph the linear inequality. Use your graph to determine:i) a combination of activities that Trang can afford and still have some money left overii) a combination of activities that he can afford with no money left over

Name: ________________________ ID: A

2

8. Henri coaches a women’s lacrosse team of 12 players. He plans to buy new practice jerseys and lacrosse sticks for the team. The supplier sells practice jerseys for $55 each and lacrosse sticks for $75 each. Henri can spend no more than $1700 in total. He wants to know how many jerseys and sticks he should buy.a) Write a linear inequality to represent the situation.b) Use your inequality to model the situation graphically.c) Determine a reasonable solution to meet the needs of the team, and provide your reasoning.

9. For every bouquet that is sold at a fundraising banquet, $5 goes to charity. For every ticket that is sold, $18 goes to charity. The organizers’ goal is to raise at least $8000. The organizers need to know how many bouquets and tickets must be sold to meet their goal.a) Define the variables and write a linear inequality to represent the situation.b) Graph the linear inequality to help you determine whether each of the following points is in the solution set. The first coordinate is the number of bouquets and the second is the number of tickets.i) (200, 400) ii) (600, 300) iii) (1000, 100)

Free Plain Graph Paper from http://incompetech.com/graphpaper/plain/





1

Chapter 6.1/2 rewrite

Short Answer

1. Which side of the boundary line is the solution set for the linear inequality 4y + 8x 2?

2. Graph the solution set for the linear inequality 3y – 6x < –1.

Problem

3. Henri coaches a men’s lacrosse team of 10 players. He plans to buy new practice jerseys and lacrosse sticks for the team. The supplier sells practice jerseys for $60 each and lacrosse sticks for $95 each. Henri can spend no more than $1500 in total. He wants to know how many jerseys and sticks he should buy.a) Write a linear inequality to represent the situation.b) Use your inequality to model the situation graphically.c) Determine a reasonable solution to meet the needs of the team, and provide your reasoning.

4. For every calendar that is sold at a fundraising banquet, $8 goes to charity. For every ticket that is sold, $25 goes to charity. The organizers’ goal is to raise at least $6000. The organizers need to know how many calendars and tickets must be sold to meet their goal.a) Define the variables and write a linear inequality to represent the situation.b) Graph the linear inequality to help you determine whether each of the following points is in the solution set. The first coordinate is the number of calendars and the second is the number of tickets.i) (400, 100) ii) (500, 100) iii) (100, 200)

5. A banquet room is set up to seat, at most, 750 people. Each rectangular table seats 24 people, and each circular table seats 5 people. a) Define the variables and write a linear inequality to represent the number of each type of table needed.b) The organizers of the banquet would like to have as close to the same number of rectangular tables and circular tables as possible.What combination of tables could they use? Explain your choice.

Name: ________________________ ID: A

2

6. A banner is being created for a school glee club.• The length must be less than 280 cm.• The perimeter must be 740 cm or less.Use a graph to choose three possible combinations of length and width. Explain your choices.

7. Odette is setting up her social networking page:• She wants to have no more than 460 friends on her new social networking page.• She also wants to have at least two school friends for every karate friend.a) Define the variables and write a system of inequalities that models this situation.b) Describe the restrictions on the domain and range of the variables.

z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09-3.4 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0002-3.3 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0003-3.2 0.0007 0.0007 0.0006 0.0006 0.0006 0.0006 0.0006 0.0005 0.0005 0.0005-3.1 0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 0.0007-3.0 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010

-2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014-2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019-2.7 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 0.0028 0.0027 0.0026-2.6 0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038 0.0037 0.0036-2.5 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048

-2.4 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064-2.3 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084-2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.0110-2.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143-2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183

-1.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233-1.8 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294-1.7 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367-1.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455-1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559

-1.4 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681-1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823-1.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.0985-1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170-1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379

-0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611-0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867-0.7 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148-0.6 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451-0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776

-0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.3121-0.3 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.3594 0.3557 0.3520 0.3483-0.2 0.4207 0.4168 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859-0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.42470.0 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641

Standard Normal Cumulative Probability Table

Cumulative probabilities for NEGATIVE z-values are shown in the following table:

z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.090.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.53590.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.57530.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.61410.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.65170.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879

0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.72240.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.75490.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.78520.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.81330.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389

1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.86211.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.88301.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.90151.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.91771.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319

1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.94411.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.95451.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.96331.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.97061.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767

2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.98172.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.98572.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.98902.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.99162.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936

2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.99522.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.99642.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.99742.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.99812.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986

3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.99903.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.99933.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.99953.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.99973.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998

Standard Normal Cumulative Probability Table

Cumulative probabilities for POSITIVE z-values are shown in the following table:

Documents

ExamView - Untitled - MrTrenholm - homemrtrenholm.wikispaces.com/file/view/Quizzes+2011.pdfName: _____ ID: A 3 9. Austin made the following conjecture: As you travel farther south,