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Applied Math 30S

Exam Review Booklet

*No proportional reasoning

Name: Answer Key

*Note: full solutions available in the

classroom*

When completing this review and your exam, remember to:

Show ALL work – even when using the calculator

Include UNITS in final answers

Round answers to TWO decimal places (unless otherwise stated)

Applied Math 30S Exam

Date

Time

Room #

Good Luck!

Quadratic Functions

1. Ms. Wagner cranks a fly ball deep into left field (probably another home run). The formula

for the height of the ball as a function of time is

h(t) = -4.9t2 + 25t + 1.5 where h is the height of the ball in meters and t is the time in seconds.

(Give all answers to 2 decimal places.)

a) At what time is the ball at the highest point in the sky? 2.55s

b) When does the ball hit the ground (no doubt over the fence)? 5.16 s

c) How high is the ball at the highest point? 33.39 m

d) How high is the ball when the time of flight is 1.5 sec? 27.98 m

e) When is the ball at a height of 28 m? 1.50 s and 3.60 s

2. A farmer has 1000 m of fencing and wishes to enclose a rectangular area and divide it into

three parts by two other fences parallel to one of the sides.

a) Sketch a diagram to represent the fencing and show your lists.

*List data may vary

b) Define your variables and write an equation.

L1 x = width

L2 y = area y = -2x2 + 500x

c) What dimensions of the largest field will yield the maximum area?

Width = 125 m Length = 250 m

d) What is the maximum area?

Area = 31 250 m2

3. Which of these quadratic functions corresponds to the parabola?

A. y = 2x(6 — x) — 8

B. y = 12x — 8 — 2x2

C. y = -2(x — 3)2 + 10

D. all of these choices

4. What is the vertex of the parabola defined by y = (3 — x)(x + 2)?

A. (1, 3) B. (-1, -4) C. (-0.5,-6.25) D. (0.5,6.25)

5. a) Complete this table of values for the function

f(x) = -0.5x2+ 4.5x - 7.

b) Determine the equation of the axis of symmetry:

x = 4.5

c) Determine the coordinates of the vertex:

(4.5 , 3.125)

-12

-3

0

2

3

3

2

6. Given the function f(x) = - 3x2 + 24x — 18

a) Determine the y-intercept: (0,_-18 ).

b) Determine another point with the same y-coordinate as the y-intercept:

( 8 . -18 )

d) Determine the equation of the axis of symmetry: x = 4 .

e) Determine the vertex: (4 , 30 ).

7. A quadratic function is given y = 4(x + 5)2 - 35. Determine:

a) the coordinates of its vertex: (-5 , -35)

b) its y-intercept: 65 (0, 65)

c) its domain and range: D: (-∞, ∞) and R: [-35, ∞)

8. Determine the vertex of the parabola defined by the quadratic function

y = 2x2 - 1Ox + 7.

Vertex (2.5, - 5.5)

9. A pole vaulter can jump a height of 6.8 m. During his jump he covers a distance of is 3.8 m. Write an equation of the parabola which describes his jump. y = -1.88x2 + 7.16x (1 mark)

10. For the function

21( 3) 2

2y x

find the following: a) vertex b) axis of symmetry c) domain d) range e) x-intercept f) y-intercept g) max or min h) graph the function

a) Vertex (3, -2) b) X = 3 c) D: (-∞, ∞) d) R: [-2, ∞) e) X-int: 1 and 5 f) Y-int: 2.5 g) Min: -2 h) On calculator(zoom standard)

11. A construction company has 360 m of fencing and wishes to enclose a rectangular area with a fence. The area borders on a ravine and does not require fencing on that side.

Define your variables and write an expression for the total area as a function of one of the two linear dimensions (length or width). See solution book in classroom for help with lists and window settings List 1 (x) represents = width (or length) (1 mark) List 2 (y) represents = area (1 mark)

y = -2x2 + 360x (1 mark) a) What dimensions of the largest field will yield the maximum area? Width = 90 m Length = 180 m b) What is the maximum area? Area = 16 200 m2

12. Four hundred people will attend a sidewalk display if tickets cost $1 each. Attendance

will decrease by 20 people for each 10-cent increase in ticket price. What ticket price will

yield the maximum income, and what is the maximum income from ticket sales?

X = ticket price Y = income Y = -200x2 + 600x Ticket price is $1.50 to generate maximum income of $450.

Applied Math 30S Exam Review 2018

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13. A golf ball has an initial velocity of 35 metres/second after being hit. The formula for the height of the ball as a function of time is h(t) = -4.9t2 + 35t + 0.1 whre h is the height of the ball in metres and t is the time in seconds. (Round all answers to 2 decimal places.)

a) At what time is the ball at the highest point in the sky? 3.57 s

b) When does the ball hit the ground? 7.15 s c) How high is the ball at the highest point? 62.6 s d) How high is the ball when the time is 1.2 seconds? 35.04 s e) When is the ball at a height of 25 m? 0.80 s and 6.34 s 14. An apple grove now has 24 trees per acre. The average yield is 200 apples per tree. It is estimated that for each additional tree the average yield per tree will decrease by 6 apples.(Round all answers to the nearest integer.) List 1 (x) represents = # of trees (1 mark) List 2 (y) represents = total # of apples (1 mark)

y = -6x2 + 344x (1 mark) a) How many trees per acre should be added to produce the maximum yield of apples? 28-29 trees produces maximum, therefore, 4-5 trees should be added (to the 24 there is now). b) What is the maximum yield of apples? Max yield is 4930-4931 apples.


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Inductive and Deductive Reasoning

1. Pierre is thinking about even numbers. He makes this conjecture: the sum of any 3

consecutive even integers is divisible by 4. Which of the following sets of numbers

does NOT support the validity of Pierre's conjecture?

A. 2, 4, 6 B. 8, 10, 12 C. 10, 12, 14 D. 14, 16, 18

2. What are the traits of good inductive reasoning?

A. Looking for patterns, identifying properties, gathering evidence, making a

reasonable conjecture

B. Examining the data, making calculations, making guesses

C. Looking for patterns, making guesses

D. None of the above

3. Determine which square completes the pattern: Answer: E

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

All people who work do so from 9 a.m. to 5 p.m., with one hour for lunch.

Bill works, so he works from 9 a.m. to 5 p.m.

A. a false assumption or generalization

B. an error in reasoning

C. an error in calculation

D. There is no error in the deduction.


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5. Kevin claims that the midpoints of any quadrilateral, when joined, form a rhombus

(Definition of a rhombus: A quadrilateral with all four sides equal in length).

Which of the following is a counterexample to Kevin’s conjecture? Answer: C

6. This proof seems to show that 4 = 2. Where is the error?

A. Multiply by a. (Subtract 4b2)

B. Factor.

C. Divide by (a - 2b). (Substitute a = 2b.)

D. Divide by b.

7. Prove that the sum of two consecutive numbers is equal to the difference of the

squares of those numbers. Use algebra or give at least 3 numerical examples to support

the conjecture.

Let x = first number and

x+1 = consecutive number

OR

Examples #1 3 + 4 = 42 − 32 #2 4 + 5 = 52 − 42 #3 5+6 = 62 − 52

7 = 16 - 9 9 = 25 – 16 11 = 36 - 25

7 = 7 9 = 9 11 = 11

𝑥 + (𝑥 + 1) = (𝑥 + 1)2−𝑥2 2𝑥 + 1 = 𝑥2 + 2𝑥 + 1 − 𝑥2

2𝑥 + 1 = 2𝑥 + 1

http://www.mathopenref.com/quadrilateral.html


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8. A 3 X 3 magic square is a square grid in which each whole number from 1 to 9 appears

once, so that the sums of each row, each column, and each diagonal are all equal.

a) What is the sum of each row, column, and diagonal of a 3 X 3 magic square?

15

b) Complete this 3 X 3 magic square.

9. Show the each statement is false by finding a counterexample:

a. If you live in Alberta, you live in a province that shares borders only with

other Canadian provinces.

South border of Alberta borders Montana

b. Any animal that has wings can fly.

ostriches

c. All animals that live in the water are fish.

whales

d. If a quadrilateral has four right angles, then it is a square.

rectangle

e. The sum of two prime numbers is an even number.

2 + 1 = 3

8 3 4

6

9


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

All videos have large groups of dancers. The western band is recording a

new video, so it must have a large group of dancers.

False premise

11. What type of error, if any, occurs in each deduction?

a. All people take public transit to work each day. Lita goes to work each day.

Therefore, Lita takes public transport.

False premise

b. Suppose that: 𝑥 + 𝑦 = 𝑧

Then: (3𝑥 − 2𝑥) + (3𝑦 − 2𝑦) = (3𝑧 − 2𝑧) 3𝑥 + 3𝑦 + 3𝑧 = 2𝑥 + 2𝑦 + 2𝑧 3(𝑥 + 𝑦 + 𝑧) = 2(𝑥 + 𝑦 + 𝑧)

3 = 2

Error in reasoning (can’t divide by 0)

c. All runners can run for one mile without stopping. Leif is a runner.

Therefore, Leif can run for one mile without stopping.

False premise

d. Most students do not go to public school on Sunday. Therefore, most

students should wear blue clothing on Sunday.

Error in reasoning (faulty logic)

e. 2 = 2 4(2) = 4(1 + 1)

4(2) + 3 = 4(1 + 1) + 3 8 + 3 = 6 + 3

11 = 9

Error in calculation (didn’t follow BEDMAS)

f. On the first day of school last year, it was raining. Therefore, it will rain on

the first day of school next year.

Error in reasoning (faulty logic)


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12. You are escaping from an underground maze and encounter two guards, each

standing in front of a door. A mysterious voice tells you that one door leads

to freedom, the other to eternal imprisonment. The voice also tells you that

one guard always tells the truth and the other always lies, but does not tell you

which is which. You are allowed to ask only one question of only one guard.

If you ask the right question, you will be able to escape.

a) Does it matter which guard you ask a question? Explain why or why not.

Eg) No. If it mattered, you might not be able to escape, as you would have to know

already which guard to question.

b) What question should you ask?

Eg) “If I asked the other guard which door he was guarding, what would he say?”

13. a) Make a conjecture about the sum of two consecutive perfect squares.

Eg) The sum of two consecutive perfect squares is always an odd number.

b) List evidence that supports or disproves your conjecture (give examples here

using actual number values).

Eg) Examples in support 22 + 32 = 13, 32 + 42 = 25, 1002 + 1012 = 20 201

c) If possible, prove your conjecture (you must use algebra here).

𝑠 = 𝑥2 + (𝑥 + 1)2

𝑠 = 𝑥2 + 𝑥2 + 2𝑥 + 1 𝑠 = 2𝑥2 + 2𝑥 + 1 𝑠 = 2(𝑥2 + 𝑥) + 1

Since you multiply the brackets by 2 it starts out as an even number, but

when you add one the answer will always be an odd number


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14. Determine the unknown term in each pattern:

15, 45, 135, 405, 1215, 3645

18, 9, 4.5, 2.25, 1.125, 0.5625

2, 2, 4, 6, 10, 16, 26, 42, 68, 110

15. Does the following statement demonstrate inductive reasoning or deductive

reasoning?

For the past three years, a bush has produced roses. Therefore, the bush will

produce roses this year. Inductive reasoning

16. Does each statement show inductive or deductive reasoning?

a) A certain tree has produced oranges each year for the past six years.

Therefore, the tree will produce oranges this year. inductive

b) All reptiles have scales. Iguanas are reptiles.

Therefore, iguanas have scales. deductive

c) Every multiple of 6 has a factor of 3. 24 is a multiple of 6.

Therefore, 24 has a factor of 3. deductive

d) The unknown term in this pattern is 64: 1,4, 16, ____, 256, 1024 inductive

e) Every Tuesday at 10:00 p.m., the news is broadcast on television. deductive

Today is Tuesday; therefore, the news will be broadcast tonight at 10:00 p.m.

f) Every high school student in western Canada must take English. deductive

You are a high school student in western Canada; therefore, you must take English.


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Systems of Linear Inequalities

1. Solve the following system by graphing (pencil and paper):

3 7

2 8

x y

x y

Line 1: 𝑦 ≤ −𝑥

3−

7

3

Line 2: 𝑦 ≥𝑥

2− 4

*Note: inequality sign flips when dividing by negative number


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2. Solve the following system by graphing.

3 6

5

y x

x y

Line 1: 𝑦 ≤𝑥

3− 2

Line 2: 𝑦 > −𝑥 + 5


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3. Mr. Krahn makes Blokus math games. He uses 10 sheets of cardboard and 15

sticks of glue for a basic game and 15 sheets of cardboard and 45 sticks of glue

for a super-deluxe-supreme game. He has available 60 sheets of cardboard and 135

sticks of glue. If Mr. Krahn makes $390 profit on a basic game and $600 on a

super-deluxe-supreme game, how many of each type of game should Mr. Krahn build

to maximize his profit?

Solution x = # basic games y = # super-deluxe-supreme games Define inequalities 10𝑥 + 15𝑦 ≤ 60 Equation of Maximum Profit: 15𝑥 + 45𝑦 ≤ 135 390𝑥 + 600𝑦 = max 𝑝𝑟𝑜𝑓𝑖𝑡 Evaluating possibilities: Sketch of inequalities 390(0) + 600(3) = $1800 390(3) + 600(2) = $2370

390(6) + 600(0) = $2340

Statement (final answer):

Making 3 basic games and 2 super-deluxe

games gives profit of $2370.

Restrictions

Variables

Totals


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4. Solve the following inequalities. Show your answer on the number line and with

interval notation.

2 4 5 2x x Interval solution: (-, -2/3)

−3𝑥 − 4 > −2

−3𝑥 > 2

𝑥 < −2/3 *Note: inequality sign flips when dividing by negative number Number Line -2/3 0

5. Which of the following accurately describes how the solution set for the linear

inequality 3𝑥 − 2𝑦 > 5 should be graphed?

A . dashed line, above line shaded B. solid line, above line shaded

C. dashed line, below line shaded D. dashed line, below line shaded

6. A system of linear inequalities is defined by: 3𝑥 − 2𝑦 < 12 and 𝑥 + 𝑦 ≥ 5.

Which of these points is in the solution set of the system?

A. (5,2.5) B. (5.5,-1) C. (6,3) D. (1,2)

7. Which graph represents the solution set of the given system?

3𝑦 + 𝑥 ≥ 6 and 𝑥 < 5 Answer: A


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8. Ms. Nato makes chocolate chip muffins and all-bran muffins. Each chocolate chip

muffin requires 4 minutes mix time and 3 minutes bake time. Each all-bran muffin

requires 3 minutes mix time and 1 minute bake time. The mixer is available only 2

hours each day, and the oven is available only 1 hour each day.

a) If the profit on a chocolate chip muffin is $3 and the profit on an all-bran

muffin is $5.50, how many of each should be baked each day to maximize her

profit?

b) What is the maximum profit?

Solution x = # bran muffins y = # chocolate chip muffins Define inequalities 3𝑥 + 4𝑦 ≤ 120 Equation of Maximum Profits 𝑥 + 3𝑦 ≤ 60 5.5𝑥 + 3𝑦 = max 𝑝𝑟𝑜𝑓𝑖𝑡𝑠 Evaluating possibilities: Sketch of inequalities 5.5(0) + 3(20) = $60

5.5(24) + 3(12) = $168 5.5(40) + 3(0) = $220


Making 40 bran muffins games gives profit

of $220.

Restrictions

Variables

Totals


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9. A system of linear inequalities is defined by:

x > 3 - 2y and y 5

a) Determine whether (0, 2) is a solution of this system.

Solution? Yes/No (circle one)

b) Is (0.1, 2.1) a solution of the system?

Solution? Yes/No (circle one)

10. Verify that the point ( - 3, 3) is a solution to this system:

5y - x 7

x + 2y < 5

Substitute the point into both inequalities. If it holds true for both, it is a

solution to the system.

(-3, 3) 5𝑦 − 𝑥 ≥ 7 𝑥 + 2𝑦 < 5 5(3) − (−3) ≥ 7 (−3) + 2(3) < 5 15 + 3 ≥ 7 −3 + 6 < 5 18 ≥ 7 True 3 < 5 True

Therefore, (-3, 3) is part of the solution.


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11. Snappy Cards makes two types of greeting cards: scratch'n sniff, or with a

recorded tune that plays when the card is open. The company can make at

most 250 scratch'n'sniff cards and at most 175 tune cards per day. However,

they can make 300 or more cards in total per day. The profit on scratch’n’sniff

cards is $1.25 and on tune cards a $1.75.

What is the optimum number of cards that can be made to maximize the profits.

Show all work for full credit. Define variables x = # scratch and sniff cards y = # recorded tunes cards Define inequalities 𝑥 ≤ 250 𝑦 ≤ 175 Equation of Maximum Profit 𝑥 + 𝑦 ≥ 300 1.25𝑥 + 1.75𝑦 = max 𝑝𝑟𝑜𝑓𝑖𝑡 Evaluating possibilities: Sketch of inequalities 1.25(125) + 1.75(175) = $462.50 1.25(250) + 1.75(175) = $618.75 1.25(250) + 1.75(50) = $400.00


Making 250 scratch and sniff cards and

175 recorded tunes cards profits

$618.75.


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12. Zoe is creating party favours for her sister Janine’s wedding. She can make little

"travel totes" for $1.60 each and small "bling baskets" for $2.30 each.

Janine has asked Zoe to make sure that:

• there are at most 48 favours altogether

• there are at least 24 travel totes

• at least one-third of the favours are bling baskets

Define variables x = # travel totes y = # bling baskets Define inequalities 𝑥 ≥ 24

𝑦 ≥1

3(𝑥 + 𝑦) OR 2𝑦 ≥ 𝑥 Equation of Minimum Costs

𝑥 + 𝑦 ≤ 48 1.60𝑥 + 2.30𝑦 = min 𝑐𝑜𝑠𝑡𝑠 Evaluating possibilities: Sketch of inequalities 1.60(24) + 2.30(24) = $93.60

1.60(32) +2.30(16) = $88 1.60(24) + 2.30(12) = $66


Making 24 totes and 12 baskets costs

$66.


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13. Consider the system of linear inequalities:

3x + y 12

x < 2y - 6

a) Graph the system.

b) For each inequality, determine where to shade (upper or lower).

c) Graph the solution set of the system on the grid provided. Identify two

points in the solution set.

(answers vary – must be coordinates in

the shaded solution area)

14. Consider the system of linear inequalities:

2y - 5x < 7

x > 4


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a) Graph the system below.

b) Identify two

points in the solution set above.

(answers vary – must be

coordinates in the shaded

solution area)


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15. Lorel and Shaida are making shakes and smoothies for the drinks stand at

their school fair. They can make a maximum of 280 drinks altogether, of

which at most 120 can be shakes. They plan to sell shakes for $3.50 each and

smoothies for $2.75 each.

Define variables x = # shakes y = # smoothies Define inequalities 𝑥 ≤ 120 𝑥 + 𝑦 ≤ 280 Equation of Maximum Profits 3.5𝑥 + 2.75𝑦 = max 𝑝𝑟𝑜𝑓𝑖𝑡𝑠 Evaluating possibilities: Sketch of inequalities 3.5(0) + 2.75(280) = $770

3.5(120) + 2.75(160) = $860

3.5(120) + 2.75(0) = $420 Statement (final answer):

Making 120 shakes and 160 smoothies

profits $860.


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Trigonometry

1. You are asked to solve this triangle. Which law, in which form, should you use first?

A. sine law: sin 𝐴

𝑎=

sin 𝐵

𝑏

B. sine law: sin sin

a b

A B

C. cosine law: c2 = a2 + b2 - 2ab cos C

D. cosine law: ab

cbaC

2

222

2. In JKL,j = 38 mm, k = 32 mm, and J = 107°. How many triangles are possible

with these dimensions?

A. 0 B. 1 C. 2 D. not enough information to determine

3. Determine the measure of the indicated angle, to the nearest degree.

A. 31° B. 65°

C 69° D. 80°


A. 62° B. 56°

C. 52° D. 46°


26 | P a g e


A. 16° B. 60°

C. 32° D. 74°

6. Determine the indicated side length, to the nearest tenth.

A. 18.1mm C. 23.5 mm

B. 18.6 mm D. 29.2 mm


A. 1.9 m C. 26.1m

B. 6.8 m D. 46.6 m


A. 7.4 cm B. 5.8 cm

C. 4.8 cm D. 4.7 cm


27 | P a g e

9. Simon knows lengths a and c in ABC. He also knows one of the angles, and this

gives him enough information to use the cosine law to determine b. Which angle

could be the one Simon knows?

A. LA B. LB C. LC D. any of these

10. Which of the following ratios is the same for each side—angle pair in a triangle?

A. a

Asin B.

A

a

sin C. both D. neither

11. You are given three pieces of information about the measures of the angles and

sides in a triangle. In which of the following situations can the sine law NOT be

used to solve the triangle?

A. SSA B. SAS C. ASA D. AAS

12. In XYZ, x = 4.3 cm, y = 3 . 1 cm, and z = 5.9 cm. Which is the largest angle,

and is it obtuse?

A. LY; yes B. LZ; yes C. LZ; no D. LY; no

13. Which set of measurements results in no possible triangles?

A. LP = 25°, p = 3.5 m, q = 6.2 m C. LP = 135°, p = 3.8 m, q = 4.0 m

B. LP = 96°, p = 5.2 m, q= 5.0 m D. LP = 48°, p = 7.4 m, q = 7.1 m

14. The cosine law does not have an ambiguous case. Why not?

A. The cosine law does not apply to obtuse triangles.

B. The cosine of an obtuse angle is always negative.

C. The principal value of a square root is always positive.

D. The cosine law cannot be used if the unknown angle is obtuse.


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15. Solve DEF. Round to the nearest tenth of a centimetre or the nearest degree.

Triangle #1 F = 52.48° E = 86.52° e = 10.19 cm

Triangle #2 F = 127.52° E = 11.48° e = 2.03 cm

16. Solve PQR. Round to the nearest tenth of a metre or the nearest degree.

P = 51.33° E = 61.67° e = 6.48 cm


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17. Martin determines the height of a pylon on the far side of a railway line by taking

measurements from two positions, A and B. The base of the pylon is at C, and its top is

directly above C at D. The diagram shows the positions of A, B, C, and D, as well as

the measurements Martin took. Determine the following, to the nearest tenth.

a) What is the length of AC? 20.89 m

b) What is the height of the pylon? 25.80 m

18. Solve PQR. Round lengths to the nearest

tenth of a centimetre and angles to the nearest degree.

∠R = 30°

q = 4.36 cm

r = 2.37 cm

19. Solve UVW. Round angles to the nearest degree and

lengths to the nearest tenth of a metre.

w = 6.68

∠V = 60.26°

∠U = 47.74°


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20. Ricardo is landscaping part of a garden in the shape of an acute triangle. He

wants the sides of the triangle to be 13 m, 17 m, and 19 m long. Determine,

to the nearest degree,

a) the measure of the smallest angle in Ricardos triangle: 41.88 °

b) the measure of the largest angle in Ricardo s triangle: 77.32 °

21. Richard has copied down a question about XYZ. He knows that ∠X

measures 50° and that two of the side lengths are 11 cm and 15 cm, but he

does not know which given side length is x and which is y. However, Richard’s

friend Pam assures him that there is a possible solution for XYZ.

a) What are the given side lengths? x =_15 cm y =_11 cm

b) Solve XYZ. Round to the nearest degree or the nearest tenth of a cm.

z = 19.5 cm

∠Y = 34°

∠Z = 96°


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22. In ABC, AB = 14 cm, BC = 15 cm, and AC = 16 cm.

a) Which is the smallest angle in ABC? Which is the largest? Explain using a

diagram.

Smallest ∠C (across from smallest side 14 cm)

Largest ∠B (across from largest side 16 cm)

b) Determine the measure of the largest angle in ABC to the nearest degree.

∠B = 67°

23. In XYZ, x= 1.1 m, y = 1.3 m, and X = 52°.

a) Draw sketches of all possible triangles XYZ.

Ambiguous case – two triangles exist

b) Solve each possible triangle XYZ. Round to the nearest degree or the nearest

tenth of a metre.

Triangle #1 ∠Y = 69° ∠Z = 59° z = 1.2 m

Triangle #2 ∠Y = 111° ∠Z = 17° z = 0.4 m


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24. Zenab and Krista set out on a canoe trip. Starting from the dock, they paddle

northeast for 5.4 km until they reach Foggy Island, then turn due east,

reaching Brousseau Township after another 2.6 km. Krista wonders how far it

is from Brousseau back to the dock. Zenab remembers that the angle between

the bearings from the dock to Foggy Island and to Brousseau is about 25°.

a) Sketch the situation.

See solution key

b) Determine the return distance from Brousseau to the dock, to the nearest

tenth of a kilometre.

Ambiguous triangle – two triangles exist without knowing the

directions of the locations (either 6.2 km or 3.6 km are possible

answers)

25. A tree standing on the side of a hill casts a shadow uphill. The hill slopes at

an angle of 12°. When the angle of elevation of the Sun is 37°, the shadow is

48 m long. How tall is the tree, to the nearest metre?

45 m

26. The base of a cliff, A, is surveyed from two different points,

C and D, at the same horizontal level. The elevation of

the top of the cliff, B, is taken from C.

a) What is the height of the cliff (AB), to the nearest metre?

240 m

b) To the nearest degree, what is the elevation of the cliff (to the top at B) taken

from D?

65°


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27. a) Determine the diagonal length AC of the rectangle,

to the nearest millimetre.

12 mm

b) Determine the longer side length of the rectangle, to the nearest millimetre.

11 mm

28. Marina’s tiger kite has the measurements shown.

What is the length of AC (from tip to tail of the kite)

to the nearest tenth?

52.4 cm


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Statistics

1. Based on their standard deviations, which of these two sets of test scores

(both out of 100) is more dispersed?

A. Class A is significantly more dispersed.

B. Class B is significantly more dispersed.

C. The classes are about equally dispersed.

D. The standard deviations do not give enough information to decide.

2. The lengths of a sample of fully grown monarch butterfly caterpillars are normally

distributed, with a mean of 4.9 cm and a standard deviation of 0.3 cm.

What percent of caterpillars would you expect to be longer than 5.5 cm?

A. 5% B. 95% C. 2% to 3% D. 17%

3. For which of these data sets are the mean, median, and mode equal?

A. 5.5 cm, 6.0 cm, 7.5 cm, 9.0 cm, 9.5 cm

B. 1.0 m, 4.0 m, 4.0 m, 4.5 m, 5.0 m, 5.5 m

C. 8 g , 11 g , 13 g, 13 g, 16 g, 17 g

D. sizes: 21, 22, 24, 24, 25,29


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4. Predict which data set has the smallest standard deviation.

A. data set A B. data set B

C. data set C D. not enough information to decide

5. Which of the following increases the width of a confidence interval and the margin

of error?

A. an increased confidence level B. a reduced confidence level

C. an increased sample size D. none of these choices

6. Art scores 87 on a chemistry test and 79 on a French test. The mean and standard

deviation on both tests are shown. Determine Art’s z-scores on each test, to the

nearest hundredth:

Chemistry 0.64

French 0.90


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7. A telephone survey of 900 randomly selected respondents determined that 68% of

Canadian adults watch at least one hockey game per month during the regular and

post season. The results are accurate within 3 percent points, 19 times out of 20.

a) State the confidence level: 95%

b) State the margin of error: ± 3 %

c) Determine the confidence interval: 65% to 71%

d) If the adult population of Canada is 24 986 000, what is the range of people

that this survey predicts will watch at least one game per month?

Between 16 240 900 and 17 740 060 Canadians

8. Twin brothers Eric and Basil are arguing about who did better overall in recent

math tests. Eric scored 83 in Algebra and 92 in Geometry, while Basil scored 87 in

Algebra and 90 in Geometry Suppose the scores in Algebra were approximately

normally distributed with mean 67 and standard deviation 15, and the scores in

Geometry were approximately normally distributed with mean 69 and standard

deviation 18.

a) What are Eric's z-scores on the tests?

Algebra: 1.07 Geometry: 1.28

b) What are Basils z-scores?

Algebra: 1.33 Geometry: 1.17

c) Based on each brothers average z-score, who did better overall?

Basil


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9. The table shows reported sales by shoe size from two shoe stores on the same

day in June 2011. To the nearest tenth,

a) what was the mean shoe size sold at store A?

45.1

At store B? 45.3

b) what was the standard deviation for store A?

4.1

For store B? 4.5

c) Which store sold the greater proportion of sizes 39 or smaller?

Store B

10. a) Complete the frequency table for the following mass data for sea shells, in mg:

168, 290, 224, 254, 189, 268, 210, 156, 227, 254, 181, 193, 260, 303, 295, 259,

330, 217, 175, 284, 232, 205, 250, 172, 248, 278, 348, 317, 320, 193

b) Draw a histogram for this data on the grid

provided. Masses of Seashells

3

5

4

3

6

4

3

2

200-225

225-250

325-350

300-325

275-300

250-275


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11. a) Based on the frequency distribution shown in the table, construct a histogram for

this height data on the grid provided.

b) Calculate the mean and median for the data.

12. Using the tally chart and grid, create a histogram for the following data:

Heights of Bean Plants

1

3

4

4

3

1

1

2

20-24

25-29

45-49

40-44

35-39

30-34

5

2

4

50-54

55-59

60-64

65-69

70-74


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13. Cartons of a brand of breakfast cereal have a mean net mass of 300 g. The quality

control officer wants to ensure that regularly taken samples of cartons have a mean mass

between 299.5 g and 300.5 g. The table guides the sampling process.

a) What confidence interval and margin of

error are being used?

Confidence interval: 299.5 – 300.5 g

Margin of error: ±0.5 g

b) Approximately how many cartons should be sampled to ensure the mean

mass is within the acceptable range 99% of the time?

164 cartons

a) What happens to the sample size as the confidence level increases? Why?

The sample size increases when the confidence level increases. Eg) A larger

sample must be taken to be more certain that samples have a mean mass in

the acceptable range.


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For the exam you will need to bring:

o Your test notes (one page 2 sides)

o Your graphing calculator – MAKE SURE

TO HAVE AAA BATTERIES THAT

WORK!

o A ruler and a pencil

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