Applied Math 30S Exam Review - Ms. Turnbull's Math ...msturnbullmath.weebly.com/uploads/1/0/9/4/10943432/... · Web view1. Ms. Wagner cranks a fly ball deep into left field (probably

Applied Math 30S

Exam Review Booklet

Name: _______________

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 ExamJanuary ___, 2012

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? __________________

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

c) How high is the ball at the highest point? _______________________

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

e) When is the ball at a height of 28 m? ________________________

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.

b) Define your variables and write an equation.

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

d) What is the maximum area?

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 =___________

c) Determine the coordinates of the vertex:

(__________ , __________)

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

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

b) Determine another point with the same y-coordinate as the y-intercept:( _____ . ______ )

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

e) Determine the vertex: (_______ , _______ ).

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

a) the coordinates of its vertex: (______ , _______)

b) its y-intercept:

c) its domain and range:

8. Determine the vertex of the parabola defined by the quadratic function y = 2x2 - 1Ox + 7.

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 mark)

10. For the function find the following:a) vertexb) axis of symmetryc) domaind) rangee) x-interceptf) y-interceptg) max or minh) graph the function

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).

List 1 (x) represents = ______________________ (1 mark)

List 2 (y) represents = ______________________ (1 mark)

y = ______________________ (1 mark)

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

b) What is the maximum area?

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?

Applied Math 30S Exam Review 2012

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?

b) When does the ball hit the ground?

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

d) How high is the ball when the time is 1.2 seconds?

e) When is the ball at a height of 25 m?

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 = ______________________ (1 mark)

List 2 (y) represents = ______________________ (1 mark)

y = ______________________ (1 mark)

a) How many trees per acre should be added to produce the maximum yield of apples?

b) What is the maximum yield of apples?

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Proportional and Deductive Reasoning

1. It is the day before Halloween and you are out shopping. You see a sign for toilet paper: Bounty 2 Rolls 64-sheets per roll for $2.69

Royale Extra 2 Rolls 75-sheets per roll for 2.89Viva 2 Rolls 100-sheets per roll for $3.09.

Which is the better buy? Justify your answer and don’t even think about toilet papering your teacher’s house.

2. 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

3. Richard is roasting a chicken with a mass of 1.85 kg. His cookery book says to allow 15 min cooking time per pound, plus an extra 15 min. Given that 2.2 lb = 1 kg, how long should Richard leave the chicken in the oven?

A. 1 h 1 min B. 43 min C. 1 h 11 min D. 1 h 16 min

4. Michael was solving the equation x2 + 2x + 1 = x - 1. Where did he make an error?

A. line 2 B. line 3 C. line 4 D. line 5

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5. Two similar objects have a scale factor of 1:2.5 associated with them.The volume of the smaller object is 400 cm3. What is the larger objectsvolume?A. 1000 cm3 B. 2500 cm3 C. 6250 cm3 D. none of these

6. 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 Kevins conjecture?

7. 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.

8. a) How many ways can you colour the edges of pentagon ABCDE so that each edge is

either red, blue, or green, and two edges that meet at a vertex are different colours?

_________ways

b) How many ways can you colour the edges of square ABCD in the same way as the pentagon in part a)?

__________ways

9. Solve the Kakuro puzzle.

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


10. 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?

b) Complete this 3 X 3 magic square.

11. Nina and Franco are comparing their SUV and sedan fuel costs. On a 250 km trip, the SUV uses 45.3 L of gas. On a similar trip, of 180 km, the sedan uses

28.7 L of gas. Rounding to the nearest tenth, what is the fuel economy

a) of the SUV? __________L/100 km

b) of the sedan? __________L/100 km

c) By how much, to the nearest percent, is the sedan more fuel efficient?______%

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12. The scale diagram represents the net for a gift box. The base of the box is 15 mm wide on the diagram. The actual box will be 22.5 cm wide.

a) What is the scale ratio of the diagram? 1:________

b) How many times larger is the surface area of theactual box than the area of the diagram?

________times larger

13. This floor plan was sketched at a scale ratio of 1 : 200. Not all the room measurements were recorded. What is the actual area of the largest room? _______________m2

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14. Prove that the sum of two consecutive numbers is equal to the difference of the squares of those numbers.

15. The sum of the squares of three consecutive odd integers is 683.

a) Develop an algebraic equation to represent this situation.

b) What are the integers (positive or negative whole numbers)?

16. Brian uses a cookie dough recipe that calls for 250 mL of water per 400 mLof flour. Erin's cookie dough recipe calls for 200 mL of flour per 150 mL ofwater.

a) Which recipe uses the greater proportion of flour?

b) Brian and Erin agree to share a 1 kg bag of flour equally. How much waterwill each of them use?

17. a) What is the ratio of the radii of the two cylinders?

b) Determine the ratio of the surface areas of the cylinders. Show your work.

Note: SA of a cylinder is 2π r2+2 πrh

18. You are escaping from an underground maze and encounter two guards, eachstanding in front of a door. A mysterious voice tells you that one door leadsto freedom, the other to eternal imprisonment. The voice also tells you thatone guard always tells the truth and the other always lies, but does not tell

youwhich 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.

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

b) What question should you ask?

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

b) List evidence that supports or disproves your conjecture (give examples here using actual number values).

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

20. Murray is wrapping a number of identical boxes for gifts for co-workers. Eachbox needs a length of 57 cm from a roll of gift wrap. There are two gift-wrapoptions, at different stores: 3 m rolls at $16.49 or 4 m rolls at $19.99. To saveon shopping time, Murray wants to get only one kind of wrap.

a) If Murray has 15 gifts to wrap, should he buy 3 m or 4 m rolls?

b) If Murray has many extra gifts to wrap, which rolls should he buy?

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x-10 -5 5 10

y

-10

-5

5

10

x-10 -5 5 10

y

-10

-5

5

10


Systems of Linear Inequalities

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

2. Solve the following system by graphing.

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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 =

y =

Define inequalities

_____________________________ Equation of Maximum Profit:

_____________________________ __________________________________

_____________________________ Evaluating possibilities:

Sketch of inequalities __________________________________

__________________________________

__________________________________

Statement (final answer):

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

Interval solution: __________________

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Number Line

5. Which of the following accurately describes how the solution set for the linear inequality 3 x−2 y>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: 3 x−2 y<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?3 y+x≥6 and x<5

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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 =

y =

Define inequalities

_____________________________ Equation of Maximum Profits:

_____________________________ __________________________________

_____________________________ Evaluating possibilities:

Sketch of inequalities __________________________________

__________________________________

__________________________________


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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 ¿ 7x + 2y < 5

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11. Snappy Cards makes two types of greeting cards: scratch'n sniff, or with arecorded tune that plays when the card is open. The company can make atmost 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 =

y =

Define inequalities

_______________________________

_______________________________

Sketch of graphed inequalities – all possible solutions

Equation of Maximum Profits:

__________________________________

Evaluating possibilities:

__________________________________

__________________________________

__________________________________


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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

What is the most they can make will spending minimum costs?

Define variables

x =

y =

Define inequalities

_______________________________

_______________________________


Equation of Minimum Costs:

__________________________________


__________________________________

__________________________________

__________________________________


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x-10 -5 5 10

y

-10

-5

5

10

x-10 -5 5 10

y

-10

-5

5

10


13. Consider the system of linear inequalities:3x + y ¿ 12x < 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 twopoints in the solution set.

14. Consider the system of linear inequalities:2y - 5x < 7x > 4

a) Graph the system below.

b) Identify two points in thesolution set above.

15. Lorel and Shaida are making shakes and smoothies for the drinks stand attheir school fair. They can make a maximum of 280 drinks altogether, ofwhich at most 120 can be shakes. They plan to sell shakes for $3.50 each

andsmoothies for $2.75 each. What is their maximum profit they can make?

Define variables

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x =

y =

Define inequalities

_______________________________

_______________________________


Equation of Maximum Profits:

__________________________________


__________________________________

__________________________________

__________________________________


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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 Aa = sinBb

B. sine law: a

sin A= bsinB

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

D. cosine law: C=a

2+b2−c2

2ab

2. In Δ 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°

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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

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9. Simon knows lengths a and c in ΔABC. 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. sin Aa B.

asin A 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 ΔXYZ, 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 ΔDEF. Round to the nearest tenth of a centimetre or the nearest degree.

F =__________ ° E =___________ ° e =__________

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

P =__________ ° R =___________ ° q =__________

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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? ________________m

b) What is the height of the pylon? ___________m

18. Solve ΔPQR. Round lengths to the nearest tenth of a centimetre and angles to the nearest degree.

19. Solve ΔUVW. Round angles to the nearest degree and lengths to the nearest tenth of a metre.

20. Ricardo is landscaping part of a garden in the shape of an acute triangle. Hewants 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:__________ °

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

21. Richard has copied down a question about ΔXYZ. He knows that ∠Xmeasures 50° and that two of the side lengths are 11 cm and 15 cm, but hedoes not know which given side length is x and which is y. However,

Richard’sfriend Pam assures him that there is a possible solution for ΔXYZ.

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

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

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

a) Which is the smallest angle in ΔABC? Which is the largest? Explain using a diagram.

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

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

a) Draw sketches of all possible triangles XYZ.

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

tenth of a metre.

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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 itis from Brousseau back to the dock. Zenab remembers that the angle betweenthe bearings from the dock to Foggy Island and to Brousseau is about 25°.

a) Sketch the situation.

b) Determine the return distance from Brousseau to the dock, to the nearest tenth of a kilometre.

25. A tree standing on the side of a hill casts a shadow uphill. The hill slopes atan angle of 12°. When the angle of elevation of the Sun is 37°, the shadow is48 m long. How tall is the tree, to the nearest metre?

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?

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

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

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

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?

28.

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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 cmB. 1.0 m, 4.0 m, 4.0 m, 4.5 m, 5.0 m, 5.5 mC. 8 g , 11 g , 13 g, 13 g, 16 g, 17 gD. 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 levelC. 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___________

French_____________

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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: __________%

b) State the margin of error: __________%

c) Determine the confidence interval: __________% to __________%

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_______________ and _______________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:_____________ Geometry:_______________

b) What are Basils z-scores?

Algebra:_____________ Geometry:_______________

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

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9. The table shows reported sales by shoe size from two shoe stores on the sameday in June 2011. To the nearest tenth,

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

At store B?

b) what was the standard deviation for store A?

For store B?

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

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.

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

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12. 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?

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

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

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

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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

Documents

Applied Math 30S Exam Review - Ms. Turnbull's Math ...msturnbullmath.weebly.com/uploads/1/0/9/4/10943432/... · Web view1. Ms. Wagner cranks a fly ball deep into left field (probably