High School Math - Others Questions

grams a How many different anagrams including nonsensical words can be made from SUCCESS b How many can be made if we require that the first and last letters must both be S c How many distinct arrangements of the word SUCCESS are there with the condition that con sonants always should come together as one block Examples SSSCCUE SSSCCEU CSSSCEU etc

You and your friend want to take graduation pictures with a few of your fellow computer science class mates making 10 of you in total You hired a very expensive photographer for the occasion and want to make the most of the experience You want to select four students to stand in the front of the group in a line In how many ways is it possible to take the pictures such that a you have a place at the front of the group photo b you and your friend have a place together at the front of the group photo

5 Binomial Theorem Using the Binomial Theorem what is the coefficient of a x 13 in x 2 30 b y13 in 2 y 30

Sketch the graph of the function Include two full periods Use a graphing utility to verify your result y 2 sec 2x 1 I 4 U 4 3 4 2 y

Changes in the timbre or tone color in a piece of music

c Write down the minimum height of point P 1 Later the cat is tired and it takes twice as long for point P to complete one revolution at a new constant rate d Write down the new value of b

follow a periodic pattern of rise and fall called the tides The graph below shows the sea level at a certain beach in feet over two days where time t is measured in hours after 12 00 a m midnight on the first day Sea level in feet 8 5 24 20 5 24 25 0 Time in hours 14 5 0 Write an equation in terms of y the sea level in feet and t time in hours to represent the given context

The pressures caused by pure tones on the eardrum are sinusoidal The change in pressure P in pounds per square foot on a person s eardrum from a pure tone at time t in seconds can be modeled using the equation P Asin 2xft d where f is the frequency in cycle per second and is the phase angle When P is positive there is an increase in pressure and the eardrum is pushed inward when P is negative there is a decrease in pressure and the eardrum is pushed outward A graph of a tone P t 008 sin 2x 274 42 t shown to the right Complete parts a through c below 2 274 421 is 008 Q 005 Q 008 a Determine algebraically the values of t for which P 0 over 0 005 The solution set is Round to five decimal places as needed Use a comma to separate answers as needed b From the graph and your answer in part a determine the interval for which P 0 over 0 005 Type your answer in interval notation c Would an eardrum hearing this tone be vibrating outward or inward when P 0 Outward

Irina uses a set of coordinate axes to draw her design of a window The base of the window is on the 2 axis the upper part of the window is in the form of a quadratic curve and the sides are vertical lines as shown on the diagram The curve has end points 0 10 and 8 10 and its vertex is 4 12 Distances are measured in centimetres The quadratic curve can be expressed in the form ya br c for 0 8 a Write down the value of c a ill Hence find the equation of the quadratic curve b Find the area of the shaded region In Irina s design

Mr Young built a greenhouse 42 feet wide 110 feet long 5 feet to the eaves and 14 feet to the ridge cap How many square feet of plastic does it take to enclose the greenhouse

18 What happened to Wade the day after he completed the first task that changed his life for the better

Question 3 A baker uses the expression 5 75c 3 45p to calculate his profit when he sells c cakes and p pies What is the baker s profit in dollars when he sells 33 cakes and 42 pies

To which of the following rules does this example apply There were about 500 guests at Richard and Roselle s wedding party If the possessive case is a singular noun or an indefinite noun then the apostrophe is put at the end of the noun along with an s If the possessive case is a plural noun that end in s then the apostrophe is put at the end of the plural noun after the final s If the possessive case is a plural noun that does not end in s then the apostrophe is put at the end of the plural noun along with an s If there are two or more possessors of a certain object then the apostrophe is put at

7 P Q R are points on the sides BC CA AB respectively of the triangle ABC such that BP CQ AR are respectively one third of BC CA AB Prove that the area of the triangle PQR is one third that of the triangle ABC

11 Find w to find the measure of the exterior angle 13 Find mZH W 68 6x 1 H 126 F G 5x 17 12 Find x to find the measure of the remote interior angle 46 134 14 Determine the measure of the indicated exterior angle in the diagram 3x 4 15 Match each angle with its corresponding measure given m21 130 and m 7 70 Indicate a match by writing the letter for the angle on the line in front of the corresponding angle measure A mz2 B m23 C m24 D m25 E mZ6 50 60 70 110 120 16 The map of France commonly used in the 1600s was significantly revised as a result of a triangulation survey The diagram shows part of the survey map Use the diagram to find the measure of ZKMJ Note that ZKMJ ZNKM LA ROCHELLE 104 Rochefort 88 48 M N

4 A polygon has an interior angle sum of 3060 How many sides must the polygon have 3080 5 Two of the angles in a triangle measure 50 and 27 Find the measure of the third angle Solve for the unknown angle measures of the polygon 6 A pentagon has angle measures of 100 105 110 and 115 Find the fifth angle measure 116 7 The measures of 13 angles of a 14 gon add up to 2014 Find the fourteenth angle measure 8 Determine the unknown angle measures for the quadrilateral in the diagram 9 The cross section of a beehive reveals it is made of regular hexagons What is the measure of each angle in the regular hexagon 22

4 Euclid Algorithm Use Euclid s algorithm to compute the following Show all your steps 1 gcd 781 994 2 gcd 67457 43521

2 Divisibility What are the quotient and remainder when 1 44 is divided by 6 2 994 is divided by 13 3 221 is divided by 16

9 In the triangle shown XY 222 272 2 22 27 cos 39 Label all the sides and angles of the triangle with their measures to the nearest tenth Y Z

Find the length of segment JK Round to the nearest hundredth J 23 H 29 31

8 Which of the following sets of conditions for AABC requires the Law of Cosines to solve the triangle A mZA mZB c B mZA mZC a C mZA b c D mZA a b

3 SECTION 3 1 a c 3 5 3 2 33 5 e A b 2 B 2 2 7 d d30 d5 x d6 f 5s 2 x 125s3 36

7 State the number of possible triangles that can be formed using the given measuremen a m s 136 PS 14 MP 11 b BC 30 mZA 71 AB 22

Write name date and period Show all sketches and work 1 Solve for m F Round to the nearest tenth F E 107 9 7 G

About 3 2 108 people live in the United States About 3 9 x 107 people live in Canada And about 1 1 x 108 people live in Mexico About how many people live in all three countries altogether a 4 69 x 107 b 4 69 x 108 c 8 2 x 107 lt over blow 10 d 8 2 108

1 Onto one to one bijection Consider the function f NU 0 NU 0 where f is defined as x 1 if x is even x 1 f x x 1 if x is odd 1 Is f is one to one If yes prove it otherwise provide a counter example 2 Is f is onto If yes prove it otherwise provide a counter example 3 Is f is bijection If so find f 1 inverse of f

Bir m teri bir mal n sat fiyat nda 20 indirim yap l rsa elindeki parayla bu maldan 5 adet daha fazla al yor Buna g re m teri elindeki parayla indirimli maldan ka

4 Proof by induction Assume n is a positive integer Use induction to prove the following 1 5 9 4n 3 2n2 N

Simplify the expression 1 cos 59 78 sin 59 78 1 cos 59 78 sin 59 78 Simplify your answer Use integers or decimals for any numbers in the expression Do not include the degree symbol in your a

Two teams of scientists explore a cave system inside a mountain From the entrance to the cave Team A hikes 192 ft down to an underground lake Team B hikes 175 ft up to explore an open space Which statement is correct regarding the position of the two teams relative to the cave s entrance O Team A is farther from the entrance than Team B because 192 175 O Team A is farther from the entrance than Team B because 192 175 O Team B is farther from the entrance than Team A because 192 175 O Team B is farther from the entrance than Team A because 192 175

17 3 8 18 19 20 10 7 5 7 7 12 4 54 x 7 35

ement of the progress bar may be uneven because questions can be worth more or less including zero depending on your answer Which of the writing prompts below calls for an evaluative thesis O Analyze the roles of exercise and diet in a healthy lifestyle O Compare and contrast the costs and savings of buying and renting a home O Use Shakespeare s plays to argue whether comedy or drama stands the test of time better Compare and contrast vegetarian and vegan diets and summarize their nutritional concerns

b Convert the equation to vertex form algebraically using complete the square method Write the equation using function notation c Describe the transformations applied to y x2 to get the resulting equation Task 3 Analyzing the situation a Determine the zeros algebraically and explain what these mean for b Determine the vertex and explain what this means for your situation your situation

29 What was Dennis s plan when he told Jeremiah to unbuckle himself a To fight Anna b To hide from Anna c To run away from Anna d To stay near the truck

2 The amount of dry matter in tomatoes measured in grams is the amount of solid content of the fruit subtract the water content The table below shows weights of dry matter in 10 tomatoes grown in soil with different amounts of calcium Ca measured in mg cm Ca in soil mg cm x Weight of dry matter g y 12 13 15 17 18 19 21 22 23 25 2 9 31 47 4 5 47 5 3 6 1 65 62 68 a 1 ii b 1 Find the Pearson s product moment correlation coefficient r for this data 0 96 Comment on the strength of the r value found Strong Poative linear correlation Find the Spearman s rank correlation coefficient r for this data ii Comment on the strength of the r value found c In the context of this question and the data provided comment on if both correla coefficients should be considered when determining the relationships between calcium content and dry matter weight or if one should be used in favour of the

B If DE 16x 3 EF 9x 11 and DF 52 find HG E D H

The table gives temperatures in degrees Fahrenheit in a certain town on a given day The sinusoidal functioni F t 8 cos t c 30 models the data where F t is the temperature in F at time t in hours past 12 midnight and c is a constant Which of the following is true about the value of e A B D The value of cis 2 because this accounts for a phase shift of g t 8 cos t 30 that aligns a minimum value of the data set with a minimum value of g The value of cis 2 because this accounts for a vertical shift of g t 8 cos t 30 that aligns a minimum value of the data set with a minimum value of g The value of c is 14 because this accounts for a phase shift of g t 8 cos t 30 that aligns a maximum value of the data set with a maximum value of g The value of cis 14 because this accounts for a vertical shift of g t 8 cos t 30 that aligns a maximum value of the data set with a maximum value of g

Study the following information The process below details the Federal Government s actions involved combating which which of the following economic issues The Federal in Households and Ag Government reduces taxes individuals cut spending d A recession O Unemployment

Task 1 Modelling a real world situation You have been asked to sell tickets to a charity event You know that as the price of the ticket increases there will be less people who are able to attend Your task is to come up with the equation which would best model the ticket price in compared to the revenue Let x represent the price of the ticket and y represent the revenue in you would be able to raise for charity Unit Price 5 Profit 11250 10 12000 15 12250 20 12000 25 11250 30 10000 35 8250 6000 3250 40 45 a Copy the table and graph the points you see and include the line of the best fit You may use the graphing software to help you have to adjust this after you have completed task 2

ask 3 Analyzing a Determine the zeros algebraically and explain what these mean for your situation b Determine the vertex and explain what this means for your situation

Task 2 Equation of the situation a Determine the equation of the situation in standard form Write the equation using function notation Use a graphing app Like Desmos GeoGebra or Google Sheets create the graph and include it in your submission b Convert the equation to vertex form algebraically using complete the square method Write the equation using function notation c Describe the transformations applied to y x2 to get the resulting equation

Drag the tiles to the correct boxes to complete the pairs Not all tiles will be used C B 90 5 3 Match the trigonometric ratios with their values based on the triangle shown in the diagram sin D cos Cx tan D sin C sin D x cos D tan Cx tan D 22 310 199

Let S and T be two sets defined as S 1 2 3 5 and T 2 4 6 7 8 9 10 Let f be a binary relation from S to T defined by the set of ordered pairs 1 Is fa function f 1 2 2 4 3 4 5 6 2 What is the domain of f codomain of f 3 What is the image of f 4 What is the image of 2 and the image of 3 5 What is the pre image of 2 6 Is this a one to one function

4 Composition of functions For each of the following pairs of functions f and g calculate go f and fog 1 f 1 2 3 4 5 6 and g 2 1 4 3 6 5 2 f x 2x 1 and g x 4x 5 for all x Z

a Consider the three following Hasse diagrams representing three poset relations RA RB and Rc a a b 3 4 b b C a 1 2 A B C 1 For each poset list all the ordered pairs that belong to the relation 2 For each relation provide all least minimal greatest and maximal elements b Which of the following posets are lattices Justify your work for the non lattices only 1 1 2 2 3 A B 3 2 3 3 D

5 Inverse functions Let f be a bijective function f RR defined by f x 4x 5 1 Find the inverse of f 2 Calculate f 1 of and fof 1 What do you notice

In 1 m and n are direction cosine of a vector then a 12 m n 1 c 12 m n 1 2 b 12 m n 1 d 1 m n 1

B C R 2 3 as MAX es 06 In the figure shown point B and the center of each circle lie on AC The ratio of AB to BC is 4 to 1 If the area of the small circle is 72 what is the area of the shaded region TE

13 Let A 4 3 be the initial side and B 2 5 be the terminal side a Find the ordered pair for vector AB Find the horizontal and vertical components b Find the magnitude of AB Round o the nearest thousandth 0 Find the direction Round to the nearest thousandth

TASK 2 Modelling a function 1 The following function h x 2 x 12 5 has undergone a horizontal transition o the right a vertical transition up by 3 and stretched by the factor of 4 What would be function 3 marks