High School Math - Others Questions

f Boris recorded the number of daylight hours on the first day of each month in a northern hemisphere town This data was plotted onto a scatter diagram The points were then joined by a smooth curve with minimum point 0 8 and maximum point 6 16 as shown in the following diagram hours of daylight each day 16 12 6 9 12 month of the year Let the curve in the diagram be y f t where t is the time measured in months since Boris first recorded these values Boris thinks that f t might be modelled by a quadratic function leng a Write down one reason why a quadratic function would not be a good model for the number of hours of daylight per day across a number of years Paula thinks that a better model is f t a cos bt d t 0 for specific values of a b and d For Paula s model use the diagram to write down b the amplitude c the period d the equation of the principal axis e Hence or otherwise find the equation of this model in the form f t a cos bt d For the first year of the model find the length of time when there 10 hours and 30 minutes of daylight per day 1

2 a Write an equation of the form y a x h k with vertex 2 10 that models the flight path for the toy rocket assuming the rocket leaves the ground at 0 0 5 marks Hint to find the value of a use the coordinates of a point where rocket leaves the groung and your knowledge of h and k values of the vertex form b What are the domain and range of the function What do they represent in this situation 3 marks

Sylvia makes pizzas at an Italian restaurant A large pizza is listed on the menu as being 16 inches Sylvia wants to know how accurate she is at throwing dough to that size A coworker measures all the pizzas Sylvia throws and they randomly select 35 data points They use this data to calculate the following 95 confidence interval 15 85 16 10 Use this to recommend a strategic decision 1 point Sylvia should use more dough since the least value of the confidence interval is less than 16 inches Sylvia should use less dough since the greatest value of the confidence interval is greater than 16 inches Sylvia should continue using the same amount of dough since 16 inches is contained within the confidence interval O Sylvia should use more dough so that the entire confidence interval is greater than 16 inches

approximafely modelled by the equation P asin bt c a b c R where t is measured in mont is from the time of the initial measurements In a 12 month period the maximum population is 2600 and oceurs when t 3 and the minimum population is 800 and occurs when t 9 Find the value of t at which the population first reaches 2200 P 3 2600 80 a i Find the value of a a ii Find the value of b 9 800 12 t a iii Find the value of c Find the value of t at which the population first reaches 2200

Consider the function f x ax2 bx c The graph of y f x is shown in the diagram The vertex of the graph has coordinates 0 5 12 5 The graph intersects the x axis at two points 2 0 and p 0 diagram not to scale 2 0 p 0 10

The graph of the quadratic function f x x 2 x 8 intersects the y axis at 0 c a Find the value of c C 8 The vertex of the function is 3 12 5 b Write down the equation for the axis of symmetry of the graph The equation f x 12 has two solutions The first solution is x 10 c d e Use the symmetry of the graph to show that the second solution is x 4 om Write down the x intercepts of the graph On graph paper draw the graph of y f x for 10 x 4 and 14 y 14 Use a scale of 1 cm to represent 1 unit on the x axis and 1 cm to represent 2 units on the y axis

A player throws a basketball The height of the basketball is modelled by h t 4 75t2 8 75t 1 5 t 0 where h is the height of the basketball above the ground in metres and t is the time in seconds after it was thrown a b Find how long it takes for the basketball to reach its maximum height 6 909 maximum Assuming that no player catches the basketball find how long it would take for the basketball to hit the ground Another player catches the basketball when it is at a height of 1 2 metres 1 2 4 75 t 8 75 1 5 9 bns 0 c Find the value of t when this player catches the basketball U 20 9

2 x 2

7 Juan is planning the seating for a table dinner with his 9 friends They will all sit in a straight line along the table Find the probability that Tom will sit beside Jerry but Chip and Dale will not be seated together T I 4

plane Two children are playing with a ball The girl throws the ball to the boy The ball travels in the air curves 3 m to the right and falls 5 m away from the girl as shown in Figure 5 46 If the plane that contains the trajectory of the ball is perpendicular to the ground find its equation 5m 3m

Classify each function as even odd or neither 101 B 8 4 2 8 10L f x 3x 4 h x 2x 3x Even Odd g x 2x 4x Odd

1 Consider the linear transformation T R3 R3 given by 21 22 2x3 T 3x2 6x3 3x12x2 4x3 a Find a basis for the subspace that consists of all ER such that T 0 Is T injective b Find a basis for the image of T Is T surjective

2 Consider the following general 3 3 matrix a b A d e f ghi a Let B be the matrix obtained from A by switching row 2 and row 3 Show via an expli calculation that det A det B b Let C be the matrix obtained from A by replacing R3 row 3 with R3 t R1 row 3 plus t tim row 1 for some scalar t Show via an explicit calculation that det A det C hint expand along its third row

Please explain to your new client the differences between servers and consumer personal computers as well as the differences between intranet or local networks and the internet WAN Provide at least four suggestions that will help keep your client s data safe and secure

Mary and Pat are getting divorced and decide to split the house and their savings using the method of Sealed Bids Each person will make a confidential bid to the attorney and if they present the highest bid for an item they will own it but will have to pay the other person their fair share of the cash value of the item Neither Mary nor Pat will know what the other bid Here are the results the attorney gathered House Bid Cash Mary Pat 280 000 1 000 220 000 80 000 I According to Pat what should be his perceived fair share cash value amount to the nearest dollar

190 10 300 y asinibx f C 180 1 30 360 4 acos bx d

150 yasin x 2 380 b 120 yacos x d 360

1 Which number is the location of Ayer s Rock 02 03 05 9 6 7

Which point represents the opposite of 11 b d 3 2 1 0 1 2 3 O a Ob Oc d

Which of the following points is NOT a negative number W X Y Z 6 4 2 0 OW OX OY 2 6

Which integers on the number line are opposites a b 10 8 6 4 2 02 4 6 8 10 a and b Ob and c Oc and d O a and d

5 Proof on relations Let R and S be relations from A to B Prove that RCS R CS

4 Congruence relations Recall the congruence relation of numbers congruence modulo n Let s define R4 the binary relation of congruence modulo 4 on Z Let R x y ZxZ x y mod 4 1 Calculate 0 1 2 3 4 5 You can enumerate the elements 2 How many distinct equivalence classes are there Justify your answer 3 Are the equivalence classes disjoint empty intersection What is their union

Let R and S be relations on the set A 1 2 3 4 5 represented by the figures below 1 Write the two sets of ordered pairs corresponding to R and S 2 Represent R and S using boolean matrices 3 Draw digraphs for the relations RS and RUS 2 3 8 2 5 3

3 Proving equivalence relations Let x and y be two real numbers x y E R We define a relation R between real numbers as follows xRy IFF xy EZ In other words two real numbers are related by the relation R provided their difference in an integer Prove that R is an equivalence relation Show all your work to receive full credit

Let R S and T be relations on the set A 0 1 2 3 represented by the figures below State for each relation whether it is reflexive not reflexive symmetric not symmetric antisymmetric transitive Check all that apply No need to justify your answers but make sure you understand the properties 0 R 3 0 1 2 3 2 3 2 S Reflexive Irreflexive Symmetric Anti symmetric Transitive R S T T

The amount of food needed for proper nutrition in cups C for a puppy weighing a certain aw b where a and b are amount in pounds w can be determined by the equation C constants For a puppy weighing 9 pounds the correct amount of food is 4 cups and for a puppy weighing 11 pounds the correct amount of food is 6 cups a Determine the values for a and b b Find the correct amount 2

Make sure to label all the graphs Use your preferred internet search engine to explore different types of businesses and business owners that you might be able to adapt your business model to in completing the assessment To get you started use the search term Shop First Nations to find an example of a resource that might be helpful This search term is just a suggestion and you are encouraged to research different resources to help you find inspiring examples of businesses and business owners Task 1 Understanding the equation Your company has a profit that is represented by the equation P 2 4x 60 where P is the profit in millions and x is the number of years starting in 2020 Hint You might want to factor out the common denomenator first HINT this means when x 0 it is 2020 Therefore so today being 2023 would be represented by x 4 2024 2020 4 a Graph the relation b Is this relation linear quadratic or neither Explain your answer in two different ways c What is the direction of opening and does profit have a maximum or minimum How do you know d What is the P intercept of this relation What does it represent Do you think it would make sense that this is a new company given the P intercept Explain Task 2 Solving for break even point s A break even point for a company is when they are neither making nor losing money This is when the profit is P 0 a How many break even point s will there be What do you use to determine this b Determine in which year s the company will break even using any algebraic method you wish c Determine in which year s the company will break even using a different algebraic method than you chose in b d Which mothed th

consider equation E x y N We Suppose that xy is a caple solutias of the equation E 1 Can x x and y have the same parity 2 KEN copy and complete the tablet E 5 1 2 3 4 2 5 3 Deduce x 1 5 or x 4 5 Find a non triviale solution different from 1 0

3 y 2 3 tan 3 x 2 Choose the correct graph below O A Ay B C Q Q Ay E

The position of a weight attached to a spring is s t 2 cos 4 t inches after t seconds Complete parts a d belo a What is the maximum height that the weight rises above the equilibrium position in b What are the frequency and period The frequency of the oscillation is cycles per sec Type an integer or a fraction Type an exact answer using as needed The period of the oscillation is sec Type an integer or a fraction Type an exact answer using it as needed c When does the weight first reach its maximum height after sec Type an integer or a fraction Type an exact answer using as needed d Calculate and interpret s 1 2 s 1 2 Round to the nearest integer as needed Interpret s 1 2 Choose the correct answer below OA After 2 sec the weight is about 1 2 in above the equilibrium position OB After 1 2 sec the weight is about 2 in above the equilibrium position 1 OC After 1 2 sec the weight is about in above the equilibrium position

5 Domain Range Leading Coefficient Degree Number of REAL roots Number of Maxima Number of Minima 0 500 5

n 6 11 Find the value of each variable drawings are not to scale 105 7 X 15 65 37 N 2 lo 58 8 x y 63 72

1 Let T R Rm be a linear transformation a If T is injective what can you determine about the relationship between m and n If T is surjective what can you determine about the relationship between m and n Make sure to briefly explain your answers b Let L Rm Rk be another linear transformation Prove that the composition LoT R RA L T is a linear transformation Clearly indicate where you use defined by LoT 7 linearity of L and T

Write three to four sentences presenting your prediction about the main conflict in the novel based on how the characters feel about their lives Include evidence to support your prediction

An object is attached to a coiled spring It is pulled down a distance of 4 units from its equilibrium position and then released The time for one complete oscillation is 3 seconds a Give an equation that models the position of the object at time t s t Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers in the expression b Determine the position at time t 1 82 sec units Round to the nearest hundredth as needed c Find the frequency oscillation per sec Use integers or fractions for any numbers in the expression

4 1 point Question 3 workbook Solve each system of equations a 2x 4y 20 and x 4 b y 6x 11 and 2x 3y 7 a type your answer type your answer b type your answer Q o type your answer

If mTA 42 and mMI 130 find m C C A T I M

Organize the steps to solve the given equation 3 x 5 29 10 Subtract 14 from each side Subtraction Property Distribute 3 to the binomial expression Distributive Property Divide both sides by 3 Division Property Combine like terms on the left side of equation Simplify

3 Complete the chart below Assume a one year investment period Return on Investment ROI Net Profit 4 30 25 4 10 4 000 Investment 60 100 10 ROI 100 20 40

Given the following preference schedules for a class of student voters on favorite restaurants determine the plurality winner if one exists Five Guys Chic fil a Zaby s Wendy s 7 Wendy s Chic fil a Five Guys Zaxby s a Zaxby s b Five Gur 4 Zarby s Chic fil a Wendy s Five Guys 8 Chic fil a Wendy s Zaxby s Five Guys 1

1 4 26r 40x n 5n 1 5 4n 18n 20 7 5k 26k 5k 2 3p 17p 10 4 3x 8x 3 6 3n 20n 25n 8 6b 3b

State all transformations 11 2 x 3 4 Factor 12 25x 49 13 25x 70X 49 by Ex 265 7 57

1 0 0081 8 2 2 5 8 5 2x 3 4 2 25 2 2 5 3 96 ti 4 24 Solve each equation Give the answer in radical form and then use a calculator to approximate solution to two decimal places if necessary 6 6x 21 33 7 6 2 24 2 6245 14 6 6 x 20 9 7x 10 18

The function is given by 0 4 5 D 0 426 1016 1 025 1444 The function g is given by o a f e For which of the following values does g a 3

Given the following preference schedules for a class of student voters on their favorite school subject determine the Condorcet Winner if one exists Math Science Electives ocial Studi Science Language Arts Electives Science Language Arts Language Arts Electives Science

Which best describes the type of Winner defined by the following The candidate that received the most votes is the winner a Sequential Run Off Winner b Condorcet Winner c Borda Count Winner d Run Off Winner el Approval Vote Winner

Which of the following best describe the Run Off Winner a Start by eliminating a single candidate with the least number of first place votes from all of the preference schedules re tally the votes and again eliminate the next candidate with the least number of first place votes Continue repeating this process until only one candidate remains and is the winner O b Assign points based on the ranking of the preference schedule Assign 1 point for each last place vote Assign 2 points for each vote that is the next place above last place and continue adding a point for each place above last place such that a first place vote receives the most points The candidate with the most points is the winner received more than half of the votes is the winner

the values of the following polynomials for the given values of x 1 P x x 3x x 8 find P 2 2 f x x 2x x 11 find f 5 3 g x x5 2x4 3x 2x 1 find g 3 4 f x x 4x x 6 find f 2 2 5 P x 4x 4x 8x find P 1

fue for all values of a and B ether the identity of costa B cosacos sinasing is Let P cosa sina and Q cos sin be any two points on the circle O with radius 1 If POA a and QOA 8 then POQ a B P cosa sina Q cos sia p 2 1 1 Make use of the cosine rule to determine the length of PQ 4 1 0 Make use of the distance formula to determine the length of PQ