Sequences & Series Questions and Answers

12 Replace the with the correct symbol or which will make a true statement from the following expression 2 3 120 42

4 Find the inverse of the function f x 9 x x

Show that the given set has a cardinality of No by establishing a one to one correspondence between the elements of the given set and the elements of N 1 1 125 5 1 5 25 125 50 Let N 1 1 1 1 2 3 Then a one to one correspondence between the given set and the set of natural numbers N is given by the following general correspondence

15 You want to rent a dune buggy for some weekend fun The rental company employee says it s a flat fee of 72 to rent the dune buggy and an additional 24 per day used Also you may only keep the dune buggy for a maximum of 32 days What is the domain of the function O positive real numbers O all real numbers between 0 and 32 O all real numbers between 24 and 840 O all real numbers

Before you upload your file ensure your name appears on the top of every page of your document MAP4C 1 The following are the test results for a grade 12 math class of 20 students 82 79 68 72 85 81 86 84 94 97 83 97 96 65 72 81 72 91 92 75 a Calculate the mean median and mode from the class s test results Round answers to one decimal place where applicable b Calculate ti c Determine the

3 Perform the following tasks a Do the following problems without a calculator For each problem display the answer you get Then check on the calculator Display your answers 1a 12 5 4 3 2a 2 5 6 2 0 3a 168 4 4a 16 8 4 5a 12 2 9 2 6a 8 2 2 1 7a 2 5 9 8a 2 x 5 2 9 9a 8 2 1 10a 3 11a 100 5 2 12a 100 5 2 b What steps did you use to get the answers c What do we learn from the calculator about Order of Operations

Find the 5 number summary for the data shown X 6 5 8 5 17 5 18 9 19 1 20 5 20 7 21 3 28 29 1 5 number summary Use the Locator Percentile method described in your book not your calculato

2 How many ounces of pure salt must be added to 11oz of 10 salt solution to produce a 30 solution Pure salt is 100 Round your answer to the nearest hundredth of an oz OZ

Rewrite into Radican Form 1813 315 Otx th Simpliky 3 165 4 647 3 2

18 There are 64 cupcakes in a bag 32 pairs 2 pair s are silver 12 pairs are brown and the rest are black If you took out a black cupcake and you didn t put it back what is the probability that you pull out another black cupcake If you enter your answer as a decimal round to the thousandths place

12 If an 8 hour workday includes a total break time of 16 how many hours are used for breaks Round your answer to the nearest hundredth of an hour or the nearest minute O 1 43 hours or 1 hour and 26 minutes O 1 45 hours or 1 hour and 27 minutes O 1 35 hours or 1 hour and 21 minutes

21 Solve for x O O O O 1 11 O 0 32 O 0 55 O 0 08 8x 1 7

27 How much water should be added to 125 oz of 30 acid solution to dilute it to a 20 acid solution 6 25 oz 59 52 oz 62 5 oz

4 Describe two different ways to graph the equation y without using a calculator Which methods do you prefer Why 1 X 5

5 In the graph below an equation of line J is y x y ITThat Tr y x HHH 11 I 11 2 X

3 Find y when x 6 and z 6 if y varies jointly as x and z and y 38 and x 6 when z 3 Round your answer to the nearest thousandth y

and y 34 when x 5 O 157 44 O 163 2 O 165 61 167 6 7 Find y when x 88 if y varies inversely as x and y 31 when x 139 Round your answer to the nearest thousandth y 8 Find y when x 6 and z 6 if y varies jointly as x and z and y 38 and x 6 when z 3 Round your answer to the nearest thousandth

2 A stone is thrown upward with an initial speed of 800 feet per second It is given that h 13t 910t his the height of the stone at any given time Factor the given equation completely Oh t 13t 910 Oh 13 t 70t Oh 13t t 70 This equation is already completely factored

The parents of a 9 yr old boy have agreed to deposit 5 in their son s bank account on his 10th birthday and to double the size their deposit every year thereafter until his 18th birthday a How much will they have to deposit on his 18th birthday b How much will they have deposited by his 18th birthday

Markeeta a recent college graduate received two job offers Company A offered her an initial salary of 39 000 with guarante annual increases of 1800 year for the first 5 years Company B offered an initial salary of 40 300 with guaranteed annual increases of 1700 year for the first 5 years a Which company is offering a higher salary for the fifth year of employment Company A Company B b Which company is offering more money for the first 5 years of employment Company A Company B

Which of the following statements is are correct a C d e If the side length of a square is doubled then the area of the square is quadrupled The weight of the Earth is 5 97 104 kg whereas the weight of the Moon is 7 35 1022 kg Then the Earth is 81 22 times as heavy as the Moon rounded to two digits after the decimal point If a y 0 zy 256 and a b 4 then a 2ab b zy 64 For any positive integers z y the value y is a rational number The sum of all positive multiples of 7 that are less than 1000 can be written as 7 1 2 143

For the series SA n 1 9n0 7 8 calculate the sum of the first 4 terms S Include several decimals in your answer Now find a bound for the error error

O 27 O 11 O 11 38 Convert the following equation to its alternate form standard to slope intercept or vice versa y 2 x 3 O 8x 12y 9 O 8x 12y 9 3 1 x y 20 O x y 2 10

Use the binomial series to expand the function as a power series 01 1 12 5 3n 4 n 3 n 01 x 3n 4 xn n O 1 x n 1 00 R 01 x 3 n 2 n 0 n 2 00 01 2 5 00 n 2 2 5 1 n 3n 4 n 3 3n 4 n n 2 5 3n 4 xn 3 n State the radius of convergence R

17 f x g x can be written in the form of x 1 x 2 x 1 The possible anwsers for f x and g x are a A a constant or b Az B a linear function f x is in the form of input a or b and g x is in the form of input a or b The partial fraction decomposition of

A survey shows that 55 will vote yes and 45 will vote no on an issue with a 7 margin of error Explain whether there is a clear preference on the issue Paragraph

1 A boy named Bechton would like to celebrate his birthday at a private beach He has saved 120 for admission to the beach Admission price is 6 for adults x and 3 for children y The beach has a rule that for large parties there must be one adult x for every two children y Explain how you would use the following strategies to help Bechton invite enough people to spend exactly 120 for admission and maintain the proper ratio of children and adults Explain your work a First write the equations you would use to figure out how many people to invite b Show the steps or explain how you would solve this problem by elimination c Show the steps or explain how you would solve this problem by substitution d What steps would you take to solve this by graphing e How many adults and children should Bechton invite to the beach party

1 Tahlia needs to buy shredded wood for her children s playground The shredded wood costs 15 per ton and there is a delivery cost of 14 with each order If Tahlia needs 6 5 tons what will the cost be C

29 Solve for x Round to the nearest hundredth 9 7x 2 7 x 1 X 30 Solve the inequality set Graph the solution on a nu 3x 18 and 6x 0 O x 6 Ox 6 and x 0 0 x 0 O x 6 and x 0 O all real numbers O

0 Multiple answers may be correct Mark all correct answ rational numbers whole numbers irrational numbers real numbers integers counting or natural numbers No number set describes this number The following are the low temperatures in New York fo cross the stato

is not a function and begins with y is not a function and begins with x is a function and begins with x is a function and begins with y 40 Solve for x x 6 7 x 4 Write your answer as a fraction If no solution exists write none in the space provid X 41 Tahlia needs to buy shredded wood for her children s The shredded wood costs 15 per ton and there is a d of 14 with each order If Tahlia needs 6 5 tons what will the cost be

38 The perimeters of two similar trapezoids are 4 cm and 8 cm What is the ratio of the lengths of corresponding sides State your answer as a fraction C

32 In a two hour TV event the commercials show 16 of the tim How many minutes of commercials are shown each hour Round to the nearest tenth of a minute minutes

Solve the following inequality for y 9y 7x 9 Identify the statements which represent the inequality There may be more than one correct answer select all The graph has a solid line The graph has a dotted line The correct inequality begins with y The correct inequality begins with y None of these statements are true In a two hour TV event the commercials show 16 of How many minutes of commercials are shown each hou Round to the nearest tenth of a minute

form standard to slope intercept or vice versa 10 y 110 X O 3x 10y 100 Ox y 10 3x 10y 100 Ox y 10 x y 10 25 Given the equation y 5 the y intercept is 26 If c represents the hypotenuse of a right triangle sol for the unknown side length a 25 b 20 c Round your answer to the nearest hundredth

1 ITE 4 3 2 11 234 1 N 3 43254 9 88 43 S 678 S 34 IIII I 2 W t L 1 3 2 1 1 4321SSL7 432 Y

Graph the function y 6 2 40 20 20 1 40 40 20 20 2 2 20 20 40 40 20 20 y 2 X MY

19 The distributive property is best illustrated by which equation O 10a 4b 2 5a 2b O 10a 4b 4a 106 O 10a 4b 10 4 a b O 10a 4b 2 5 a 2 2 b

If a satellite travels 33000 feet per second how many m per minute does the satellite travel about 426 14 miles per minute about 304 88 miles per minute about 375 miles per minute about 457 32 miles per minute

8 Piper pays 27 to join the cycling team She pays 11 each time she enters a race She does not want to spend more than 296 dollars on cycling How many races can she enter

9 Decide if the following is rational or irrational 91 O rational O irrational 10 The best way to mathematically write the phrase the number n is increased by four is 11 Evaluate 56 25

Determine if the following data represents a direct var Y 10 20 30 x 2 4 6 O yes no

5 Rewrite the following expression as a fraction times the variable 7a

Refer to the functions and g and evaluate the function for the given value of x Select Undefined if applicable f 0 3 3 5 4 3 1 1 5 4 and g 1 0 2 2 1 2 2 2 gof 1 is Undefined

Refer to function p Find the function pop x and write the domain in interval notation Write any number in the intervals as an integer or a simplified fraction p x x 6x Part 0 2 Part 1 of 2 pop x

Find two functions f and g such that h x g x and f x g x x h x x 8 f x and g x

Refer to functions m and q Evaluate qm x and write the domain in interval notation Write your answers as integers or simplified fractions m x x 5 9 x Part 0 2 Part 1 of 2 x 10

22 Given the two points 1 8 and 1 line passing through both these points Om 0 Om 6 O m 43 m 6 m undefined 23 Given 11 w 4 w 07 O 15 O O 15 2 wha

Given the functions f x x 7x g x 5x h x 3x 5 Evaluate the function g f x for x 2 Write your answer in exact simplified form Select Undefined if applicable g f 2 is Undefined

11 If w represents the width of a rectangle that is 10 inches long with a perimeter of 118 inches the best algebraic representation of the rectangle s perimeter is in terms of w p