Basic Math Questions and Answers

3 7 5 7 8 Type a response 9 Elisha wants to buy book marks to give to her teachers she has a total of 60 to spend Each book mark costs 6 00 and she wants to also buy her mom a cookbook that costs 23 00 Write and solve an inequality to find the greatest number of book marks she can buy Click on show your work to type or write your work The greatest number of bookmarks she can buy is enter number only

You may use a calculator or spread sheet application to work on this quiz 5 pts 1 The prevalence of Hutchinson Guilford Progeria is 1 per 22 million individuals in Japan The disease is caused by a Mendelian dominant mutation The disease mimics premature aging and affected persons rarely live past 13 years old With an average mutation rate in this population estimated at 1 x 10 5 what is the predicted selection against this allele Explain your calculated result 1 sentence

5 Determine the nature of roots a 2x 8x 14 6 c 8n 7n 16 b 4a 4a 6 0 d 8b 6b 3 5b

Emma hits the ball is given by y 0 01x 0 5x 0 2 where y is the vertical height in yards above the ground and x is the horizontal distance from the tee in yards Round all answers to one decimal place a How far does Emma hit the golf ball

8 An object is through off a building h t 16t 48t 160 where h is the height in meters and t is the time meas seconds a What was the height of the building where the object was launched from b How long will it take the object to strike the ground c What time s is the object at a height of 192m d What is the height of the hall after 3 5 seconds

Evaluate the following expressions given the functions below g x 4x 5 b f 8 f x x 3x a g 6 d Find x if h x 9 Solve the following quadratics by factoring a 15a 3a 3 7a 6n 18n 18 6 h x 2x 1 c h 7 e Find x if g x 13 b n 10n 22 2 d 3r 16r 7 5

The domain and range of some relations are given Each relation consists of five points Is the relation given a function Justify your answer a Domain 1 2 3 4 5 Range 4 b Domain 3 1 1 3 5 Range 0 9 c Domain 2 3 6 Range 4 6 7 11 15 d Domain 2 Range 9 10 11 12 13

son science and The new education system was initiall soon Soviet model of education In particular it was geared to the drive technology As a result a privileged technological intelligentsia for industrial development with the greatest emphasise emerged widening the separation between intellectual and manual work equal opportunities for all also appeared Educational expansion was Other social inequalities despite the CCP s formal commitment to greater in urban than rural areas in addition admissions to schools beyond the primary level tended to favour the children of Party cadre government employees and technicians primary education throughout China the lack of surplus finance meant this had Although the government aimed to provide free and universal p 1950s most village children had some primary education and the numbers in by no means been achieved by 1955 Nonetheless by the mid secondary education had almost tripled ACTIVITY Carry out some additional research on the educational reforms of the period 1949 55 Then write a couple of paragraphs to explain why full educational equality was not achieved by these reforms Health and living standards During the 1950s there were important advances in health care which Defore 1949 had been almost completely absent from rural areas The CCP quickly established clinics in most counties and health workers were sent to deal with the most common diseases Young people were ained to help people in rural areas identify and report contagious seases and to give instruction in the importance of hygiene d sanitation

3 Given f x 2x 3 x 5 x 2 answer the following questions a List the zeros of the function b What is the degree of f x c As x o f x d As x o f x IDDLESEX

2 Here are graphs of x 4 and x y 12 Complete the graphs by shading regions and adjusting line types as needed to show all the allowable numbers of widgets and zurls that the factory can produce in one day 11 1 12 4 12 10 8 6 4 2 3 Does each ordered pair represent an allowable combination of widgets and zur produced in one day 4 5 10 12 3 9

M MEASUREMENT AND MATTER Counting significant digits when measurements are added or Add or subtract the following measurements Be sure each answer you enter contains the correct number of significant digits 2 800 g 1 57 g g 0 670 g 1 07 g g 7 82 g 0 500 g g X

Construct a Binomial probability distrubtion table using n 5 and P 0 24 Next record the mean and standard deviation of the distribution below Where necessary round all numbers to four decimal places P x 0 1 2 3 st 4 5 X OF 0 0 2536 0 4003 0 2529 0 0798 0 0126 0 0008

Wages and Salaries Personal Income Taxes Payroll Taxes e g Social Security tax Income Receipts from Rest of the World Income Payments to Rest of the World Indirect Business Taxes Corporate Income Taxes Government Transfer Payments US Exports Undistributed Corporate Profits Gov t Purchases of Goods and Services 188 Gross Private Domestic Investment US Imports Net Private Domestic Investment Statistical Discrepancy Personal Consumption Expenditure 1300 90 85 128 147 50 240 522 78 237 257 96 112 8 1220

Wages and Salaries Personal Income Taxes Payroll Taxes e g Social Security tax Income Receipts from Rest of the World Income Payments to Rest of the World Indirect Business Taxes Corporate Income Taxes Government Transfer Payments 1300 90 85 128 147 522 US Exports 78 Undistributed Corporate Profits 237 Gov t Purchases of Goods and Services 188 Gross Private Domestic Investment 257 US Imports Net Private Domestic Investment Statistical Discrepancy Personal Consumption Expenditure 50 240 96 112 8 1220

Consider the proposition p x y Student a has taken class y over the universe where x is any student at UML and math class at UML Express each quantified proposition in English 1 3x 3y p x y 2 Ey Vx p x y 3 3x Vy p x y 4 Vy Vx p x y A Every class has been taken by at least one student B Every student has taken every math class C Every student has taken a math class D There is a student who has taken some math class E There is a student who has taken every math class I There is a math class that has been taken by every student

Match each quantified proposition over R with its negation 1 3x x 2 x 0 2 3x y x y 17 3 Vx 2 2 V x 0 4 3 Vy x y 17 5 Vr Vy x y 17 2 A 3x Vy x y 17 B 3x y x y 17 C Vac x 2 V x 0 D Vx x 2 A x 0 E V Vy x y 17 F 3x x 2 x 0 G Ve y x y2 17 H Va Vy x y 17 I 3x x 2 x 0

Let p n be the following proposition over Z the set of integers p n n 7n 12 0 Consider the following propositions over Z Which of the following propositions does p imply i e which a satisfy p q Select all that apply A g n n is a divisor of 24 OB g n 4n 12 OC g n tn 16 OD g n n 8 n 8 n 64 Be able to justify your answers using truth sets

Suppose that p 91 92 96 are propositions over the set of integers with the following truth sets Tp 3 7 10 Tq 3 Tq2 7 10 Tq 1 3 7 10 Tq 1 2 7 10 Tas 3 7 10 Tq 1 7 a Which of the following propositions imply p That is for each proposition does q p Select all that apply DA 92 B q OC 94 OD 96 b Which of the following propositions does p imply That is for each proposition does p qi Select all that apply DA gs B 92 OC 93

Which of the following propositions are OA p q OB pV q OC p q OD q OE pa OF P implied by p p q Select all that apply

Consider the following proposition p over the set S 1 2 10 p x x 16 10x a Compute the truth set of p Answer Tp b Which of the following propositions over S is equivalent to p OA g x 8x 16 OB q x 3 x 66 OC q x x 5 3

Solve 7 3 4

15 1 point Frogh measures the amount of water in her backyard well each day during a dry spell in her area 6 4 7 1 3 0 2 26 22 34 46 50 42 38 Day Amount of Water L 5 30 The rate of change of the amount of water with respect to the number of days is measured in units of

1 1 point Tracy reads part of her novel between 15 min and 30 min each day and the time she spends reading varies each day What type of relation best describes how Tracy s reading time is related to the price of gasoline BLERTEL IN

3 1 point A scatter plot is created for a set of data A linear model for the data has a coefficient of determination of R 0 7106 A quadratic model for the data has a coefficient of determination of R 0 7531 An exponential model for the data has a coefficient of determination of R 0 7278 Which model best fits the data

3 1 point Consider the data in the following table This relationship is 3 4 5 137 192 269 y 1 70 98 CEREEEEEE

1 point Mareta and Mikias are having a race The distance in metres that Mareta can travel while riding her bike in seconds follows a quadratic model d 22 The distance in metres that Mikias can travel on his motorized scooter in t seconds follows a linear model d 81 Who is ahead in the race at 4 s

7 1 point More than one model can sometimes seem to fit a set of data is this statement true or false

Section 4 Application Directions For each of the questions in this section show all work to get full marks 19 4 points The table shows the number of visitors to a Web site since it was put online Days 1 2 Daily Visitors 750 780 810 3 4 840 870 5 900 Determine a linear and an exponential model for the data How many more visitors does the exponential model predict on the 10th day than the linear model

1 point The following number sequence is an example of 1 3 9 27 81 TELITI growth

9 2 points Sasi roller blades at a constant speed travelling 8 km from her home to the library in 0 5 h What was the rate of change of distance with respect to time

18 3 points Solve 7 3 4 1

Directions For each of the questions in this section show all work to get full marks 16 2 points Solve Give the answer as a fraction 5 1 5 50

17 3 points Solve

irections For each of the questions in this section write your final answer

2 Let f x 5x 1 Find f 0 3 Given f x 2x 3 x 5 x 2 answer the following question a List the zeros of the function b What is the degree of f x c As x o f x d As x f x MIDDLESEX

Simplify the following Show the steps PEMDAS 2 5 16 7 2 5 16 57 2 Evaluate the expressions Show the substitution and the steps z x y use x 6 y 8 and z 6 10 p q 5 5 use p 1 and q

51 Most introductory economics textbooks have a section on market failure It is here that students learn that markets may fail to achieve their potential leaving people worse off than they theoretically could be The existent of market failure is often taken as an excuse for government intervention to do whatever markets fail to do In just a couple of sentences explain why economists and others particularly politicians must accept the possibility of government failure as well That is tell me why government solutions to perceived market failures may themselves fail to achieve their own stated goals The U S Drug war is an apt example of a discrepancy between a stated political policy goal and the actual attainment of that goal

46 What type of economic system does the United States have A traditional economy B free market economy C command economy D mixed economy

47 In Mark Skousen s article What is Economics Anyway he bemoans the apparent fact that the modern definition of economics is incomplete What does he say is missing A relationship between means and ends B the concept of scarcity C the process of transformation of resources D allocation toward competing ends

36 To be binding a price ceiling must be set at a price lower than the equilibrium price higher than the equilibrium price C the same as the equilibrium price D any price ceiling is binding A B

32 A decrease in the price of eggs will result in A an increase in the demand for eggs an increase in the supply of eggs a shift in the supply curve for eggs B C D a movement along the demand curve for eggs

Use the following to answer questions 12 13 Figure Consumer and Capital Goods Consumer goods per period Curve 2 Curve 1 Capital goods per period 12 Figure Consumer and Capital Goods Look at the figure Consumer and Capital Good The movement from curve 1 to curve 2 indicates A economic growth B C D a change from unemployment to full employment a decrease in the level of technology instability 13 Figure Consumer and Capital Goods Look at the figure Consumer and Capital Goods Point Z A is unattainable all other things unchanged B is attainable if the economy is able to reach full employment C is attainable if the quantity and or quality of factors decreases D will be attained as soon as the economy becomes efficient and moves to curve 2

Figure Rent Controls Rent per period Rent Renta Rent Rent Rento S D Qo Q1 Q2 Q3 Q4 Quantity of rental units per period 39 Figure Rent Controls Look at the figure Rent Controls If rent controls are set at Rento renters would be willing to pay a price at least as high as A Rent for Qo units B Rent4 for Q units C Renta for Q units D No one would be willing to pay a higher actual price than Rento 40 Figure Rent Controls Look again at the figure Rent Controls If rent controls are set a Rent

54 The logic of politics often leads to very different market outcomes than if the logic of economics were being used to allocate scarce resources In our discussions we covered a concept called concentrated benefits dispersed costs that might help one understand this disparity Briefly explain what the concept means and then give an example of applying it to say farm price supports a type of price control we covered but other examples may be used

Is the following claim logical Explain your answer Actor Matt Damon will be more likely to buy a court side Boston Celtics basketball seat beca they are more expensive up to 10 points

52 How might price controls on gasoline lead to human fatalities in an area where there is an oncoming hurricane 4 points

53 From and economic perspective why do governments tend to mismanage scarce resources

Figure The Market for Milk Price P P P a b P o C e S question 42 02 S D Q Quantity 42 Figure The Market for Milk Look at the figure The Market for Milk If there we binding price floor in the market for milk the price could be equal to and producers would supply consumers would demand A P Q1 Q3 B P 02 02 C P Q Q1 D P3 Q Q1

14 Find the optimum number of batches to the nearest whole number of an item that should be produced annually in order to minimize cost if 50 000 units are to be made it costs 4 to store a unit for one year and it costs 500 to set up the factory to produce each batch Assume that units of this item will be sold off throughout the year so the cost equation will use the average cost A 14 batches B 12 batches D 16 batches C 10 batches

48 An increase in the good s own price will cause the supply the shift left A True B False 2 points