Survey of Math Exam 2 Name

Transcription

1 Survey of Math Exam 2 Name 1. Graph y = 2x 2, by letting x = 3, 2, 1,0,1,2, and 3 and finding corresponding values for y. SEE MARIANNE FOR SOLUTION 2. Use the x- and y-intercepts to graph 4x 2y = 8 SEE MARIANNE FOR SOLUTION

2 3. If f (x) = 3x 2 7x 5, find f ( 2) f ( 2) = 3( 2) 2 7( 2) 5 = 3(4) = = Find the slope of the line passing through (-3,4) and (-5,-2). m = 4 ( 2) / 3 ( 5) = / 3+ 5 = 6 / 2 = 3 5. Graph y = 2 using the slope and the y-intercept. 3 x 1 SEE MARIANNE FOR SOLUTION

3 6. Solve the system by graphing: x + y = 6 4x y = 4 SEE MARIANNE FOR SOLUTION 7. Solve the system by substitution: x = y + 4 3x + 7y = 18 Substituting the expression from the first equation into the second, 3(y + 4) + 7y = 18 3y y = 18 10y +12 = 18 10y = 30 y = 3 x = 3+ 4 x = 1 (1, 3)

4 8. Solve the system by elimination by addition: 5x + 4y = 10 3x + 5y = 7 Multiplying the first equation by 3 and the second by -5, 15x +12y = 30 15x 25y = 35 13y = 65 y = 5 5x + 4( 5) = 10 5x = 30 x = 6 (6, 5) 9. A CD player with an original price of $120 is on sale at 15% off. What is the sale price of the CD player? 120(0.85) = You earned wages of $46,500, received $790 in interest from a savings account, and contributed $1100 to a tax-deferred savings plan. You are entitled to a personal exemption of $3800 and a standard deduction of $5950. The interest on your home mortgage was $7300, you contributed $350 to charity, and paid $1395 in state taxes. Find your taxable income. (Remember to base your taxable income on the greater of the standard deduction or an itemized deduction.) AGI = 46, = taxable = = 33, You borrow $2000 from a friend and promise to pay back $3000 in two years. What simple interest rate will you be paying? A = P(1+ rt) 3000 = 2000(1+ r2) 3000 = r 1000 = 4000r r = 0.25 = 25% 12. You would like to have $3000 in four years for a special vacation by making a lump-sum investment in an account that pays 9.5% compounded annually. How much should you deposit now? Round to up to the next dollar. A 3000 P = 1+ r nt = = (4)

5 13. Use the 2012 marginal tax rates in the table to calculate the federal income tax owed by the following person: *single, no dependents *gross income, $36,500 *$2000 paid to a tax-deferred IRA *$4700 mortgage interest *$1300 property taxes *no tax credits Single Married filing separately Married filing jointly Head of Household 10% up to $8700 up to $8700 up to $17,400 up to $12,400 15% $8701 to $35,350 $8701 to $35,350 $17,401 to $70,700 $12,401 to $47,350 25% $35,351 to $85,650 $35,351 to $71,350 $70,701 to $142,700 $47,351 to $122,300 28% $85,651 to $178,650 $71,351 to $108,725 $142,701 to $217,450 $122,301 to $198,050 33% $178,651 to $388,350 $108,726 to $194,175 $217,451 to $388,350 $198,051 to $388,350 35% more than $388,350 more than $194,175 more than $388,350 more than $388,350 Stnd Deduct Exempt ns $5950 $5950 $11,900 $8700 $3800 $3800 $3800 $3800 AGI = 36, = 34,500 taxable = 34, = 24,700 15% marginal tax rate tax = 0.10(8700) (24, ) = 3,270

6 14. Suppose that you decide to save money for a down payment to buy a home in five years by depositing $6000 in an account that pays 6.5% compounded monthly. How much will you have as a down payment after five years? A = P 1+ r nt = = (5) 15. Suppose that instead of making a lump-sum deposit to save for a down payment, you deposit $100 at the end of each month in an annuity that pays 6.5% compounded monthly. How much will you have as a down payment after five years? P 1+ r nt 1 A = r = = 7, (5) Suppose that you want to retire in 40 years. How much should you deposit at the end of each month in an IRA that pays 6.25% compounded monthly in order to have $1,500,000 in 40 years? Round up to the next dollar. A r P = 1+ r = nt 1 = 704 1,500, (40) 1

7 17. Convert 807mm to hm. Move decimal 5 places to the left hm 18. Given 1 inch =2.54 centimeters, use dimensional analysis to convert 635 centimeters to inches. 1in 635cm 2.54cm = = 250in 19. If 1 mile 1.6 kilometers, express 80 miles per hour in kilometers per hour. 80 m hr 1.6km 1m = 128 km hr 20. Australia has a population of 20,090,400 and an area of 2,9667,908 square miles. Find Australia s population density to the nearest tenth. DIDN T GRADE DUE TO TYPO 21. Given 1 acre 0.4 hectare, use dimensional analysis to find the area of a property measured at 18 hectares. 1acre 18hectares 0.4hectares = 45acres

8 22. A swimming pool has a volume of 10,000 cubic feet. Given that 1 cubic foot has a capacity of about 7.48 gallons, how many gallons of water does the pool hold? 10,000cu ft 7.48gallons = 74,800gallons 1cu ft 23. Convert 137g to kg. Move decimal 3 plces to left kg 24. Convert 176 F to Celsius. C = 5 ( 9 F 32) ( ) = = Comfortable room temperature is approximately a. 70 C b. 50 C c. 30 C d. 20 C From above, we know that 70C is close to 176F. 50C is halfway to boiling point of water. Solving the formula F = 9 for 30C and 20C, we see 30C = 86F and 20C=68F, so 5 C + 32 d is the correct answer.