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Name _____________________________________________ Math 130A.050 – Exam II – Review – October 13, 2004 1. 2. Change to a) an improper fraction: 5 ½ = ___________ b) to a mixed number 25/7 = __________ c) to a decimal: 5/8 = _________________ d) to fraction in simplest form: 0.004 = ___________ Write in words. 201.021 → ______________________________________________________ Write in standard form ( numbers). Five thousand one and 2 ten thousandths. _________________ Round to the nearest ten-thousandth → 30,204.02345 → ____________ 3. Which of the following numbers are real numbers. _________________ -2, a) 0 2/3, 5 c) 0 and - 2 d) -2, 0, 2/3 0, b) 0 and 2/3 e) all are Which of them are not rational ? ____________ Which of them are whole numbers ? ________ 4. Match. ___________ a) a + b = b + a ___________ c) (ab) c = a ( bc ) ___________ d) a(b + c ) = ab + ac 5. 1) associative law of addition 2) commutative law of addition 3) associative law of multiplication 4) commutative law of multiplication 5)distributive law 6) none of these We call 1 the multiplicative identity because for any real number x, 1 • x = x • 1 = x We call ________ the additive identity because for any real number x → x + ___ = ___ + x = x What is the opposite of - 2/3 ? ______ What is the reciprocal of - 2/3 ? ________ 6. Evaluate. Write in simplest form. a) -ab = ___________ if a = - 2 ¼ and b = 5 ½ b) -2a - b2 = ___________ if a = 4 1/3 and b = - 2 ½ f) NONE 6c) ab - b = ____________ if a = 3.12 and b = - 1.2 d) ( a + b ) ÷ b = ______ if a = -1.47 and b = 2.1 7. Find the solution of each of the following equations. a) - 2x + 5/2 = - 4/3 x = __________________ b) 2.1 - 2x = 4.9 x = ___________________ c) x–1 x+2 ----------- = -------3 3 d) x = ________________ 0.3x = 62.7 x = _____________ 8. Write the correct symbol between the expressions ( < , > , or = ) a) 2/3 __________ c) 1/3 _________ 9. 8/13 0.3333 b) 0.21___________ 0.201 d) 2/3 _________ 18 / 27 Find a) 3/n + 4/n - c) 8/n = ___________ 3/12 ÷ 8/15 ÷ 6/20 = __________ e) 12 - 4 ½ = __________ b) 5 5/12 - 6 ¼ d) 5 • 2 ¼ = _________ f) 8 ÷ 2 2/3 10. Write as simple fraction. ½ - 1/3 ----------------- = ____________ ¼ 11. Simplify a) ( 0.1)3 = __________ c) b) 32.16 ÷ 1.6 = ____________ 2.3 - 0.23 = _____________ 12. Simplify the following radicals. ___ a) 2 \/ 64 = __________ ___ b) 8 - 3 \/ 16 ____ c) \/ 9/16 = ________ = __________ _____ d) - \/ 9 + 16 = __________ 12.5 More radicals. a) 2+ 2 9 = ________ 13. Plot on a number line. b) 3 3 = ________ c) 24 = ____ x≤ 3 Write as an inequality ____________ 14. Find a) 4 ( 3x ) = _________ b) ( 2x) ( 3x ) = __________ c) - ( 2 – 3x ) = __________ d) ( -3 ) ( x ) = ___________ 15. Word Problems. a) Your cellular phone company charges $19.99 per month which includes 20 minutes of free air time, and $0.75 for each additional minute after the first 20. What is your cellular phone service bill for a month in which you had 42 minutes of calls ? ____________________ 15b) The relationship between the velocity of a car and its braking distance is given by the formula v = 20d , where v is the velocity in miles per hour and d is its braking distance in feet. How fast is a car going when its braking distance is 80 feet ? _________________ c) A one year subscription to a monthly magazine costs $45. The price of each issue at the newsstand is $4.90. How much would you save per issue by buying a year’s subscription rather than buying each issue at the newsstand ? __________ d) Find the length of fencing needed to surround a rectangular dog pen that 20 ½ feet long by 12 ¼ feet wide. ________ e) A bicyclist rode ¾ hours at a rate of 5 ½ mph. How far did he travel ? _____________ f) If a car can go 18 ½ miles per gallon and you traveled ____________ then how many gallons did you use ? 16. What is the degree of each of the following polynomials a) 2 + x + x 3 → _________ b) 3 – 2xy + y3 → ____________ c) 4x2 y5 17. Write in scientific notation 23.2 = ____________ 18. 0.00345 = ________________ Write in standard form 3.2 x 10-2 = ________________ 1.01 x 105 = ____________ 19. Use the rules of exponents to simplify a) 2x3 • 4x4 = _____________ b) ( -4x5 ) ÷ ( 2x3 y) = _________ c) ( 2x4y2 )3 = _____________ d) 4 xy 3 = ________________ 6x 4 y 2 20. More with scientific notation and exponents. a) ( 2.1 x 102 ) • ( 5.0 x 105 ) = _________________________(in scientific notation ) b) ( 1.2 x 103 ) ÷ ( 6 x 102 ) = __________________________ ( in scientific notation ) 21. Perform the given operation and simplify by combining similar terms. a) 4 + 3a = _________ b) ( 2a + 3 ) ( 2a + 3 ) = _____________ c) ( x +2 )2 = ____________ d) ( 2x2 + 2x + 3 ) - ( x2 – 2x – 3 ) = _____________ e) 2x + x( x – 2 ) = _________ 22. Write in simplest form without negative exponents. a) -40 = _________ b) ( - 2 ) 0 = ________ c) -22 = __________ d) 4-2 = _________ e) - 2-3 = ___________ f) m-2 = _________