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________________________ Name Math 1302 College Algebra Exam I March 6, 2003 1. Complete each of the following blanks. a) The set of _________________ is made up entirely of the set of whole numbers and their opposites. b) Every ___________________ number can be written as a fraction and there is no other real number that can be written as a fraction except for these numbers. c) Real numbers are made of numbers that must be members of one of two sets, the set of ___________________________ or the set of _____________________ 2. Complete the following by using the a) commutative law of addition: 3 + x = ______________ b ) the distributive law: ( - 3 ) ( x + b ) = ____________________ 3. Give me an example of the associative law of multiplication. ________________ 4. Simplify to a single number in simplest form. a) -42 = _______ b) 02 = __________ e) -4- 2 = _________ e) c) - 16 ½ = _________ - 2 0 = ________ d) ( 4/ 9 ) – 3/2 = _______ f) (-8 )-2/3 = _______ 5. Evaluate if x = -1 and y = - 2, z = - 3, and r = 0 a) xy = _______ b) ( y r )z = __________ 6. Find each of the following absolute values. Do not combine any of the numbers. Write without absolute values and without parenthesis or grouping symbols of any kind. __ a) | 4 - 7 | = ___________ b) | 8 - \/ 50 | = _____________ c) - | 4 | - | - 2 | = _____________ d) | 7 - 2 | = ___________ 1 7. True or False. _____________ a. Every integer can be written as a fraction. _____________ b. all rational numbers are either positive or negative _____________c. 1 is the smallest positive whole number _____________d. ( x + 2y )2 = x2 + 4y2 _____________ f. two is the smallest prime number 8. Perform the given operations and simplify. a) 4 – 3 [ 2 – ( 4 – 5 ) ] = __________________ b) 4 – 22 3 + 8 2 = _________ 9. Use the rules of exponents to simplify a) ( 3x2 )3 = ________________ c) ( - 2x - 2 )2 ( 4x3 )2 = ________ f) h) ( 4x2y4 ----------- = ___________ 8xy7 - 6 x - 2y - 3 -----------2x 2y – 4 )2 b) ( 4x2 ) ( - 2x4 y ) = _____________ d) ( 4x-2)-1/2 = ____________ e) ( 2/3)-2 = _________ -4x -1y -3 g) -------------------- = ______________ 2x - 3y2 =____________________ 2 10. Use the rules of radicals and fractional exponents to simplify. _______ 3 _____ a) \/ 16x4y2 = ______________ b) \/ 8x6 = ________________ ___ c) 4 - 2 \/ 9 = _____________ d) ( 16x24y8 )1/4 = _____________ 11. Perform the given operation -- Do not factor. a) ( 3x2 - 4x + 6 ) - 2(x2 - 2x + 3) =_________________________ b) 3x2y ( x + 2y ) = _______________________ c) 2x + 3 ( x + 2 ) = _____________ 12. Factor each of the following polynomials - All of these should factor. Factor completely ! a) 4x2 + 4x - 15 = __________________ c) 5x4 - 20x2y2 = __________________________ b) 3( x – 2y ) + 5( x – 2y ) = ____________________ d) x4 - 16y4 = ___________________________ e) x4 - 8x = _________________________________ 13. Find the GCF of the following a) GCF( 80, 120 ) = _____________ b) GCF( 12x2y4, 16xy5 ) = ___________ 3 14. Find the LCM of b) LCM ( 12xy2, 8x3y4 ) = _______ a) LCM (24, 30 ) = ________________ 15. Find the degree of each of the following polynomials. a) 4 _____________ b) 82x3y5 _____________ c) 1 + 5x8 - 2x4y5 _______________ 16. Simplify. a) ( 9 ) – 3/2 = ___________ c) - 8- 2/3 = _____________ 18. A polynomial that has three factors but only one term is called a ________________________ A monomial will always have only one ____________ 19. Reduce each of the following algebraic fractions to lowest terms. a) x3 - y3 ----------------- = _____________ x2 - y2 3 - xy b) ---------------- = _______________ xy - 3 20. Simplify by performing the given operation and reducing to lowest terms. 3- x x -1 a) --------- ---------- = ______________ x- 2 x -2 4 x2 - 4x 3x2 + 3x b) ------------ ------------------ = ________________ x2 - 16 x2 + 5x + 4 c) x2 - 4x - 12 x2 - 4 ------------------- ------------------- = ____________________ x2 - 12x + 36 x2 - 5x - 6 21. More radicals a) \/ 64x6y4 b) \/ 4x6y4 = ____________ c) \/ 24 = ____________ d) \/ 8 + 2 \/18 = __________ 1 c) --------- = \/ 9x 22. A dress sells for $60 and there is an 8 % sales tax. How much change will you get back if you paid with three twenties and a ten dollar bill ? 5 23. Simplify by using the rules of exponents. No radicals in your final solution. No negative exponents in your final solution. b) x1/4 x1/2 = _______________ a) x1/2 x1/4 = ____________ c) ( -2x1/3y-1/2 ) -6 = ____________ 24. Find the solution of each of the following equations. Complex solutions are acceptable – make sure not to use the phrase “ no real solution” a) 2 – x ( x – 2 ) = ( 3 – x )(3 + x ) b) 3/x = 3 - 1/x x = ___________ c) 4 / ( 1 – x ) = 2 / x d) x/2 + x/3 = 1 x = ___________ x = _________________ ==> x = __________ 6 25. Write in standard form of a quadratic equation. 4 - x2 = - 2x find a = _______ b= _______ c = ___________ 25. Find the solution of each of the following equations. a) x2 = 4x , x = ___________ b) 9 - 16x2 = 0 , x = ______________ c) 2x ( x + 4 ) = 0 , x = _________________ d) x2 – x – 6 = 0 , x = _________________ 26. Simplify by performing the given operation and reducing to simplest form. a) 4 – x ------ + 2–x 2 --------- = ____________ x–2 x2 - x 3x2 – 9x b) ----------- --------------- = _____________ x2 + 2x - 3 x2 - 9 c) 1 + 1 ---------- = __________________ 1 - 1/x 7