Name. Unit 1 Worksheets Math 150 College Algebra and Trig

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1 Name Unit 1 Worksheets Math 10 College Algebra and Trig Revised: Fall 009

2

3 Worksheet 1: Integral Eponents Simplify each epression. Write all answers in eponential form. 1. (8 ). ( y). (a b ). y 6. (7 8 y) 6. (wt) (wt) 7. (-a )(-a ) 8. (a b c) (ab c ) 9. (z ) (z ) ( 6y) 11. 9w y 1. r st n 1. () () 1. (-6q) (-6q) b ( ) ( ab ) 19. (z ) (z ) 0. ( y ) (y ) 1. 7a b. km p n 6. (-pq) (-pq). ( yz ) ( y) - 1 -

4 Evaluate each eponential epression, writing without eponents.. (-) (-1) (-) (-6) (-7) (-) 0 + (-) (-1) (-) r

5 Worksheet : Integral Eponents Simplify each epression, writing with positive eponents 1) 8-1 ) ) t 7 t -9 ) a -1 b ) (vw - )(v - w 7 b c ) 6) bc 7) 8) 9) (a -1 b ) - 10) ( - y - ) -1 11) ( - y )(-6 y - ) 1) ( y - ) - 1) (-a b - ) (a - b y ) 1) 7 10 y 0a b 1) a b 16) y ) w 1 z 1 18) a b 19) y 0) y 1) y ) a b ) ( ) -1 ( ) - ( ) - ) (a - ) (a - ) (a - ) - ) y z 6 Epress without fractions, using negative eponents where needed: 6) 9 7) 8) y a 1 9) 0) b y - -

6 Worksheet : Division of Polynomials Divide, using long division. Write any remainder as a fraction. 1. (r - r - 0) (r - ). (a - 11a + 16) (a + ). z z + 8z+ 6 z+ 1. y 1 y

7 Worksheet : Radicals I. Evaluate: II. Simplify: III: Simplify y 7. a 8. 1 m 9. 1 a y. 0 a a. y 6. 0 m - -

8 IV: Simplify 7. m y m a b z y 1. 1 m. 19 a. 17 m. y. y 1 z 6 6. a 1 m a m m z 1 9. a y 0. 1 m V: Simplify y m y y. 6 a 6 y 1. m y y 7. y m y a 9 b 60. m 16 y m n m 9 y a y m 16 z - 6 -

9 Worksheet : Radicals Perform the indicated operations and epress answer in simplest form: ( 7) 19. y z ( ) ( mn m)( mn m ) ( a b)( a b) ( b) a a a ( )( )

10 Worksheet 6: Literal Equations 1) Solve for : + m = b ) Solve for : m + c = + d ) Solve for W: P = L + W ) Solve for n: L = a + (n 1)d ) Solve for d: L = a + (n 1)d 6) Solve for m: Ft = m(v V 1 ) 7) Solve for V : Ft = m(v V 1 ) 8) Solve for a: 7y + b = m + a 9) Solve for b : A h( b + ) 1 = 10) Solve for B : A= B C 1 1 b 11) Solve for : b + c = a 1) Solve for : a( c) = a + c - 8 -

11 Worksheet 7: Radical Equations Solve for the variable. Be sure to check your roots = 6. y =. = 1. y+ 1+ 7=. 7a 1= 6. 6 = 7. = + 8. a 16 = + a - 9 -

12 9. a+ 6= a + 7a 10. 9a + a a= 11. The marketing department of a computer manufacturer determines that the demand for its computers depends on the price it charges. The relationship of price to demand is given by the formula: p= , 0, where p is the price and is the number of computers sold at that price. Find the number of computers sold if the price is $ For a group of 0,000 births, the number of people surviving (N) to age is given by the formula: N= To what age will 0,000 in the group survive?

13 Solve each problem algebraically using one variable. Worksheet 8: Word Problems 1. Find a number such that the sum of 1 and the number is four times the number.. When nine is added to seven times a certain number, the result is equal to the result of subtracting three from ten times the number. Find the number.. The labor costs for a certain project were $ per day for a total of 17 technicians and helpers. If the technicians earned $10 per day and the helpers earned $18 per day, how many technicians were employed on the project?. When seven times the sum of two and some number is subtracted from four times the sum of three and twice the number, the result is equal to zero. Find the number.. Two cars are at the same location. One travels at a speed of 0 mph and the other at mph in the opposite direction. How long will it take (in hours) for them to be 67. miles apart? 6. An item costs $0., which includes 8% ta. How much did the item cost, to the nearest cent, before the ta was added on? 7. A person goes shopping with a certain amount of money and spends one-half of it on clothes, one-quarter of it on shoes, one-twelfth of it on lunch and has $0 left for gas. How much did the person have to start?

14 Worksheet 9: Inequalities 1. When is it necessary to reverse the direction of the inequality sign when solving an inequality? Solve each inequality. Epress the solutions set using INTERVAL NOTATION and GRAPHICALLY.. + > 6. y - 8 > m + 7. > 8. -a < b > y + (y - 1) y 11. -(z - 6) > z < - < k < p + 6 < z + 16 m <

15 Review Test #1 Match each vocabulary term on the left with its eample on the right. 1. Two term epression A. 0 a. Third degree epression B. ( - ) + ( + )( - ). Undefined C. (-). When evaluated, equals 16 D. 0. Zero E. - F G. ( + 1)( - 6) 6. Simplify: ( ) + ( ) 7. Subtract from Simplify: (7 y 0 z ) ( y z ) 0 9. Simplify using only positive eponents: - - y 10. Simplify and epress answer with positive eponents: a) w y 1 b) ( y - ) - (7y ) 11. Multiply: ( - )( ) 1. a) Square ( - 8) b) Cube ( + 1) 1. Divide (1 y - 6 y + y) by ( y) 1. Divide using long division and writing any remainder as a fraction: (6y - 8y - ) (y - ) - 1 -

16 1. Referring to 9 + y, answer the following three questions: a) What is the radicand? b) What is the inde? c) Epress this radical epression in eponential form. 16. What is the conjugate of? 17. One use of the conjugate is to get a number in the denominator of a radical fraction. 18. Epress the following in eponential form: a) y b) 9 a c) n a b 19. Epress the following in radical form: a) y b) ( ) 1 y c) d) ( ) 0 -: Simplify each epression as much as possible: y.. 80 a b c.. 6-9: Combine the following epressions: : Multiply: 0. ( ) 1. ( 8 )( 8+ ) -: Divide so that the denominator is rational:

17 . Solve for p: 7 (1 p) = + p. Solve for : ( ) = 6. Solve the formula h = vt 16t for v. For problems 6-7, solve the inequality, epress the solution set using interval notation and graphically: < < Write the equation for the following number problems using one variable and solve the resulting equation. Only an algebraic solution will be accepted! 0. When three times the sum of 6 and an unknown number is subtracted from 1 times the unknown number, the result is 6. Find the number. 1. When twice the sum of five and an unknown number is subtracted from 8 times the unknown number, the result is equal to times the sum of 8 and twice the unknown number. Find the number.. Find consecutive even integers such that times the sum of the last two is 0 more than times the first. -7: Solve the following radical equations for the variable. Check your answers = 7. 7a 1=. 9= = =

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