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1 Math 70 : Intermediate Algebra Name : ____________________ Test 3 : System of linear equations, Polynomial and Exponents Use the appropriate method to solve the problem. Must show your work. Circle your answers. Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Points 5 5 5 6 12 6 10 5 5 5 5 5 5 5 6 5 5 5 5 Total 110 Your points Comments Your test score = _____________________________ Your current course grade = __________________________ 1 Fall 2010 2 5 x 2 y 11 [5] 1. Use the substitution method to solve . x 2 y 9 x 4 y 8 [5] 2. Use addition method to solve . 3x 12 y 24 3 [5] 3. Flying with the wind, a plane flew 1000 miles in four hours. Against the wind, the plane required 5 hours to fly the same distance. Find the rate of the plane in calm air and the rate of the wind. [Use two variables and two equations to solve this problem.] (i) Describe your variables. The rate of the plane in calm air = __________. The rate of the wind = __________. (ii) Setup the equations. (Distance= rate • time) (iii) Solve the equations and present your answers. 4 [6] 4. A coin bank contains only nickels, dimes and quarters. The value of the 19 coins in the bank is $2. There are twice as many nickels as dimes. Find the number of each type of coin in the bank. (i) Describe your variables. n = number of nickels in the bank. d = number of dimes in the bank. q = number of quarters in the bank. (ii) Setup three equations. (iii) Solve the equations and present your answers. 5 5. [4] (a) Simplify 2x y 5x 5 2 1 x 2 y 3 [5] (c) Simplify 2 5 4x y 4 y 3 2 [3] (b) Multiply ( 2x5) ( 3x+2 ) . 2 [6] 6. Divide by using synthetic division. x 3 x 2 x 1 . Present your answer. 6 x y 4 [10] 7. Graph the solution set. 2 x 3 y 6 x 0 (a) Use a ruler. (b) Write the equation next to the line. (c) Find the point that the line x y 4 and the line 2 x 3 y 6 intersect. (d) Mark the point of intesection on your graph. (e) Shade the area of the souliton set. 7 (8) [5] Divide by using the long division method. (9) [5] Simplify (9 x y ) 2 x y 2 3 2 1 11. [5] Factor completely. x 2 y 2 x 2 y 2 8x 3 9 2 x 3 9ab2 10. [5] Simplify 2 8a b 3 8 12. [5] Factor 6x 2 17 x 10 . (Use grouping method) a = ____, b =_____, c =_____ Find ac = ________ ac = ( )( ) ( )+( ) = ______ Finish the problem. 13. [5] Factor 64 x 3 1 . 14. [5] Use the Remainder theorem to evaluate P (3) when P( x) x 3 3x 2 3 . [Use synthetic division, show your work clearly.] 9 15. [6] Find 3x 2 2 x 1 if x( x 6) 16 . 16. [5] The square of a number is 195 more than twice the number. Find the number. 17. [5] The length of a rectangle is (5x+3) ft. The width is (2x-7) ft. Find the area of the rectangle in terms of the variable x. 18. [5] Solve for x, 3x(2 x 5) 0 . 19. [5] Given that 4 is in the range of the function defined by f ( x) x 2 x 2 , find two values of c for which f (c) 4. 10