# pt_sol - Sample Math Placement Exam Question solutions:...

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Sample Math Placement Exam Question solutions: Please note that many printers will not interpret some of the notation correctly so after you print this you may want to double check some of the answers. Algebra: 1. 88 0 425 2 x ± == ± 2. 2x(x-4)=0 or x=0 or x=4 3. () x yx y x y x yx y x x +− + + •= −+ 4. (2 ) (3 ) 1 1 5 3 28 ( 3)( 2) ( 5)( 3) 3 5 ( 3)( 5) ( 3)( 5) xx x x x x x + += + −− 5. Let x be the time it takes them both to mow the lawn. 11 1 2 1431 2 h o u r s 34 7 x x x + = = 6. Multiplying by LCD gives the equation: 2( 3) 4( 3) which gives 18. x x =+ = This answer checks in the original equation. 7. Let x be the rate of the current and t be time. The system of equations is: 20 = (15+x)(t) 10 = (15-x)(t) Using substitution as a technique for solution, we have: 20 15 t x = + so 20 10 (15 ) 15 x x ⎛⎞ =− ⎜⎟ + ⎝⎠ Solving this last equation by multiplying both sides by 15+x results in the equation: 10(15+x)=20(15-x) or x = 5 mph.

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8. 11 1 1 17 72 98 7 2 1 7 −− ⎛⎞ += = ⎜⎟ ⎝⎠ 9. x yy x xy x x •= + + 10. (1 ) 1 p p qp q qpp q pq p q pq p + = = = 11. 21 2 2 4 4 22 44 1 2 32 5 59 x yz x −−− = 12. 2{-3x+4[8+x]} = 2{x+32}=2x+64 13. 5+2x-6=2[5-4x-12] so -1+2x=-14-8x or x= 13/10 x = − 14. (1/8)(2) = 1/4 15. Let x be the length. Then 1/2 x will be the width. The perimeter is 24 so the equation would be: 2(1/2 x)+ 2(x) = 24. This gives a solution x = 8. The length is 8 inches, the width is 4 inches. 16. Using the point slope formula: 7 4( 3 ) 4 yx =+ which results in the equation: 75 =− 17. The slope of the given line is 2/5 so the slope of a perpendicular line would be -5/2 . Using the point (-3,1) and the point slope formula, we have: 5 1( 3 ) 2 −= + which reduces to 51 3 = . 18. f(-3) = 2(-3) P 2 P -5 or f(-3) = 13. 19. Domain: {-4, -2, 3}; Range: {0,2,5}. This is not a function. 20. Using the ordered pairs: (0, .75) and (40, 4.25) and the point slope formula, we have: 7 () .75 80 Wt t .
-1 8 21. First graph the line 2x-3y=6 and then shade the appropriate region: 22. 16 2 2 8 1 xx −≤ −≤⇒≥≥ . In interval notation: [-1,8] . 23. Simplifying each side: -3x+14>2x-6 which simplifies to x < 4 . Interval notation: (- , 4) . 24. -3<2x+5<3 which simplifies to -4<x<-1. In interval notation: (-4, -1) . 25. Using substitution and solving the first equation for y results in : y = -9-5x. Substituting this for y in the second equation results in : 20x+3(-9-5x) = -2.

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## This note was uploaded on 10/20/2009 for the course MATH 241 taught by Professor Wang during the Spring '08 term at University of Delaware.

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pt_sol - Sample Math Placement Exam Question solutions:...

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