ࡱ> }| )dbjbj 4j0@@///8g/~ (555HHHxzzzzzz$/ђ9{DH{{55׍!!!{l55x!{x!!FX,j5PXΐ/ojTd0UYUjj&UH>,!$HHH1 HHH{{{{UHHHHHHHHH@ I:  Name: __________________________ COLLEGE ALGEBRA MIDTERM STUDY GUIDE QUARTER 1 / SEMESTER 1 30 Multiple Choice Questions ______________________________________________________________________________________ Problem Solving and Critical Thinking Estimation, graphs, and mathematical models Problem solving Algebraic Expressions Evaluating expressions Distributive property Combining like terms Translating from word problems to expressions Algebraic Linear Equations Solving one step and two-step equations including fractions Solving multi-step equations with distributive property and combining like terms Solving multi-step equations with variables on both sides of the equation Solving multi-step equations with no solutions or infinite solutions Solving literal equations Applications of linear equations Functions Function notation Evaluating functions Vertical line test Function mapping Domain and range Problem Solving and Critical Thinking Write an algebraic rule for the total number of tiles, T, in terms of the figure, n.  n2 + 4 2n + 2 2(n + 1) 3n + 2 2. Write an algebraic rule for the total number of tiles, T, in terms of the figure, n.  n + 1 n(n + 1) 3n n2 + 1 3. Which equation best describes the relationship between the values of x and y shown in the table? xy-1-70-52-143y = x 5 y = 2x 5 y = 3x 7 y = 4x 7 Algebraic expressions 4. Two enterprising college students decide to start a business. They will make up and deliver helium balloon bouquets for special occasions. It will cost them $39.99 to buy a machine to fill the balloons with helium. They estimate that it will cost them $2.00 to buy the balloons, helium and ribbons needed to make each balloon bouquet. Which of the following expressions could be used to model the total cost for producing b balloon bouquets? $2.00b + $39.99 $37.99b $39.99b + $2.00 $41.99b 5. A plumber charges $13.50 per hour for a plumbing job that requires more than 3 hours to complete. For any job requiring 3 hours or less, there is a flat charge of $40.50. If h represents the number of hours the job requires, which of the following expressions gives the charge, in dollars, for a job requiring more than 3 hours to complete? 13.5h + 40.5 13.5h 13.5h 40.5 40.5 6. You help in the school cafeteria by emptying the trash barrels. You are paid $4 for each day you work. Let d be the number of days you work in a month. Which of the following expressions represent your pay for that month, in dollars? d4  EMBED Equation.3  4 + d 4d 7. What is the value of the expression (x y)2 when x = 5 and y = -1? 4 16 24 36 8. If a = - EMBED Equation.3 , b = 4, and d = -3, what is the value of  EMBED Equation.3 ? -25 EMBED Equation.3  -6 75 102 9. What is the value of  EMBED Equation.3  if x = 6? -3 3 6 9 10. For all x, 5 3(x 4) = ? -3x + 17 -3x 7 -3x + 1 -3x 4 11. (6x 4) (2x + 8) is equivalent to: 4(x + 4) 4(x 1) 4(x 3) 4(x 12) 12. The expression (3x2 + 5x 12) 2(x2 + 4x +9) is equivalent to which of the following: x2 3x 30 x2 + 13x + 6 5x2 + x 18 x2 + 3x 21 Algebraic Linear Equations 13. A Fahrenheit temperature F can be approximated by doubling the Celsius temperature C and adding 32. Which of the following expresses this approximation method? F =  EMBED Equation.3 C + 32 F = 2C + 32 F = 2(C + 32) F = C2 + 32 14. Roy is saving to buy a new bike, which costs $258. He has $16 towards this purchase. Express how much more Roy needs in the form of an equation. A. x + 258 = 16 B. x 16 = 258 C. x = 258 + 16 D. x + 16 = 258 15. Solve for r: 3r + 2 r = -4 A. 3 B. -3 C. 4 D. -4 16. Patricia pays $1.19 each to download songs to her MP3 player. If n is the number of downloaded songs, which equation represents the cost C in dollars? C = 1.19n n = 1.19C C = 1.19 n C = n + 1.1 17. Solve the equation EMBED Equation.3 . A.  EMBED Equation.3  B.  EMBED Equation.3  C.  EMBED Equation.3  D.  EMBED Equation.3  18. An equation is shown below: -2x + 9 = -17 What is the solution to the equation? x = -13 x = -4 x = 4 x = 13 19. If a + b = 6, then  EMBED Equation.3  A. 3 B. 7 C. 10 D. 14 20. Solve for y: 3x 4y = 12 A. y = 3x 4 B.  EMBED Equation  C.  EMBED Equation  D. 3x 4y = 12 21. The sum of one fifth of a number and three is equal to half of the number. What is the number? 5 10 15 20 22. Given y + 36 = 102, y + 14 = ? (Hint: solve for y first, then find y + 14) 66 76 80 124 23. When n basketball uniforms are purchased, the cost, C, of each uniform is given by the equation EMBED Equation.3 . If the cost of each uniform was $60, how many uniforms were purchased? A. 5 B. 6 C. 8 D. 13 E. 26 Functions 24. What is the value of f(2) if f(x) =  EMBED Equation.3 ?  EMBED Equation.3  15 125 500 25. What are the domain and range for the relation EMBED Equation.3 . A. Domain = {all real numbers} Range = {all real numbers} B. Domain = {all real numbers `" 5} Range = {all real numbers} C. Domain = {all real numbers `" "5} Range = {all real numbers} D. Domain = {all real numbers} Range = {all real numbers `" 5} 26. If f(x) = 3x  2, find f(8)  f(-5) A. 7 B. 9 C. 37 D. 39 27. If f(x) = 2x 4 find f(q + 1): A. 2q + 4 B. 2q + 2 C. 2q 6 D. 2q 2 28. If f(x) = -4x2 + 15, then f(-3) = ? -21 -9 39 51 29. Find the range of the function given the domain: f(x) = 5 4x; domain = {-1, 0, 1} A. {1, 5, 3} B. {9, 5, 1} C. {9, 5, 3} D. {1, 5, 5} 30. A function g(x) =  EMBED Equation.3 . For which value of x will g(x) = 0? 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