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Review for College Mathematics

Review for College Mathematics. A selection of problems intended to maintain students essential algebra skills Instructor Copy. Equations and Modeling. A moving company charges $46 to move a certain machine 10 miles and $58 to move the same machine 30 miles.

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Review for College Mathematics

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  1. Review for College Mathematics A selection of problems intended to maintain students essential algebra skills Instructor Copy

  2. Equations and Modeling A moving company charges $46 to move a certain machine 10 miles and $58 to move the same machine 30 miles. • Find an equation that defines this relationship if it is linear. • What will it cost to move the machine 25 miles? • What is the minimum charge for moving the machine? • What is the rate for each mile the machine is moved? Solution: a) b) c) d) C = 0.6 m + 14 $55 $40 $0.60 per mile MATHEMATICS for COLLEGE READINESS

  3. Equations and Modeling The total cost of producing a certain item consists of paying rent for the building and paying a fixed amount per unit for material. The total cost is $250 it 10 units are produced and $330 if 30 units are produced. a) Find the equation that defines this relationship if it is linear. b) What will it cost to produce 100 units? c) How much is paid in rent? d) What is the cost of the material for each unit? Solution: a) b) c) d) C = 4x + 210, where x = number of units produced. $610 $210 $4 per unit MATHEMATICS for COLLEGE READINESS

  4. Equations and Modeling If x2 + 2x = 3, demonstrate algebraically which of the following is a possible value for x. – 3 • –2 • –1 • 0 • 3 Solution: a) – 3 MATHEMATICS for COLLEGE READINESS

  5. Equations and Modeling How many solutions are there to the systems of equations? Solve algebraically. Solution: Infinite: the lines coincide so the solution is MATHEMATICS for COLLEGE READINESS

  6. Equations and Modeling The sum of the square of a number and the product of the number and 3 equals 40. Write an equation to model this situation. What are the positive answer(s)? Solution: a) b) n =5 MATHEMATICS for COLLEGE READINESS

  7. Equations and Modeling Two truckers start on a trip at the same time. One heads west at 60 mph while the other heads east at 55 mph. Their CB radios work for a distance up to 500 miles apart. How long will they be able to communicate with each other? Model and solve algebraically. Solution: 4 hr 20 min. MATHEMATICS for COLLEGE READINESS

  8. Equations and Modeling Solve the system of equations algebraically. Solution: empty set: The lines are parallel. MATHEMATICS for COLLEGE READINESS

  9. Equations and Modeling Solve for w: p = 2 ( l + w ) Give your answer in two forms, one answer with a single fraction and the other as a sum or difference of two terms. Solutions: MATHEMATICS for COLLEGE READINESS

  10. Equations and Modeling Solve for a: Solution: MATHEMATICS for COLLEGE READINESS

  11. Equations and Modeling Solve for x: Solution: MATHEMATICS for COLLEGE READINESS

  12. Equations and Modeling The Boosters Club held a spaghetti dinner as a fundraiser. They sold 300 tickets and collected $2200. If an adult’s ticket cost $8.50 and a child’s ticket cost $3.50, how many of each were sold? Solution: 230 adult tickets 70 children’s tickets MATHEMATICS for COLLEGE READINESS

  13. Equations and Modeling Admission to a school football game was $2 for students and $3 for nonstudents. How many of each group attended if there were 900 people and $1920 collected? Model and solve algebraically. Solution: 120 nonstudents. 780 students. MATHEMATICS for COLLEGE READINESS

  14. Equations and Modeling Solve algebraically: x2 – 5 = 3x Solutions: MATHEMATICS for COLLEGE READINESS

  15. Equations and Modeling Bill needs to make 1000 copies before the meeting that starts in 15 minutes. He begins using a machine that makes 30 copies per minute after laminates, a newer machine which copies at 45 pages per minutes become free . Using both machines, will Bill be able to make all the copies before the meeting? Explain algebraically. Solution: No, it will take almost 17 min to make the copies. MATHEMATICS for COLLEGE READINESS

  16. Equations and Modeling Find the equation of a line with slope of 0 through (6, 10). • Solution: • y = 10 MATHEMATICS for COLLEGE READINESS

  17. Function Theory Which of the following are functions? x3y = 12 x2 + y2 = 20 x3 + y = 15 x (x+2) = 5 + y e. y(y + 2) = 4 + x g. x = 4 h. y = 5 c, d, e, h Solution: MATHEMATICS for COLLEGE READINESS

  18. Function Theory If f(x) = x2 – 5, find f(b) – f( c) . Solution: b2 – c2 MATHEMATICS for COLLEGE READINESS

  19. Function Theory If f(x) = 2x2 – x + 3, find f(x + h) . Solution: MATHEMATICS for COLLEGE READINESS

  20. Function Theory If f(x) = x2 – 4, find f(a + 5) . Solution: a2 +10a+21 MATHEMATICS for COLLEGE READINESS

  21. Function Theory If f(x) = x2 – 3 x + 5, find f(x + h) – f(x) . 2xh + h2– 3h Solution: MATHEMATICS for COLLEGE READINESS

  22. Function Theory If f(x) = 3x4 – 4x3 -2x2 +x - 5, find f(-x). Solution: 2xh + h2– 3h MATHEMATICS for COLLEGE READINESS

  23. Expressions with Exponents Simplify: Solution: MATHEMATICS for COLLEGE READINESS

  24. Expressions with Exponents Simplify. Give the answer with positive exponents only: Solution: MATHEMATICS for COLLEGE READINESS

  25. Expressions with Exponents Simplify. Give the answer with positive exponents only: Solution: MATHEMATICS for COLLEGE READINESS

  26. Expressions with Exponents Multiply a. b. c. d. e. • Solution: MATHEMATICS for COLLEGE READINESS

  27. Expressions with Exponents Multiply • Solution: MATHEMATICS for COLLEGE READINESS

  28. Expressions with Exponents Multiply • Solution: MATHEMATICS for COLLEGE READINESS

  29. Expressions with Exponents If the area of a circle if what is the area of a circle if the radius is 3a? • Solution: MATHEMATICS for COLLEGE READINESS

  30. Expressions with Exponents If the volume of a sphere is what is the volume of a sphere with radius 3a? • Solution: MATHEMATICS for COLLEGE READINESS

  31. Expressions with Exponents If the volume of a cylinder is find the volume of a cylinder with radius 3x and a height that is twice the radius. • Solution: MATHEMATICS for COLLEGE READINESS

  32. Exponential and Logarithmic Functions If , then x = a. 3 + ln t b. c. d. ln ( t – 3 ) e. ln t – 3 Solution: e. lnt – 3 MATHEMATICS for COLLEGE READINESS

  33. Exponential and Logarithmic Functions If 7x = 3, then x = a. b. c. d. e. • Solution: MATHEMATICS for COLLEGE READINESS

  34. Simplifying Expressions Simplify a. b. c. d. • Solution: • a MATHEMATICS for COLLEGE READINESS

  35. Simplifying Expressions Simplify a. b. c. d. • Solution: • c MATHEMATICS for COLLEGE READINESS

  36. Simplifying Expressions Simplify • Solution: 5k2 + 250k -16 MATHEMATICS for COLLEGE READINESS

  37. Simplifying Expressions Evaluate the following expression using x = -3.1 and y = 4.23 4x-2 + y3 • 76.103 • Solution: MATHEMATICS for COLLEGE READINESS

  38. Algebraic Expressions Factor completely using integer coefficients. Solution: • 12 m2n3 (m2 + 4) MATHEMATICS for COLLEGE READINESS

  39. Algebraic Expressions Factor completely using integer coefficients. Solution: (4m – 3) (3m + 2) MATHEMATICS for COLLEGE READINESS

  40. Algebraic Expressions Which of the following is a factor of a. b. c. d. not factorable c. (4x + 3) Solution: MATHEMATICS for COLLEGE READINESS

  41. Algebraic Expressions Which of the following is a factor of a. b. c. d. Solution: b. (x + 2) MATHEMATICS for COLLEGE READINESS

  42. Algebraic Expressions Write in simplest radical form. Solution: MATHEMATICS for COLLEGE READINESS

  43. Algebraic Expressions Write in simplest radical form. Solution: 7x2y MATHEMATICS for COLLEGE READINESS

  44. Algebraic Expressions Write in simplest radical form. Solution: MATHEMATICS for COLLEGE READINESS

  45. Algebraic Expressions Write in simplest radical form. Solution: MATHEMATICS for COLLEGE READINESS

  46. Algebraic Expressions Perform the indicated operations and reduce answers to lowest terms. a. b. c. d. Solution: d MATHEMATICS for COLLEGE READINESS

  47. Quadratic Equations Solve algebraically. Solution: MATHEMATICS for COLLEGE READINESS

  48. Quadratic Equations Solve algebraically. Solution: MATHEMATICS for COLLEGE READINESS

  49. Quadratic Equations Solve algebraically. Solution: MATHEMATICS for COLLEGE READINESS

  50. Quadratic Equations Solve algebraically. Solution: MATHEMATICS for COLLEGE READINESS

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