Introductory Algebra Final Exam Review Note to students: The final exam for this course will consist of 0 multiple-choice questions and a few openended questions. The exam will cover Lessons from your Introductory Algebra Student Workbook. You may use a calculator on the exam, but no notes of any kind will be permitted. This review consists of sample questions which are not to be considered identical to those found on the exam. ) Perform the indicated operations. Reduce your answer to lowest terms. 6 75 B) 5 C) 75 6 5 5 D) ) ) Evaluate the expression a b, given a =, b = ) 7 B) 6 C) 6 D) 7 ) Simplify. 7(r 6) (r ) ) r + 7 B) 6r + 0 C) 6r + 5 D) 6r + 5 ) Solve. ( x ) ( x ) ) 5 B) C) D) 5) Solve. 8 0 x 5) 7 B) C) D) 6) Jon works for a vacuum cleaner sales business. He receives $8 per week in salary plus a commission of 8% of his weekly sales. How much will Jon earn in a week when his sales total $67? $5.00 B) $8.08 C) $.6 D) $8.80 6) 7) Solve the inequality 7 x > Write your answer in interval notation. 7) (, ) B) (, ) C) (, ) D) (, ) 8) A / cup serving of cereal contains 0 calories. How many calories are there in a ½ cup serving? 8) 0 calories B) 60 calories C) 80 calories D) 0 calories
) Jon has 006 points in his math class. He must have 76% of the 00 points possible by the end of the term to receive credit for the class. What is the minimum number of additional points he must earn by the end of the term to receive credit for the class? ) 58 points B) 06 points C) points D) 765 points 0) Given x y =, solve for y. 0) y x B) y x C) y x D) y x ) Given A P PRT, solve for T. ) PR P A A P A T B) T C) T D) T A P PR PR R ) Give the coordinates of the points C and D on the graph. ) C (, 5); D (, ) B) C (5, ); D (, ) C) C ( 5, ); D (, ) D) C (, 5); D (, ) ) Determine whether the ordered pair (6, ) satisfies the equation y 0 x ) Yes B) No ) Determine whether this set of ordered pairs represents a function. {( 6, ), (, 7), (, ), ( 7, )} ) Function B) Not a function
5) Determine whether this table of values represents a function. Input Output 7 8 0 Function B) Not a Function 5) 6) Determine whether the graphed relation is a function. 6) Function B) Not a Function 7) Given f ( x) x x x 6, evaluate f ( 6). 7) 50 B) 00 C) 56 D) 0 8) Given f (x) = x determine x when f (x) = - 8) -5 B) -5 C) 0 D) -0.5 ) The function C( d) d 0 describes the total cost of renting a truck for d days. How many days can the truck be rented for $6? ) 0 days B) days C) 7 days D) 7 days 0) Suppose the sales of a particular brand of appliance satisfy the relationship S( t) 0t 800, where S(t) represents the number of sales in year t, with t = 0 corresponding to 8. Find the number of sales in. 6570 B) 70 C) 770 D) 6570 0)
) Determine the slope of the line shown below ) B) 00 C) 0 D) -5 ) Determine the slope of the line shown below. ) B) 0 C) Undefined D) / ) The slope of a decreasing linear function is always ) Zero B) Positive C) Undefined D) Negative ) y x Determine the vertical intercept. (, 0) B) (-, 0) C) (0, ) D) 0, ) 5) x 5 Determine the vertical intercept. ( 5, 0) B) (0, 0) C) (0, 5) D) None 5)
6) y x Find the slope. 6) B) C) D) 0 7) x Find the slope. B) 0 C) Undefined D) 7) 8) y x Find the slope. 8) B) C) D) ) y x Determine the horizontal intercept. (, 0) B) (, 0) C) (0, ) D) 0, ) 0) x y = Determine the horizontal intercept. ) (, 0) B) (8, 0) C) (0, 6) D) (0, ) ) Write the equation of the linear function that generates the table below ) x y..8 5. y 0.x. B) y = 0.6x +. C) y.x 0. D) y 0.x. ) Write the equation of the linear function with slope =, passing through (, ). 8 7 y x B) y x C) y x D) y x 8 8 8 8 ) ) Write the equation of the horizontal line passing through (7, -). ) y 7 B) x 7 C) x D) y ) Write the equation of the line passing through the point (-, 5) that is parallel to y = 8 x. ) y = x + 5 B) y = x + 8 C) y = x D) y = x + 7
5) Write the equation of the line passing through the points (6, ) and (-, -) 5) 5 y x B) y x C) y x D) y x 5 5 5 5 6) When a new charter school opened in 005, there were 50 students enrolled. Since then, the student population has decreased by 00 students every two years. Write a formula for the function N(t) representing the number of students attending this charter school t years after 005. 6) N(t) = 50 00t B) N(t) = 50 50t C) N(t) = 50 t D) N(t) = 00 50t 7) Simple interest is given by the formula A = P + Prt. Where A is the accrued value of the investment after t years, and P is the starting principal invested at an annual percentage rate of r, expressed as a decimal. Sally buys a $,000 savings bond that pays % simple interest each year. How much will the bond be worth after 5 years? 7) $6.65 B) $578. C) $00 D) $000 8) Determine whether the ordered pair (-6, -) is a solution to the system. x y x y 7 8) Yes B) No ) Solve the system of equations. Write the solution as an ordered pair. 5x y 6x 5y (, ) B) (, ) C) (, ) D) (, ) ) 0) Mark the electrician charges $0 for a house call, and then $5 per hour for labor. Sara the electrician charges $00 for a house call, and then $50 per hour for labor. Write a cost equation for each electrician, where y is the total cost of the electirical work, and x is the number of hours of labor. Mark: y 5x 0 B) Mark: y 50x 00 Sara: y 50x 00 Sara: y 5x 0 C) Mark: y 0x 5 Sara: y 00x 50 D) Mark: y 00x 50 Sara: y 0x 5 0)
) Solve the system of equations. Write the solution as an ordered pair. 7x 6y 5x y 0 ( 6, 5) B) (6, 5) C) (6, 5) D) (5, 6) ) ) Choose the ordered pair which is a solution of the inequality. x y 8 ) (, ) B) (0, 0) C) (, ) D) (, 0) ) The Science Museum charges $ for adult admission and $ for each child. The total bill for 68 people from a school field trip was $78. How many children went to the museum? 56 B) C) 7 D) ) ) The bill for dinner (after tax) was $85.0. You decide to leave a 5% tip. Calculate the total amount paid. $.78 B) $7.8 C) $7. D) $.5 ) For problems 5 50, simplify the expressions. Write all answers with positive exponents. Assume variables represent nonzero quantities. 5 5) ( x ) 5) 8 x B) 5 x C) 8 x D) 5 x 6) x (5x ) 6) 6 0x B) 0x C) 0x D) 6 50x 7) n 5 6n 5 B) n 5 C) 6n 65 D) n 65 7) 8) 6 mp mp p m m p B) C) m p D) mp 8)
) B) C) D) ) 50) x 50) 8 B) C) D) x 8x x x 5) Evaluate (x) when x = 5) 6 B) C) D) 7 78 08 7 5) Multiply and simplify. ( x 6)( x 8) 5) x x B) x x 8 C) x 8x D) x x 8 5) Multiply and simplify. (a ) 5) a a B) a C) a a D) a 5) Divide. Assume the variables represent nonzero quantities. 7 6x x 7 x 6 7 6 x B) C) 6x x D) x 6x 5) 55) The amount of waste in a landfill over a 5 year period (in tons) is shown in the table below. Years t 6 5 Amount of Waste (in tons) W(t).5 0 5.5 7.5 For what value of t is W(t) = 5? Include units in your answer. 55) 6 years B) 6 tons C) 7.5 years D) 7.5 tons
56) In 5, the cost of tuition at a large Midwestern university was $ per credit hour. In 005, tuition had risen to $8 per credit hour. Determine a linear equation to represent the cost, C, of tuition as a function of x, the number of years since 5. 56) C( x) x B) C( x) 8 x C) C( x). x D) C( x). x 57) The function V(m) represents value of an investment (in thousands of dollars) after m months. Explain the meaning of V() = 8. After months, the investment will be worth $8. B) After months, the investment will be worth $8,000. C) After 8 months, the investment will be worth $. D) After 8 months, the investment will be worth $,000. 57) Problems 58 60 refer to the graph of f(x) shown below 58) Determine the domain of f(x). 58) 0 x 0 B) x 6 C) x 8 D) 0 x 5) Determine the range of f(x). 5) 0 f(x) B) f(x) 6 C) f(x) 8 D) 0 f(x) 8 60) Determine f(). 60) B) 0 C) D)