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MATH 0930 Beginning Algebra Part 1 K.Rigdon Name_________________________ Practice Test for Exam 3 – 2.6 & 3.1-3.2 Due (optional) Test Day – Mon., 11/3/2014 This practice test will give you a good idea of the type and number of problems you will see on the actual test. Working through this practice test will, therefore, provide you with a good idea of how well you know the material you will be tested over. I am providing the answers on the last sheet for you to check your answers. You have the opportunity to earn 3 extra credit points toward your test grade if you show all work for all the problems and, of course, get all the answers correct (partial points can be earned as well). If you would like to earn these extra points, you will need to turn in this packet, with your work attached (on your own notebook paper), on test day. I will be including 5-6 Cumulative Review problems at the beginning this time. These problems will be like the Problems on the Cumulative Review Worksheets you’ve had and/or like Cumulative Review type problems assigned in Homework assignments… p149: #119-122, p193: #136-138, 140 p204: #75-77 In terms of points possible, you should expect the application problems to be worth a little more than the others….. Remember, also, ….. you are allowed to use a calculator with this test!!!!! ALSO – at the end of the Practice Test Questions, but before the Answers, I will be including a “Formula/Fact Sheet” like what I will be including in the actual text. One more thing – attached to the very back of this packet, you will see a sample of what the application problems will look like on the test…… I don’t want you to be surprised! Practice Test questions continued on next page! PRACTICE TEST QUESTIONS….. Use the formula given to find the value of the variable indicated (round answers to the nearest hundredth, if necessary): 7) m = a + b + c; find m when a = 43.2, b = 90, and c = 46.8 8) S 4 r 2 r 2 ; find S when r = 10 Use the information from the Formula/Fact Sheet attached for the following problems (round answers to the nearest hundredth, if necessary): 9) A rectangular tablecloth is 3 yards long and 2 yards wide. Find the perimeter and area. 10) An advertisement sign, in the shape of a trapezoid, is 5 feet tall and has bases that are 8 and 10 feet. What is the area of the sign? 11) A can of soup in the shape of a right circular cylinder is 5 inches tall and has a radius of 1.5 inches. How much soup will the can hold? 12) How much interest will Bill pay on his car loan if he finances $17,000 at a 13% simple interest rate for 4 years? 13) What speed would you be traveling if you drove 330 miles in 5.5 hours? For the following application problems, select & define a variable and other unknown: 14) Justin’s test score was 12 points less than the average test score. 15) Kristen and Kyle paid for their dinner separately. Their restaurant bills totaled $54.35. 16) The width of the rectangular garden is 5 feet less than half the length. For the following application problems, write the expression indicated. 17) At a football game, the stands were filled with 1200 spectators. Let m represent the number of male fans. Write an algebraic expression for the number of female fans at the game. 18) The larger of two numbers is two more than three times the smaller number. Let n represent the smaller number. Write an expression for the sum of the two numbers. 19) The sales tax in a particular state is 6.5%. Let x represent the price of an item to be purchased in this state. Write an algebraic expression for the complete purchase total. For the following application problems, be sure to define your variable (and other unknowns), write and solve an equation, and answer the question(s). 20) The sum of two integers is 121. Find the two integers if the larger one is 7 more than twice the smaller. 21) The sum of two consecutive integers is 69. Find the two integers. 22) Ronnie purchased a lawn mower. The cost of the mower, including an 8% sales tax, was $648. Find the cost of the mower before tax. 23) The town of Marthasville currently has a population of 808. If its population is increasing at a rate of 112 people per year, how long will it take for the population to reach 2264?. 24) Josephine ordered some candles from an online company. The company charged $10.25 per candle, plus $15 for shipping and handling. How many candles did Josephine order if her bill was $179? 25) Nine less than five times a number is 76. Find the number. Formula/Fact Sheet (I will include one like this with the test too!) Perimeter, P, is the sum of the lengths of the sides of a figure. Area, A, is the total surface within the figure’s boundaries. 2 Square P = 4s A= s Rectangle A=lw P = 2l + 2w Parallelogram A = lh P = 2l + 2w Trapezoid Triangle Circle A= 1 2 A= h (b + d) 1 2 bh A r 2 P=a+b+c+d P=a+b+c C 2r is approximately 3.14. (If you use the key on your calculator, you will need to round your answers to the nearest hundredth.) Rectangular solid V = lwh 2 Right circular cylinder Right circular cone Sphere V r h V 13 r 2 h V 43 r 3 Two angles are supplementary angles when the sum of their measures is 180 . Each angle is the supplement of the other. Perpendicular lines are lines that intersect at 90 angles. An acute triangle is one with three acute angles (angles < 90 ). An obtuse triangle has one obtuse angle (an angle > 90 ). A right triangle has one right angle (an angle equal to 90 ). An isosceles triangle has two sides of equal length. The angles opposite the equal sides have the same measure. An equilateral triangle has three sides of equal length. It also has three equal angles that measure 60 each. When two sides of a right triangle are known, the third side can be found using the Pythagorean Theorem, a 2 + b 2 = c 2 , where a and b are the legs and c is the hypotenuse of the triangle. A triangle that contains two sides of equal length is called an isosceles triangle. In isosceles triangles, the angles opposite the two sides of equal length have equal measures. The sum of the angles of any triangle measures 180 degrees. When two lines intersect four angles are formed. The pair of opposite angles formed by the intersecting lines are called vertical angles. Vertical angles have equal measures. A quadrilateral is a four-sided figure. Quadrilaterals include squares, rectangles, parallelograms, and trapezoids. The sum of the measures of the angles of any quadrilateral is 360 degrees. Two angles are complementary angles when the sum of their measures is 90 . Each angle is the complement of the other. Simple Interest formula Interest = principal or I = prt Distance formula Distance = rate rate time or d = rt time Practice Test Answer Key 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 180 753.6 P = 10 yards, A = 6 square yards Area = 45 square feet Volume = 35.33 cubic inches or 35.34 cubic inches $8840 60 mph x = average test score, x – 12 = Justin’s score x = Kristen’s bill (or Kyle’s), 54.35 – x = Kyle’s bill (or Kristen’s) x = length, ½ x – 5 = width Female fans = 1200 – m Larger number = 3n + 2, so Sum of the two numbers = n + 3n + 2 Complete purchase total = x + .065x Define: x = smaller integer 2x + 7 = larger integer Equation: x + 2x + 7 = 121 Solve: x = 38 Answer: The integers are 38 & 83. Define: x = first consecutive integer x + 1 = second consecutive integer Equation: x + x + 1 = 69 Solve: x = 34 Answer: The consecutive integers are 34 & 35. Define: x = cost of mower before tax .08x = tax on mower Equation: x + .08x = 648 Solve: x = 600 Answer: The cost of the mower before tax was $600. Define: x = years Equation: 808 + 112x = 2264 Solve: x = 13 Answer: It would take 13 years. Define: x = number of candles Josephine ordered Equation: 10.25x + 15 = 179 Solve: x = 16 Answer: Josephine ordered 16 candles. Define: x = number Equation: 5x – 9 = 76 Solve: x = 17 Answer: the number is 17 Sample of what application problems will look like on the test (I may change the point values – haven’t decided yet)……… For the following application problems, be sure to define your variable (and other unknowns), write and solve an equation, and answer the question(s). These items will receive credit as follows: Define your variable & other unknowns: 2 points Write and solve an equation: 5 points Answer the question(s): 2 points 10) The sum of two integers is 121. Find the two integers if the larger one is 7 more than twice the smaller. Define variable (& other unknowns): Write and solve an equation: Answer the question(s):