COMPASS Math Practice Test - Heartland Community College
COMPASS Math Practice TestDirections: The practice questions in this study guide are separated by mathematical level,similar to how the adaptive COMPASS placement test may ask you questions in different levels,depending on how accurately you answer each question.To try and place into a college level Math class, it is recommended that you focus most of yourpractice in the levels of College Algebra (pg. 1-2) and Geometry (pg. 3-7). However, if you findthese practice questions too difficult at first, some easier questions in Intermediate Algebra (pg.8-9), Elementary Algebra (pg. 10-11), and Pre-Algebra (pg. 12-13) are provided for extrapractice before moving on to College Algebra/Geometry.Tip: You are not limited to this one study guide as a form of test practice. We also recommendKhanacademy.org and Mathhelp.com for online/interactive practice.
Page 1College Algebra Placement Practice1.For π 1, if 3π(2 5π) π₯ 6π, then x ?A.2.B. 5C. 5iD. 15iE. 27iIf f(4) 0 and f(6) 6, which of the following could represent f(x)?A.3.-152π₯3 4B. x 2C. x β 4D.3π₯2 6E. 3x β 121What is the next term in the geometric sequence 16, 4, 1, 4 , ?1A. 81B. 0C. 16D.18E.124.A manufacturing company processes raw ore. The number of tons of refined material thecompany can produce during t days using Process A is π΄(π‘) π‘ 2 2π‘ and using Process B isπ΅(π‘) 10π‘. The company has only 7 days to process ore and must choose 1 of the processes.What is the maximum output of refined material, in tons, for this time period?A. 8B. 10C. 51D. 64E. 705.For the two functions, f(x) and g(x), tables of values are shown below. What is the value ofg(f(3))?x-5-213A.6.B. -3C. -1g(x)3-1-3-5D. 2E. 7For positive real numbers x, y, and z, which of the following expressions is equivalent toπ₯1 2 5 2π¦ 3π§ 6A.7.-5x-2123f(x)7-5323 π₯π¦ 2 π§ 3If π΄ [A.0[0?6B. π₯π¦ 2 π§ 56C. π₯ 3 π¦ 2 π§ 56D π₯ 3 π¦ 4 π§ 511E. π₯π¦ 2 π§ 52 4 2 4] and π΅ [], then A β B ?6 0 6 00]0B. [1 0]0 1C. [0 8]0 0 4 0D. [] 12 0E. [4 8]12 0
Page 28.Listed below are 5 functions, each denoted g(x) and each involving a real number constant c 1.If π(π₯) 2π₯ , which is these 5 functions yields the greatest value for f(g(x)), for all x 1?A.9.ππ(π₯) ππ₯B. π(π₯) π₯π₯C. π(π₯) πD. π(π₯) π₯ πE. π(π₯) log π π₯If the function f satisfies the equation π(π₯ π¦) π(π₯) π(π¦) for every pair of real numbers xand y, what are the possible values of f(0)?A. Any real number B. Any positive real number C. 0 and 1 only D. 1 only E. 0 only10. The imaginary number I is defined such that π 2 1. What does π π 2 π 3 π 23 equal?A. iB. βiC. -1D. 0E. 111. In an arithmetic series, the terms of the series are equally spread out. For example, in 1 5 9 13 17, consecutive terms are 4 apart. If the first term in an arithmetic series is 3, and the lastterm is 136, and the sum is 1,390, what are the first three terms?A. 3, 10, 17B. 3, 23, 4313C. 3, 36 , 7012D. 3, 69 , 136E. 3, 139, 1,251Correct Answer Choices for Sample College Algebra Questions1. A7. E2. E8. A3. C9. E4. E10. C5. B11. A6. D
Page 3Geometry Placement PracticeThis document provides practice problems to complete as you prepare to take the placement test forGeometry at Heartland Community College. The questions are from the COMPASS website, 2014ACT, Inc.1.In the figure below, line m is parallel to line n, and line t is a transversal crossing both m and n.Which of the following lists has 3 angles that are all equal in measure?2.Μ Μ Μ Μ equal to the length ofAs shown in the figure below, ΞABC is isosceles with the length of π΄π΅Μ Μ Μ Μ . The measure of π΄ is 40 and points B, C, and D are collinear. What is the measure ofπ΄πΆACD?3.The diagram below shows a pasture which is fenced in. All but one section of fence run straightnorth-south or east-west. Consecutive fence posts are 10 feet apart except for the one diagonalsection. Which of the following statements best describes P, the perimeter of the pasture, infeet?
Page 44.A person had a rectangular-shaped garden with sides of lengths 16 feet and 9 feet. The gardenwas changed into a square design with the same area as the original rectangular-shaped garden.How many feet in length are each of the sides of the new square-shaped garden?5.Μ Μ Μ Μ is 6 units and the length of πΆπ΅Μ Μ Μ Μ is 3In the figure below, π΄π΅πΆ is right triangle. The length of π΄π΅Μ Μ Μ Μ ?units. What is the lengths, in units, of π΄πΆ6.If a central angle of measure 30 is subtended by a circular arc of length 6 meters, as isillustrated below, how many meters in length is the radius of the circle?
Page 57.A rectangular box with a base 2 inches by 6 inches is 10 inches tall and holds 12 ounces ofbreakfast cereal. The manufacturer wants to use a new box with a base 3 inches by 5 inches.How many inches tall should the new box be in order to hold exactly the same volume as theoriginal box? (Note: The volume of a rectangular box may be calculated by multiplying the areaof the base by the height of the box.)8.In the figure below, the circle centered at B is internally tangent to the circle centered at A. TheΜ Μ Μ Μ is 5 units. If thesmaller circle passes through the center of the larger circle and the length of π΄π΅smaller circle is cut out of the larger circle, how much of the area, in square units, of the largercircle will remain?9.In the figure below,andare parallel, and lengths are given in units. What is the area, insquare units, of trapezoid ABCD?
Page 610. A 6-foot spruce tree is planted 15 feet from a lighted streetlight whose lamp is 18 feet abovethe ground. How many feet long is the shadow of that tree?Μ Μ Μ Μ are given, in units. What is the area, inΜ Μ Μ Μ , Μ Μ Μ Μ 11. In the figure below, the lengths of π·πΈπΈπΉ , and πΉπΊsquare units, of π·πΈπΊ?
Page 712. In the figure below , , and are parallel, and intersects all 3 lines at points R, S,and T, respectively. If the measure of QTF is 33 , what is the measure of PRB ?A.B.C.D.E.13.33 57 66 123 147 In MPB below,. If , then ?A.B.C.D.E.Answers:1. A2. C3. A4. C5. B6. D7. A8. C9. B10. B11. C12. E13. C
Page 8Intermediate Algebra Placement Practice (MATH 093)1.For 4 , which of the following is equivalent to the expressionA.2.B. x 8C. x 113xB. x 3?D. x 16Which of the following is a simplified expression equal toA.3.x 3π₯ 2 12π₯ 32π₯ 4C. x β 39 π₯ 2π₯ 3E. x 28?D. βx 3E. βx β 3What is the slope of the line with the equation 2x 3y 6 0?A.-6B. -32D. 3C. -2E.234.Point A (-4, 1) is in the standard (x,y) coordinate plane. What must be the coordinates of point BΜ Μ Μ Μ ?so that the line x 2 is the perpendicular bisector of π΄π΅A. (-6, 1)B. (-4, -1)C. (-4, 3)D. (-2, 1)E. (8,1)5.What is the sum of the polynomials 3π2 π 2π2 π 2 and ππ 2 π2 π 2 ?A.3π2 π ππ 2 3π2 π 2B. 3π2 π ππ 2 2π2 π 2D. 2π2 π 3 2π4 π 46.E. 3π3 π 3 2π4 πFor all nonzero r, t, and z values,A.4π§3 2π‘ π2B. 16π 3 π‘π§ 5 4ππ‘ 3 π§ 24ππ§C. π‘4π2 π§3π‘2π₯ 2 1If x -3, what is the value ofA.-48.For all x 0 and y 0, the radical expressionπ₯ 1B. -23π₯ π₯π¦9π₯ π¦B.3π₯ π₯π¦3π₯ π¦ ?D. 4π 4 π‘ 4 π§ 7E. 4π 2 π‘ 2 π§ 3?7.A.C. 2π2 π 3π2 π2C. 22D. 3 3 π₯is equivalent to:3 π₯ π¦3π₯ π₯π¦3π₯ π₯π¦C.D.9π₯ π¦3π₯ π¦E. 5E.π₯3π₯ π¦
Page 99.If x -3, what is the value ofA.-4π₯ 2 1π₯ 1?B. -2C. 22D. 3 3E. 510. Doctors use the term maximum heart rate (MHR) when referring to the quantity found bystarting with 220 beats per minute and subtracting 1 beat per minute per each year of apersonβs age. Doctors recommend exercising 3 or 4 times each week for at least 20 minuteswith your heart rate increased from its resting heart rate (RHT) to its training heart rate (THR)where,THR RHR 0.65(MHR β RHR)Which if the following is the closest to the THR of a 43 year old person whose RHR is 54 beatsper minute?A. 197B. 169C. 162D. 134E. 8011. If x -1 and y 2, what is the value of the expression 2π₯ 3 3π₯π¦ ?A. 8B. 4C. -1D. -412. For all πA.π 3π 2 2,π 2 5π 6π 2 4B.π 2π 2E. -8 ?C.π 2π 3D.π 3π 2E.π 3π 213. Write the equation of the line that contains the points with (x,y) coordinates (-3,7) and (5, -1).A.y 3x β 2 B. y x 1013C. π¦ π₯ 832D. π¦ π₯ 114E. y -x 4Correct Answer Choices for Sample Intermediate Algebra Questions1. B7. C2. E8. A3. D9. D4. E10. B5. A11. A6. B12. E
Page 10Elementary Algebra Placement Practice (MATH 092)1.In scientific notation, 20,000 3,400,000 ?A.2.C. 2 x 31533B. 6 41C. 10 296 D. 4 x 9E. 16 x 81D. 11E. οΏ½οΏ½οΏ½π¦π₯E.ππ₯π¦15B. 16C. 21D. 30E. 480%B. 10%C. 15%D. 30%E. 45%70B. 72C. 84D. 96E. 98A total of 50 juniors and seniors were given a mathematics test. The 35 juniors attained anaverage score of 80 while the 15 seniors attained an average of 70. What was the average scorefor all 50 students who took the test?A.9.B. 0 x 65Adam tried to compute the average of his 7 test scores. He mistakenly divided the correct sumof all of his test scores by 6, which yielded 84. What is Adamβs correct average test score?A.8.0 x 5This year, 75% of the graduating class of Harriet Tubman High School had taken at least 8 mathcourses. Of the remaining class members, 60% had taken 6 or 7 math courses. What percent ofthe graduating class had taken fewer than 6 math courses?A.7.E. 3.60 1012On a math test, 12 students earned an A. This number is exactly 25% of the total number ofstudents in the class. How many students are in the class?A.6.D. 3.60 107If the total cost of x apples is b cents, what is a general formula for the cost, in cents, of yapples?A.5.C. 3.42 107What value of x solves the following proportion?A.4.B. 3.60 106Saying that 4 π₯ 9 is equivalent to saying what about x?A.3.3.42 10673B. 75C. 76D. 77Which of the following is a factor of the polynomial π₯ 2 π₯ 20?E. 78
Page 11A.xβ5B. x β 4C. x 2D. x 5E. x 10D. -3E. 210. If 2(x β 5) -11, then x ?A. 212C. B. -8112111. When getting into shape by exercising, the subjectβs maximum recommended number ofheartbeats per minute (h) can be determined by subtracting the subjectβs age (a) from 220 andthen taking 75% of that value. This relation is expressed by which of the following formulas?A. h 0.75(220 β a)D. 0.75h 220 β a12. IfA.453B. h 0.75(220) β aE. 220 0.75(h β a)C. h 220 β 0.75a1 ( 10) π₯ 1 2 , then x ?2B. 1C. -1D. -2E. -1013. An airplane flew for 8 hours at an airspeed of x miles per hour (mph), and for 7 more hours at325 mph. If the average airspeed for the entire flight was 350 mph, which of the followingequations could be used to find x?A. x 325 2(350)D. 8x 7(325) 2(350)B. x 7(325) 15(350)E. 8x 7(325) 15(350)C. 8x β 7(325) 35014. Which of the following is a factor of π₯ 2 5π₯ 6?A.x 2B. x β 6C. x β 3D. x β 2E. x β 1D. 9a bE. 9a 7b15. Which of the following is equivalent to 3a 4b β (-6a β 3b)?A.16abB. -3a bC. -3a 7bCorrect Answer Choices for Sample Elementary Algebra Questions1. E9. A2. E10. E3. E11. A4. D12. C5. E13. E6. B14. B7. B15. E8. D
Page 12Prealgebra Placement Practice (MATH 091)This document provides practice problems to complete as you prepare to take the placement test forGeometry at Heartland Community College. The questions are from the COMPASS website, 2014ACT, Inc. (http://www.act.org/compass/sample/math.html)1.54 β 6 2 6 ?A. 62.B. 24B. 8 E. 57321C. 16 D. 24 E. 32 1If ( ) ( ) is calculated and the answer reduced to simplest terms, what is the4323denominator of the resulting fraction?A. 244.D. 30The lowest temperature on a winter morning was β8 F. Later that same day the temperaturereached a high of 24 F. By how many degrees Fahrenheit did the temperature increase?A. 3 3.C. 2712A.B. 122345B.1727C. 6D. 4E. 3 (3 4) (5 6)11613C. 1875D. 9E. 635. Mr. Brown went grocery shopping to buy meat for his annual office picnic. He bought 7 41pounds of hamburger, 17.85 pounds of chicken, and 62 pounds of steak. How many pounds ofmeat did Mr. Brown buy?A. 32.10B. 31.31C. 26.25D. 22.10E. 21.106. Four students about to purchase concert tickets for 18.50 for each ticket discover that theymay purchase a block of 5 tickets for 80.00. How much would each of the 4 save if they can geta fifth person to join them and the 5 people equally divide the price of the 5-ticket block?A. 1.507.B. 2.50C. 3.13D. 10.00E. 12.50What is the average (arithmetic mean) of 8, 7, 7, 5, 3, 2, and 2?4564A. 3 7B. 4 6C. 4 7D. 5E. 6 5
Page 138.Ben is making wooden toys for the next arts and crafts sale. Each toy costs Ben 1.80 to make.If he sells the toys for 3.00 each, how many will he have to sell in order to make a profit of 36.00?A. 12B. 20C. 30D. 60E. 1089.How many yards of material from a 24-yard length of cloth remain after 3 pieces, each 3 2 yards11long, and 5 pieces, each 2 4 yards long are removed?A.1241B. 4 45C. 4 61D. 10 45E. 10 610. Phillip charged 400 worth of goods on his credit card. On his first bill, he was not charged anyinterest, and he made a payment of 20. He then charged another 18 worth of goods. On hissecond bill a month later, he was charged 2% interest on his entire unpaid balance. How muchinterest was Phillip charged on his second bill?A. 8.76B. 7.96C. 7.60D. 7.24Correct Answer Choices for Sample Pre-algebra . 6.63
practice in the levels of College Algebra (pg. 1-2) and Geometry (pg. 3-7). However, if you find these practice questions too difficult at first, some easier questions in Intermediate Algebra (pg. 8-9), Elementary Algebra (pg. 10-11), and Pre-Algebra (pg. 12-13) are provided for extra practice before moving on to College Algebra/Geometry.
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compass reading (a) Fe-rich rock bodies can only use sun compass C. Using clinometer 1. align vertical edge of compass with angle of plane 2. adjust bubble level of clinometer 3. read angle from vernier scale on compass D. Computing vertical elevation 1. measure eye height from ground surface (E.H.) 2. sight compass to top of object (e.g. top .
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Introduction to the Brunton Compass Geo420k, Lab 1. M. Helper, Jackson School of Geosciences, UT Austin Mirror Lift Pin for Needle Compass Card Sighting Arm Parts of the Brunton Compass . Compass must be horizontal (bullβs eye bubble centered), with compass edge flush to the tilted plane Strike.
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COMPASS SURVEYING 1. Familiarity with instruments used in compass surveying - prismatic compass. 2. Setting up the compass - observation of bearings. 3. Traversing with prismatic compass and chain calculation of included angles and check. 4. Traversing with prismatic compass and chain closed traverse covering the given area recording. 5.
