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North Carolina Communit College Sstem (NCCCS) Diagnostic and Placement Test The NCCCS Diagnostic and Placement test contains 96 questions that measure proficienc in eight content areas. The eight content areas are as follows: Operations with Integers Topics covered in this categor include: Problem events that require the use of integers and integer operations Basic eponents, square roots and order of operations Perimeter and area of rectangles and triangles Angle facts and the Pthagorean Theorem Fractions and Decimals Topics covered in this categor include: Relationships between fractions and decimals Problem events that result in the use of fractions and decimals to find a solution Operations with fractions and decimals Circumference and area of circles The concept of π Application problems involving decimals Proportions, Ratios, Rates and Percentages Topics covered in this categor include: Conceptual application problems containing ratios, rates, proportions and percentages Applications using U.S. customar and metric units of measurement Geometr of similar triangles Polnomials and Quadratic Applications Topics in this categor include: Graphical and algebraic representations of quadratics Finding algebraic solutions to contetual quadratic applications Polnomial operations Factoring polnomials Appling factoring to solve polnomial equations Rational Epressions and Equations Topics covered in this categor include: Graphical and algebraic representations of rational equations Finding algebraic solutions to contetual rational applications Identifing and simplifing rational epressions Radical Epressions and Equations Topics covered in this categor include: Manipulating radicals to solve real-world applications involving radical equations Simplifing and performing operations with radical epressions and rational eponents Epressions, Linear Equations and Linear Inequalities Topics covered in this categor include: Graphical and algebraic representations of linear epressions, equations and inequalities Application problems using linear equations and inequalities Graphs and Equations of Lines Topics covered in this categor include: Graphical and algebraic representations of lines Interpretation of basic graphs (line, bar, circle, etc.) 0 The College Board. Diagnostic and Placement Test Sample Questions
Operations with Integers For each of the questions below, choose the best answer from the four choices given. You ma use the paper ou received as scratch paper.. On a summer da in Benton, the low temperature of 75 F was reached at 6 in the morning. The high temperature was reached 9 hours later, after the temperature rose 6 F. What was the high temperature in Benton that da? 8 F B. 84 F 9 F 96 F A B C D 4 0 4. Which of the four labeled points on the number line above has the greatest absolute value? A B. B C D Fractions and Decimals For each of the questions below, choose the best answer from the four choices given. You ma use the paper ou received as scratch paper. feet Table. A large dining room table is in the shape of a semicircle of diameter feet, as shown above. Of the following, which is closest to the area of the table? (Use π =.4. ) 8 square feet B. 57 square feet 75 square feet square feet. (- - 4) 8 = -48 B. -6 6 48 4. The sum of Cherl s scores on the first four quizzes in her histor class was 64 points. If she scores 96 points on her net quiz, what will be her average score for the five quizzes? 89 points B. 9 points 9 points 94 points. The large square above has area 9 and is divided into 9 smaller squares of equal area. What is the length of the path drawn in bold?. B. 4 5 6 0.6 0 - = 60 B. 6 0.06 0.006 5. 59 = 7 B. 6 7 0 The College Board. Diagnostic and Placement Test Sample Questions
4.,590 = B. 5.59 0 4.59 0.59 0.59 0 O 75 Proportions, Ratios, Rates and Percentages For each of the questions below, choose the best answer from the four choices given. You ma use the paper ou received as scratch paper.. During a basketball practice, two plaers, Sidell and Jeron, each attempted 5 free throws. Sidell made 40% of his free-throw attempts, whereas Jeron made 5% of them. How man more free-throws did Jeron make than Sidell? B. 4 5 6 5. The circle above has center O. The fraction of the area of the circle that is shaded represents a value on the number line between B. 5 and 5 5 and 4 5 4 5 and 5 5 5 5 and 6 5. A bo skis 4 miles down a mountain slope in 0 minutes. What is his average speed, in miles per hour (mph), over that time interval? 48 mph B. 6 mph mph 4 mph. There are children in a line to bu a hot dog. If ever 4th child in line, starting with the fourth in line, gets a to, what is the ratio of the number of children in line who get a to to the number of children in line who do not get a to? :8 B. 5 : 5 :8 6 : 4. 5 is what percent of 60? 0% B..5% 5% 8.5% 5. Jenna is driving at a speed of 65 miles per hour. What is Jenna s driving speed in kilometers per hour? (There are about.6 kilometers in mile.) kilometers per hour B. 04 kilometers per hour 96 kilometers per hour 9 kilometers per hour 0 The College Board. Diagnostic and Placement Test Sample Questions
Epressions, Linear Equations and Linear Inequalities For each of the questions below, choose the best answer from the four choices given. You ma use the paper ou received as scratch paper. 0. The tick marks on the number line above are equall spaced. The epression + is equal to 5. If - = 5 -, then = B. 0-5 5 5 8 - B. 0 8 6. A part suppl store charges an initial charge of $0 to rent a costume plus an additional $8 per da for each da the costume is rented. Which of the following represents the cost, in dollars, to rent a costume for n das? 8n B. 0 + 8n (0)(8 n) 0-8n. Julie purchased a treadmill that originall cost t dollars at a discount of 8%. Which of the following represents the amount, in dollars, that Julie paid for the treadmill after the discount? t- 0.8t B. t + 0.08 t+ 0.08t t- 0.08t 4. A long distance cell phone service offers a plan that costs $0 per month plus $0.40 per minute of use. Which of the following represents the total cost of this service for a month in which n minutes were used? (0)(0.04 n ) B. 0.40n 0 +.4n 0 + 4n 0 The College Board. Diagnostic and Placement Test Sample Questions 4
Graphs and Equations of Lines For each of the questions below, choose the best answer from the four choices given. You ma use the paper ou received as scratch paper. Total Amount of Mone Saved (in dollars),000 0,000 8,000 6,000 4,000,000 B. Number of Shirts Sold (each month) 00 80 60 40 0 00 80 60 40 0 00 O 4 5 6 7 8 Years After the Compan Opened. The linear equation graphed above gives the amount of mone Compan H has saved ears after the compan opened. According to the graph, how man ears after the compan opened did the save $0,000? B. 4 5 6. Anita s department store determined that if a specific shirt is priced at $50 each, on average there would be 00 shirts sold each month the shirt is available for sale. The number of shirts sold per month would decrease b 0 for each $5 of increase in the price. If p presents the price of the shirt, in dollars, and s represents the average number of shirts sold per month, which of the following graphs best represents the relationship between p and s? Number of Shirts Sold (each month) 00 80 60 40 0 00 80 60 40 0 00 Number of Shirts Sold (each month) Number of Shirts Sold (each month) 00 80 60 40 0 00 80 60 40 0 00 00 80 60 40 0 00 80 60 40 0 00 5 40 45 50 55 60 65 70 75 80 85 Price of Shirt (in dollars) 5 40 45 50 55 60 65 70 75 80 85 Price of Shirt (in dollars) 5 40 45 50 55 60 65 70 75 80 85 Price of Shirt (in dollars) 5 40 45 50 55 60 65 70 75 80 85 Price of Shirt (in dollars) 0 The College Board. Diagnostic and Placement Test Sample Questions 5
. A computer help-service charges an initial fee to join the service plus an additional charge for each hour of helpservice a customer uses. If the computer service compan charges a total of $40 for the initial fee and a -hour help session and a total of $0 for the initial fee and a 4-hour help session, which of the following epressions gives the computer compan s charge for each hour of help-service that a customer uses? B. $0 - $40 4- $0 + $40 4+ 4- $0 - $40 4+ $0 + $40 4. Jen scored 6 points in a new card game, where each plaer could receive either or 4 points in each round. If Jen received amount of point scores, and amount of 4 point scores, what does the -intercept of the graph in the -plane of the equation + 4 = 6 indicate? Jen scored points in 8 rounds and she didn t score 4 points in an round. B. Jen scored points in rounds and 4 points in rounds. Jen scored points in 4 rounds and 4 points in rounds. Jen didn t score points in an round, but she scored 4 points in 4 rounds. 0 9 8 7 6 5 4 6 5 4 O 4 5 6 7 8 9 0 4 5. Which of the following is true about the line graphed in the -plane above? The line has slope and -intercept -. B. The line has slope and -intercept. The line has slope and -intercept -. The line has slope and -intercept. 0 The College Board. Diagnostic and Placement Test Sample Questions 6
Polnomials and Quadratic Applications For each of the questions below, choose the best answer from the four choices given. You ma use the paper ou received as scratch paper. t 4. If -- 8 = 0, which if the following is a possible value for of? -6 B. 6 9 z. All of the line segments in the figure above meet at right angles, and the lengths of four of the si sides are given. Which of the following represents the area of the figure, in terms of, t,, and z?. z - t B. z + t z - t + t z + t + t 4 4 ( z )( - - z - ) B. z z z z = 00 50 00 50 00 50 O 5 0 5 0 5 0 5 40 5. The function f( ) = - + 40-75 is graphed in the -plane above. For what value of is the value of f( ) greatest? 5 B. 0 0 5. a - b B. a - ab + b a - ab + b a - ab + b 4 a - ab + b 4 0 The College Board. Diagnostic and Placement Test Sample Questions 7
Rational Epressions and Equations For each of the questions below, choose the best answer from the four choices given. You ma use the paper ou received as scratch paper.. Kala is going to bike the entire length of a 90-mile scenic bike path. She will take a -hour break during her ride. If Kala s average speed while biking is s miles per hour, how man hours will it take from the time she leaves the start of the bike path until she reaches the end of the bike path? B. 90 s - 90 s + 90 s - 90 s + 4 O 4 5 6. Which of the following could be an equation of the function graphed in the -plane above? + 9 = + -6. ( ) - 7 B. + 7-7 + 7 4. + = + B. + + + 5. If + = 8, + - -- B. 0 - then = B. = = + = - = + 0 The College Board. Diagnostic and Placement Test Sample Questions 8
Radical Epressions and Equations For each of the questions below, choose the best answer from the four choices given. You ma use the paper ou received as scratch paper.. The formula v = 0 fd is used to estimate the speed v, in miles per hour, a car was traveling if it skids d feet after the application of its brakes. The number f is a coefficient that measures the slipperiness of the road. If a car skids 55 feet and f = 0.9, how fast was the car traveling when its brakes were applied? (Round our answer to the nearest tenth of a mile per hour.) 8.5 mph B. 4.6 mph 45.0 mph 48.5 mph 5. If -- 0 = -, what is the value of? B. 4 6 0. ( 49) - = - 7 B. 7 7 49. 7 + 00 = + 0 B. 0 9( + 0) 4. If and are positive numbers, then ( 5 )( - - ) B. = 0 The College Board. Diagnostic and Placement Test Sample Questions 9
Answer Ke Question Number Correct Answer Operations with Integers Rationale C Choice (C) is correct. The low temperature of 75 F was reached at 6 in the morning, and the high temperature was6 F higher. So the high temperature in Benton that da was 75 F + 6 F = 9 F. A B C D A 4 0 4 Choice (A) is correct. The absolute value of point A is - 4 = 4. The absolute values of points C, and D, respectivel, are - =, =, and =. Therefore, of the four labeled points, point A has the greatest absolute value. A Choice (A) is correct. The value of -- 4 is - + (- 4) = - 6. Therefore, (- - 4) 8 = - 6 8 = -48. 4 C Choice (C) is correct. Cherl s average score for the five quizzes will be the sum of the scores divided b 5, the number of quizzes. She scored a total of 64 points on the first four quizzes, and if she scores 96 points on her net quiz, the sum of the scores will be 64 + 96 = 460 points. Therefore, her average score for the five quizzes will be 460 5 = 9 points. 5 B Choice (B) is correct. The square root of 59, denoted 59, is, because = = 59. 0 The College Board. Diagnostic and Placement Test Sample Questions 0
Question Number Correct Answer Fractions and Decimals Rationale B Choice (B) is correct. Since the table is a semicircle of diameter feet, the radius of the semicircle is 6 feet. The area of the table is 6 π square feet, or approimatel 8.4 = 56.5 square feet. Therefore, of the choices given, the closest to the area of the table is choice (B), 57 square feet. D Choice (D) is correct. Since the large square has area 9, each of its sides is of length. Hence each of the 9 smaller squares has sides of length. Since the path drawn in bold is made up of si of the sides of smaller squares, its length is 6 = 6. A 4 C Choice (A) is correct. The division 0-0.6 = 0.6 0 = 0.6 00 = 60. 0.6 0 - is equivalent to the multiplication Choice (C) is correct. The number,590 is equal to the product.59,000, which can be rewritten as.59 0. Choice (D) is correct. Since a circle has 60 degrees of arc, the shaded 75 -degree sector of the 5 D circle represents between 75 5 = of the circle, which is equal to the decimal 0.08. This value lies 60 4 5 0.0 5 = and 6 = 0.4 on the number line. 5 0 The College Board. Diagnostic and Placement Test Sample Questions
Question Number Correct Answer Proportions, Ratios, Rates and Percentages Rationale 40 A Choice (A) is cworrect. Since 40% of 5 is 5 0, 00 = and 5% of 5 is 5 5, 00 = Jeron made more free-throws attempts than Sidell did. Choice (D) is correct. Since there 60 minutes in an hour, the 0-minute interval is equivalent to D 6 of an hour. The bo s average speed can be calculated as number of miles skied, time which is 4 6 = 4 = 4 miles per hour. 6 C Choice (C) is correct. Since ever 4th child in line, starting with the fourth in line, gets a to, it follows that the children who get a to are in line in positions 4, 8,, 6 and 0. Hence, of the children in the line, 5 get a to, and - 5 = 8 do not get a to. Therefore, the ratio of the number of children in line who get a to to the number of children in line who do not get a to is 5 :8. 4 B Choice (B) is correct. Since 5 = = 0.5, it follows that 5 is.5 percent of 60. 60 40 5 B Choice (B) is correct. Since there are about.6 kilometers in mile, it follows that Jenna s speed in kilometers per hour is 65.6 = 04 kilometers per hour. 0 The College Board. Diagnostic and Placement Test Sample Questions
Epressions, Linear Equations and Linear Inequalities Question Number Correct Answer Rationale 0 C Choice (C) is correct. The value of on the number line is -, and the value of on the number line is. Substituting these values into the epression + gives 4 8 + - = 4 - =. B Choice (B) is correct. The rental fee for the costume consists of the initial charge of $0 and a dail charge of $8. Thus if the costume is rented for n das, the total cost, in dollars, is 0 + 8 n. D Choice (D) is correct. If the original cost of the treadmill is t dollars, an 8% discount on that price is 0.08t dollars. Therefore, the discounted price is the original price, in dollars, minus the discount, which is t- 0.08 t. 4 C Choice (C) is correct. The cost, in dollars, of n minutes of use is 0.4 n. Therefore, the total cost of this service, in dollars, for a month in which n minutes were used is 0 + 0.4 n. 5 B Choice (B) is correct. The equation - = 5 - is equivalent to = 5. Multipling both sides of this equation b gives 5 =. It follows that 4 = 0, so = 0. 0 The College Board. Diagnostic and Placement Test Sample Questions
Question Number Correct Answer Graphs and Equations of Lines Rationale C Total Amount of Mone Saved (in dollars),000 0,000 8,000 6,000 4,000,000 O 4 5 6 7 8 Years After the Compan Opened Choice (C) is correct. The -value represents the total amount of mone that the compan saved. From the graph, after 5 ears the compan was opened, the saved $0,000. 00 A Number of Shirts Sold (each month) 80 60 40 0 00 80 60 40 0 00 5 40 45 50 55 60 65 70 75 80 85 Price of Shirt (in dollars) Choice (A) is correct. The graph in (A) is a line with a slope of -0 that contains the point (50, 00). A $0 - $40 Choice (A) is correct. The epression represents the difference of dollars charged for 4- two different help sessions divided b the difference in the number of hours of help-service used, giving the amount, in dollars, the compan charges for each hour of help-service a customer uses. 0 The College Board. Diagnostic and Placement Test Sample Questions 4
4 A Choice (A) is correct. Since represents the amount of points Jen scored, and the -intercept is the value of that satisfies equation + 4 = 6 when = 0, Jen must have scored onl points each round. Since she scored a total of 6 points, she must have scored points in 8 rounds. 5 B 6 5 4 0 9 8 7 6 5 4 O 4 5 6 7 8 9 0 4 Choice (B) is correct. The -value of the line increases units for ever units of increase in the -value. Therefore, the slope of the line is. The line also intersects the -ais at, and therefore the -intercept is. 0 The College Board. Diagnostic and Placement Test Sample Questions 5
Question Number Correct Answer Polnomials and Quadratic Applications Rationale t C z Choice (C) is correct. The figure can be divided into three nonoverlapping rectangles. One has area z ( - t), one has area t( - ), and one has area t. The sum of the areas is then ( z - t) + ( t - t) + t = z - t + t. B Choice (B) is correct. B the law of eponents, 4 4 0 z Therefore, ( z )( - - z - ) = - z. This is equivalent to 4 4 ( 4) ( ) (4 ). ( z )( - - z - ) - - z -. =. z. = C a Choice (C) is correct. B definition, the epression - b a a a epression is equivalent to -b - b+ b a ab ab - - + b, a which simplifies to - ab + b 4. is a a -b -b. This a It follows that - b. is equivalent to 4 C Choice (C) is correct. The epression -- 8 factors as ( - 6)( + ). Since -- 8 = 0, either - 6= 0 or + = 0. It follows that = 6 or = -. Of the options given, onl 6 is a possible value for. 0 The College Board. Diagnostic and Placement Test Sample Questions 6
5 B 00 50 00 50 00 50 O 5 0 5 0 5 0 5 40 Choice (B) is correct. The quadratic epression - + 40-75 factors as ( -5)(5 - ). It follows that the graph of f( ) = - + 40-75 intersects the -ais at = 5 and at = 5. The greatest value of f( ) occurs at the verte, and the -coordinate of the verte of the parabola 5-5 is the point halfwa between 5 and 5 on the -ais. This is 5 + = 0. So the value of for which f( ) is greatest is = 0. 0 The College Board. Diagnostic and Placement Test Sample Questions 7
Question Number Correct Answer Rational Epressions and Equations Rationale D Choice (D) is correct. Since Kala s average speed while biking is s miles per hour, it will take her 90 hours of biking to ride the entire 90-mile bike path. In addition to this time, Kala s break will s add hour to the time it takes her to reach the end of the bike path. Therefore, it will take Kala 90 + hours from the time she leaves the start of the bike path until she reaches the end of the s bike path. Choice (B) is correct. The graph could be of a rational function that is not defined at = 0 and has B a horizontal asmptote at =. Of the given choices, (A) at = 0, and of these, onl (B) = and (B) = + are not defined = + has a horizontal asmptote at =. Therefore, of the given choices, onl (B) = + could be an equation of the graph shown. C Choice (C) is correct. The quadratic epression + - 6 factors as + - 6 = ( + 9)( - 7), 9. ( 9)( 7) 7 and so ( + 9) + -6 can be rewritten as ( ) + = + - - 4 C Choice (C) is correct. The epression can be rewritten as, + + =. as and so + can be rewritten 5 D Choice (D) is correct. Since -- = ( + )( - ), the equation + = 8 + - -- - ( + ) 8 4 8 can be rewritten as + =, or =. -- -- -- -- -- It follows that 4 = 8, or =. 0 The College Board. Diagnostic and Placement Test Sample Questions 8
Question Number Correct Answer Radical Epressions and Equations Rationale A Choice (A) is correct. Substituting 55 for d and 0.9 for f in the formula v 0 fd gives v = (0)(0.9)(55) 8.54 miles per hour, which, to the nearest tenth, rounds to 8.5 miles per hour. C D m Choice (C) is correct. For an nonzero number a and rational number, n integers and n > 0, the epression m n a - is defined as n. m a Therefore, ( ) where m and n are - 49 = =. 49 7 Choice (D) is correct. Since 7 = 9 = and 00 = 00 = 0, it follows that 7 + 00 =. 4 A Choice (A) is correct. If and are positive numbers, then - - - - ( )( ) ( )( ) 5 5 = = =. 5 B Choice (B) is correct. Squaring both sides of the equation - - 0 = - gives - - 0 = - 4 + 4, which simplifies to = 4. Substituting 4 for in the original equation, one can see that 4 is a solution of the equation. Therefore, the value of is 4. 0 The College Board. Diagnostic and Placement Test Sample Questions 9