North Carolina Early Mathematics Placement Testing Program, 9--4. Multiply: A. 9 B. C. 9 9 9 D. 9 E. 9 Solution and Answer to Question # will be provided net Monday, 9-8-4
North Carolina Early Mathematics Placement Testing Program, 9-8-4 4. Solve this absolute value equation: 8m 4 A. B., C., D., E. 4 4 Answer to Question #, 9--4, is B:. Multiply: A. 9 B. C. 9 9 9 D. 9 E. 9 Solution: To multiply two binomials the distributive property must be used. This is sometimes referred to as the FOIL method. 9 9
North Carolina Early Mathematics Placement Testing Program, 9--4. A wheel has a circumference of 4 inches. Approimately how many revolutions does the wheel make when it rolls mile (,80 feet)? A. 78 B. 448 C. 7 D.,08 E.,408 Answer to Question #4, 9-8-4, is D: 4. Solve this absolute value equation: 8m 4 A. B., C., D., E. 4 4 Solution: Isolate the absolute value term first by subtracting from both sides. In general, if a, then a or a. Use this rule to find two solutions. 8m 4 8m 8m or 8m 8m 6 or 8m 0 6 0 m or m 8 8 4
North Carolina Early Mathematics Placement Testing Program, 9--4 6. The smallest angle in a triangle measures one-third of the measure of the largest angle. The third angle is 0 degrees more than the measure of the smallest. Find the measure of the smallest angle. A. 6 B. C. 40 D. E. 96 Answer to Question #, 9--4, is E:. A wheel has a circumference of 4 inches. Approimately how many revolutions does the wheel make when it rolls mile (,80 feet)? A. 78 B. 448 C. 7 D.,08 E.,408 Solution: With a circumference of 4 inches, the wheel covers 4 inches of ground in one revolution. The total distance given is mile. This must be changed to inches so that the units of measure agree. mile =,80 feet foot = inches So mile =,80 ft in/ft = 6,60 inches Now divide the total inches covered by the inches in one revolution: 6,60 4 =,408 turns or revolutions of the wheel in mile.
North Carolina Early Mathematics Placement Testing Program, 9-9-4 7. Simplify: 64a b 4 A. 4 4 4a b a b B. 4 4 4ia b a b C. 4 4 a b D. 4ab a b E. 4a b a b 4 4 Answer to Question #6, 9--4, is B: 6. The smallest angle in a triangle measures one-third of the measure of the largest angle. The third angle is 0 degrees more than the measure of the smallest. Find the measure of the smallest angle. A. 6 B. C. 40 D. E. 96 Solution: Remember that the sum of the measures of the three angles of any triangle is 80 degrees. Let = measure of largest angle; = measure of smallest angle; 0 = measure of third angle One equation that can be used to solve for is: 0 80 0 80 60 60 96 largest angle. So the smallest angle 96
North Carolina Early Mathematics Placement Testing Program, 0-6-4 8. Simplify this comple fraction: a b a A. B. b a a b C. b a b D. b E. b a Answer to Question #7, 9-9-4, is A: 7. Simplify: 64a b 4 A. 4 4 4a b a b B. 4 4 4ia b a b C. 4 4 a b D. 4ab a b E. 4a b a b 4 4 Solution: First, rewrite the radicand with as many perfect cube factors as possible. These factors are in red. Then take the cube root of each of the red factors. The remaining black factors stay under the cube root symbol. 64a b 4 64 a a b b 4a b a b 4 4
North Carolina Early Mathematics Placement Testing Program, 0--4 9. The population of the earth increased from.9 billion to 6 billion from one year to the net. What number best describes the percent increase in the population that year? A. 0.069% B. % 60 C..69% D. % 9 E. 98.% Answer to Question #8, 0-6-4, is C: 8. Simplify this comple fraction: a b a A. B. b a a b C. b a b D. b E. b a Solution: Recall this definition of a term with a negative eponent: a and use it to rewrite the terms of a the comple fraction. Then choose a least common denominator (LCD) of the three smaller fractions. Multiply the numerator and denominator of the comple fraction by the LCD and clear out the smaller fractions. a b b a a ab ab ab a b a b = a b = = ab ab a a a = b
North Carolina Early Mathematics Placement Testing Program, 0-0-4 40. The measures of rainfall for five consecutive days during the winter are: 6 0 For the measure of those five days, which of the following is true? I. The median equals the mode. II. The median equals the arithmetic mean. III. The range equals the median. A. I only B. II only C. III only D. I and II only E. I and III only Answer to Question #9, 0--4, is C: 9. The population of the earth increased from.9 billion to 6 billion from one year to the net. What number best describes the percent increase in the population that year? A. 0.069% B. % 60 C..69% D. % 9 E. 98.% Solution: To find percent increase (or decrease), use this formula: change 00 starting point 6 billion -.9 billion 0. billion 0. 0.06949.9 billion.9 billion.9 Convert 0.06949 to a decimal by multiplying by 00.69% increase
North Carolina Early Mathematics Placement Testing Program, 0-7-4 4. Solve: 8 A. 4 B. C. 8 D. 4 E. 70 Answer to Question #40, 0-0-4, is B: 40. The measures of rainfall for five consecutive days during the winter are: 6 0 For the measure of those five days, which of the following is true? I. The median equals the mode. II. The median equals the arithmetic mean. III. The range equals the median. A. I only B. II only C. III only D. I and II only E. I and III only Solution: First, reorder the data from smallest to largest:,,, 6, 0. median = middle term = mean = average = 6 0 mode = most often occurring = range= largest smallest = 0- = 8 Therefore, only statement II is correct.
North Carolina Early Mathematics Placement Testing Program, --4 4. The mathematical model of the relationship between time and the remaining number of kilobytes to be downloaded from a web site is n.t 40, where n is the number of kilobytes remaining to be downloaded at time t in seconds. From the numbers below, select the amount of time nearest to when 00 kilobytes remain to be downloaded. A. 0 sec B. 770 sec C. 7 sec D. 0 sec E. 09 sec Answer to Question #4, 0-7-4, is D: 4. Solve: 8 A. 4 B. C. 8 D. 4 E. 70 Solution: Since this equation is fractional, it would be best to find the least common denominator (LCM) and use it to clear out the fractions. The first two denominators are prime, but the last denominator can be factored. So multiply each term of the equation by the LCM. into. The LCM is 8 8 40 70 4 8 Always check your solutions when solving a fractional equation! Avoid values for that would make the denominator of any fraction in the original equation 0. In this case,.
North Carolina Early Mathematics Placement Testing Program, -0-4 4. If P 0 m is multiplied by Q 0 n, the product is equivalent to which of the following? A. ( P + Q) 0 D. 00 m PQ n mn B. 0 m PQ n E. PQ n m C. PQ 0 mn Answer to Question #4, --4, is E: 4. The mathematical model of the relationship between time and the remaining number of kilobytes to be downloaded from a web site is n.t 40, where n is the number of kilobytes remaining to be downloaded at time t in seconds. From the numbers below, select the amount of time nearest to when 00 kilobytes remain to be downloaded. A. 0 sec B. 770 sec C. 7 sec D. 0 sec E. 09 sec Solution: Substitute 00 in the place of n in the given equation and then solve for t. n.t 40 00.t 40 0.t t 09 seconds
North Carolina Early Mathematics Placement Testing Program, -7-4 44. If a square carpet, 8 feet long on a side, is cut up into smaller squares each feet long on a side, what is the largest number of smaller squares that can be formed? A. 8 B. 6 C. D. 64 E. 8 Answer to Question #4, -0-4, is B: 4. If P 0 m is multiplied by Q 0 n, the product is equivalent to which of the following? A. ( P + Q) 0 D. 00 m PQ n mn B. 0 m PQ n E. PQ n m C. PQ 0 mn Solution: The two epressions given are written in scientific notation. Use the associative and commutative m n properties of multiplication to rearrange. When multiplying 0 and 0, remember to keep the base and add the eponents. m n ( P 0 )( Q 0 ) m n = ( P Q)(0 0 ) = PQ 0 mn
North Carolina Early Mathematics Placement Testing Program, -4-4 4. How long is the hypotenuse of a right triangle whose legs measure and 4 units? A. 7 B. C. D. 7 E. cannot be determined Answer to Question #44, -7-4, is B: 44. If a square carpet, 8 feet long on a side, is cut up into smaller squares each feet long on a side, what is the largest number of smaller squares that can be formed? A. 8 B. 6 C. D. 64 E. 8 Solution: The area of the carpet before it is cut is l w 8 8 = 64 sq ft. The area of each smaller square is l w = 4 sq ft. To determine how many 4 sq ft areas can be cut from 64 sq ft, divide 64 by 4. This equals 6 squares of carpet. No scraps of carpet would remain, so 6 is the largest number of smaller squares that can be formed.
North Carolina Early Mathematics Placement Testing Program, --4 46. Solve this equation: ( ) 4. A. 6 B. 4 C. 6 D. E. 6 Answer to Question #4, -4-4, is C: 4. How long is the hypotenuse of a right triangle whose legs measure and 4 units? B. 7 B. C. D. 7 E. cannot be determined Solution: Since this is a right triangle, the Pythagorean Thm. can be used to find the missing side measure. ( leg) ( leg) ( hypotenuse) a b c ( ) (4 ) c 9 6 c c Now take the square root of both sides of the equation. c
North Carolina Early Mathematics Placement Testing Program, -8-4 47. Find the quotient and remainder when 6 is divided by 4. A. Quotient: C. Quotient: E. Quotient: ; remainder: B. Quotient: ; remainder: 7 D. Quotient: ; remainder: ; remainder: ; remainder: 7 Answer to Question #46, --4, is A: 46. Solve this equation: ( ) 4. A. 6 B. 4 C. 6 D. E. 6 Solution: Use the distributive property to remove the parentheses on the left side of the equation. You will notice that the equation is quadratic. Set the equation equal to 0. Write the terms on the left in descending order. Despite your best efforts it will not factor, so another method is to use the quadratic formula. ( ) 4 6 4 6 0 Let a, b 6, c. b b 4ac a () ( 6) ( 6) 4()() 6 6 6 4 6 4 6 6 6 6 6 6 ( 6) 6 6 6
North Carolina Early Mathematics Placement Testing Program, --4 48. Rationalize the denominator and simply: A. 7 B. 4 C. 7 D. E. Answer to Question #47, -8-4, is D: 47. Find the quotient and remainder when 6 is divided by 4. A. Quotient: C. Quotient: E. Quotient: ; remainder: B. Quotient: ; remainder: 7 D. Quotient: ; remainder: ; remainder: ; remainder: 7 Solution: Long division is used here. First, be sure to put the divisor ( 4 ) and the dividend ( 6) in descending order for the powers of. Also note that the dividend is missing a second power of, so insert a placeholder of 0. 7 4 4 0 6 4 4 6 4 8 4 7
North Carolina Early Mathematics Placement Testing Program, -- 49. Determine the equation for the inverse function of y ( ) 8. A. y ( ) 8. B. y 8 C. y 6 D. y 0 E. y 8 Answer to Question #48, --4, is A: 48. Rationalize the denominator and simply: B. 7 B. 4 C. 7 D. E. Solution: The irrational number,, must be removed from the denominator. Since is part of the binomial, the quickest way to remove the irrational part is to multiply the denominator by the conjugate of. You must also multiply the numerator by this same quantity. ( ) ( ) 9 ( ) ( ) 9 9 4 6 = 9 4 (7 ) 7 4
North Carolina Early Mathematics Placement Testing Program, -- 0. Solve this system of equations for y : 0 y 8 y A. B. C. D. E. no solution Answer to Question #49, --, is E: 49. Determine the equation for the inverse function of y ( ) 8. A. y ( ) 8 B. y 8 C. y 6 D. y 0 E. y 8 Solution: The domain and range of a function and its inverse are reversed. So the first step is to switch the letters and y in the equation of the original function. y ( ) 8 becomes: ( y ) 8 To isolate the new y, add 8 to both sides. 8 ( y ) Take the cube root of both sides. 8 ( y ) 8 y Subtract from both sides. 8 y y 8 Rearrange.
North Carolina Early Mathematics Placement Testing Program, -9-. Simplify this epression: A. B. C. 4 D. 7 6 E. Answer to Question #0, --, is D: 0. Solve this system of equations for y : 0 y 8 y A. B. C. D. E. no solution Solution: Since the second equation is already solved for y, the Substitution Method would be easy to use. So substitute in the place of y in the first equation. 0 ( ) 8 0 6 6 8 4 6 8 4 4 Now substitute for in the second equation: y y y
North Carolina Early Mathematics Placement Testing Program, -6-. Find the equation of the line that passes through points, and 4,. A. y B. y 4 C. y 4 D. y E. 7 y Answer to Question #, -9-, is A:. Simplify this epression: A. B. C. 4 D. 7 6 E. Solution: Follow the correct order of operations. Simplify each term with an eponent first. Then divide before you subtract. 9 9 9 7 =
North Carolina Early Mathematics Placement Testing Program, --. If g ( ) 6, then g( c) g() A. c 4c B. c 4 C. c 8 D. c 4c 4 E. c 4 Answer to Question #, -6-, is B:. Find the equation of the line that passes through points, and 4,. A. y B. y 4 C. y 4 D. y E. 7 y Solution: First find the slope of the line that passes through the two points. Then choose one of the two points. Then use the slope and the coordinates of the point to fill in the point-slope form of a line. slope = y y m = 4 6 point chosen is 4, since three of the answers begin with y. y y m y ( ( 4)) y ( 4)
North Carolina Early Mathematics Placement Testing Program, -9-4. Solve this equation for : 0.4.7. Round the answer to the nearest hundredth. A. 0.4 B..6 C. 0.4 D. 0.6 E. 0.6 Answer to Question #, --, is C:. If g ( ) 6, then g( c) g() A. c 4c B. c 4 C. c 8 D. c 4c 4 E. c 4 Solution: First find g(c) by substituting a "c" in the place of in the function. Then find g() by substituting a "" in the place of in the function. Then find the sum of these answers. g c g c 6 6 4 6 g c g c ( ) () ( 6) ( ) c 8
North Carolina Early Mathematics Placement Testing Program, -6-. A tire has a circumference of 6 inches. Approimately how many revolutions does the tire make when the tire rolls mile (,80 ft)? A. 47 B. 440 C.,760 D.,760 E.,840 Answer to Question #4, -9-, is E: 4. Solve this equation for : 0.4.7. Round the answer to the nearest hundredth. A. 0.4 B..6 C. 0.4 D. 0.6 E. 0.6 Solution: First move the constant term from the right to the left side of the equation by subtracting. Then divide both sides by. Round your answer to two decimal places. Be sure you can do this problem without a calculator!! 0.4.7.7.7.. ( ) ( ) 0.66 0.6
North Carolina Early Mathematics Placement Testing Program, -- 6. If the zeros of a quadratic function are zeros is: and, one possible quadratic function having these A. f ( ) ( )( ) B. f ( ) C. f ( ) 4 0 D. f ( ) E. f ( ) Answer to Question #, -6-, is C:. A tire has a circumference of 6 inches. Approimately how many revolutions does the tire make when the tire rolls mile (,80 ft)? A. 47 B. 440 C.,760 D.,760 E.,840 Solution: It is important to use a consistent unit of measure. Since mi =,80 ft, it would be wise to convert 6 in to ft. The circumference of a tire is the measure of the distance around the tire. It also tells how far a tire will roll in one revolution. To find the number of revolutions of the tire, divide the total distance of,80 ft by the distance covered in one revolution:,80 ft ft =,760 revolutions.
North Carolina Early Mathematics Placement Testing Program, -- 7. Given: -/ This is an illustration of the solution set for which inequality below? A. B. C. D. E. Answer to Question #6, --, is D: 6. If the zeros of a quadratic function are zeros is: and, one possible quadratic function having these A. f ( ) ( )( ) B. f ( ) C. f ( ) 4 0 D. f ( ) E. f ( ) Solution : Solution : One method of solving a quadratic equation is to set the equation =0, factor the polynomial, set each factor =0, and then solve for. Since you are given the two zeros, or solutions, in this problem, work in reverse to find the equation: 0 0 ( )( ) 0 0 Use this formula if given the roots of a quadratic eq: (sum of roots) (product of roots) = 0 ( ) ( )() 0 ( ) ( ) 0 0
North Carolina Early Mathematics Placement Testing Program, -9-8. Solve the equation 7 7 for. A. 4 B. C. 49 D. E. 49 Answer to Question #7, --, is A: 7. Given: -/ This is an illustration of the solution set for which inequality below? A. B. C. D. E. Solution: Quickly solve each of the inequalities in the five possible answers for by dividing by the coefficient of. Remember that dividing both sides of a linear inequality by a negative number causes the inequality to become false. So remember to reverse the inequality sign after you divide to make it true. Answer choices A, B, and E all require division by. Answer choices C and D require division by so the inequality sign will not change. The possible answers can now be written as: A. B. C. D. E. Answer choice A correctly matches the graph given.
North Carolina Early Mathematics Placement Testing Program, -6-9. After a % reduction, the sale price of a pair of flip-flops was $9.46. Before the reduction, the original price was A. $8. B. $9.4 C. $9.8 D. $0.7 E. $0.88 Answer to Question #8, -9-, is B: 8. Solve the equation 7 7 for. A. 4 B. C. 49 D. E. 49 Solution: Notice on the left side of the equation that 7 and 7 can be condensed by using the law of eponents for multiplying epressions with the same base, that is, keep the base and add the eponents. 7 7 7 0 It would be helpful if both sides of the equation had the same base of 7. So rewrite the number as 7. Then if both sides of the equation have the same base of 7, then the eponents must also have the same values. 7 7 7 0 0
North Carolina Early Mathematics Placement Testing Program, -- 60. If the coordinates of one endpoint of a line segment are, 4 and the midpoint of the segment has coordinates (, ), what are the coordinates of the other endpoint of the segment? A. (7, 0) B. (,) C. (, ) D. (, ) E. (,8) Answer to Question #9, -6-, is D: 9. After a % reduction, the sale price of a pair of flip-flops was $9.46. Before the reduction, the original price was A. $8. B. $9.4 C. $9.8 D. $0.7 E. $0.88 Solution: Let represent the original price of the flip-flops. To find the amount of reduction in price from the original price, multiply by %. original price reduction sale price. 9.46. 9.46.88 9.46 $0.7
North Carolina Early Mathematics Placement Testing Program, -0-6. When, find the value of this epression: A. B. C. D. E. The value is undefined. Answer to Question #60, --, is E: 60. If the coordinates of one endpoint of a line segment are, 4 and the midpoint of the segment has coordinates (, ), what are the coordinates of the other endpoint of the segment? A. (7, 0) B. (,) C. (, ) D. (, ) E. (,8) Solution: Let and y represent the coordinates of the unknown endpoint. The midpoint of a segment formula indicates that to find the coordinates of the midpoint, the coordinates of the two endpoints must be averaged and, likewise, the y coordinates of the two endpoints must be averaged. See the two equations that involve these averages below: Endpoints of segment are ( y, ) and (, 4). Midpoint is (,). y ( 4) and y 4 4 y 8
North Carolina Early Mathematics Placement Testing Program, 4-6- 6. Solve 0. A. B.,0 C. D.,0 E. 0 Answer to Question #6, -0-, is B: 6. When, find the value of this epression: A. B. C. D. E. The value is undefined Solution: Substitute for in the epression. Simplify under the radical and take the square root. Remember that the correct order of operations involves multiplying or dividing from left to right (whichever comes first) and then subtracting. 6 0 6 0 0 =
North Carolina Early Mathematics Placement Testing Program, 4-- 6. If the average weight of four football players listed in the table below is 0 pounds, what is the weight, in pounds, of Player D? Player Weight in lbs A. 0 B. 0 C. 40 A 70 B 0 D. 0 E. 60 C 40 D? Answer to Question #6, 4-6-, is B: 6. Solve 0. A. B.,0 C. D.,0 E. 0 Solution: This is a second degree quadratic equation. First set the equation equal to 0. As a first method of solution, try factoring. (As a second method of solution, the quadratic formula may also be used where a 0, b, and c 0.) 0 0 0 () 0 0 or 0 0 Note: Avoid dividing both sides of an equation by. have a value of 0. Division by 0 is undefined. In this equation, dividing both sides by as a first step would cause you to lose the solution of 0. This is a dangerous move because could
North Carolina Early Mathematics Placement Testing Program, 4-0- 64. In a right triangle, the measure of one leg is 6. The measure of the hypotenuse is. Find the measure of the other leg. A. 6 B. C. 9 D. 6 E. 4 Answer to Question #6, 4--, is E: 6. If the average weight of four football players listed in the table below is 0 pounds, what is the weight, in pounds, of Player D? Player Weight in lbs A. 0 B. 0 C. 40 A 70 B 0 D. 0 E. 60 C 40 D? Solution: Let represent the weight, in pounds, of Player D. To find the average of 0 pounds, the sum of the four weights must be calculated and then the sum divided by the number of players. 70 0 40 4 0 740 4 0 740 000 60
North Carolina Early Mathematics Placement Testing Program, 4-7- 6. Simplify: 6 A. B. C. D. E. Answer to Question #64, 4-0-, is C: 64. In a right triangle, the measure of one leg is 6. The measure of the hypotenuse is. Find the measure of the other leg. A. 6 B. C. 9 D. 6 E. 4 Solution: If the lengths of two sides of a right triangle are known, the length of the third side can be found by using the Pythagorean Theorem. Be sure the replace c with the measure of the hypotenuse. a b c a a a a 6 6 9 9
North Carolina Early Mathematics Placement Testing Program, -4-66. A theater with a stage has 0 seats. 70% of the seats in the theater were sold for a dance recital held at the end of May. If each ticket sold for the same amount, and the total of all the ticket sales was $,06, what was the price of each ticket? A. $4.60 B. $6.0 C. $9.00 D. $.00 E. $8.80 Answer to Question #6, 4-7-, is A: 6. Simplify: 6 A. B. C. D. E. Solution: Remember the law of eponents that says if you are dividing terms with like bases, keep the base and subtract the eponents. ( 6) 6 = = = = 6
North Carolina Early Mathematics Placement Testing Program, -- 67. What is the maimum number of circles that can be made from a piece of string 00 meters long, if the radius of each circle is meters? A. B. C. 4 D. E. 6 Answer to Question #66, -4-, is C: 66. A theater with a stage has 0 seats. 70% of the seats in the theater were sold for a dance recital held at the end of May. If each ticket sold for the same amount, and the total of all the ticket sales was $,06, what was the price of each ticket? A. $4.60 B. $6.0 C. $9.00 D. $.00 E. $8.80 Solution: First find the number of seats (tickets) that is represented by 70% of 0 seats in the theater. Let cost for each seat (ticket). Multiplying the cost of each seat by the number of filled seats results in the total ticket sales. 70% of 0 seats =.70(0) = 4 seats (tickets) sold. Let cost for each seat (ticket). 4 $06 $9.00 per ticket
North Carolina Early Mathematics Placement Testing Program, -8- This is the last question for the 04- school year. The solution will be available on Monday, --. A new set of questions for 0-6 is now being planned, the first of which will be available in early September 0. Thank you for making the most of this NC EMPT resource! 68. Find the verte and ais of symmetry of the graph of the function f ( ) 4 4. A. (, 07); B. (, ); y C. (, 7); y D. (, 7); E. (, 07); Answer to Question #67, --, is B: 67. What is the maimum number of circles that can be made from a piece of string 00 meters long, if the radius of each circle is meters? A. B. C. 4 D. E. 6 Solution: First find out how much string is needed for one circle of radius. Find the circumference of the circle since circumference measures the distance around a circle. Then divide the total length of string by the amount needed for each circle. There will be some string left over, but not enough to create another circle. C r C () C.49 meters 00 meters.49 meters =.8 full circles can be made.
North Carolina Early Mathematics Placement Testing Program, 9-- 69. Simplify: 4 6 A. B. 8 C. D. 8 8 E. Answer to Question #68, -8-, is D: 68. Find the verte and ais of symmetry of the graph of the function f ( ) 4 4. A. (, 07); B. (, ); y C. (, 7); y D. (, 7); E. (, 07); Solution: This parabola opens up since the variable is squared and this term s coefficient of 4 is positive. Therefore, the ais of symmetry will be a vertical line that passes through the verte. One way to find the b -value of the verte is to use the formula:. Once the -value is found, substitute it into the a equation of the parabola to find the matching y -value. b 4 a 4 f ( ) y 4( ) 4( ) = 4(9) 7 = 7 verte is (, 7) and the ais of symmetry is.