Florida Algebra I EOC Online Practice Test

Transcription

1 Florida Algebra I EOC Online Practice Test Directions: This practice test contains 65 multiple-choice questions. Choose the best answer for each question. Detailed answer eplanations appear at the end of the test.

2 FCAT.0 Algebra I 1 A Universal set U contains 80 elements. Sets P and Q are disjoint subsets of U. There are 85 elements in the Cartesian product P Q. If each of P and Q contains more than one element, how man elements in U do NOT belong to either P or Q? =. What is the value of? 4 The perimeter of a square is Which of the following represents its area? (A) + 4 (B) (C) (D) Tona is a qualit control manager is a large department store. In a recent shipment of 900 new blouses for women, there were 1 that had defects. If she randoml selects a sample of 5 of these blouses, how man of these would be epected NOT to have an defects? 5 Which of the following is a factor of 48? (A) 4 (B) 16 (C) + 4 (D) 16 6 Set R contains 65 elements, set R T contains 14 elements, and set R T contains 91 elements. How man elements does set T contain? (F) 1 (G) 6 (H) 40 (I) 77

3 Online Practice Test 7 The slope of a line is. The coordinates of two of its points are (7, 9) and (, 5). What is the value of? ( cd 1 e 5 ) 8 Fred will write the epression c d e in the form c d e z. What is the least common multiple of,, and z? 9 What is the value of in the equation ( 14) ( + 1) =? (A) 9. (B) 8.8 (C) 8.0 (D) 7.6 Over the last five months, Laura has been tracking the number of major projects she has managed each month and the corresponding total number of hours she spent on these projects. The following chart is to be used for questions 10 and 11. Month June Jul August September October Number of Projects Number of Hours Assuming that the number of hours () is a linear function of the number of projects (), which of the following equations matches the given data? (F) = (G) = (H) = (I) =

4 4 FCAT.0 Algebra I 11 Laura anticipates that she will manage 8 projects in November. Assuming that the linear function of question 10 applies, what will be the mean number of hours spent per project for all si months? 1 Line m is parallel to line n. The slope of line m is 5. One point on line n is ( 4, 1). Which of the following could represent another point on line n? 1 14 (F) (1, ) (G) (6, 7) (H) ( 1, 6) (I) ( 10, 11) What is the simplified epression for ( )( + ) ( 6)? (A) + 5 (B) 7 (C) + 5 (D) 7 At Joe s Hardware Store, a state ta of 5% is collected for ever item. In addition, a municipal ta of 1.5% is collected for an item that eceeds $100. Steve recentl purchased two items, one for $10 and the other for $90. In dollars and cents, how much ta did he pa? 15 What is the solution for in the inequalit 6(7 ) < ( + 5)? (A) < 1 (B) > 1 (C) > 8.5 (D) < 8.5

5 Online Practice Test 5 16 Marcia operates a catering business. In preparing meals for a banquet, she uses the following table to determine the number of pounds of meat to prepare. Number of Guests Pounds of Meat Based on the pattern in the table, how man pounds of meat are needed for 180 guests? 17 What is the value of the -intercept of the line that has a slope of 4 and contains the point (, 1)? 18 Velma is given the function f () = + 7 and calculates the value of f (). Dave is given the function h() = 5 9. What value of should Dave use so that h() = f ()? 19 If the -intercept of a line is (0, 8) and its -intercept lies to the left of the origin, which of the following could be the equation of this line? (A) = 4 (B) = (C) = 40 (D) = 16

6 6 FCAT.0 Algebra I 0 Which of the following represents the graph of a line whose slope is a negative number greater than 0.5? (F) (H) L (,1) (,1) L 1 (G) (I) (,1) (,1) L 4 L 1 Given that V = W + XY, which of the following is the correct epression for X? V W (A) Y V W (B) Y V W (C) Y V W (D) Y

7 Online Practice Test 7 The graph of a function is known to contain the points (, 4), (5, ), and (8, 7). Which of the following points CANNOT lie on this graph? (F) (4, ) (G) ( 5, ) (H) (1, 4) (I) (8, ) If ( 100 ) 7 < 8 m, and m is an integer, what is the MINIMUM value of m? 4 5 For which of the following intervals are ALL its values solutions to the inequalit 4 < 6? 1 (F) < < 1 (G) < < 7 (H) < < (I) < < 10 The domain of the function f () = + 50 is {,, 4}. What is the least common multiple of the range values? 6 The dimensions of a large rectangular storage tank are follows: 150 feet long, 100 feet wide, and 5 feet deep. A scale model of this tank has a length of 18 inches. What is the sum, in inches, of the length, width, and height of the scale model? (F) 6 (G) (H) 0 (I) 7

8 8 FCAT.0 Algebra I 7 8 The slope of line L is 5 and its -intercept is (6, 0). Which of the following points lies on L? (A) (5, 6) (B) (4, 10) (C) (, 9) (D) (, ) At 1:00 pm, car A traveled west at an average speed of 4 miles per hour from a certain location. One hour later, car B traveled east from that same location. At 6:00 pm, the two cars were 60 miles apart. What was the average speed in miles per hour of car B? 9 Caitlin sells art paintings from a booth at a flea market. She pas $100 per month to rent the booth. Each of her paintings sells for $0. Her profit (P) per month is given b P = 0 100, where is the number of paintings sold. She sold 5 paintings in Januar and paintings in Februar. What is the minimum number of paintings she must sell in March in order for her profit for all three months to be at least $000? (A) 18 (B) 19 (C) 0 (D) 1

9 Online Practice Test 9 0 A line is shown on the coordinate grid below, including points A and B. A B Which of the following points lies on this line? (F) (60, 45) (G) (70, 56) (H) (80, 6) (I) (90, 66) n c + ( n c) 1 Which of the following is equivalent to nc 1 5 4? 4 c (A) + n n c 5 (B) + n n c 5 (C) + n 4 n c (D) + n 4 n What is the simplified form for ( mp r ) ( m p r ) (F) m p 5 r (G) m 10 p r (H) m 15 p 14 5 r (I) m p 11 r 5 4?

10 10 FCAT.0 Algebra I For which one of the following sets are ALL its elements included in the solution set for the inequalit 6 < 1 4 < 0? (A) { is a positive integer less than 7} (B) { = { 1, 0, 1,,, 4} (C) { is a negative number greater than } (D) { = { 0.5, 1.5,.5,.5, 4.5} 4 What is the simplified form for ( 18 )( ) ? (F) 4+ (G) 7+ (H) 1 5 (I) 75 For which of the following does the simplified form contain a radical sign? (A) (B) (C) (D) Given that 5 and are zeros of the equation + a + c = 0, which of the following represent the values of a and c? (F) a = and c = 10 (G) a = and c = 10 (H) a = 10 and c = (I) a = 10 and c =

11 Online Practice Test 11 7 A compan that makes home heating sstems finds that its profit equation is P = , where represents the number of heating sstems sold and P is the profit in thousands of dollars. If the compan made a profit of $148,000 last ear, how man heating sstems did it sell? 8 Suppose that the Universal set U consists of all prime numbers less than 40. Set R consists of prime factors of 60, and set S consists of prime factors of 75. How man elements are in neither R nor S? (F) 8 (G) 7 (H) 6 (I) 5 9 Which of the following is the graph of = + 9? Note that each bo = units. (A) (C) (,5) (,0) (4,0) (, 6) (0, 9) (0, 9) (B) (D) ( 4,6) (, ) (,) (0, 6) ( 4, 6) (0, 6)

12 1 FCAT.0 Algebra I 40 According to several studies, the suggested number of calories per da that a person needs is between 1,800 and,00, inclusive. If represents the number of calories, which one of the following inequalities models the preceding sentence? (F) 11, ,700 (G) 6, ,900 (H) 6, ,900 (I) 11, ,50 41 Which of the following represents a graph with a zero slope and a -intercept of 4? (A) L (C) (0,4) (0, 4) L (B) (D) L L 4 (4,0) ( 4,0)

13 Online Practice Test 1 4 Look at the following Venn diagram. U = 00 P Q The Universal set has 00 elements and of them do not belong to either set P or set Q. Set P has 75 elements and set Q has 110 elements. How man elements belong to eactl one of P and Q? 4 In simplifing ( )( + 7) ( 5)( 5), which of the following will NOT be a final term? (A) 18 (B) (C) 46 (D) What is the reduced form of the fraction (F) 8 (G) 4 (H) + (I) +?

14 14 FCAT.0 Algebra I 45 Jerr has joined a roller skating club for which he pas dues of $75 each month, plus a dail rate of $10 for each da that he uses the club s skating rink. The function shown below can be used to determine the cost in dollars per month for being a member of this club. f(d) = d, where d is the number of das. Jerr spent $155 in Januar, $195 in Februar, and $5 in March. If he spent a total of $850 for the months of Januar, Februar, March, and April, what was the total number of das that he spent at the club for those four months? 46 At the Joll World Entertainment Center, the cost of four children and three adults is $ The cost of four children and two senior citizens is $ The cost of one adult and one senior citizen is $5.00. In dollars and cents, what is the cost of three children, five adults, and si senior citizens? + 5, if 0 < 5 47 A function is defined as follows: f ( ) =. What is the value of f (4) f (6) + f (8)? 5, if> 5 (A) 1 (B) 5 (C) 19 (D) 1 48 What is the product of 5 4 and + subtracted b one half of 4 10? (F) 6 18 (G) (H) + 6 (I) 6 1

15 Online Practice Test A 40-gallon solution of acid and water contains 15% acid. How man gallons of water must be removed in order to increase the amount of acid to 0%? (A) 10 (B) 8 (C) 5 (D) can be epressed in simplest form as m n? What is the value of mn? 51 Given that the relation {(1, 10), (15, 8), (9, 1), (, 18)} is NOT a function, what is the MINIMUM value of the sum of the elements in the domain? 5 Which of the following represents the graph of = A + B + C, for which B < 4AC? (F) (H) (G) (I)

16 16 FCAT.0 Algebra I The lines L 1 and L are perpendicular to each other. The equation of line L 1 is 4 = 1. If line L contains the point (14, 5), what is the -intercept of L? (A) (0, 4.5) (B) (0, 5.5) (C) (0, 6.5) (D) (0, 7.5) What is the product of the values of that satisf the following proportion? + 11 = 6 (F) 6 (G) 0 (H) 4 (I) 1 Consider the function = +. What is the maimum value? 56 Look at the Venn diagram shown below of sets A, B, and C. The Universal set U = {cat, dog, horse, lion, mouse, rat, snake, tiger, turtle, zebra} A B lion rat mouse horse turtle snake tiger zebra cat dog Which of the following is equivalent to {mouse, snake, tiger}? C (F) A C (G) C B (H) A C (I) A B C

17 Online Practice Test Mr. Jung writes the following table of and values on the chalkboard. He tells his students that is a linear function of p q 8 Which of the following statements is correct? 58 (A) The sum of p and q is 0. (B) The product of p and q is 80. (B) The quotient of p and q is 15. (C) The difference of p and q is 5. Joe and Johanna are owners of tai companies. Let C represent the cost in dollars and cents and let represent the number of miles of travel. Here are the equations for each of these companies. Joe : C = Johanna: C = What is the number of miles for which the cost is the same for both companies?

18 18 FCAT.0 Algebra I 59 Look at the following Venn diagram. M N U a b h i z c d The Universal set U consists of all 6 letters of the alphabet. The elements a, b, h, and i belong to set M but not to set N. Likewise, the elements c and d belong to set N but not to set M. The elements that do not lie in either M or N are not shown. Which of the following is a subset of M? 60 (A) {c, d, i, z} (B) {c, d,,, z} (C) {c, d, 1, } (D) {c, d, e, u, v} Sall has a collection of nickels, dimes and quarters. She has five more dimes than nickels and twice as man quarters as dimes. The total value of her collection is $ How man coins does she have? 61 Given the equation d 5 e 1= 0, which of the following is the correct epression for e? (A) (B) (C) (D) 4d d 4d+ 1 5 d d 1

19 Online Practice Test 19 6 Kenn had three more than twice as man coins as Marlene. After he gave her 7 of his coins, Marlene then had nine fewer coins than Kenn. How man coins did Kenn originall have? 6 What is the value of in the sstem of equations shown below? = 0 5= 5 64 Which of the following has zeros of 1 and 6? (F) = 0 (G) 5 6 = 0 (H) = 0 (I) = 0 65 To the nearest hundredth, what is the larger of the two solutions to the following equation? = 0 (A) 0.86 (B).1 (C).8 (D) 4.64 STOP

20 Answers for Practice Test

21 Online Practice Test 1 PRACTICE TEST FLORIDA ALGEBRA 1 END OF COURSE Question Number Benchmark Answer 1 MA.91.D MA.91.A MA.91.A.4. B 4 MA.91.A MA.91.A.4. D 6 MA.91.D.7.1 H 7 MA.91.A MA.91.A MA.91.A..1 A 10 MA.91.A..11 G 11 MA.91.A MA.91.A..9 I 1 MA.91.A.4. C 14 MA.91.A MA.91.A..4 A 16 MA.91.A MA.91.A MA.91.A MA.91.A..9 D 0 MA.91.A..8 F 1 MA.91.A.. B MA.91.A.. I MA.91.A MA.91.A..4 G 5 MA.91.A..4,016 6 MA.91.A.5.4 G 7 MA.91.A..9 B 8 MA.91.A MA.91.A..5 C 0 MA.91.A..10 H 1 MA.91.A.4.1 C MA.91.A.4.1 I MA.91.A..4 B Question Number Benchmark Answer 4 MA.91.A.6. G 5 MA.91.A.6. C 6 MA.91.A.4. F 7 MA.91.A.7. 8 MA.91.D.7.1 F 9 MA.91.A.7.1 A 40 MA.91.A..5 G 41 MA.91.A..8 C 4 MA.91.D MA.91.A.4. A 44 MA.91.A.4. F 45 MA.91.A MA.91.A..14 $ MA.91.A.. B 48 MA.91.A.4. H 49 MA.91.A..5 A 50 MA.91.A MA.91.A MA.91.A.7.1 I 5 MA.91.A..10 B 54 MA.91.A.5.4 G 55 MA.91.A MA.91.D.7. G 57 MA.91.A.. D 58 MA.91.A MA.91.D.7. D 60 MA.91.A MA.91.A.. B 6 MA.91.A MA.91.A MA.91.A.7. G 65 MA.91.A.7. D

22 FCAT.0 Algebra I 1 The correct answer is 58. The Cartesian product contains 85 elements, so the number of elements in each of P and Q can either be 1 and 85 or 5 and 17. Since each of P and Q contains more than one element, the onl possible combination is 5 and 17. (It does not matter which of P and Q has either number.) We are given that P and Q are disjoint, so there are no common elements. Therefore, the number of elements that belong to neither P nor Q is = 58. The correct answer is = 49 = 7 and 00 = 100 = 10. Thus, = 17 = 89 = 578. (B) Each side of the square is = +. Thus, the area is ( + ) = The correct answer is. Let represent the epected number of defective blouses in a sample of 5. Then 1 =. Cross-multipl to get 900 =,700. Then = Therefore, the number of blouses that do not have defects is 5 =. (D) Using Common Term factoring, 48 = ( 16). Thus, besides 1 and 48, the factors of 48 are,,, 16, 48, and 16. (H) Let represent the number of elements in set T. The cardinalit of an set X is denoted as n(x). For an two given sets R and T, nr ( T) = nr ( ) + nt ( ) nr ( T). B substitution, 91 = Then 91 = 51 +, so = The correct answer is 1. The slope (m) is given b the formula m = 1. B substitution, the slope is =. Cross-multipl to get + 14 = ( 4)() = 1. 7 Now subtracting 14 from each side results in = 6. Thus, = 6 = 1. ( cd 8 The correct answer is e 5 ) 6 10 c d e 6 ( 9) ( 6) 10 ( 0) 8 10 = = c d e = cde. We c d e c d e can write 8 as and 10 as 5. Thus, the least common multiple of, 8, and 10 is 5 = 10.

23 Online Practice Test Answer Ke (A) Using the Distributive Law of Multiplication over Addition, we can simplif the equation to 1 =. Then = +, which becomes = 5. Thus, = ( ) 5 = 9.. (G) The general form of the linear equation is = m + b, where m is the slope and b is the -intercept. Two of the points on the graph of this line are (5, 4.5) and (4, 0). The slope equals = 4.5. Then = b. Now substitute either point to solve for 4 5 b. Using the point (4, 0), we have 0 = (4.5)(4) + b. So 0 = 18 + b, which means that b = 1. Thus, the correct equation is = The correct answer is 6.. Using the linear model derived from question #10, the projected number of hours for November is (4.5)(8) + 1 = 48. Then the mean number of hours per project for all si months equals = = 6.. (I) Since line n is parallel to line m, their slopes must be equal. B substituting the point ( 10, 11) into the slope formula, we find that the slope is 11 ( 1) = ( 4) 6 = 5. For answer choices (F), (G), and (H), in conjunction the point ( 4, 1), the slopes would be 5, 5, and 5, respectivel. (C) ( )( + ) ( 6) = = + ( ) + ( + 6 ) = + 5. The correct answer is 1.0. For the $10 item, the ta is 5% + 1.5% = 6.5%. For the $90 item, the ta is 5%. Thus, the total ta for Steve s purchases is ($10)(0.065) + ($90)(0.05) =$ $4.50 = $1.0. (A) Using the Distributive Law, the inequalit becomes < Subtract from each side to get < 10. Net, add 4 to each side to get 4 < 5. Thus, < 1.

24 4 FCAT.0 Algebra I The correct answer is 70. First note that = = = =. This means that pounds of meat are needed for ever guests. Let represent the number of pounds of meat needed for 180 guests. Then =. Cross-multipl to get = 540. Thus, 180 = The correct answer is 5. Since the slope is 4, we can write the equation as = 4 + b. (b is the -intercept.) Then, substituting (, 1), we get 1 = ( 4)( ) + b. So b = 1 8 = 0. To determine the -value of the -intercept, substitute zero for in the equation = 4 0. Thus, 0 = 4 0, which means that = The correct answer is 7.. f () = + ()() 7 = = 7. Then h() = 5 9 = 7. Add 9 to each side to get 5 = 6. Thus, = (D) To determine the -intercept, substitute = 0. Answer choices (A) and (B) are wrong because (0, 8) is the -intercept for each of them. Each of answer choices (C) and (D) does have the -intercept (0, 8). The - intercept is found b substituting = 0. For answer choice (C), the -intercept is (10, 0), which lies to the right of the origin. This means that answer choice (C) is wrong. The -intercept for answer choice (D) is 16 (,0), which does lie to the left of the origin. (F) This line has a negative slope. With respect to points on this line, notice that for =, the corresponding value is less than 1. This implies that the slope is greater than 0.5. For eample, assume that L 1 contains the point (, 0.75). Now use the fact that (0, 0) lies on L 1. Then the slope would be = 0.75, which is greater than 0.5. The 0 slopes of L, L, and L 4 are a positive number, a negative number less than 0.5, and zero, respectivel. (B) First multipl the entire equation b to get V = W + XY. Subtracting W, leads to V W V W = XY. The last step is to divide b Y, so that = X. Y

25 Online Practice Test Answer Ke 5 4 (I) For an function, each value ma correspond to onl one value. Thus, for the graph of an function, no two points ma have the same -coordinate. Since (8, 7) is a point on the graph, this means that (8, ) cannot be a point on the graph. The correct answer is 4. The left side of the inequalit can be written as 700 and the right side can be written as ( ) m = m. Then 700 < m, which simplifies to m >.. Since m must be an integer, the minimum value would be 4. (G) 4 < 6 is equivalent to 6 < 4 < 6. Then 9 < 4 <, so its solution is 9 < <. All the members of the inequalit in answer choice (G) are contained in < < 4 4. Answer choice (F) is wrong because its upper bound of eceeds 9 4. So, for eample an value of 11 belongs to choice (F) but not to < < An value such as 4 belongs to each of answer choices (H) and (I) but does not belong to 5 9 < <. So, (H) and (I) are wrong The correct answer is,016. The range values are as follows: () + 50 = 4, () + 50 =, and (4) + 50 = 18. Using prime factorization, 4 = 7, = 5, and 18 =. Thus, the least common multiple is 5 7 = (G) Let w and d represent the width and depth, respectivel, of the scale model. Then =. Reduce 100 w 100 to, so that = 18. Cross-multipl to get w = 6. So, w w = 1. Similarl, =. We can reduce 5 d 5 to 6 1. Then 6 = 18, which leads to 1 d 6d = 18. So, d =. Therefore, the sum of the length, width, and depth of the scale model is = inches.

26 6 FCAT.0 Algebra I (B) The equation ma be written as = 5 + b, where b is the -intercept. Substitute (6, 0) so that 0 = 5(6) + b. Then b = 0. Now the equation becomes = Note that (4, 10) satisfies this equation because 10 = 5(4) + 0. None of answer choices (A), (C), and (D) satisf this equation. The correct answer is 7.5. Let represent the average speed in miles per hour of car B. Since car A traveled for 5 hours (1:00 pm to 6:00 pm), the distance traveled was (4)(5) = 10 miles. Car B traveled for 4 hours, so its distance was 4. The two cars traveled in opposite directions, so = 60. Then 4 = 150, which means that = 7.5 miles per hour. (C) Caitlin s profit in Januar was (0)(5) 100 = $650. Here profit in Februar was (0) () 100 = $860. In order that her profit for Januar, Februar, and March eceed $000, she must make a profit of at least $000 $650 $860 = $490 in March. Let represent the number of paintings sold in March. Then This inequalit becomes so Since we must round up, she must sell at least 0 paintings. 0 (H) Point A is located at ( 4, 1) and point B is located at (0, ). Then the slope of the line 1 is 0 ( 4) =. The equation of this line becomes = 4 4. B substitution, we find that 6 = (80). This implies that (80, 6) is a point on this line. Each of 4 answer choices (F), (G), and (I) is wrong because 45 (60), (70), and 66 4 (90). 1 (C) n c + ( n c) 4 nc n c nc c 8 4 = + = + n c 4 c = + n 5. (Remember that c 0 = 1.) nc nc n n (I) ( mp r ) ( m p r ) 5 4 = ( mpr 6 9 )( m 1 pr 8 0 ) m p = m p r = r

27 Online Practice Test Answer Ke 7 (B) Given 6 < 1 4 < 0, subtract 1 from each part to get 18 < 4 < 8. Then divide each part b 4 (and reverse the sense of the inequalit) to get the solution of 9 < <. Each element of answer choice (B) is contained in < < 9. Answer choice (A) is wrong because it contains 5 and 6. Answer choice (C) is wrong because 9 numbers such as.5 do not belong to < <. Answer choice (D) is wrong because it contains 4.5, which is equal to 9. 4 (G) ( 18 )( ) = ()( 9)( )( 16)( ) 4 + ( 49)( ) = ()()(4)() = (C) 4 7 = 6 = (6)( )( ) = 6 6, which still contains a radical sign. For answer choice (A), = 9 = 80. For answer choice (B), = 16 = For answer choice (D), = 5 = 5 4. (F) Since 5 and are zeros of the equation + a + c = 0, the factors must be ( 5) and ( + ). So we can write ( 5)( + ) = 0. We note that ( 5)( + ) = = 10. Thus, a = and c = 10. The correct answer is. Substituting 148 for P, we get 148 = , which becomes = 0. Dividing b 8 leads to 0 44 = 0. Then ( ) ( + ) = 0. The two answers are and, but we reject an negative answer. (F) The Universal set = {,, 5, 7, 11, 1, 17, 19,, 9, 1, 7} Since 60 = 5, R = {,, 5}. Since 75 = 5 1, S = {5, 11}. Therefore, the set that does not contain an elements from R or S must contain the eight elements 7, 1, 17, 19,, 9, 1, and 7.

28 8 FCAT.0 Algebra I (A) First note that when = 0, = 9. This means that onl answer choices (A) and (C) are possible. Assume that choice (C) is correct and substitute the point (4, 0). We need to check if 0 = (4) + (4) 9. However, the right side simplifies to ()(16) = 5. This means that (4, 0) does not lie on the graph of = + 9. Onl answer choice (A) could be correct. We note that b substitution, ( ) + ( ) 9 = ()(9) 9 9 = 0 and () + () 9 = ()(4) = 5. Thus, both (, 0) and (, 5) lie on the graph of = + 9. (G) In order to solve 6, ,900, first subtract 500 from each part to get 6,600 5,400. The last step is to divided each part b and reverse the inequalit smbols. Thus, the solution is 1,800,00. The solutions to answer choices (F), (H), and (I) are 1,800,00, 1,700,00, and 1,750,00, respectivel. (C) A horizontal line has a slope of zero, so this eliminates answer choices (B) and (D). Answer choice (A) is wrong because the line crosses the -ais at (0, 4). Note that the graph in answer choice (C) crosses the -ais at (0, 4). The correct answer is 169. Let represent the number of elements that belong to both P and Q. Then 75 represents the number of elements that belong onl to P. Similarl, 110 represents the number of elements that belong onl to Q. So, (75 ) + + (110 ) + = 00. This equation simplifies to 08 = 00. Solving, we get = 8, which represents the number of elements inboth P and Q. Thus, the number of elements that belong to eactl one of P and Q is 00 8 = 169. An alternative solution after finding that = 8 is as follows: The number of elements that belong to onl P is 75 8 = 67. Likewise, the number of elements that belong to onl Q is = 10. Thus, the number of elements that belong to eactl one of P and Q is = 169. (A) ( )( + 7) ( 5)( 5) = = Thus, 18 is not a part of the final simplified result.

29 Online Practice Test Answer Ke 9 44 (F) (4 )( 5 1) (4 )(+ )( 4) ()( 4) = = =, which is 8 18 ( )(4 9) ( )(+ )( ) 8 equivalent to. (Note that CANNOT be canceled from the numerator and denominator because it is not a factor of either binomial.) 45 The correct answer is 55. The dollar amount in April was $850 $155 $195 $5 = $75. The number of das for Januar can be found b solving the equation 155 = d. Subtract 75 from each side to get 80 = 10d. Then d = 8. In a similar manner, the number of das for each of Februar, March and April can be determined b solving the equations 195 = d, 5 = d, and 75 = d, respectivel. We find that Jerr spent 1 das in Februar, 15 das in March, and 0 das in April. Thus, the total number of das spent at the club was = The correct answer is $1.50. Let = number of children, = number of adults, and z = number of senior citizens. Then we can form three equations, namel: 4 + = 15, 4 + z = 10, and + z = 5. Subtract the second equation from the first equation to get z = 5. Net, double all terms of the third equation to get + z = 10. Adding this equation to z = 5 will result in 5 = 15. So, = $, which is the cost per adult. Using the equation + z = 5, we can easil find that z = $, which is the cost per senior citizen. Use the first equation to find the value of. Then 4 + ()() = 15, which simplifies to 4 = 6. So = $1.50. Thus, the cost of three children, five adults, and si senior citizens is ()($1.50) + (5)($) + (6)($) = $1.50. (B) f (4) = = 1, f (6) = ()(6) 5 = 7, and f (8) = ()(8) 5 = 11. Then = 5. (H) (5 4)( + ) = = One half of 4 10 is 5. Then ( 5) = + 6.

30 0 FCAT.0 Algebra I 49 (A) Let represent the number of gallons of water that must be removed. The original 40-gallon solution contains (0.15)(40) = 6 gallons of acid. When gallons of water are removed, the resulting solution will contain 40 gallons of both water and acid. 6 Since no acid is being removed, there will still be 6 gallons of acid. Then 40 = 0.0. Multipl both sides b (40 ) to get 6 = (0.0)(40 ) = Subtracting 8 from each side leads to = 0.0. Thus, = = 10 gallons The correct answer is 115. B using a factor tree, we can determine that 18 = 8 5 and 45 = So = = = 5. Therefore, mn = ()(5) = The correct answer is 54. In order that the relation not be a function, there must be at least two different ordered pairs in which the first element is repeated. The lowest given domain value is 9. Thus, if the fourth ordered pair is (9, 18), then the sum of the domain values is = 54. (I) B < 4AC is equivalent to B 4AC < 0. The quantit B 4AC is called the discriminant of the quadratic formula used to determine the solutions to 0 = A + B + C. Whenever the discriminant is less than zero, both solutions must be comple. This implies that the graph of = A + B + C does not intersect the -ais, as shown in answer choice (I). (B) The slope of L must be the negative reciprocal of the slope of L 1. So the slope of L must be 4. The equation of L must be of the form = + b, where b is 4 the -intercept. Now substituting the point (14, 5), we get = 5 + b 4 (14). Then 5 = b, which means that b = 5.5. The -intercept is therefore (0, 5.5).

31 Online Practice Test Answer Ke (G) Using cross-multiplication for the given proportion, we have ( )( ) = 6( + 11). This equation becomes = , which simplifies to = 0. For an quadratic equation of the form a + b + c = 0, the product of the roots is given b the quantit c a. Thus, for = 0, the product of the roots is 60 = 0. Note that an alternative solution, following = 0, is to use factoring on the left side of this equation. Then ( + 5)( 1) = 0, from which we get the values of 5 and 1. Thus, the product is 5 (1) = 0. The correct answer is 0.5. Since the coefficient of is negative, the graph has a maimum value at its verte. The -value of the verte of an function in the form = a + b + c is given b the quotient b. For our current function, this value a is ()( 1) =. Thus, the corresponding value is = + = 4 1 4, which is equivalent to 0.5. (G) Note that C B means the set of all elements in C that do not eist in B. This is equivalent to listing all elements of C, then subtracting out those elements common to both B and C. Now C ={mouse, snake, tiger, turtle, zebra} and the elements common to B and C are turtle and zebra. Thus, C B = {mouse, snake, tiger}. Answer choice (F) is wrong because its elements are lion, rat, and horse. Answer choice (H) is wrong because its elements are mouse and turtle. Answer choice (I) is wrong because its onl element is turtle. (D) Let the graph of the line be represented b = m + b, where m is the slope and b is the -intercept. Since (0, 7) is a point on this line, we know that b = 7. We can substitute the point (, 10) to find m. Then 10 = (m)() + 7, which simplifies to = m. This means that m = 1.5, so the equation of this line is = To find the value of p, substitute = 8. Then p = (1.5)(8) + 7 = 19. To find the value of q, substitute = 8. Then 8 = 1 1.5q + 7. This equation simplifies to 1 = 1.5q. So q = = 14. Finall, we note that 1.5 the difference of p and q is 5.

32 FCAT.0 Algebra I 58 The correct answer is.5. We need to solve the equation = Subtract 6 from each side to get 0.50 = Net, subtract 0.0 from each side to get 0.0 = Thus, = 4.50 =.5 miles. (Note that for.5 miles, the cost for each compan is $17.5) (D) The set M consists of all elements that do not belong to M. This includes c, d, and all elements that are not listed in either M or N. Each element in answer choice (D) is either c, d, or an element outside of M and N, (but within U ). Answer choice (A) is wrong because it contains the elements i and z. Answer Choice (B) is wrong because it contains the elements,, and z. Answer choice (C) is wrong because the elements 1 and do not belong to the Universal set. 60 The correct answer is 6. Let = number of nickels, + 5 = number of dimes, and ( + 5) = + 10 = number of quarters. The value of each of her nickels, dimes, and quarters is 0.05, (0.10)( + 5), and (0.5)( + 10), respectivel. Then ( + 5) + (0.5)( + 10) = 10.80, which becomes = This equation simplifies to = Then 0.65 = 7.80, so = 1, the number of nickels. So Sall must also have = 17 dimes and ()(17) = 4 quarters. Therefore, Sall has a total of = 6 coins (B) 5 e to each side to get d 1= 5 e. Now di- d 1 = e. Finall, square both sides so that a 5 Rewrite the given equation b adding vide both sides b 5, which results in d 1 4d 4d+ 1 e = =. 5 5 The correct answer is 1. Let n = number of coins Marlene originall had and let n + = number of coins Kenn originall had. After Kenn gave Marlene 7 coins, he had n + 7 = n 4, and she had n + 7. Since she still had nine fewer coins, we can write n 4 = n Subtracting n from each side leads to n 4 = So n = = 60. Thus, the number of coins that Kenn originall had was ()(60) + = 1.

33 Online Practice Test Answer Ke 6 The correct answer is 9. Multipl the first equation b and the second equation b. The result is the following set of equations: 6 4= = 159 Adding these equations ields 11 = 99. Thus, = (G) Factoring the left side of the equation, we get ( + 1)( 6) = 0. So + 1 = 0 or 6 = 0. Thus, the solutions (zeros) are 1 and 6. Answer choice (F) is wrong because its zeros are and. Answer choice (H) is wrong because its zeros are and. Answer choice (I) is wrong because its zeros are 1 and 6. (D) Using the Quadratic equation, the solutions are given b ± ( 11) ( 11) (4)()(8) = ()() 11± = 11± 57 11± and The larger solution is