Florida Algebra I EOC Online Practice Test


 Anabel Lyons
 7 years ago
 Views:
Transcription
1 Florida Algebra I EOC Online Practice Test Directions: This practice test contains 65 multiplechoice 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 40gallon 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 =. Crossmultipl 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 =. Crossmultipl 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 =. Crossmultipl 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. Crossmultipl 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 40gallon 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 crossmultiplication 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
Review of Intermediate Algebra Content
Review of Intermediate Algebra Content Table of Contents Page Factoring GCF and Trinomials of the Form + b + c... Factoring Trinomials of the Form a + b + c... Factoring Perfect Square Trinomials... 6
More informationMATH REVIEW SHEETS BEGINNING ALGEBRA MATH 60
MATH REVIEW SHEETS BEGINNING ALGEBRA MATH 60 A Summar of Concepts Needed to be Successful in Mathematics The following sheets list the ke concepts which are taught in the specified math course. The sheets
More information135 Final Review. Determine whether the graph is symmetric with respect to the xaxis, the yaxis, and/or the origin.
13 Final Review Find the distance d(p1, P2) between the points P1 and P2. 1) P1 = (, 6); P2 = (7, 2) 2 12 2 12 3 Determine whether the graph is smmetric with respect to the ais, the ais, and/or the
More informationFINAL EXAM REVIEW MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
FINAL EXAM REVIEW MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether or not the relationship shown in the table is a function. 1) 
More informationSolving Quadratic Equations by Graphing. Consider an equation of the form. y ax 2 bx c a 0. In an equation of the form
SECTION 11.3 Solving Quadratic Equations b Graphing 11.3 OBJECTIVES 1. Find an ais of smmetr 2. Find a verte 3. Graph a parabola 4. Solve quadratic equations b graphing 5. Solve an application involving
More informationSUNY ECC. ACCUPLACER Preparation Workshop. Algebra Skills
SUNY ECC ACCUPLACER Preparation Workshop Algebra Skills Gail A. Butler Ph.D. Evaluating Algebraic Epressions Substitute the value (#) in place of the letter (variable). Follow order of operations!!! E)
More informationNorth Carolina Community College System Diagnostic and Placement Test Sample Questions
North Carolina Communit College Sstem Diagnostic and Placement Test Sample Questions 0 The College Board. College Board, ACCUPLACER, WritePlacer and the acorn logo are registered trademarks of the College
More informationFlorida Algebra 1 EndofCourse Assessment Item Bank, Polk County School District
Benchmark: MA.912.A.2.3; Describe the concept of a function, use function notation, determine whether a given relation is a function, and link equations to functions. Also assesses MA.912.A.2.13; Solve
More informationINVESTIGATIONS AND FUNCTIONS 1.1.1 1.1.4. Example 1
Chapter 1 INVESTIGATIONS AND FUNCTIONS 1.1.1 1.1.4 This opening section introduces the students to man of the big ideas of Algebra 2, as well as different was of thinking and various problem solving strategies.
More informationAlgebra II. Administered May 2013 RELEASED
STAAR State of Teas Assessments of Academic Readiness Algebra II Administered Ma 0 RELEASED Copright 0, Teas Education Agenc. All rights reserved. Reproduction of all or portions of this work is prohibited
More informationPOLYNOMIAL FUNCTIONS
POLYNOMIAL FUNCTIONS Polynomial Division.. 314 The Rational Zero Test.....317 Descarte s Rule of Signs... 319 The Remainder Theorem.....31 Finding all Zeros of a Polynomial Function.......33 Writing a
More informationUse order of operations to simplify. Show all steps in the space provided below each problem. INTEGER OPERATIONS
ORDER OF OPERATIONS In the following order: 1) Work inside the grouping smbols such as parenthesis and brackets. ) Evaluate the powers. 3) Do the multiplication and/or division in order from left to right.
More informationAlgebra EOC Practice Test #4
Class: Date: Algebra EOC Practice Test #4 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. For f(x) = 3x + 4, find f(2) and find x such that f(x) = 17.
More informationA Quick Algebra Review
1. Simplifying Epressions. Solving Equations 3. Problem Solving 4. Inequalities 5. Absolute Values 6. Linear Equations 7. Systems of Equations 8. Laws of Eponents 9. Quadratics 10. Rationals 11. Radicals
More informationSummer Math Exercises. For students who are entering. PreCalculus
Summer Math Eercises For students who are entering PreCalculus It has been discovered that idle students lose learning over the summer months. To help you succeed net fall and perhaps to help you learn
More informationMATH 21. College Algebra 1 Lecture Notes
MATH 21 College Algebra 1 Lecture Notes MATH 21 3.6 Factoring Review College Algebra 1 Factoring and Foiling 1. (a + b) 2 = a 2 + 2ab + b 2. 2. (a b) 2 = a 2 2ab + b 2. 3. (a + b)(a b) = a 2 b 2. 4. (a
More information{ } Sec 3.1 Systems of Linear Equations in Two Variables
Sec.1 Sstems of Linear Equations in Two Variables Learning Objectives: 1. Deciding whether an ordered pair is a solution.. Solve a sstem of linear equations using the graphing, substitution, and elimination
More informationIOWA EndofCourse Assessment Programs. Released Items ALGEBRA I. Copyright 2010 by The University of Iowa.
IOWA EndofCourse Assessment Programs Released Items Copyright 2010 by The University of Iowa. ALGEBRA I 1 Sally works as a car salesperson and earns a monthly salary of $2,000. She also earns $500 for
More informationSection 5.0A Factoring Part 1
Section 5.0A Factoring Part 1 I. Work Together A. Multiply the following binomials into trinomials. (Write the final result in descending order, i.e., a + b + c ). ( 7)( + 5) ( + 7)( + ) ( + 7)( + 5) (
More information1.3 Algebraic Expressions
1.3 Algebraic Expressions A polynomial is an expression of the form: a n x n + a n 1 x n 1 +... + a 2 x 2 + a 1 x + a 0 The numbers a 1, a 2,..., a n are called coefficients. Each of the separate parts,
More informationTHE POWER RULES. Raising an Exponential Expression to a Power
8 (5) Chapter 5 Eponents and Polnomials 5. THE POWER RULES In this section Raising an Eponential Epression to a Power Raising a Product to a Power Raising a Quotient to a Power Variable Eponents Summar
More information5.2 Inverse Functions
78 Further Topics in Functions. Inverse Functions Thinking of a function as a process like we did in Section., in this section we seek another function which might reverse that process. As in real life,
More informationSolution of the System of Linear Equations: any ordered pair in a system that makes all equations true.
Definitions: Sstem of Linear Equations: or more linear equations Sstem of Linear Inequalities: or more linear inequalities Solution of the Sstem of Linear Equations: an ordered pair in a sstem that makes
More informationMath 0980 Chapter Objectives. Chapter 1: Introduction to Algebra: The Integers.
Math 0980 Chapter Objectives Chapter 1: Introduction to Algebra: The Integers. 1. Identify the place value of a digit. 2. Write a number in words or digits. 3. Write positive and negative numbers used
More informationFactoring Polynomials
UNIT 11 Factoring Polynomials You can use polynomials to describe framing for art. 396 Unit 11 factoring polynomials A polynomial is an expression that has variables that represent numbers. A number can
More informationZeros of Polynomial Functions. The Fundamental Theorem of Algebra. The Fundamental Theorem of Algebra. zero in the complex number system.
_.qd /7/ 9:6 AM Page 69 Section. Zeros of Polnomial Functions 69. Zeros of Polnomial Functions What ou should learn Use the Fundamental Theorem of Algebra to determine the number of zeros of polnomial
More informationAnswer Key for California State Standards: Algebra I
Algebra I: Symbolic reasoning and calculations with symbols are central in algebra. Through the study of algebra, a student develops an understanding of the symbolic language of mathematics and the sciences.
More information1. a. standard form of a parabola with. 2 b 1 2 horizontal axis of symmetry 2. x 2 y 2 r 2 o. standard form of an ellipse centered
Conic Sections. Distance Formula and Circles. More on the Parabola. The Ellipse and Hperbola. Nonlinear Sstems of Equations in Two Variables. Nonlinear Inequalities and Sstems of Inequalities In Chapter,
More informationM122 College Algebra Review for Final Exam
M122 College Algebra Review for Final Eam Revised Fall 2007 for College Algebra in Contet All answers should include our work (this could be a written eplanation of the result, a graph with the relevant
More informationMath 152, Intermediate Algebra Practice Problems #1
Math 152, Intermediate Algebra Practice Problems 1 Instructions: These problems are intended to give ou practice with the tpes Joseph Krause and level of problems that I epect ou to be able to do. Work
More informationFSCJ PERT. Florida State College at Jacksonville. assessment. and Certification Centers
FSCJ Florida State College at Jacksonville Assessment and Certification Centers PERT Postsecondary Education Readiness Test Study Guide for Mathematics Note: Pages through are a basic review. Pages forward
More informationHow many of these intersection points lie in the interior of the shaded region? If 1. then what is the value of
NOVEMBER A stack of 00 nickels has a height of 6 inches What is the value, in dollars, of an 8foothigh stack of nickels? Epress our answer to the nearest hundredth A cube is sliced b a plane that goes
More information6. The given function is only drawn for x > 0. Complete the function for x < 0 with the following conditions:
Precalculus Worksheet 1. Da 1 1. The relation described b the set of points {(, 5 ),( 0, 5 ),(,8 ),(, 9) } is NOT a function. Eplain wh. For questions  4, use the graph at the right.. Eplain wh the graph
More informationMATH 185 CHAPTER 2 REVIEW
NAME MATH 18 CHAPTER REVIEW Use the slope and intercept to graph the linear function. 1. F() = 4   Objective: (.1) Graph a Linear Function Determine whether the given function is linear or nonlinear..
More informationThe SlopeIntercept Form
7.1 The SlopeIntercept Form 7.1 OBJECTIVES 1. Find the slope and intercept from the equation of a line. Given the slope and intercept, write the equation of a line. Use the slope and intercept to graph
More informationLINEAR FUNCTIONS OF 2 VARIABLES
CHAPTER 4: LINEAR FUNCTIONS OF 2 VARIABLES 4.1 RATES OF CHANGES IN DIFFERENT DIRECTIONS From Precalculus, we know that is a linear function if the rate of change of the function is constant. I.e., for
More informationAlgebra 1 EndofCourse Exam Practice Test with Solutions
Algebra 1 EndofCourse Exam Practice Test with Solutions For Multiple Choice Items, circle the correct response. For Fillin Response Items, write your answer in the box provided, placing one digit in
More informationAnswers to Basic Algebra Review
Answers to Basic Algebra Review 1. 1.1 Follow the sign rules when adding and subtracting: If the numbers have the same sign, add them together and keep the sign. If the numbers have different signs, subtract
More informationSkills Practice Skills Practice for Lesson 1.1
Skills Practice Skills Practice for Lesson. Name Date Tanks a Lot Introduction to Linear Functions Vocabular Define each term in our own words.. function A function is a relation that maps each value of
More informationPolynomial Degree and Finite Differences
CONDENSED LESSON 7.1 Polynomial Degree and Finite Differences In this lesson you will learn the terminology associated with polynomials use the finite differences method to determine the degree of a polynomial
More informationMath Review. for the Quantitative Reasoning Measure of the GRE revised General Test
Math Review for the Quantitative Reasoning Measure of the GRE revised General Test www.ets.org Overview This Math Review will familiarize you with the mathematical skills and concepts that are important
More informationy intercept Gradient Facts Lines that have the same gradient are PARALLEL
CORE Summar Notes Linear Graphs and Equations = m + c gradient = increase in increase in intercept Gradient Facts Lines that have the same gradient are PARALLEL If lines are PERPENDICULAR then m m = or
More informationLESSON EIII.E EXPONENTS AND LOGARITHMS
LESSON EIII.E EXPONENTS AND LOGARITHMS LESSON EIII.E EXPONENTS AND LOGARITHMS OVERVIEW Here s what ou ll learn in this lesson: Eponential Functions a. Graphing eponential functions b. Applications of eponential
More informationScope and Sequence KA KB 1A 1B 2A 2B 3A 3B 4A 4B 5A 5B 6A 6B
Scope and Sequence Earlybird Kindergarten, Standards Edition Primary Mathematics, Standards Edition Copyright 2008 [SingaporeMath.com Inc.] The check mark indicates where the topic is first introduced
More informationD.2. The Cartesian Plane. The Cartesian Plane The Distance and Midpoint Formulas Equations of Circles. D10 APPENDIX D Precalculus Review
D0 APPENDIX D Precalculus Review SECTION D. The Cartesian Plane The Cartesian Plane The Distance and Midpoint Formulas Equations of Circles The Cartesian Plane An ordered pair, of real numbers has as its
More informationCore Maths C1. Revision Notes
Core Maths C Revision Notes November 0 Core Maths C Algebra... Indices... Rules of indices... Surds... 4 Simplifying surds... 4 Rationalising the denominator... 4 Quadratic functions... 4 Completing the
More information1.6. Piecewise Functions. LEARN ABOUT the Math. Representing the problem using a graphical model
. Piecewise Functions YOU WILL NEED graph paper graphing calculator GOAL Understand, interpret, and graph situations that are described b piecewise functions. LEARN ABOUT the Math A cit parking lot uses
More informationLinear Inequality in Two Variables
90 (7) Chapter 7 Sstems of Linear Equations and Inequalities In this section 7.4 GRAPHING LINEAR INEQUALITIES IN TWO VARIABLES You studied linear equations and inequalities in one variable in Chapter.
More informationSolving Quadratic Equations
9.3 Solving Quadratic Equations by Using the Quadratic Formula 9.3 OBJECTIVES 1. Solve a quadratic equation by using the quadratic formula 2. Determine the nature of the solutions of a quadratic equation
More information10.1. Solving Quadratic Equations. Investigation: Rocket Science CONDENSED
CONDENSED L E S S O N 10.1 Solving Quadratic Equations In this lesson you will look at quadratic functions that model projectile motion use tables and graphs to approimate solutions to quadratic equations
More informationSECTION P.5 Factoring Polynomials
BLITMCPB.QXP.0599_4874 /0/0 0:4 AM Page 48 48 Chapter P Prerequisites: Fundamental Concepts of Algebra Technology Eercises Critical Thinking Eercises 98. The common cold is caused by a rhinovirus. The
More informationChapter 3 & 8.18.3. Determine whether the pair of equations represents parallel lines. Work must be shown. 2) 3x  4y = 10 16x + 8y = 10
Chapter 3 & 8.18.3 These are meant for practice. The actual test is different. Determine whether the pair of equations represents parallel lines. 1) 9 + 3 = 12 27 + 9 = 39 1) Determine whether the pair
More informationMath 120 Final Exam Practice Problems, Form: A
Math 120 Final Exam Practice Problems, Form: A Name: While every attempt was made to be complete in the types of problems given below, we make no guarantees about the completeness of the problems. Specifically,
More informationREVIEW OF ANALYTIC GEOMETRY
REVIEW OF ANALYTIC GEOMETRY The points in a plane can be identified with ordered pairs of real numbers. We start b drawing two perpendicular coordinate lines that intersect at the origin O on each line.
More informationExponential and Logarithmic Functions
Chapter 6 Eponential and Logarithmic Functions Section summaries Section 6.1 Composite Functions Some functions are constructed in several steps, where each of the individual steps is a function. For eample,
More informationMTH 092 College Algebra Essex County College Division of Mathematics Sample Review Questions 1 Created January 17, 2006
MTH 092 College Algebra Essex County College Division of Mathematics Sample Review Questions Created January 7, 2006 Math 092, Elementary Algebra, covers the mathematical content listed below. In order
More information7 Literal Equations and
CHAPTER 7 Literal Equations and Inequalities Chapter Outline 7.1 LITERAL EQUATIONS 7.2 INEQUALITIES 7.3 INEQUALITIES USING MULTIPLICATION AND DIVISION 7.4 MULTISTEP INEQUALITIES 113 7.1. Literal Equations
More informationACT Math Vocabulary. Altitude The height of a triangle that makes a 90degree angle with the base of the triangle. Altitude
ACT Math Vocabular Acute When referring to an angle acute means less than 90 degrees. When referring to a triangle, acute means that all angles are less than 90 degrees. For eample: Altitude The height
More informationC3: Functions. Learning objectives
CHAPTER C3: Functions Learning objectives After studing this chapter ou should: be familiar with the terms oneone and manone mappings understand the terms domain and range for a mapping understand the
More informationSECTION 2.2. Distance and Midpoint Formulas; Circles
SECTION. Objectives. Find the distance between two points.. Find the midpoint of a line segment.. Write the standard form of a circle s equation.. Give the center and radius of a circle whose equation
More informationEQUATIONS OF LINES IN SLOPE INTERCEPT AND STANDARD FORM
. Equations of Lines in SlopeIntercept and Standard Form ( ) 8 In this SlopeIntercept Form Standard Form section Using SlopeIntercept Form for Graphing Writing the Equation for a Line Applications (0,
More informationVocabulary Words and Definitions for Algebra
Name: Period: Vocabulary Words and s for Algebra Absolute Value Additive Inverse Algebraic Expression Ascending Order Associative Property Axis of Symmetry Base Binomial Coefficient Combine Like Terms
More informationTSI College Level Math Practice Test
TSI College Level Math Practice Test Tutorial Services Mission del Paso Campus. Factor the Following Polynomials 4 a. 6 8 b. c. 7 d. ab + a + b + 6 e. 9 f. 6 9. Perform the indicated operation a. ( +7y)
More informationQuadratic Equations and Functions
Quadratic Equations and Functions. Square Root Propert and Completing the Square. Quadratic Formula. Equations in Quadratic Form. Graphs of Quadratic Functions. Verte of a Parabola and Applications In
More informationMidterm 2 Review Problems (the first 7 pages) Math 1235116 Intermediate Algebra Online Spring 2013
Midterm Review Problems (the first 7 pages) Math 15116 Intermediate Algebra Online Spring 01 Please note that these review problems are due on the day of the midterm, Friday, April 1, 01 at 6 p.m. in
More informationD.3. Angles and Degree Measure. Review of Trigonometric Functions
APPENDIX D Precalculus Review D7 SECTION D. Review of Trigonometric Functions Angles and Degree Measure Radian Measure The Trigonometric Functions Evaluating Trigonometric Functions Solving Trigonometric
More informationAlgebra I Vocabulary Cards
Algebra I Vocabulary Cards Table of Contents Expressions and Operations Natural Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers Absolute Value Order of Operations Expression
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA. Tuesday, January 24, 2012 9:15 a.m. to 12:15 p.m.
INTEGRATED ALGEBRA The Universit of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA Tuesda, Januar 4, 01 9:15 a.m. to 1:15 p.m., onl Student Name: School Name: Print our name and
More informationSection 7.2 Linear Programming: The Graphical Method
Section 7.2 Linear Programming: The Graphical Method Man problems in business, science, and economics involve finding the optimal value of a function (for instance, the maimum value of the profit function
More informationALGEBRA 1 SKILL BUILDERS
ALGEBRA 1 SKILL BUILDERS (Etra Practice) Introduction to Students and Their Teachers Learning is an individual endeavor. Some ideas come easil; others take timesometimes lots of time to grasp. In addition,
More informationALGEBRA 2: 4.1 Graph Quadratic Functions in Standard Form
ALGEBRA 2: 4.1 Graph Quadratic Functions in Standard Form Goal Graph quadratic functions. VOCABULARY Quadratic function A function that can be written in the standard form y = ax 2 + bx+ c where a 0 Parabola
More informationZeros of Polynomial Functions
Zeros of Polynomial Functions The Rational Zero Theorem If f (x) = a n x n + a n1 x n1 + + a 1 x + a 0 has integer coefficients and p/q (where p/q is reduced) is a rational zero, then p is a factor of
More informationDISTANCE, CIRCLES, AND QUADRATIC EQUATIONS
a p p e n d i g DISTANCE, CIRCLES, AND QUADRATIC EQUATIONS DISTANCE BETWEEN TWO POINTS IN THE PLANE Suppose that we are interested in finding the distance d between two points P (, ) and P (, ) in the
More informationALGEBRA I FINAL EXAM
ALGEBRA I FINAL EXAM A passing score of 9 on this test allows a student to register for geometry. JUNE 00 YOU MAY WRITE ON THIS TEST . Solve: 7= 6 6 6. Solve: =. One tai cab charges $.00 plus 7 cents per
More informationBig Bend Community College. Beginning Algebra MPC 095. Lab Notebook
Big Bend Community College Beginning Algebra MPC 095 Lab Notebook Beginning Algebra Lab Notebook by Tyler Wallace is licensed under a Creative Commons Attribution 3.0 Unported License. Permissions beyond
More information1.1 Practice Worksheet
Math 1 MPS Instructor: Cheryl Jaeger Balm 1 1.1 Practice Worksheet 1. Write each English phrase as a mathematical expression. (a) Three less than twice a number (b) Four more than half of a number (c)
More informationMore Equations and Inequalities
Section. Sets of Numbers and Interval Notation 9 More Equations and Inequalities 9 9. Compound Inequalities 9. Polnomial and Rational Inequalities 9. Absolute Value Equations 9. Absolute Value Inequalities
More informationWhat are the place values to the left of the decimal point and their associated powers of ten?
The verbal answers to all of the following questions should be memorized before completion of algebra. Answers that are not memorized will hinder your ability to succeed in geometry and algebra. (Everything
More information2.3 Quadratic Functions
88 Linear and Quadratic Functions. Quadratic Functions You ma recall studing quadratic equations in Intermediate Algebra. In this section, we review those equations in the contet of our net famil of functions:
More informationA.3. Polynomials and Factoring. Polynomials. What you should learn. Definition of a Polynomial in x. Why you should learn it
Appendi A.3 Polynomials and Factoring A23 A.3 Polynomials and Factoring What you should learn Write polynomials in standard form. Add,subtract,and multiply polynomials. Use special products to multiply
More informationAlgebra II A Final Exam
Algebra II A Final Exam Multiple Choice Identify the choice that best completes the statement or answers the question. Evaluate the expression for the given value of the variable(s). 1. ; x = 4 a. 34 b.
More informationMTH 100 College Algebra Essex County College Division of Mathematics Sample Review Questions 1 Created June 6, 2011
MTH 00 College Algebra Essex County College Division of Mathematics Sample Review Questions Created June 6, 0 Math 00, Introductory College Mathematics, covers the mathematical content listed below. In
More informationLesson 9.1 Solving Quadratic Equations
Lesson 9.1 Solving Quadratic Equations 1. Sketch the graph of a quadratic equation with a. One intercept and all nonnegative yvalues. b. The verte in the third quadrant and no intercepts. c. The verte
More information5.1. A Formula for Slope. Investigation: Points and Slope CONDENSED
CONDENSED L E S S O N 5.1 A Formula for Slope In this lesson ou will learn how to calculate the slope of a line given two points on the line determine whether a point lies on the same line as two given
More informationFunctions and Graphs CHAPTER INTRODUCTION. The function concept is one of the most important ideas in mathematics. The study
Functions and Graphs CHAPTER 2 INTRODUCTION The function concept is one of the most important ideas in mathematics. The stud 21 Functions 22 Elementar Functions: Graphs and Transformations 23 Quadratic
More informationHigher. Polynomials and Quadratics 64
hsn.uk.net Higher Mathematics UNIT OUTCOME 1 Polnomials and Quadratics Contents Polnomials and Quadratics 64 1 Quadratics 64 The Discriminant 66 3 Completing the Square 67 4 Sketching Parabolas 70 5 Determining
More informationAlgebra EOC Practice Test #2
Class: Date: Algebra EOC Practice Test #2 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which of the following lines is perpendicular to the line y =
More informationChapter 4. Polynomial and Rational Functions. 4.1 Polynomial Functions and Their Graphs
Chapter 4. Polynomial and Rational Functions 4.1 Polynomial Functions and Their Graphs A polynomial function of degree n is a function of the form P = a n n + a n 1 n 1 + + a 2 2 + a 1 + a 0 Where a s
More information2.1 Increasing, Decreasing, and Piecewise Functions; Applications
2.1 Increasing, Decreasing, and Piecewise Functions; Applications Graph functions, looking for intervals on which the function is increasing, decreasing, or constant, and estimate relative maxima and minima.
More informationSolve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. Solve word problems that call for addition of three whole numbers
More informationExpression. Variable Equation Polynomial Monomial Add. Area. Volume Surface Space Length Width. Probability. Chance Random Likely Possibility Odds
Isosceles Triangle Congruent Leg Side Expression Equation Polynomial Monomial Radical Square Root Check Times Itself Function Relation One Domain Range Area Volume Surface Space Length Width Quantitative
More informationSAMPLE. Polynomial functions
Objectives C H A P T E R 4 Polnomial functions To be able to use the technique of equating coefficients. To introduce the functions of the form f () = a( + h) n + k and to sketch graphs of this form through
More informationSection A3 Polynomials: Factoring APPLICATIONS. A22 Appendix A A BASIC ALGEBRA REVIEW
A Appendi A A BASIC ALGEBRA REVIEW C In Problems 53 56, perform the indicated operations and simplify. 53. ( ) 3 ( ) 3( ) 4 54. ( ) 3 ( ) 3( ) 7 55. 3{[ ( )] ( )( 3)} 56. {( 3)( ) [3 ( )]} 57. Show by
More informationSection 23 Quadratic Functions
118 2 LINEAR AND QUADRATIC FUNCTIONS 71. Celsius/Fahrenheit. A formula for converting Celsius degrees to Fahrenheit degrees is given by the linear function 9 F 32 C Determine to the nearest degree the
More informationSAT Math Hard Practice Quiz. 5. How many integers between 10 and 500 begin and end in 3?
SAT Math Hard Practice Quiz Numbers and Operations 5. How many integers between 10 and 500 begin and end in 3? 1. A bag contains tomatoes that are either green or red. The ratio of green tomatoes to red
More informationAmerican Diploma Project
Student Name: American Diploma Project ALGEBRA l EndofCourse Eam PRACTICE TEST General Directions Today you will be taking an ADP Algebra I EndofCourse Practice Test. To complete this test, you will
More informationDefinition 8.1 Two inequalities are equivalent if they have the same solution set. Add or Subtract the same value on both sides of the inequality.
8 Inequalities Concepts: Equivalent Inequalities Linear and Nonlinear Inequalities Absolute Value Inequalities (Sections 4.6 and 1.1) 8.1 Equivalent Inequalities Definition 8.1 Two inequalities are equivalent
More informationTHE PARABOLA 13.2. section
698 (3 0) Chapter 3 Nonlinear Sstems and the Conic Sections 49. Fencing a rectangle. If 34 ft of fencing are used to enclose a rectangular area of 72 ft 2, then what are the dimensions of the area? 50.
More informationAlgebra I. In this technological age, mathematics is more important than ever. When students
In this technological age, mathematics is more important than ever. When students leave school, they are more and more likely to use mathematics in their work and everyday lives operating computer equipment,
More information