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EOCT Review Pull out paper & pencil 1) Solve –2x + 13 ≤ 23: a)x = 5 c) x > 5 b)x ≤ −5 d) x ≥ −5 2) What is not a solution to 3 ∗ 2 + 1 < 25? a) 3 c) –5 b) 0 d) 2 3) What would the graph look like for the solution to 4x – 5 > 7? a. Closed circle at 3 and shaded to the right b. Open circle at 3 and shaded to the right c. Open circle at 3 and shaded to the left d. Closed circle at 3 and shaded to the left 4) Which inequality represents the sum of 2 consecutive integers is greater than 73? a) 2n + 1 > 73 b) 2n > 73 c) 2n + 2 ≥ 73 d) n + (2n + 1) > 73 5) Which is a solution to the system of inequalities: 6 − 9 > 2 + 19 10 − > 7 a) All real #’s b) No solution c) 3 d) -4 6) In the expression, 3y + 8x + 12, what is the constant? a) 3 b) 8 c) y d) 12 7) A plumber charges a flat fee for each job, plus an hourly rate for the number of hours the job takes to complete. The total cost of the job, in dollars, can be modeled by the equation y = 50 + 65x. What does the independent variable in the expression represent in this situation? A) B) C) D) The number of jobs, y The number of hours to complete the job, x The cost per hour, $65 The total cost for the job, y 8) A plumber charges a flat fee for each job, plus an hourly rate for the number of hours the job takes to complete. The total cost of the job, in dollars, can be modeled by the equation y = 50 + 65x. What does the coefficient in the expression represent in the situation? A) B) C) D) The number of hours to complete the job, x The cost per hour, $65 The flat fee, $65 The flat fee, $50 9) A plumber charges a flat fee for each job, plus an hourly rate for the number of hours the job takes to complete. The total cost of the job, in dollars, can be modeled by the equation y = 50 + 65x. What does the constant term in the expression represent in this situation? A) B) C) D) The number of jobs, x The cost per hour, $65 The cost per hour, $50 The flat fee, $50 10) A plumber charges a flat fee for each job, plus an hourly rate for the number of hours the job takes to complete. The total cost of the job, in dollars, can be modeled by the equation y = 50 + 65x. What does the dependent variable in the expression represent in this situation? A) B) C) D) The number of jobs, y The number of hours to complete the job, x The total cost for the job, y The flat fee, $65 11) The owner of a pool cleaning business wants to know how much time, on average, his workers spend cleaning a pool. Last week, 7 employees each worked a 6-hour shift. In all, they cleaned 42 pools. Which is the most appropriate unit in which to calculate an answer to his question? A) B) C) D) Pools per employee Pools per day Employees per pool Hours per pool 12) Which is equivalent to 21.76 grams per minute? A) 1.306 kg/h B) 13.06 kg/h C) 36.267 kg/h D) 362.67 kg/h 13) Which of the following represents an exact quantity? A) The weather forecast for today calls for a high temperature of 81. B) The rise of a hill is about 15. C) A cat had a litter of 6 kittens. D) The maximum capacity of a bridge is 20,000 pounds. 14)For which of the following situations is an exact answer most needed? A) The maximum number of passengers on an airplane B) The number of spectators at a baseball game C) The number of blueberries in a batch of blueberry pancakes D) The number of people in a town 15) Which is not an exponential function? 1 8 a) =6∗ b) = c) = −12 10 d) = 4−5 16) Which function is represented in this graph: 1 6 A) = B) ∗ 3 1 =4 2 1 +1 C) = 2 D) = 41/2 17) Enrollment at a preschool has dropped by 4.5% each year. The variable y gives the number of students at school after x years. What is the base for the equation in the form y = a*bx that represents this situation? A) 0.045 B) 0.955 C) 1.91 D) 0.09 18) A beekeeper pays $30 to rent a booth at a farmers’ market. She charges $5 for each jar of honey. Which of the following is true? A) The value of x can be negative. B) The value of y can be negative. C) The value of x can be fractional. D) The value of y cannot be zero. 19) Which of the following is equivalent to the equation 4r + 7s = q? A) r = 4q – 28s B) r = q−7s 4 C) s = 7q + 28r D) s = q+4r 7 20) Which of the following is not equivalent to the equation a – 3b = 5c + 9? A) a = 3b + 5c + 9 B) b = 1 (a 3 – 5c – 9) C) a – 3b – 5c = 9 D) c = a−3b+9 5 21) Ohm’s Law of Electricity states that V = IR, where V = voltage, I = current, & R = resistance. If V = 9 volts and I = 0.5 amperes, how many Ohms (R) are used? A) 4.5 Ohms B) 18 Ohms C) 9.5 Ohms D) 8.5 Ohms 22) At a baseball game, hot dogs cost $2.25 and sodas cost $1.75. If Bob spent $18.25 and bought 5 hot dogs, how many sodas did he buy? A) 4 B) 7 C) 10 D) 9.5 23) A rectangle’s length is twice its width. Its perimeter is 156 meters. What is the rectangle’s length? A) 13 m B) 26 m C) 52 m D) 54 m 24) A seamstress is making dresses to sell at a local craft fair. She charges $35 for each dress and pays a $75 fee to rent her booth at the fair. The expression 35d – 75 gives the amount she earns at the fair, where d is the number of dresses sold. Which of the following is not true? A) B) C) D) The value of d can by any whole number. The value of d can be any integer. The value of d cannot be irrational. The value of d can be 0. 25) The sum of 22 and five times a number is 57. What is the number? A) 307 B) 7 C) 10 D) 9.5 26) What property is used in the equation below? 9+d=d+9 A) Associative property B) Commutative property C) Identity property D) Zero property 27) Sarah used the steps below to solve the 3 4 equation: ∗ 7 ∗ = 49. 4 3 Step 3 One: 4 ∗ 4 ∗ 3 7 = 49 Step Two: 1 ∗ 7 = 49 Step Three: 7 = 49 Step Four: = 7 Which step can be justified by the commutative property of multiplication? A) Step 1 C) Step 3 B) Step 2 D) Step 4 28) Sarah used the steps below to solve the 3 4 equation: ∗ 7 ∗ = 49. 4 3 Step 3 One: 4 ∗ 4 ∗ 3 7 = 49 Step Two: 1 ∗ 7 = 49 Step Three: 7 = 49 Step Four: = 7 Which step can be justified by the multiplicative identity property? A) Step 1 C) Step 3 B) Step 2 D) Step 4 29) Which is the solution to the equation: 8 ∙ 1 − 2 +1=1 ? 2 A) n = –4 B) n = –2 C) n = 2 D) n = 4 30) What step could be written within the solution to the equation: 4 ∙ 53 = 500? A) 53 = 53 B) 43 = 100 C) 53 = 2000 D) 203 = 500 31) A system of three equations is shown on the graph below. What is the solution to the system? A) (1, 1) B) (0, –2) C) (4, –2) D) No solution 32) At what amount of minutes does it not matter which cell phone company you choose? A) 10 B) 15 C) 20 D) 5 33) What step comes next if you solve the following system by substitution? 3 − 5 = 13 2 − = −3 –y = –2x – 3 y = 2x + 3 A) B) C) D) 3x – 5(2x + 3) = 13 3(2x + 3) – 5y = 13 3x = 5y + 13 None of the above 34) What step would come next if you solve the following system by elimination? − 2 = 5 −2 + 7 = −4 A) 2y – 4x = 10 B) y = 2x + 5 C) y – 7x = 5 D) –y + 5x = 1 35) Sonjit has a collection of quarters and dimes worth $3.70. He has a total of 19 coins. Which equation would be part of a system used to solve this problem? A) x + y = 3.7 B) x + y = 19 C) 19(x + y ) = 3.7 D) 0.25x – 0.1y = 3.7 36) Which system of inequalities is represented in the graph? ≤ 2 + 2 A) <−2 B) ≤ 1 2 +2 ≤ 2 + 2 C) >−2 D) ≥ 2 + 2 37) Which ordered pair is a solution to the system of inequalities represented in the graph? A) (–3, 2) B) (–7, –10) C) (–1, –2) D) (4, –10) 38) Which of the following is true about the system of inequalities represented in the graph below: A) (–4, –6) is a solution. B) The white section within the graph is the only area where solutions for this system can be found. C) Any ordered pair that falls on the y > x – 2 line is a solution. D) None of the above 39) Which table of values is not a function? Input Output Input Output a. 2 4 6 8 -2 -4 -6 -8 b. 1 1 2 2 4 5 6 7 Input Output Input Output c. -1 0 1 2 3 3 4 5 d. 1 3 5 7 -1 -2 -3 -4 40) Which value could not be substituted for a in the table if the table represents a function? A) 1 B) 0 C) –1 D) –3 x g(x) –3 24 a 4 1 4 2 –1 41) Which value or values could be substituted for b in the table to ensure that the table represents a function? A) 1 only B) 3¼ only C) 18 only D) Any real number x h(x) –1 2¼ 0 3 1 b 4 258 42) Which is true of the function shown below: A) B) C) D) It is increasing on the interval (−∞, ∞). It is decreasing on the interval [0, −∞). It is linear. It has a constant rate of change. 43) What is the x and y intercept of the function below? A) B) C) D) x-int (4, 0) & y-int (0,2) x-int (2, 0) & y-int (0,4) x-int: none & y-int (0,2) x-int: (2, 0) & y-int: none 44) What is the x-intercept of the table below: A) –9.9 B) –1 C) 1 D) –9 x –2 –1 0 1 2 g(x) –9.99 –9.9 –9 0 90 45) Which statement about this function is not true? A) Its domain is: {–6≤ x ≤ 9} B) Its range is: {–5≤ x ≤ 7.5} C) It has a y-intercept at (0,0) D) It has a maximum at 9. 46) The table below shows some ordered pairs for an exponential function. Which statement about this function is not true? A) Its x-intercept is the same as its y-intercept. B) It is positive on the interval (0,∞). C) It is increasing on the interval (–∞, ∞). D) As x approaches –∞, f(x) approaches ∞. x –1 f(x) 0 1 2 3 0 5 35 215 – 5 6 47) What is the rate of change for a line containing the points (7, 5) and (–2, 1)? A) 4 9 B) 4 5 C) 9 4 D) 5 4 48) Which statement is true when f(x) = 5x + 3 and g(x) = 6 9 + 9 for x1 = 0 and x2 = 3? A) The rate of change of f(x) is greater from x1 to x2. B) The rate of change of g(x) is greater from x1 to x2. C) The rate of change of f(x) is the same as g(x) from x1 to x2. D) None of the above is true. 49) Which two functions can be written from the equation 4x + 5 = 0.5x – 2? A) y = 4x + 5; y = 0.5x – 2 B) y = 3.5x; y = 3 C) y = x; y = 3.5x + 7 D) None of the above 50) Solve the equation for x by using the given table. A) 2 B) 3 C) 4 D) 25 x 2 3 4 5 6 f(x) = 5x – 2 g(x) = 25 1 25 5 25 25 25 125 25 625 25 51) The graph below shows f(x) = 1.5x and the graph of g. Which equation could represent g(x) in terms of f(x)? A) g(x) = f(x) + 6 B) g(x) = f(x) – 6 C) g(x) = f(x + 6) D) g(x) = 6f(x) 52) The graph below shows f(x) = 2x and the graph of g. Which equation could represent g(x) in terms of f(x)? A) g(x) = f(x) – 4 B) g(x) = f(x) + 4 C) g(x) = f(x – 4) D) g(x) = f(x + 4) 53) Describe the transformation from the parent function f(x) = x when given f(x) = x + 5. A) Left 5 units B) Right 5 units C) Up 5 units D) Down 5 units 54) Which function shows the transformation of left 7 units, a vertical stretch, and up 8 units when compared to its parent function? A) f(x) = 4*3x+7 – 8 B) g(x) = 1 x–7 *3 + 4 8 C) h(x) = 5*3x–7 + 8 D) m(x) = 5*3x+7 + 8 55) The graphing calculator screen below shows f(x) = 2x and its reflection g. Which could represent g(x)? A) g(x) = 2x B) g(x) = 2–x C) g(x) = –(2x) D) g(x) = –(2– x) 3 x 2 56) The graphing calculator screen below shows f(x) = – – 6 and its reflection g. Which is not true of the functions? A) g(x) = f(–x) B) Function f was reflected across the y-axis to form g. C) Both f and g have the same y-intercept. D) Both f and g have the same slope. 57) The equation A(t) = 900(0.85)t represents the value of a motor scooter t years after it was purchased. Which statement is also true of this situation? A) When new, the scooter cost $765. B) When new, the scooter cost $900. C) The scooter’s value is decreasing at a rate of 85% each year. D) The scooter’s value is decreasing at a rate of 0.15% each year. 58) Which function could be used to model the table: A) linear B) quadratic C) exponential D) cubic x 0 1 2 3 4 f(x) 16 8 4 2 1 59) The formula an = –10(3)n-1 describes a geometric sequence. Which recursive formula also describes this sequence? A) a1 = 1; an = an-1 ∙ –30 B) a1 = 3; an = an-1 ∙ –10 C) a1 = –10; an = an-1 ∙ 3 D) a1 = –1; an = an-1 ∙ 30 60) Which formula can be used to find the nth term in the sequence below? 128, 96, 72, 54, … A) an = 128 ∙ B) an = 128 ∙ C) an = 128 ∙ D) an = 128 ∙ 3 −1 4 4 −1 3 3 4 4 3 61) The formula an = 10 – 4n describes an arithmetic sequence. What are the first four terms in the sequence? A) 6, 2, –2, –6 B) 6, 2, 0, –2 C) 10, 6, 2, –2 D) 14, 18, 22, 26 62) For an arithmetic sequence a1 = 21, the recursive formula is an = an-1+11. Which explicit formula can be used to find the nth term in the sequence? A) an = 10 – 11n B) an = 10 + 11n C) an = 21 – 11n D) an = 21 + 11n 63) Based on the graph below, which statement is not true? A) Functions f and g have the same y-intercept. f(x) 1 ) 2 B) The ordered pair (–1, is a solution for both functions. C) The ordered pair (1, 2) is a solution for f(x). D) The value of f(x) begins to exceed g(x) during the interval between x = 2 and x = 3. g(x) 64) Which statement accurately compares the average weight of a puppy from the 2nd litter to the average weight of a puppy from the 1st litter? 1st Litter 3½, 4, 4, 4½ 2nd Litter 4½, 5, 7, 7½ A) The average weight is about the same for both litters. B) The average weight of a puppy from the 2nd litter is about ½ as great. C) The average weight of a puppy from the 2nd litter is about 1½ times as great. D) The average weight of a puppy from the 2nd litter is about 2½ times as great. 65) To compare two shipments, five packages from each shipment were chosen at random and weighed. Which measure or measures of center would be best to use if you wanted to compare the weight of a typical package from each shipment? 1st Shipment 2, 4, 6, 8, 10 2nd Shipment 3, 3, 5, 8, 50 A) Median would be the best measure of center. B) Mean would be the best measure of center. C) Median and mean would both be equally good measures of center. D) Neither the mean nor the median would be a good measure of center. 66) What is the mean of the dot plot below? A) 26 B) 30 C) 31 D) 29 67) What is the median of the dot plot below? A) 25 B) 30 C) 35 D) 40 68) Which is true about the histograms below? A) B) C) D) The non-obese graph is bimodal. The obese graph is uniform. The non-obese graph is skewed right. The obese graph is unimodal. 69) Which histogram is skewed left and has a gap? 70) What is the mean absolute deviation of the dot plot if the mean is about 4.2? A) 0.9 B) 3.9 C) 4.2 D) 1.7 71) Which statement is true concerning the two dot plots given below? Dot Plot #1 A) Dot Plot #1 has more variation than Dot Plot #2. B) Dot Plot #2 has more variation than Dot Plot #1. C) Both dot plots vary the same. D) The amount of variation for Dot Plot #2 is 3. Dot Plot #2 72) A teacher determined the median scores and interquartile ranges of scores for a test she gave to two classes. • In Class 1, the median score was 70 points, and the interquartile range was 15 points. • In Class 2, the median score was 75 points, and the interquartile range was 12 points. • Both classes had the same third quartile score. Which range includes only the numbers that could be third quartile scores for BOTH classes? A 70 to 87 points B 70 to 85 points C 75 to 87 points D 75 to 85 points 73) The box and whisker plot below shows the quiz scores of 20 history students. Which of the following statements is NOT a correct interpretation of the box-and-whicker plot? ● 20 25 30 35 40 A. The median quiz score was 30. B. Approximately 5 students had quiz scores of 36 or above. C. The lowest quiz score was 21. D.Approximately half of the students had a quiz score of 30. 74) The box plot shows the test scores earned by students in a biology class. Which statement about the test scores is not true? ● 60 70 80 90 100 A. The scores ranged from 65 to 100. B. The median score earned was an 85. C. 25% of students scored less than 75 points on the test. D.50% of students had scores that ranged from 75 to 85 points. 75) The box plot shows the prices of 20 skirts for sale at a boutique. Which statement about the prices is true? ● 10 20 30 40 50 60 70 80 90 100 A. The highest-priced skirt costs $100. B. The median half price of a skirt is $70. C. Half of the skirts have prices that range from $20 to $70. D.The prices of the skirts are close to the median and not very variable. 76) Given the table below, what is the value of the missing marginal frequency? Washington, D.C. Williamsburg, VA TOTAL Boys Girls TOTAL 77 20 97 28 75 ? A) 103 C) 93 B) 75 D) 95 105 95 200 77) Given the table below, what percentage of girls want to go to Williamsburg? Washington, D.C. Williamsburg, VA TOTAL Boys Girls TOTAL 77 20 97 28 75 ? A) 73% C) 27% B) 38% D) 79% 105 95 200 78) Given the table below, how many students want to go to Washington D. C.? Washington, D.C. Williamsburg, VA TOTAL Boys Girls TOTAL 77 20 97 A) 97 C) 105 B) 103 D) 95 28 75 ? 105 95 200 79) A scatter plot has a correlation coefficient of r = –0.895. What does this mean? A) The scatter plot shows strong positive correlation. B) The scatter plot shows weak positive correlation. C) The scatter plot shows strong negative correlation. D) The scatter plot shows weak negative correlation. 80) Find the equation of the line of best fit for the scatter plot below. A) y = 2 x 3 +1 B) y = x + 2 C) y = 2x D) y = 1 81) Find the equation of the line of best fit for the scatter plot below. A) f(x) = 50 3 5 B) f(x) = 135 2 C) f(x) = 125 2 5 D) f(x) = 100 6 82) Which equation is the best model for the table of values shown below? A) y = –0.55x + 3.55 B) y = 0.55x + 3.55 C) y = 3.55x – 0.55 D) y = –3.55x – 0.55 x 1 2 3 4 5 f(x) 3 6.5 10 14 17 83) Which equation is the best model for the table of values shown below? A) y = 4(2.99-x) B) y = 4(2.99x) C) y = 2.99(4-x) D) y = 2.99(4x) x 1 2 3 4 5 f(x) 12 48 190 770 3,070 84) What does the screenshot on the right show about the data being considered? LinReg y=ax+b a=–26.18521429 b=58.89810714 r2 = .5700873883 r=–.7550413156 A) A line with positive slope is a good fit for the data. B) A line with negative slope is a good fit for the data. C) A linear function is not a good model for the data. D) An exponential function is the only good model for the data 85) Quadrilateral ABCD and its reflected image are shown. Which statement is true of these two quadrilaterals? A) The image shows the result of a reflection across the x-axis. B) The path that point D takes across the line of reflection is perpendicular to the line of reflection. C) Each point (x,y) on quadrilateral ABCD maps to a point (-y,x) on its image. D) Corresponding sides of quadrilateral ABCD and its image are parallel. 86) Triangle ABC is transformed to triangle A’B’C’. Which statement is not true of these two figures? A) The transformation shows the image of ∆ABC after a 270 rotation about the origin. B) This transformation preserved the distances and angle measures of the original figure. C) Sides and ′′ lie on lines that are parallel to one another. D) Sides and ′ ′ lie on lines that are perpendicular to one another. 87)Which does not describe a way to map this regular octagon back onto itself? A) B) C) D) Reflect it across the x-axis. Reflect it across the y-axis. Rotate it 45. Rotate it 80. 88) Which sequence of transformations can be used to map ∆ABC to ∆A’B’C’? A) Dilation by a factor of ½ followed by a translation 4 units down. B) Dilation by a factor of ½ followed by a 270 rotation. C) Vertical shrink by a factor of ½ followed by a translation 4 units down. D) Vertical shrink by a factor of ½ followed by a 270 rotation. 89) What is the perimeter of quadrilateral TUVW? A 14 inches B 14.1 inches C 17.2 inches D 24 inches 90) Which equation represents a line that is perpendicular to the line shown below? A) y = 3x + 3 B) y = 1 − x 3 +3 C) y = –3x + 3 D) y = 1 x 3 +3 91) Which equation represents a line that is parallel to the line shown below? A) y = 3x + 2 B) y = 1 − x 3 +2 C) y = –3x + 2 D) y = 1 x 3 +2 92) Which describes the lines y = 8 7 7 x 8 + 12 and y = – x + 7? A) parallel B) perpendicular C) Neither parallel nor perpendicular D) coincidental 93) Which describes the lines x – 2y = –6 and 4y + 4 = 2x? A) parallel B) perpendicular C) Neither parallel nor perpendicular D) coincidental 94) Is ∆ABC a right triangle? A) B) C) D) Yes, because is perpendicular to . Yes, because is perpendicular to . Yes, because is perpendicular to . No, because none of the sides are perpendicular to one another. 95) What is the area of ∆ABC in square units? A) B) C) D) 13 21 26 52 F 96) Is DFGH a square? D G A) B) C) D) H Yes, because all of the angles are right angles and all of the sides are congruent. No, because all of the angles are not right angles. No, because opposite sides are not parallel. No, because not all of the sides are congruent. F 97) What is the perimeter of DFGH in units? D G A) B) C) D) 12 14 16 18 5 5 5 5 H 98) What is the distance between the points (1, –5) and (6, 7)? A) 11 B) 13 C) 14 D) 16 99) What is the midpoint between the endpoints (–11, –6) and (16, 22)? A) (1.5, 8) B) (–13.5, –14) C) (–13.5, –7) D) (2.5, 8) 100) A line segment has a midpoint of (–4, 6) and an endpoint of (2, 1). What is the coordinate of the other endpoint? A) (–1, 3.5) B) (–10, 11) C) (10, –11) D) (3.5, –1) 101) Find the coordinates of point P that lies along the directed line segment from M to N and partitions the segment in the ratio of 3 to 2 . Hint: Use (x + 1 – x2) + x2 and (y + 1 – y2) + y2 A) (1.2, 0) B) (2, 1.5) C) (0.5, –0.5) D) (–1, –1)