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Name ________________________________________ Date __________________ Class __________________ End-of-Year Test Modules 1–25 7. The graph represents Lea’s distance from home over time. What is happening at the part of the graph labeled “B”? 1. Which measurement is the most precise? A 5.52 m C 5.516 m B 552 cm D 550 cm 2. Solve the inequality − 3 y 1 < +1 . 4 8 4 A y < −16 C y < 16 B y > −16 D y > 16 3. For each sequence, is the common difference equal to 2? A f (n) = 2n − 4 Yes No A Lea is stopped. B f (n) = 4n − 2 Yes No B Lea is walking away from home. Yes No Yes No C f (n ) = n 2 D f (n) = 2n C Lea is walking toward home. D Lea is slowing down. 8. The formula a university uses to charge tuition is T = 500h − 275, where h is the number of class hours a student is taking. Solve the formula for h. 4. What is the range of the relation {( −1, 2), (2, 4), (3, − 5), ( −4, − 3)} ? A {2} C {−4, − 1, 2, 3} B {−5, − 3, 2, 4} D {−1, 2, 3, − 5} ________________________________________ 5. Franco has x quarters, 12 one-dollar bills, and half as many ten-dollar bills as quarters. Which expression represents the amount of money Franco has in dollars? 9. Which equation is graphed below? A 20.25 x + 12 B 10.25 x + 12 C 5.25 x + 12 D 0.25 x + 10 x + 12 6. Which is the solution to 9q + 24 = 3(3q − 4)? 1 x +3 2 A q = −2 A y= B q=2 B y = 2x + 3 C y =− 1 x+3 2 D y = −2 x + 3 C no solution D q is all real numbers. Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 208 Name ________________________________________ Date __________________ Class __________________ End-of-Year Test Modules 1–25 15. Which of the following rules for an arithmetic sequence matches the pay scale represented in the table below? 10. What is the fourth term of a sequence with the recursive rule f (1) = −3.5; f (n ) = −2f (n − 1) for n > 1? A −28 C 14 B −2.5 D 28 11. What are the x- and y-intercepts of 7 7 x − y = −49 ? 2 Hours of Work 1 2 3 4 Pay $11 $20 $29 $38 A f (n ) = 9n + 20 B f (n ) = 9n + 11 A x-intercept: (−7, 0); y-intercept: (0, −14) B x-intercept: (−7, 0); y-intercept: (0, 14) C f ( n ) = 9n + 2 C x-intercept: (14, 0); y-intercept: (0, −7) D f ( n ) = 9n D x-intercept: (14, 0); y-intercept: (0, 7) 16. What is the domain of f ( x ) = 12. A cup contains 75 milliliters of water, from which 3 milliliters of water are poured out every second. Which function shows the amount of water in the cup after t seconds? C w (t ) = 3t − 75 B −1 B x≥0 D y≥0 Yes No Yes No C y > −2 x + 17 Yes No D y + 6 ≥ x + 14 Yes No B y +4≤ 75 − t 3 13. What is the slope of a line that contains the points (−4, −8) and (2, −2)? 5 3 C x<0 A y < −4 x + 32 B w (t ) = 75 − 3t A − A all real numbers 17. Does each linear inequality have the ordered pair (0, 8) as a solution? A w (t ) = 75 + 3t D w (t ) = C 4+x ? 12 x + 10 2 18. Which type of correlation best describes the data represented in the table below? 5 3 Price of Stock Over Time D 1 14. Which best describes the solutions to −12 x ≤ 90 ? 1998 2002 2006 2010 2014 $21 $22 $20 $17 $14 A all numbers less than −7.5 A Strong positive B all numbers greater than −7.5 B Negative C all numbers less than or equal to −7.5 C Positive D all numbers greater than or equal to −7.5 D None Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 209 Name ________________________________________ Date __________________ Class __________________ End-of-Year Test Modules 1–25 22. How many solutions does the system of equations graphed below have? 19. What is the correlation coefficient based on the scatter plot below? A −1 C 0 B −0.85 D 1 20. The squared residuals of lines of fit A and B are calculated. Line A better fits the data. Which of the following could be true? A none C 2 B 1 D infinitely many 23. Which ordered pair is not a solution of the system graphed below? A The sum of the squared residuals of A and B is 1.25. B The sum of the squared residuals of A is 1, and the sum of the squared residuals of B is 0.25. C The sum of the squared residuals of A is 0.82, and the sum of the squared residuals of B is 1.01. D The sum of the squared residuals of A is 4.5, and the sum of the squared residuals of B is 2.8. 21. Which equation would make this system have an infinite number of solutions? ⎧y = x + 2 ⎨ ⎩ ________ A 2y = 2 x + 2 C y = 2x B y −2= x D y = 3x − 1 A (−5, −10) C (0, −4) B (−4, −12) D (12, 0) 24. Alex is buying drinks and snacks for a party and wants to spend less than $45. Drinks cost $2 each, and snacks cost $4 each. He needs to buy at least 11 drinks and snacks altogether. Write a system that represents this situation. ________________________________________ Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 210 Name ________________________________________ Date __________________ Class __________________ End-of-Year Test Modules 1–25 30. Which regression equation best fits the data shown on the table? 25. A scientist is observing a dish of cells. The dish contains six cells that are dividing every minute. Which function best represents the number of cells in the dish at time x? A f (x) = 6 × 2 C f (x) = 2 × 6 x B f ( x ) = 6x y= B y =4 B D y = 32(4) C $9800 B $10,650 D $550 3 2 C 1 2 B − 1 2 D 3 2 y 5 2.3 1.3 0.63 x y ≈ 5.1× 2 x x 31. x What is the interquartile range of the data shown above? A 8 C 30 B 18 D 40 32. Which inequality is shown on the graph? 28. What is the common ratio of the sequence −8, 12, −18, 27,... ? A − 6 D y ≈ 4.4 × 0.7 x 27. A motorcycle with an initial value of $14,000 is decreasing in value at a rate of 3% each year. At this rate, approximately what will the value of the motorcycle be in 9 years? A $14,000 4 ⎛3⎞ C y ≈ 5×⎜ ⎟ ⎝2⎠ C y = 4(2)x x 2 ⎛ 1⎞ A y ≈ 5.2 × ⎜ ⎟ ⎝4⎠ D f ( x ) = 2x 8x 4 0 x 1⎞ ⎛ 26. The ordered pairs ⎜ −3, ⎟ and (2, 16) 2⎠ ⎝ are solutions to an exponential equation. What is the equation? A x 29. Would each of the following data sets be best described by an exponential model? A {(2, 4), (3, 9), (4, 16), (5, 25)} Yes No B {(−2, −1), (−3, 0), (−4, 1), (−5, 0)} Yes No A y≤ 1 x +1 3 C y ≤ 3x + 1 B y≥ 1 x +1 3 D y≤x+ C {(2, 64), (3, 16), (4, 4), (5, 1)} Yes No 1 3 Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 211 Name ________________________________________ Date __________________ Class __________________ End-of-Year Test Modules 1–25 38. Ben wants to get a 94 in math class. His grade will be the average of two test scores. He scored an 89 on the first test. What grade does Ben need to get on his second test to meet his goal? 33. Which is a recursive rule for the arithmetic sequence 22, 15, 8, 1….? A f(1) = 22; f(n) = f(n − 1) − 7 for n > 1 B f(1) = 22; f(n) = f(n − 1) + 7 for n > 1 C f(1) = 1; f(n) = f(n − 1) + 7 for n > 1 ________________________________________ D f(1) = 7; f(n) = f(n − 1) − 7 for n > 1 34. What is an equation for a line with a y-intercept of (0, −1) that contains the point (−4, −18)? A y =− 17 x −1 4 C y= 17 x −1 4 B y =− 17 x +1 4 D y= 17 x +1 4 39. What is the y-value of the solution of the ⎧6 y = 6 x − 40 system ⎨ ? ⎩4 y = 12 x + 48 ________________________________________ 40. How many significant digits does the measurement 1020 millimeters have? 35. Which functions have a rate of change greater than the function represented in the table? x 1 2 3 4 f(x) −2 3 8 13 A y= 11 x+5 2 Yes No Yes No 1 2 y= x 9 3 Yes No D y = 4.5 x − 10 Yes No B −3 x + C 1 y =3 2 ________________________________________ 41. High temperatures for five days in New York were 70 °F, 80 °F, 77 °F, 66 °F, and 59 °F. What was the range of temperatures? ________________________________________ 42. Scores on a chemistry test are normally distributed. The mean score is 80 and the standard deviation is 8. 1200 students took the test. About how many students scored less than 72? ________________________________________ 36. What is the slope of a line that contains the points (−4, −8) and (−2, −8)? 43. ________________________________________ x −5 2 3 4 y 1 3 8 13 Raj graphed the line of best fit for the data above. What is the slope of the line? 37. The sum of the measures of two angles is 180°. The difference between the angle measures is 70°. What is the measure of the smaller angle? ________________________________________ 44. What is the x-value of the solution to the ⎧ y = 2x ⎪ system ⎨ ? 1 ⎪⎩ y = 2 x + 6 ________________________________________ ________________________________________ Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 212 Name ________________________________________ Date __________________ Class __________________ End-of-Year Test Modules 1–25 49. Line segment PQ with endpoints P(4, 2) and Q(−2, 0) is rotated 90° clockwise around the origin. What are the coordinates of the midpoint of P ′Q′? For 45–46, use the graph. ________________________________________ 50. Use the graph. 45. Which segment is congruent to EF ? ________________________________________ 46. What is the midpoint of GH ? ________________________________________ Which transformation maps RST to R′ S′T′ ? Use the following information for 47–48. A (x, y) → (x + 6, y + 6) In the figure, m∠KJL = 32°. B (x, y) → (x + 6, y − 6) C (x, y) → (x − 6, y + 6) D (x, y) → (x − 6, y − 6) Use the figure for 51–52. 47. What is the value of x? ________________________________________ 48. What is m∠KJM ? 51. How many lines of symmetry does the figure have? ________________________________________ ________________________________________ 52. What are the angles of rotation less than 360° for the figure? ________________________________________ Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 213 Name ________________________________________ Date __________________ Class __________________ End-of-Year Test Modules 1–25 57. In the figure, m∠2 = 75°. Use the following information for 53–54. In the figures below, ABC ≅ LNM . + + 53. What is the value of x? ________________________________________ What is m∠7? 54. What is the value of y? ________________________________________ ________________________________________ 58. The measures of two complementary angles are represented by the expressions (3x + 16)° and (5x + 18)°. Find the value of x. Use the graph for 55–56. ________________________________________ 59. Write an equation for the line that passes through (1, −3) and is perpendicular to 1 y = x + 5. 2 ________________________________________ 60. Write an equation for the line that passes through (3, 2) and is parallel to 2x + 3y = 3. 55. What transformations can you use to show that quadrilaterals DEFG and D'E'F'G' are congruent? ________________________________________ ________________________________________ 61. In the figure, the measure of ∠2 is 55°. ________________________________________ 56. Express the transformations as a single mapping rule in the form of (x, y) → (?, ?). ________________________________________ What is the measure of ∠4? ________________________________________ Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 214 Name ________________________________________ Date __________________ Class __________________ End-of-Year Test Modules 1–25 62. Use the figures. 66. In the figure, PQ ≅ PS. Determine the value of x that ensures that the triangles are congruent. Explain why ________________________________________ ________________________________________ For 63–64, state the additional congruency statement or statements needed to prove ABC ≅ XYZ for the given theorem. + +PQR ≅ +PSR. ________________________________________ + 67. Use the figure. Answer True or False for each statement. 63. ASA Theorem A Angle MKL is an exterior angle of triangle JKM. ________________________________________ True 64. AAS Theorem False B Angle KML is an exterior angle of triangle JKM. ________________________________________ True 65. Look at the figure below. False C Angles MKL and KLM are complementary. True False D x = 35 True False 68. The sum of the measures of the interior angles of a regular polygon is 900°. How many sides does the polygon have? Are triangles DEF and FGH congruent? Explain why or why not. If the triangles are congruent, write a congruence statement. ________________________________________ ________________________________________ ________________________________________ Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 215 Name ________________________________________ Date __________________ Class __________________ End-of-Year Test Modules 1–25 69. Triangle RST is an isosceles triangle with m∠R = 120°. What is m∠S? Explain your reasoning. 74. In the figure, LP, MP, and NP are perpendicular bisectors. ________________________________________ ________________________________________ 70. The lengths of two sides of a triangle are 5 meters and 8 meters. If x represents the length of the third side in meters, which inequality gives all possible lengths for the third side? If LP = 5, LH = 12, HP = 13, and PM = 6, what is PJ ? A 3 < x < 13 ________________________________________ B 3 ≤ x ≤ 13 75. In the figure, point W is the incenter of triangle XYZ. C x < 3 or x > 13 D x > 3 or x < 13 For 71–72, use the figure. If RW = 5 and WY = 14, what is WT ? ________________________________________ 71. If EG = 4, what is GC? 76. ABCD is a quadrilateral with BE ≅ ED and ∠BCD ≅ ∠DAB. ________________________________________ 72. If AF = 15, what is AG? ________________________________________ 73. In the figure, MN is the midsegment of JKL. + If EC = 16 cm, m∠ABC = 64°, AE = 3x − 5, and m∠DAB = (4y − 12)°, for which values of x and y is ABCD a parallelogram? A x = 7, y = 19 B x = 32, y = 7 C x = 7, y = 32 If KM = 11 cm and KL = 24 cm, what is KN ? D x = 8, y = 19 ________________________________________ Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 216 Name ________________________________________ Date __________________ Class __________________ End-of-Year Test Modules 1–25 80. A parallelogram has vertices D(−4, −1), E(2, 5), F(4, 3), and G(−2, −3). Determine whether DEFG is a rhombus, rectangle, or neither. Explain your reasoning. 77. State whether each quadrilateral has congruent diagonals. A parallelogram Yes No B rhombus Yes No C rectangle Yes No D isosceles trapezoid Yes No ________________________________________ E kite Yes No ________________________________________ 78. GIJL is a trapezoid with midsegment HK . 81. KLMN is an isosceles trapezoid. If IJ = 18 cm and GL = 42 cm, what is HK? What is the missing x-coordinate of N? ________________________________________ ________________________________________ 79. Triangle PQR is shown in the graph. Use the following information for 82–83. The figure is symmetric about the x-axis. Use the coordinates of the vertices to determine whether each statement is True or False. A Triangle PQR is a right triangle. True 82. Find the perimeter of the figure. Round to the nearest tenth. False B Triangle PQR is scalene. True ________________________________________ False 83. What is the area of the figure? C Triangle PQR is isosceles. True False ________________________________________ D Triangle PQR is an acute triangle. True False Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 217 Answer Key End-of-Year Test Modules 1–25 1. C 36. 0 2. B 37. 55° 3. A Yes B No C No D Yes 38. 99 4. B 39. −16 5. C 40. 3 6. C 41. 21°F 7. A 42. 191 8. h = T + 275 500 43. 1.04 44. 4 9. C 45. AB 10. D 46. (3.5, −1.5) 11. B 47. x = 7 12. B 48. 70° 13. D 49. (1, −1) 14. D 15. C 50. D 16. A 51. 5 17. A Yes B No C No D Yes 52. 72°, 144°, 216°, 288° 18. B 53. x = 9 19. A 54. y = 8 20. C 21. B 55. a reflection over the y-axis, then a translation 1 unit left and 6 units down 22. A 56. (x, y) → (−x − 1, y − 6) 23. C 57. 105° ⎧2d + 4s < 45 24. ⎨ ⎩d + s ≥ 11 58. x = 7 59. y = −2x − 1 25. A 60. y = − 26. C 2 x+4 3 27. B 61. 35° 28. A 62. x = 9 29. A No B No C Yes 63. AC ≅ XZ 30. D 64. AB ≅ XY or BC ≅ YZ 31. A 65. Yes; the figure shows that DF ≅ GF and EF ≅ HF . ∠DFE and ∠ GFH are vertical angles, so ∠DFE ≅ ∠GFH . Therefore, DEF ≅ GHF by SAS. 32. A 33. A + 34. C 35. A Yes B Yes C Yes D No + Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 277 66. It is given that +PQR and +PSR are 76. C right triangles and PQ ≅ PS. PR ≅ PR by the Reflexive Property, so PQR ≅ PSR by HL Theorem. + 77. A No B No C Yes D Yes E No 78. 30 cm + 79. A False B False C True D True 67. A False B True C False D True 69. m∠S = 30°; the base angles of an isosceles triangle are congruent. Since ∠R is an obtuse angle, the unknown angles are the acute base angles of the triangle. The sum of the base angles is 180 − 120 = 60°, so each base angle is equal to 30°. 80. rectangle; using the Distance Formula, DE = FG = 6 2, EF = DG = 2 2, so the figure has opposite sides that are congruent. The slope of DE = slope of GF = 1 and slope of EF = slope of DG = −1, so the figure has two pairs of parallel sides, and consecutive sides are perpendicular. Therefore, the figure is a rectangle. 70. A 81. 2a + b 71. 8 82. 19.3 units 72. 10 83. 24 square units 68. 7 sides 73. 12 cm 74. 13 75. 5 Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 278