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Benchmark Questions Benchmark #1 Which is the graph of f(x) = x2? A. B. C. D. MM1A1 b Benchmark #2 F(x) = 4x + 6; What is f(2)? A. B. C. D. 10 12 14 16 MM1A1 a Benchmark #3 In the equation y = 3x2, 3 ________ the graph from f(x) = x2. A. B. C. D. vertically stretches vertically shrinks horizontally stretches reflects MM1A1c Benchmark #4 Solve: -6x + 9 = 21 A. -5 B. -2 C. 5 D. 6 MM1A3 d Benchmark #5 What is the pattern in the following sequence {3, 4, 5, 6, 7, …}. a. b. c. d. n n+1 n+2 n2 MM1A1 f Benchmark # 6 What is the intersection point of the graphs of the equations f(x) = 4x + 1 and g(x) = x + 2? a. (1, 3) b. ( 1 1 ) 5 ,2 5 c. (3, 1) d. (2, 4) MM1A1 i Benchmark #7 Which is the graph of f(x) = |x|? A. C. B. D. MM1A1 b Benchmark #8 What is 5 x 6 ? a. 30 b. 11 c. 35 d. 30 MM1A2 b Benchmark #9 Subtract y2 + 4 from 3y2 + 8y. a. b. c. d. 4y2 + 12y 4y2 + 8y + 4 2y2 + 8y - 4 2y2 + 8y + 4 MM1A2 c Benchmark #10 Multiply the binomials (x - 3)(x - 3). a. b. c. d. x2 - 6x + 9 x2 - 6x -9 x2 - 9 x2 + 9 MM1A2 d Benchmark #11 Multiply b. y 2x x 3y 2 x 2 y 2 y 2x and y2 x4 x3 a. x3 x2 y2 x c. d. . x 4 y 2 2x 3y 4 y 2x x2 x MM1A2 e Benchmark #12 Factor the expression x2 + x - 30. a. b. c. d. (x - 6)(x + 5) (x -10)(x + 3) (x - 2)(x + 15) (x + 6)(x - 5) MM1A2 f Benchmark #13 What is the difference between the ranges of Set A and Set B? Set A: {39, 45, 93} Set B: {1, 6, 25} A. 54 B. 24 C. 30 D. 78 MM1D2 a Benchmark #14 Given the following measures of the angles of a triangle, find the missing angle. 90, 70 and x a. 10° b. 20° c. 30° d. 40° MM1G3 a Benchmark #15 Given the following triangle, which side is J the longest? A. KJ B. JL C. KL D. Both K KL 30 ° 80° L and KJ are the same. MM1G3 b Benchmark #16 Given the two triangles, which theorem for triangles proves they are equivalent? a. b. c. d. SSS HL SAS ASA 1 2 MM1G3 c Benchmark #17 A square is __________ a rectangle. a. Always b. Sometimes c. Never MM1G3 d Benchmark #18 Given the two triangles, which theorem for triangles proves these are equivalent? a. b. c. d. AAS HL SAS ASA MM1G3 c Benchmark #19 Point Z is the orthocenter of ∆TUV. Which term accurately describes TY a. b. c. d. altitude angle bisector median of triangle perpendicular bisector MM1G3 e Benchmark #20 The point of concurrency of the angle bisectors is the _______________. a. b. c. d. centroid incenter circumcenter orthocenter MM1G3 e Benchmark #21 Sally is seven years old and goes to the store with her mother every Saturday morning. Every time they go, she notices that here mother gives the check out clerk money before they leave the store. Sally concluded that everyone has to give money in exchange for things they want to take out of the store. This is an example of: a. Deductive reasoning b. Inductive reasoning c. Analytical reasoning MM1G2 a Benchmark #22 If I make all passing grades this week, then I will go to the movies on Saturday. What is the inverse of this statement? a. If I don’t make all passing grades this week, then I won’t go to the movies on Saturday. b. If I go to the movies on Saturday, then I make all passing grades this week. c. If I don’t go to the movies on Saturday, then I didn’t make all passing grades this week. d. If I don’t make all passing grades this week, then I will go to the movies on Saturday. MM1G2 b Benchmark #23 Magdalena has 6 hats, 2 scarves, and 5 pairs of mittens. In how many different ways can she wear a hat, a scarf and a pair of mittens? A. 13 B. 14 C. 12 D. 60 MM1D1 a Benchmark #24 How many permutations can you find using the letters in the CAT? a. 3 b. 6 c. 9 d. 12 MM1D1 b Benchmark #25 If Joe rolls 2 dice, the probability of him rolling a six and a double (3, 3) is: a. Mutually exclusive b. Not mutually exclusive c. Both A & B MM1D2 a Benchmark #26 If Jonathan is rolling dice and spinning a spinner, these two events are: a. b. c. d. independent dependent mutually exclusive not mutually exclusive MM1D2 b Benchmark #27 The spinner below is divided into three equal sections. What is the probability of spinning a 3 on the spinner if you the know the arrow landed on an odd number? 1 A. 1/6 B. 1/3 C. D. 1/2 2/3 2 3 MM1D2 c Benchmark #28 There are 24 candy-coated chocolate pieces in a bag. Eight have defects in the coating that can be seen only with close inspection. What is the probability of pulling out a defective piece of candy from the bag? A. 8 B. 8/23 C. 1/4 D. 1/3 MM1D2 d Benchmark #29 What is the mean absolute deviation of the following set of numbers {2, 7, 9, 1, 6, 4}? A. 1.5 B. 2 C. 2.5 D. 3 MM1D4 Benchmark #30 y = x2 is a(n) _________ function. A. Odd B. Even C. Neither MM1A1 h Benchmark #31 The school cafeteria workers are conducting a survey of students’ likes and dislikes for the foods they serve at lunch time. Once they tally the data and begin to order the food they need, which measure of central tendency will help most to make the food purchases? A. B. C. D. Mean Mode Median Range MM1D3 a Benchmark #32 y = x3 - 2 is a(n) _________ function. A. Odd B. Even C. Neither MM1A1 h Benchmark #33 What are the solutions to y = x2 + 5x + 6? A. B. C. D. x = 3, 2 x = -3, 2 x = 3, -2 x = -3, -2 MM1A1 a Benchmark #34 x 2 5. What is x? A. 3 B. 3 C. 6 D. 9 MM1A3 b Benchmark #35 1 x = 0. What is x? A. 0 B. 1 C. 1 D. 2 MM1A3 b Benchmark #36 According to the chart, what are the solution(s), (x-intercepts) to the equation f(x) = x2 + 2x + 1? f(x) A. -1 x -2 B. 1 -1 0 C. -1, 1 0 1 D. 2, 2 1 4 2 9 1 MM1A3 c Benchmark #37 According to this chart, what are the solution(s), (x-intercepts) to the equation f(x) = -9x2 + 9? x f(x) A. 9 -2 -27 B. -1, 1 -1 0 C. -1, 1, 9 0 9 D. -2, 2 1 0 2 -27 MM1A3 c Benchmark #38 The points (0, 0), (5, 0), (0, 4) form what type of triangle? A. B. C. D. Isosceles Equilateral Scalene Right MM1G1 e Benchmark #39 Solve: 3(x - 2) - 1 = 6(x + 5) A. -4 37 B. 3 C. 4 23 D. 3 Benchmark #40 Solve: -6x + 9 = 21 A. -5 B. -2 C. 4 D. 6 Benchmark #41 What is the distance between (1, 1) and (6, 6)? A. 25 B. 5 C. 50 D. 25 Benchmark #42 What is the distance between (0, 0) and (3, 2)? A. B. C. D. 13 13 4.12 3.555 Benchmark #43 What is the midpoint of (6, 4) and (3, -4)? A. B. C. D. (4.5, 0) (0, 4.5) (-4.5, 0) (0, -4.5) Benchmark #44 Use the points A = (0, 0), B = (3, 2) and C = (0, 2) and the Pythagorean Theorem to find the distance between A and B. What is the distance? A. 13 B. 13 C. 5 D. 5 Benchmark #45 Graph the points (-2, 0), (-2, 3), (2, 2), and (2, 0) to find out what shape they create. What shape do they create? A. A square B. A rectangle C. A rhombus D. A trapezoid Benchmark #46 f(x) = -x + 1; What is f(-4)? A. B. C. D. -3 -5 3 5 Benchmark #47 1 Which is the graph of f(x) = x ? Benchmark #48 In the equation y=2x - 1_______ the graph from the function f(x)=2x. A.shifts B.shrinks C.stretches D.reflects Benchmark #49 What is the general shape of the function y=x2? A.Straight line B.Parabola C.N Shape D.V Shape Benchmark #50 What is the rate of change of 3 f(x)= - x + 2? 4 3 4 A. B. 3 4 C. 2 D. -2 Benchmark #51 What is 12 3 - 3 3 ? A. 4 B. 3 C. 9 D. 9 3 3 2 3 Benchmark #52 Add: y2 + 3y + 2 and 2y2 + 4 A. B. C. D. y2 + 5y + 6 3y2 + 3y+ 6 6y2 + 6 3y2 + 7y + 2 Benchmark #53 Multiply the binomials (x + 2) ( x + 1). A. B. C. D. x2 + 2x + 3 x2 + 2x + 2 x2 + 3x + 1 x2 + 3x + 2 Benchmark #54 Add the two fraction A. B. x 2 5x 19 2 x x 6 C. x 2 6x 1 (x 2)(x 3) D. x 2 5x 19 x2 x 6 x2 (x 2)( x 3) x3 x 2 5 and x 3 Benchmark #55 Factor the expression xy + 4x + 2b + 8 by grouping. A. x(y + 4) + 2(b + 4) B. x(y - 4) + 2(b - 4) C. x(y - 4) + 2b + 8 D. x(y + 4) + 2(b + 8) Benchmark #56 What is the area of a triangle with height h = 6 + x and base b = 13 + x? A. B. C. D. x2 + 19x + 78 1/2 x2 + 19x + 39 1/2 x2 + 19/2 x + 39 1/2 x2 + 19/2 x + 78 Benchmark #57 What are the factors of b2 -4b - 5? A. B. C. D. (b - 5) (b + 1) (b + 5) (b -1) (b - 3) (b + 2) (b - 2) (b - 3) Benchmark #58 Give the following triangle, find x. A. B. C. D. 30° 40° 50° 60° 80 ° 50º x Benchmark #59 Which of the follow can be the measure of the third side of a triangle if the other two sides are 7 and 13? A. 3 B. 4 C. 5 D. 8 Benchmark #60 Given the two triangles, which theorem for triangles proves these are equivalent? 110° 40° 110° 40° A. SSS B. HL C. SAS D. AAS Benchmark #61 Given the two triangles, which theorem for triangles proves these are congruent? A. SSS 20° B. HL C. SAS D. ASA 20° Benchmark #62 What is equivalent to A. 5 11 B. 8 50 C. 11 5 D. 17 5 45 8 5 ? Benchmark #63 A rectangle is ___________ a square. A. B. C. D. always sometimes never not enough information Benchmark #64 The ____________is equidistant from the vertices of a trinagle. A. B. C. D. centroid incenter circumcenter orthocenter Benchmark #65 A(n) ________is the center of an inscribed circle. A. B. C. D. centroid Incenter circumcenter orthocenter Benchmark #66 Which is equivalent to this expression? (7x2 + 3xy - 8y2) + (4x2 - 8y2) A. B. C. D. 11x4 + 3xy - 16y2 11x2 + 3xy -16y2 11x2 - 5xy - 8y2 11x2 + 3xy Benchmark #67 Which is a factored form of x2 - 4? A. (x - 1)(x + 4) B. (x - 2) (x + 2) C. (x + 1)(x - 4) D. (x + 2)(x -2) Benchmark #68 What is the value of this expression? (2t2 - t - 28) divided by (t - 4) A. (t + 4) B. (t + 7) C. (2t - 4) D. (2t + 7) Benchmark # 69 Which shows the expansion of (x - y)4? A. B. C. D. x4 - 4x3y + 6x2y2 - 4xy3 + y4 x4 - 4x3y - 6x2y2 - 4xy3 - y4 x4 - 5x3y - 10x2y2 - 5xy + y4 x4 - 5x3y - 10x2y2 - 5xy3 - y5 Benchmark #70 What is the product of (4a + 7b)(5a + 3b)? A. B. C. D. 20a2 + 12a + 35b + 21b2 20a2 - 47ab + 21b2 20a2 + 23ab - 21b2 20a2 + 47ab + 21b2 Benchmark #71 The table of values represent part of a function. Which equation also represents this function? A. f(x) = -3x B. f(x) = x - 1 C. f(x) = 2x - 3 D. f(x) = 3x x 0 2 4 6 f(x) -3 1 5 9 Benchmark #72 The five ordered pairs below represent a function. {(-1, 4), (-3, 5), (0, 6), (2, 5), (3, 2)} What is the range for this function? A. (-3, -1, 0, 2, 3) B. (-3, -1, 0, 2, 3, 2, 4, 5, 6) C. (2, 4, 5, 6 ) D. All real number greater than or equal to 2 and less than 6. Benchmark #73 Solve the equation below for n. 20 1 15 n 2 n 2 (n 2)(n 2) A. 5 B. 4 C. 3 D. 2 Benchmark #74 What are the solutions for x2 - 3x - 10 = 0 A. B. C. D. x = -5 and x = -2 x = 5 and x = -2 x = -5 and x = 2 x = 2 and x = 5 Benchmark # 75 4 k k 2 ? What is the value of k in: 8 6 A. 20 B. 13 C. 4 26 D. 7 Benchmark #76 What value of a makes this equation true? 2a 4 2 A. 2 B. 4 C. 9 D. 18 Benchmark #77 What values of x make this equation true? 8 x x 10 x 9 A. x = -9 and x =8 B. x = -8 and x = 9 C. x = -6 and x = 12 D. x = 6 and x = 12 Benchmark #78 All carnivores are meat eaters. Lions eat meat. Therefore, lions are carnivores. This kind of thinking is an example of ___________ reasoning. A. Applied B. Inductive C. Qualitative D. Deductive Benchmark #79 If the conditional statement is represented by pq, then the ___________ is represented by qp. A. Inverse statement B. Converse statement C. Contrapositive statement D. Conditional statement Benchmark #80 If a figure is a triangle, then it has three sides. Which of the following statements is the contrapositive statement? A. If a figure is a triangle, then it has three sides. B. If a figure is not a triangle, then it does not have three sides. C. If a figure has three sides, then it is a triangle. D. If a figure does not have three sides, then it is not a triangle. Benchmark #81 If Sara has 6 shirts and 3 pairs of pants, how many different outfits does she have? A. 9 B. 12 C. 15 D. 18 Benchmark #82 If Jessica has a bag containing 3 blue bracelets and 7 green ones, what is the probability that she draws 1 blue and then 1 green (without replacement)? A B 2 9 15 34 C 5 D 7 9 30 Benchmark #83 Greg has test scores of 77, 90, 92, and 77 in English class. If he gets a 0 on his next paper, how will it affect the mean, median and mode of his scores. A. The mean will go down. The median will go down. The mode will remain the same. B. The mean, median and mode will all remain the same. C. The mean, median and mode will all go down. D. The mean will go down. The median and mode will remain the same. Benchmark #84 A spinner is divided into 7 areas numbered 1 - 7. If the sections containing 3, 4, 6, and 7 are shaded, what is the probability of landing on a 1 or a shaded area? A. 3/7 B. 5/7 C. 4/7 D. 6/7 Benchmark #85 What is the absolute mean deviation of the following set of numbers {3, 6, 2, 9, 1, 7, 2}? A. 2 B. 2.5 C. 2.61 D. 2.75 Benchmark #86 Which fraction represents the statement, “There is a 65% probability of snow tomorrow? A. 1/6 B. 6/100 C. 13/20 D. 3/5 Benchmark #87 This spinner is spun three times. What is probability that the point stops on Blue the first spin, Yellow on the second spin and Blue on the third spin? A. 1/2 B. 1/16 C. 3/8 Yellow Blue D. 1/4 Red Benchmark #88 Using a standard deck of playing cards, the 7 of clubs is drawn and not replaced. What is the probability that a second card drawn would be a heart? A. 13/51 B. 12/52 C. 12/51 D. 13/52 Benchmark #89 Using a standard deck of playing cards, the 5 of hearts is drawn and not replaced. What is the probability that a second card drawn would be a 9? A. 9/52 B. 13/51 C. 4/51 D. 9/13 Benchmark #90 What is the number of possible outcomes when a number cube is rolled and a coin tossed at the same time? A. 2 B. 4 C. 8 D. 12 Benchmark #91 A number cube is rolled once and the result is recorded. The same number cube is rolled a second time. What is the probability that the sum of the rolls is greater than 7? A. 0/6 B. 15/36 C. 4/12 D. 5/6 Benchmark #92 Which equation is the slope-intercept form of the equation: 2x + 8y = 35 C. 35 8y A. 8y = 35 - 2x B. 1 4 x 2 35 8 D. MM1A1 b 35 2x 8 Benchmark #93 A line passes through the points (6, 4) and (3, 2). What is the slope of the line? A. C. 3 B. 2 2 D. 3 MM1A1 c 2 3 3 2 Benchmark #94 What is the equation of a line that is parallel to y = 2x + 1 and passes through the point (3, 2)? A. y = 2x + 4 B. y = 2x - 4 C. y = 1/2 x + 1 D. y = 4x - 3 MM1A1 g Benchmark #95 What is the solution set of the inequality 4|x - 6| + 4 ≥ 12? A. x ≤ 4 or x ≥ 8 B. 4 ≤ x ≤ 8 C. x ≤ -4 or x ≥ 8 D. x ≤ 4 or x ≤ -8 MM1A1 i Benchmark #96 If the graph of the line y = x is transformed by a dilation of 4, what would be the equation of the new line? A. y = 4x B. y = 1/4x C. y = x + 4 D. y = x - 4 MM1A1 c Benchmark #97 When are two lines are parallel? A. When both lines have a deflection? B. When both lines have the same x-intercept? C. When both lines have the same y-intercept? D. When both lines have the same slope? MM1A1 g Benchmark #98 An empty oil tank has a 4000-gallon capacity. If it is filled at a rate of 40 gallons per minute, how full will the tank be after 18 minutes? A. 3280 B. 720 C. 1500 D. 2500 MM1A1 g Benchmark #99 The function f(x) = |x - 7| is an example of what type of function? A. Absolute Value Function B. Linear Function C. Linear Inequality D. Inequality Function MM1A1 b Benchmark #100 Which expression is equivalent to the difference: (9x2 + 3x - 4) - (2x2 - 7x + 9) a. (7x2 - 4x + 5) b. (7x2 - 4x + 13) c. 7x2 - 10x - 13 d. 7x2 + 10x - 13 MM1A 2 c Benchmark #101 There are fice points in a plane, but no three points are colinear. How many different straight lines that pass through two of the points are possible? A. 2 B. 10 C. 15 D. 20 Benchmark #102 Danny has 3 identical color cubes. Each of the 6 faces on the color cubes is a different color. He also has two fair coins. What is the total number of possible outcomes if Danny rolls all three cubes OR flips both coins. A. 22 B. 144 C. 220 D. 864 Benchmark #103 There are 14 students in a mathematics competition. Each student will earn points during the competition. The student with the greatest number of points will be the first palce winnder, and the student with the second greates number of points will be the secon place winner. How many different ways can the 14 students finish in first place and second place? A. 27 B. 91 C. 182 D. 196 Benchmark #104 A teacher has 9 red crayons, 4 blue crayons, 7 purple crayons and 5 black crayons in a basket. A student reaches into the basket and randomly selects a crayon. What is the probability that the crayon will be either blue or black? A. 4/16 B. 9/25 C. 13/25 D. 9/16 Benchmark #105 There are 6 red apples, 4 yellow apples, and 2 green applies in a bucket. Maria will choose two apples at random without replacement. What is the probability that Maria will choose a red apple and a green apple? A. 5/121 B. 6/121 C. 1/11 D. 1/12 Benchmark #106 This table shows the probability of each possible sum when two cubes with faces numbered 1 through 6 are rolled and the numbers showing on each face are added. 2 3 Sum 2 3 4 5 36 6 7 Prob 1 36 8 9 10 11 12