Mesa Public Schools. Q3 practice test. Assessment Summary: Powered by SchoolCity Inc. Page 1 of 44

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1 Mesa Public Schools Assessment Summary: Q3 practice test Powered by SchoolCity Inc. Page 1 of 44

2 Assessment Summary: Q3 practice test Year: Subject: Math Total Items: 43 Total Possible Points: 43 Includes 0 Pilot Items Item # Standard Item ID Correct Answer Points DOK 1 8.EE.A.2 KDS A B C D 1 Level 2: Skill/Concept 2 8.G.B.7 KDS A B C D 1 Level 2: Skill/Concept 3 8.G.B.7 KDS A B C D 1 Level 2: Skill/Concept 4 8.F.B.5 KDS A B C D 1 Level 2: Skill/Concept 5 8.F.B.4 KDS Level 2: Skill/Concept 6 8.G.B.7 KDS A B C D 1 Level 2: Skill/Concept 7 8.G.C.9 KDS A B C D 1 Level 1: Recall 8 8.G.B.7 KDS A B C D 1 Level 2: Skill/Concept 9 8.G.B.7 KDS A B C D 1 Level 2: Skill/Concept 10 8.NS.A.2 KDS A B C D 1 Level 2: Skill/Concept 11 8.G.C.9 KDS A B C D 1 Level 1: Recall 12 8.G.B.7 KDS A B C D 1 Level 2: Skill/Concept 13 8.G.B.7 KDS A B C D 1 Level 1: Recall 14 8.NS.A.1 KDS A B C D E 1 Level 1: Recall 15 8.NS.A.2 KDS A B C D E 1 Level 1: Recall F 16 8.G.C.9 KDS A B C D 1 Level 2: Skill/Concept 17 8.NS.A.1 KDS A B C D 1 Level 1: Recall 18 8.EE.A.2 KDS A B C D 1 Level 2: Skill/Concept 19 8.G.B.7 KDS A B C D 1 Level 2: Skill/Concept 20 8.G.C.9 KDS A B C D 1 Level 2: Skill/Concept 21 8.G.C.9 KDS A B C D 1 Level 1: Recall Powered by SchoolCity Inc. Page 2 of 44

3 Item # Standard Item ID Correct Answer Points DOK 22 8.G.C.9 KDS A B C D 1 Level 1: Recall 23 8.F.B.5 KDS A B C D 1 Level 1: Recall 24 8.G.B.8 KDS A B C D 1 Level 2: Skill/Concept 25 8.NS.A.2 KDS A B C D 1 Level 1: Recall 26 8.G.B.7 KDS A B C D 1 Level 2: Skill/Concept 27 8.NS.A.1 KDS A B C D 1 Level 1: Recall 28 8.G.B.8 KDS A B C D 1 Level 2: Skill/Concept 29 8.NS.A.1 KDS A B C D 1 Level 1: Recall 30 8.G.B.7 KDS A B C D 1 Level 2: Skill/Concept 31 8.G.C.9 KDS Level 2: Skill/Concept 32 8.G.B.6 KDS A B C D 1 Level 2: Skill/Concept 33 8.NS.A.2 KDS A B C D E 1 Level 1: Recall 34 8.NS.A.1 KDS A B C D 1 Level 1: Recall F 35 8.NS.A.1 KDS A B C D 1 Level 1: Recall 36 8.F.B.4 KDS A B C D 1 Level 1: Recall 37 8.F.B.4 KDS A B C D 1 Level 2: Skill/Concept 38 8.NS.A.1 KDS A B C D 1 Level 1: Recall 39 8.G.B.8 KDS A B C D 1 Level 2: Skill/Concept 40 8.NS.A.1 KDS A B C D 1 Level 1: Recall 41 8.EE.A.2 KDS Level 1: Recall 42 8.F.B.4 KDS A B C D E 1 Level 2: Skill/Concept 43 8.F.B.5 KDS A B C D 1 Level 1: Recall F Powered by SchoolCity Inc. Page 3 of 44

4 Standard Summary Standard Bloom's Taxonomy Create Evaluate Analyze Apply Understand Remember N/A Total 8.NS.A.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. 8.NS.A.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π²). 8.EE.A.2 Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that 2 is irrational. 8.F.B.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. 8.F.B.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. 8.G.B.6 Explain a proof of the Pythagorean Theorem and its converse. 8.G.B.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. 8.G.B.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. 8.G.C.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems Total: Powered by SchoolCity Inc. Page 4 of 44

5 Items and Rubric / Rationale Item #: 1 ID: KDS Simplify: x 2 = A A Student(s) reduced the fraction but failed to find the root. B Student(s) found the square root but failed to remove the radical sign. B C 9 16 C Student(s) reduced the fraction but failed to find the square root. D Correct answer D 3 4 Item #: 2 ID: KDS A right triangle has legs of 8 units and 10 units. Use the Pythagorean Theorem to solve for the hypotenuse. A B 164 C D A Student(s) likely solved a + b = H squared. B Student(s) likely calculated a squared + b squared. C Correct answer D Student(s) likely calculated a + b = H squared, then simplified. Powered by SchoolCity Inc. Page 5 of 44

6 Item #: 3 ID: KDS Squares are constructed on the legs of a right triangle, as pictured. The area of the small square is 40 square units and the area of the large square is 80 square units. If another square is constructed on the remaining side of the triangle (the hypotenuse), what will its area be? A Student(s) may have only found the lengths of the legs and added them. B Student(s) likely found the lengths of the legs and multiplied them. C Correct answer D Student(s) likely multiplied areas of the squares constructed on the legs. A square units B square units C 120 square units D 3,200 square units Item #: 4 ID: KDS Damon is playing with his remote controlled car. A Correct answer Powered by SchoolCity Inc. Page 6 of 44

7 He increases its speed for 15 seconds. He stays approximately the same speed for the next 15 seconds. He increases its speed again for 10 seconds. He then slows it down to a stop for the last 20 seconds. Select the graph that best represents Damon's remote controlled car speed over time. B Student(s) may have mixed up the speed axis with the time axis. C Student(s) may not have matched up the seconds from the prompt but only chose this based on the shape. D Student(s) may have mixed up increasing with decreasing. A B Powered by SchoolCity Inc. Page 7 of 44

8 C D Powered by SchoolCity Inc. Page 8 of 44

9 Item #: 5 ID: KDS A satellite radio company charges a one time fee of $36 for installation. The company also charges $42 per month for use. Based upon this information, complete this table showing the total cost of using the satellite radio after each month listed. Month Total Cost 1 $ 2 $ 3 $ 4 $ 5 $ Correct Answer: Powered by SchoolCity Inc. Page 9 of 44

10 Item #: 6 ID: KDS Let the numbers below represent the lengths of the sides of a triangle. Which of the triangles is a right triangle? I. 4, 5, 6 II. 6, 8, 10 III. 5, 13, 14 IV. 7, 11, 13 A I B II C III D IV A Student(s) may have guessed or may not have understood that the Pythagorean Theorem was necessary to solve this problem B Correct answer C Student(s) may have guessed, or may have miscalculated to find that the square of 14 is 194, not 196. D Student(s) may have guessed, or may have miscalculated to find that the square of 13 is 170, not 169. Powered by SchoolCity Inc. Page 10 of 44

11 Item #: 7 ID: KDS A cylinder has a volume of 1200 meters cubed. What is the volume of a cone with the same radius and height? A 400 m 3 B 900 m 3 C 1600 m 3 D 3600 m 3 A Correct answer B Student(s) may have mistakenly determined that the formula for the volume of a cone is V = 4/3πr 2 instead of V = 1/3πr 2 h, and they may have mistakenly divided the volume of the cylinder by 4/3 instead of multiplying it by 4/3. C Student(s) may have mistakenly determined that the formula for the volume of a cone is V = 4/3πr 2 h instead of V = 1/3πr 2 h. D Student(s) may have correctly determined that the formula for the volume of a cone is V = 1/3πr 2 h, but they may have mistakenly divided the volume of the cylinder by 1/3 instead of multiplying it by 1/3. Powered by SchoolCity Inc. Page 11 of 44

12 Item #: 8 ID: KDS If the diameter of the circle below is 18 units and point o is the center of the circle, what is the length of side x? A Student(s) may have forgotten to square the sides before adding them together (9 + 9 = 18 instead of = 162). A B C D B Student(s) may have mistaken the diameter to be the length of the sides of the triangle and added them together without squaring each side first ( = 36 instead of = 162). C Correct answer D Student(s) may have used the diameter for the side lengths instead of the radius ( = 648). Powered by SchoolCity Inc. Page 12 of 44

13 Item #: 9 ID: KDS A ladder 16 ft long is leaning against a building. If the base of the ladder is 4 ft from the building, how high up the building will the ladder reach? A B C D A Student(s) may have improperly used the Pythagorean Theorem by setting up the equation 4+x 2 =16 instead of 4 2 +x 2 =16 2 and simplified when solving for the distance the ladder reaches up the building. B Student(s) may have improperly used the Pythagorean Theorem by setting up the equation x 2 4=16 instead of 4 2 +x 2 =16 2 and simplified when solving for the distance the ladder reaches up the building. C Correct answer D Student(s) may have improperly used the Pythagorean Theorem by setting up the equation =x 2 instead of 4 2 +x 2 =16 2 and simplified when solving for the distance the ladder reaches up the building. Powered by SchoolCity Inc. Page 13 of 44

14 Item #: 10 ID: KDS The square root of 1000 is between. A 498 and 502 B 98 and 102 C 48 and 52 D 28 and 32 A Student(s) may have divided by 2 to find the square root. B Student(s) may have mistakenly believed that since 10 is the square root of 100, 10(10) is the square root of 10(100). C Student(s) may have known 10 2 = 100 and = 10,000, and concluded that 50 2 must be near D Correct answer Powered by SchoolCity Inc. Page 14 of 44

15 Item #: 11 ID: KDS A cone with a height of 50 meters has a volume of 5400π meters cubed. What is the radius of the cone? A 6 m B 12 m C 18 m D 36 m A Student(s) may have divided 5400 by 50, divided the result by 3 instead of multiplying by 3, and then found the square root to arrive at the radius of the cone. B Student(s) may have divided 5400 by 50, divided the result by 3 instead of multiplying by 3, and then found the square root to arrive at the radius of the cone, and then they may have confused the cone's diameter with its radius. C Correct answer D Student(s) may have confused the cone's diameter with its radius. Powered by SchoolCity Inc. Page 15 of 44

16 Item #: 12 ID: KDS The sides of a square are 10 inches long. How long is the diagonal of the square? A 20 in. B C 10 in. D A Student(s) may have found the sum of the two sides instead of using the Pythagorean Theorem. B Correct answer C Student(s) may have attempted to answer the question without recognizing the need for the Pythagorean Theorem. D Student(s) may have forgotten to square the side lengths before taking the square root. Powered by SchoolCity Inc. Page 16 of 44

17 Item #: 13 ID: KDS In the right triangle shown, what is the value of PQ? A Student(s) may have thought that the height and base add up to the hypotenuse and simply subtracted 15 from 17 to get 2. A 2 cm B 4 cm C 8 cm D 16 cm B Student(s) may have thought that the height is the square root of the average between the base and the hypotenuse. Student(s) may have added the two numbers together, divided by 2, and then taken the square root. C Correct answer D Student(s) may have thought that the height is the average between the base and the hypotenuse and simply added the two numbers together and divided by 2. Powered by SchoolCity Inc. Page 17 of 44

18 Item #: 14 ID: KDS Which of the following statements is correct? Select two that apply. A 3.14 is rational, and 22 7 is rational. B 3.14 is irrational, and 22 7 is rational. C π is irrational, and 3.14 is irrational. D π is rational, and 3.14 is irrational. A Correct answer B Student(s) may have correctly determined that any number that can be written as a fraction is a rational number, but they may have not realized that 3.14 can be written as a fraction. C Student(s) may have correctly determined that π is an irrational number, but they may have mistakenly thought that 3.14 is equal to π rather than an approximation for π. E 22 7 F 22 7 is rational, and π is irrational. is irrational, and π is irrational. D Student(s) may have confused rational and irrational numbers. E Correct answer F Student(s) may have correctly determined that π is an irrational number, but they may have mistakenly thought that 22/7 is equal to π rather than an approximation for π. Powered by SchoolCity Inc. Page 18 of 44

19 Item #: 15 ID: KDS Which of the following irrational numbers are located between 6 and 8 on the number line? Select three that apply. A 2 15 B C 8 5 D A Correct answer B Correct answer C Student(s) may have thought that 5 was less than 2. D Correct answer E Student(s) may have known that 80 was approximately 9. E 80 3 Powered by SchoolCity Inc. Page 19 of 44

20 Item #: 16 ID: KDS How many cubic liters are in the cylinder below? A Correct answer B Student(s) may have used the formula 2π rh instead of π r 2 h. C Student(s) may have converted the volume in cubic milliliters to liters instead of cubic liters. A 0.8 π (L 3 ) B 4 π (L 3 ) D Student(s) may have found the volume of the cylinder in cubic milliliters instead of cubic liters. C 800,000 π (L 3 ) D 800,000,000 π (L 3 ) Powered by SchoolCity Inc. Page 20 of 44

21 Item #: 17 ID: KDS If 3 is written as a decimal, will the digits 7 after the decimal eventually repeat? A 3 Yes, because is an irrational 7 number. A Student(s) may have correctly determined that the digits after the decimal will eventually repeat, but they may have misidentified the reason why. B Correct answer B 3 Yes, because 7 number. is a rational C Student(s) may have incorrectly identified the type of number that 3/7 is. C No, because 3 7 number. D No, because 3 7 number. is an irrational is a rational D Student(s) may have correctly identified the type of number that 3/7 is, but they may have misinterpreted what this means. Powered by SchoolCity Inc. Page 21 of 44

22 Item #: 18 ID: KDS Which of these statements is true about? A It is irrational, because it can be written as a fraction with an integer in the numerator and the denominator. B It is irrational, because it cannot be written as a fraction with an integer in the numerator and the denominator. C It is rational, because it can be written as a fraction with an integer in the numerator and the denominator. D It is rational, because it cannot be written as a fraction with an integer in the numerator and the denominator. A Student(s) may have correctly determined that is irrational, but they may have misidentified the reason why. B Correct answer C Student(s) may have incorrectly determined that is rational, but they may have correctly determined the reason why it would have been rational. D Student(s) may have correctly determined that cannot be written as a fraction with an integer in the numerator and the denominator, but they may have misinterpreted what this means. Powered by SchoolCity Inc. Page 22 of 44

23 Item #: 19 ID: KDS Find the slant height of the cone. Round to the nearest tenth. A Student(s) may have misunderstood the Pythagorean theorem and only added half base plus height. B Correct answer A 20.0 B 14.4 C 10.0 C Student(s) may not have known how to proceed and halved both 16 and 12. D Student(s) may not have known how to proceed and guessed. D 8.9 Powered by SchoolCity Inc. Page 23 of 44

24 Item #: 20 ID: KDS A can of vegetables has a diameter of 3 inches and a height of 5 inches. The given formula can be used to determine the volume (V) of a cylinder: V = Bh = area of base height Which of the following is the approximate volume of the can? Use 3.14 for π. A 35 in. 3 B 47 in. 3 C 141 in. 3 A Correct answer B Student(s) may have used the circumference formula instead of the area formula when finding B. C Student(s) may have squared the diameter instead of the radius when finding the area of the base. D Student(s) may have multiplied 3 5 pi to find B, having blended the area formulas of a circle and of a quadrilateral. D 236 in. 3 Powered by SchoolCity Inc. Page 24 of 44

25 Item #: 21 ID: KDS What is the volume of a spherical water balloon with a radius of 6 inches? A 48π in 3 B 144π in 3 C 288π in 3 D 864π in 3 A Student(s) may have squared the radius instead of cubing the radius when using the formula for the volume of a sphere. B Student(s) may have squared the radius instead of cubing the radius when using the formula for the volume of a sphere, and they may have used 4 instead of 4/3 in the formula. C Correct answer D Student(s) may have used 4 instead of 4/3 in the formula for the volume of a sphere. Powered by SchoolCity Inc. Page 25 of 44

26 Item #: 22 ID: KDS Which of these cone shaped funnels has a volume of 1350π square centimeters? A a funnel with a radius of 15 cm and a height of 18 cm B a funnel with a radius of 15 cm and a height of 30 cm C a funnel with a radius of 18 cm and a height of 15 cm D a funnel with a radius of 30 cm and a height of 15 cm A Correct answer B Student(s) may have used 3 instead of 1/3 and forgotten to square the radius when using the formula for the volume of a cone. C Student(s) may have confused the radius with the height when using the formula for the volume of a cone. D Student(s) may have confused the radius with the height when using the formula for the volume of a cone, and they may have used 3 instead of 1/3 and forgotten to square the height. Powered by SchoolCity Inc. Page 26 of 44

27 Item #: 23 ID: KDS Which of these describes the function graphed below? A Student(s) may have noticed that the graph appears to be almost horizontal as x approaches negative infinity, and they may have mistakenly concluded that this means that there is a linear relationship between x and y when x is negative. A There is a linear relationship between x and y when x < 0. B There is a linear relationship between x and y when x > 0. C There is never a linear relationship between x and y. D There is always a linear relationship between x and y. B Student(s) may have noticed that the graph appears to be almost horizontal as x approaches negative infinity, and they may have mistakenly concluded that this means that there is a linear relationship between x and y when x is negative, confusing the greater than sign with a less than sign. C Correct answer D Student(s) may have confused an exponential function with a linear function. Powered by SchoolCity Inc. Page 27 of 44

28 Item #: 24 ID: KDS Ian used the Pythagorean Theorem to find the distance between two points as follows. a 2 + b 2 = c 2 (11 2) 2 + (3 15) 2 = c ( 12) 2 = c = c = c 2 c = 15 Which of these pairs of points could he have been finding the distance between? A ( 2, 15) and (11, 3) B (2, 15) and (11, 3) C (11, 2) and (3, 15) D (11, 2) and (3, 15) A Student(s) may have mistakenly put negative signs in front of the x and y coordinates of the first point, since in Ian's calculation, he is subtracting the x and y coordinates of the first point from those of the second point. B Correct answer C Student(s) may have mistakenly grouped the x coordinates of the two points together as one point and the y coordinates of the two points together as another point, and they may have put negative signs in front of the x and y coordinates of the first point, since in Ian's calculation, he is subtracting the x and y coordinates of the first point from those of the second point. D Student(s) may have mistakenly grouped the x coordinates of the two points together as one point and the y coordinates of the two points together as another point. Powered by SchoolCity Inc. Page 28 of 44

29 Item #: 25 ID: KDS Between what two integers is the value of π 2? π = A 3 and 4 B 5 and 6 C 6 and 7 D 9 and 10 A Student(s) may have mistakenly identified the two integers that π is between as the correct answer. B Student(s) may have mistakenly identified the two integers that π + 2 is between as the correct answer. C Student(s) may have mistakenly identified the two integers that 2π is between as the correct answer. D Correct answer Powered by SchoolCity Inc. Page 29 of 44

30 Item #: 26 ID: KDS Find the length (d) of the diagonal of a rectangular prism with a height of 6 cm, whose base diagonal length is 12 cm. A Student(s) may have neglected to find the sum of the squares of the legs when using the Pythagorean Theorem and solved = d 2 to find the length of the diagonal of the prism. A B C D 12 cm B Student(s) may have treated the diagonal of the base as the hypotenuse of the right triangle and solved d 2 = 12 2 to find the length of the diagonal of the prism. C Correct answer D Student(s) may have assumed that all the diagonals of the prism were the same length, and did not think it was necessary to apply the Pythagorean Theorem. Powered by SchoolCity Inc. Page 30 of 44

31 Item #: 27 ID: KDS Which of the following is equivalent to 0.2? A 1 5 B 2 9 C 2 7 D 1 2 A Student(s) may have ignored the bar above the 2. B Correct answer C Student(s) may have correctly reasoned that 2 is greater than 2/10, so if the numerator is 2, then the denominator is less than 10, but they may have mistakenly chosen a number that is greater than 2/10. D Student(s) may have mistakenly chosen the fraction with 2 in the denominator, since the decimal has a repeating 2. Item #: 28 ID: KDS What is the distance between the points (4, 2) and ( 1, 10)? A 5 units B 6 units C 12 units D 13 units A Student(s) may have mistakenly found the horizontal distance between the points. B Students may have mistakenly found the difference between the x and y coordinates of the first point. C Student(s) may have mistakenly found the vertical distance between the points. D Correct answer Powered by SchoolCity Inc. Page 31 of 44

32 Item #: 29 ID: KDS Which of the following is equivalent to 0.3? A B 1 30 C 3 10 D 1 3 A Student(s) may have ignored the bar above the 3 in the decimal, and they may have then been off by a factor of 10 in their answer. B Student(s) may have correctly interpreted the bar above the 3 in the decimal, but may have been off by a factor of 10 in their answer. C Student(s) may have ignored the bar above the 3 in the decimal. D Correct answer Item #: 30 ID: KDS Assume a and b are legs of a right triangle and c is the hypotenuse. Solve for the missing length using the Pythagorean Theorem. a = 3x, b = 4y, c = A c = 5xy B c = 9x y 2 C c = 9x y 2 D c = 5 x 2 + y 2 A Student(s) may have forgotten that terms with different variables cannot be combined. B Student(s) may have forgotten to take the square root of the sum of the squares. C Correct answer D Student(s) may have thought the coefficients could be combined separately from the variables. Powered by SchoolCity Inc. Page 32 of 44

33 Item #: 31 ID: KDS A spherical tank has a radius of 6 feet. Frankie filled the tank with gasoline at a rate of 23 cubic feet per minute. At this rate, how long will it take Frankie to completely fill the tank without it overflowing? Round your answer to the nearest minute. minutes Correct Answer: 39 Item #: 32 ID: KDS A Student(s) did not understand that a 2 + b 2 represents the adding of the two squares. B Student(s) may not have realized the sides are the same by definition in the diagram explanation. Given: ΔABC is a right triangle There are 3 shaded squares with sides a, b, and c, respectively. a, b, and c are also the lengths of the sides of the right triangle, such that the area of the square with side a is a 2 and the area of the square with side b is b 2 and the area of the square with side c is C Student(s) recognized that this fact is not relevant to the Pythagorean Theorem. D Correct answer Powered by SchoolCity Inc. Page 33 of 44

34 c 2. Prove: a 2 + b 2 = c 2 (Pythagorean Theorem) Proving which of the following will prove the Pythagorean Theorem? A When you subtract the area of the smallest square from the medium square the difference equals the area of the largest square. B The sides of a right triangle are also the sides of squares. C m A + m B = m C D The area of the two smaller squares will add up to the area of the largest square. Powered by SchoolCity Inc. Page 34 of 44

35 Item #: 33 ID: KDS Which of the following numbers is to the right of 6 on a number line? Select two that apply. A 2 B 7 C 23 D 47 E 79 F 91 A Student(s) may have mistakenly assumed that numbers on a number line decrease from left to right. B Student(s) may have mistakenly compared 6 to 7 instead of 6 to 7. C Student(s) may not have noticed the negative sign, and they may have mistakenly compared 6 to 23 instead of 6 to 23. D Correct answer E Student(s) may have not noticed the negative sign. F Correct answer Powered by SchoolCity Inc. Page 35 of 44

36 Item #: 34 ID: KDS Which of the following is equivalent to 2 11? A 0.18 B 0.18 C D A Student(s) may have correctly determined the first two digits of the decimal equivalent of the fraction, but they may have forgotten to place a bar above these digits to show that they repeat. B Correct answer C Student(s) may have correctly determined the first three digits of the decimal equivalent of the fraction, but they may have mistakenly assumed that this is the correct answer, not recognizing that the first two digits repeat. D Student(s) may have correctly determined the first three digits of the decimal equivalent of the fraction, but they may have mistakenly assumed that these three digits repeat, instead of only the first two digits. Powered by SchoolCity Inc. Page 36 of 44

37 Item #: 35 ID: KDS Can a decimal that has repeating digits after the decimal point be converted into a fraction? A Yes, because the decimal is rational, and all rational numbers can be converted to fractions. B No, because the decimal is irrational, and no irrational numbers can be converted to fractions. C It depends on the number of digits that repeat. D It depends on what the digits are that repeat. A Correct answer B Student(s) may have correctly determined that no irrational numbers can be converted to fractions, but they may have mistakenly determined that a decimal with repeating digits after the decimal point is irrational. C Student(s) may have correctly determined that a decimal with repeating digits after the decimal point is rational, but they may have mistakenly determined that only rational numbers with a certain number of repeating digits can be converted to fractions. D Student(s) may have correctly determined that a decimal with repeating digits after the decimal point is rational, but they may have mistakenly determined that only rational numbers with certain digits that repeat can be converted to fractions. Powered by SchoolCity Inc. Page 37 of 44

38 Item #: 36 ID: KDS A hot air balloon was flying at an altitude of 300 meters when the pilot decided to land by descending at a rate of 2 meters per second. For which of these functions does y represent the altitude of the hot air balloon if x represents the number of seconds since the pilot started her landing? A Student(s) may have correctly made the slope of the model equation negative, but they may have mistakenly also made the y intercept of the equation negative. B Correct answer A y = 2x 300 B y = 2x C y = 2x 300 D y = 2x C Student(s) may have mixed up the signs of the slope and y intercept of the model equation. D Student(s) may have correctly made the y intercept of the model equation positive, but they may have mistakenly also made the slope of the equation positive. Powered by SchoolCity Inc. Page 38 of 44

39 Item #: 37 ID: KDS Before a blizzard, there were already 12 inches of snow on the ground, and after the blizzard, there were 36 inches of snow on the ground. If it snowed at a constant rate during the blizzard, and if the blizzard lasted for 6 hours, for which of these functions does y represent the number of inches of snow on the ground if x represents the number of hours since the blizzard started? A Student(s) may have mistakenly determined the equation of the model function by dividing 36 inches by 12 inches to find the slope and by using the number of hours the blizzard lasted as the y intercept. B Correct answer A y = 3x + 6 B y = 4x + 12 C y = 6x + 3 D y = 12x + 4 C Student(s) may have mistakenly determined the equation of the model function by using the number of hours the blizzard lasted as the slope and by dividing 36 inches by 12 inches to find the y intercept. D Student(s) may have mixed up the slope and the y intercept of the model function. Powered by SchoolCity Inc. Page 39 of 44

40 Item #: 38 ID: KDS Does the number 30 have a decimal expansion? A No, because it is rational. B No, because not every number has a decimal expansion. C Yes, because it is irrational. D Yes, because every number has a decimal expansion. A Student(s) may have correctly determined that 30 is rational, but they may have mistakenly assumed that only irrational numbers have a decimal expansion. B Student(s) may have mistakenly assumed that there are some numbers without a decimal expansion, and 30 is one of them. C Student(s) may have mistakenly determined that 30 is irrational, and they may have mistakenly assumed that only irrational numbers have a decimal expansion. D Correct answer Powered by SchoolCity Inc. Page 40 of 44

41 Item #: 39 ID: KDS Points R and S are plotted on the coordinate plane below. A Student(s) may have found, rather than. B Student(s) may have used 6 and 4 as the horizontal and vertical distances, i.e. may not have realized that the scale of the graph was 2. C Correct answer What is the distance between points R and S, to the nearest tenth of a unit? D Student(s) may have added the horizontal and vertical distances (12 units and 8 units, respectively). A 6.3 B 7.2 C 14.4 D 20.0 Powered by SchoolCity Inc. Page 41 of 44

42 Item #: 40 ID: KDS Suppose that a number written as a decimal has an infinite number of non repeating digits after the decimal point. What is this number called? A irrational B natural C rational D unnatural A Correct answer B Student(s) may have confused a positive number that has no digits after the decimal point with a positive number that has an infinite number of non repeating digits after the decimal point. C Student(s) may have confused a number that can be written with a finite number of digits after the decimal point with a number that has an infinite number of non repeating digits after the decimal point. D Student(s) may have mistakenly concluded that since a number with an infinite number of non repeating digits after the decimal point is not natural, it must be the opposite of natural. Item #: 41 ID: KDS An equation is shown below with a missing value. Enter the missing value into the box in the equation. 8 = 3 Correct Answer: 512 Item #: 42 ID: KDS Powered by SchoolCity Inc. Page 42 of 44

43 Look at the table shown below. x y Which situation(s) could be modeled by the table shown? Select two that apply. A A driver already drove 10 miles. Now she is driving at a rate of 28 miles per hour. B A driver already drove 38 miles. Now she is driving at a rate of 56 miles per hour. A Correct answer B Student(s) may have subtracted 38 from 94 to get 56 and may have thought that the y value of 38 was the initial value. C Student(s) may have subtracted 38 from 94 to get 56 and may have thought that the rate of change was the initial value. D Correct answer E Student(s) may have subtracted 38 from 94 to get 56. C A shopper needs to buy shelves for $56 each. He will also purchase $28 in other merchandise. F Student(s) may have thought that the y value of 38 was the initial value. D A shopper needs to buy shelves for $28 each. He will also purchase $10 in other merchandise. E A student read 10 pages in her book already and is currently reading at a rate of 56 pages per hour. F A student read 38 pages in her book already and is currently reading at a rate of 28 pages per hour. Powered by SchoolCity Inc. Page 43 of 44

44 Item #: 43 ID: KDS In which of these quadrants of the graph shown is y increasing as x is increasing? Select two that apply. A Student(s) may have confused the upper right quadrant with the upper left quadrant. B Correct answer C Student(s) may have confused the lower left quadrant with the lower right quadrant. A Quadrant I (the upper right quadrant) D Correct answer B Quadrant II (the upper left quadrant) C Quadrant III (the lower left quadrant) D Quadrant IV (the lower right quadrant) Powered by SchoolCity Inc. Page 44 of 44