RELEASED. Spring 2013 North Carolina Measures of Student Learning: NC s Common Exams Common Core Math II

Transcription

1 Released Form Spring 2013 North arolina Measures of Student Learning: N s ommon Eams ommon ore Math II Public Schools of North arolina State oard of Education epartment of Public Instruction Raleigh, North arolina Student ooklet opright 2013 b the North arolina epartment of Public Instruction. ll rights reserved.

2 OMMON ORE M TH II F ORM 1 The equation s 2 5 can be used to estimate the speed, s, of a car in miles per hour, given the length in feet,, of the tire marks it leaves on the ground. car traveling 90 miles per hour came to a sudden stop. ccording to the equation, how long would the tire marks be for this car? 355 feet 380 feet 405 feet 430 feet 2 The heights of two different projectiles after the are launched are modeled b f() and g(). The function f() is defined as f() = The table contains the values for the quadratic function g. g() What is the approimate difference in the maimum heights achieved b the two projectiles? 0.2 feet 3.0 feet 5.4 feet 5.6 feet 1 Go to the net page.

3 OMMON ORE M TH II F ORM 3 cit map is placed on a coordinate grid. The post office is located at the point 5, 35, L 15, 10, and the fire station is P the librar is located at the point located at the point F 9, 25. What is the ratio of the length of PF to the length of LF? 2 : 3 3 : 2 2 : 5 3 : 5 4 Twent-one students at a school have an allerg to peanuts, shellfish, or both. Fourteen students at the school are allergic to peanuts. Twelve students at the school are allergic to shellfish. How man of the students are allergic to both peanuts and shellfish? Events M and N have probabilities such that PM ( ) 0.4, PN ( ) 0.28, PM ( N) 0.56, and PM ( N) re event M and event N independent? no, because PM ( ) PN ( ) PM ( N) no, because PM ( ) PN ( ) PM ( N) es, because PM ( ) PN ( ) PM ( N) es, because PM ( ) PN ( ) PM ( N) 2 Go to the net page.

4 OMMON ORE M TH II F ORM Which epression is equivalent to (3 17 1) ( 2 6)? Go to the net page.

5 OMMON ORE M TH II F ORM 7 Which graph displas the function f()=(2 + 3)( 2)? nswer choices and are on the following page. 4 Go to the net page.

6 OMMON ORE M TH II F ORM Go to the net page.

7 OMMON ORE M TH II F ORM 8 The sum of two numbers is 24. The sum of the squares of the two numbers is 306. What is the product of the two numbers? Which equation has eactl one real solution? = = = = 0 10 circular pond is modeled b the equation = 225. bridge over the pond is modeled b a segment of the equation 7 = 75. What are the coordinates of the points where the bridge meets the edge of the pond? (9, 12) and ( 12, 9) (9, 12) and (12, 9) (9, 12) and ( 12, 9) ( 9, 12) and (12, 9) 6 Go to the net page.

8 OMMON ORE M TH II F ORM 11 The volume, V, of a certain gas varies inversel with the amount of pressure, P, placed on it. The volume of this gas is 175 cm 3 when 3.2 kg/cm 2 of pressure is placed on it. What amount of pressure must be placed on 400 cm 3 of this gas? 1.31 kg/cm kg/cm kg/cm kg/cm 2 12 compan manufactures Vs. The compan spent $247,000 to develop its process for manufacturing the Vs. The compan spends an additional $1.25 to manufacture each V. Which function represents the average total cost per V,, for the compan to manufacture total Vs? , ,000 7 Go to the net page.

9 OMMON ORE M TH II F ORM 13 For a carnival game, a jar contains 20 blue marbles and 80 red marbles. hildren take turns randoml selecting a marble from the jar. If a blue marble is chosen, the child wins a prize. fter each turn, the marble is replaced. ase has drawn si red marbles in a row. Which statement is true? If ase selects another red marble, then 2 of her net 3 picks will be blue marbles because 2 blue marbles are selected for ever 8 red marbles selected. The probabilit that ase selects a blue marble on the net turn is higher than it was on her last turn because she has chosen so man red marbles in a row. The probabilit that ase selects a blue marble on her net turn is the same as it was on the last turn because selections are independent of each other. If ase draws 4 more times, she will select 2 blue marbles because the probabilit that a blue marble will be selected is 2 out of ever 10 turns. 14 plane intersects a regular triangular pramid. The plane is parallel to one of the faces of the pramid. What tpe of polgon is formed at the intersection? square right triangle isosceles trapezoid isosceles triangle 8 Go to the net page.

10 OMMON ORE M TH II F ORM 15 The number of bacteria in a culture can be modeled b the function N(t) = 28t 2 30t + 160, where t is the temperature, in degrees elsius, the culture is being kept. scientist wants to have fewer than 200 bacteria in a culture in order to test a medicine effectivel. What is the approimate domain of temperatures that will keep the number of bacteria under 200? 1.01 < t < < t < < t < < t < Go to the net page.

11 OMMON ORE M TH II F ORM 16 Which function is graphed below? 1 1 = sin = cos = tan = cot Go to the net page.

12 OMMON ORE M TH II F ORM 17 Which transformation will carr the rectangle shown below onto itself? +10 m a reflection over line m a reflection over the line = a rotation 90 counterclockwise about the origin a rotation 270 counterclockwise about the origin 11 Go to the net page.

13 OMMON ORE M TH II F ORM 18 Which statement must be true about the triangle below? P Q R PQ QS PR RT PQR PST ST 2 S T QR 19 The graph of f() = 2 will be translated 5 units up and 2 units to the right. Which function describes the graph produced b the translation? g() = g() = g() = g() = S T 12 Go to the net page.

14 OMMON ORE M TH II F ORM 20 n investment has a balance of $2,000 and earns 3.2% interest each ear. If $150 is added at the end of each ear b the account holder and no mone is withdrawn from the investment, which represents a function that can be used to calculate the investment balance for successive ears? n = n 1 + 2,000, o = 150 n = n , o = 2,000 n = n 1 + 2,000, o = 150 n = n , o = 2, What is the approimate length of HJ in the diagram below? 292 cm 265 cm 219 cm 196 cm 100 cm H G 30 I 60 J K 80 cm 13 Go to the net page.

15 OMMON ORE M TH II F ORM 22 ngles F and G are complementar angles. s the measure of angle F varies from a value of to a value of, sin(f) increases b 0.2. How does cos(g) change as F varies from to? It increases b a greater amount. It increases b the same amount. It increases b a lesser amount. It does not change. 23 If t is an unknown constant, which binomial must be a factor of 7m m tm 2t? 7m + t m t m + 2 m 2 24 The value, V, of a car can be modeled b the function V(t) = 13,000(0.82) t, where t is the number of ears since the car was purchased. To the nearest tenth of a percent, what is the monthl rate of depreciation? 1.5% 1.6% 9.2% 18.0% 14 Go to the net page.

16 OMMON ORE M TH II F ORM 25 Which epression is equivalent to ? This is the end of the multiple-choice portion of the test. 15 Go to the net page.

17 OMMON ORE M TH II F ORM The questions ou read net will require ou to answer in writing. 1. Write our answers on separate paper. 2. e sure to write our name on each page. 1 In the figure below, a pole has two wires attached to it, one on each side, forming two right triangles. ased on the given information, answer the questions below. How tall is the pole? How far from the base of the pole does Wire 2 attach to the ground? How long is Wire 1? Wire 1 Wire ft 38 2 The amount of time it takes to build a road varies inversel with the number of workers building the road. Suppose it takes 50 workers 8 months to build the road. What is the constant of variation? Write an equation that could be used to determine how long it would take n workers to build the road. (e sure to define the variables.) How much faster would 60 workers build the road than 50 workers? 16 Go to the net page.

18 OMMON ORE M TH II F ORM 3 The function f() is defined as f() = The function g() is defined as g() = 3f() + 2. Graph g() for 2 2. escribe the transformations that take the function f() onto g(). Write a new function, h(), that transforms g() back onto f(). 17 Go to the net page.

19 OMMON ORE M TH II F ORM This is the end of the ommon ore Math II test. 1. Look back over our answers. 2. Put all of our papers inside our test book and close the test book. 3. Place our calculator on top of the test book. 4. Sta quietl in our seat until our teacher tells ou that testing is finished. 18

20 OMMON ORE M TH II F ORM ommon ore Math II Form Spring 2013 nswer Ke Item number Tpe Ke onceptual ategor 1 M F Function 2 M F Function 3 M G Geometr 4 M S Statistics and Probabilit 5 M S Statistics and Probabilit 6 M lgebra 7 M lgebra 8 M lgebra 9 M lgebra 10 M lgebra 11 M lgebra 12 M lgebra 13 M S Statistics and Probabilit 14 M G Geometr 15 M F Function 16 M F Function 17 M G Geometr 18 M G Geometr 19 M F Function 20 M F Function 21 M G Geometr 22 M G Geometr 23 M lgebra 1

21 OMMON ORE M TH II F ORM Item number Tpe Ke onceptual ategor 24 M lgebra 25 M N Number and Quantit 26 R Rubric G Geometr 27 R Rubric lgebra 28 R Rubric F Function Item Tpes: M = multiple choice R = constructed response 2