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

Transcription

1 Released Form Spring 013 North Carolina Measures of Student Learning: NC s Common Exams Precalculus Public Schools of North Carolina State oard of Education Department of Public Instruction Raleigh, North Carolina Student ooklet Copyright 013 by the North Carolina Department of Public Instruction. ll rights reserved.

2 P RECLCULUS F ORM 1 What are the approximate rectangular coordinates for the point with polar coordinates (5, 30 )? (.5,.89) (.5, 4.33) C (.89, 4.33) D (4.33,.5) sequence is shown below. 6, 1, 0, 30, 4, 56,... Which is the recursive formula for this sequence? t n ( t 1) n n 1 n n1 t ( t 1)( n ) C n n1 t ( t ) ( n ) D t t 1 ( n 1) n n 1 Go to the next page.

3 P RECLCULUS F ORM 3 quadratic function, f, has zeros P and Q, such that P Q 5 and 1 1 P Q 8. Which choice describes f? f(x) = 8x 40x + 5 f(x) = 8x 40x 5 C f(x) = x 10x + 5 D f(x) = x 10x 5 4 Lucy invested $6,000 into an account that earns 6% interest compounded continuously. pproximately how long will it take for Lucy s investment to be valued at $5,000? 5.7 years 46.9 years C 4.5 years D 3.8 years 5 lamppost is located 418 feet from a building. The angle of elevation from the base of the lamppost to the top of the building is 3.3. pproximately how tall is the building? 3 feet 64 feet C 510 feet D 661 feet Go to the next page.

4 P RECLCULUS F ORM 6 Two functions are shown below. Tx ( ) x Px ( ) 10x What is the value of P(T(3)) T(P(3))? 8 4 C 0 D 4 7 piecewise function is shown below. x f( x) cx cx For what value of c does lim f( x) exist? 1 C 1 D 4 1, x 1, x 3 Go to the next page.

5 P RECLCULUS F ORM 8 What are the polar coordinates of (4, 9)? 97, 66 97, 114 C 13, 66 D 13, sequence is shown below. 1, 3, 3, 3 3,... How many terms of the sequence must be added together for the sum to equal 3,80? 6 7 C 8 D 9 4 Go to the next page.

6 P RECLCULUS F ORM 10 The first term of an infinite geometric sequence is. The sum of the sequence is 6. What is the common ratio of the sequence? C D Which is true of the series shown below? The series diverges. The series converges to 3. C The series converges to 4. 3 D The series converges to Go to the next page.

7 P RECLCULUS F ORM 1 Karen recursively generated a sequence of five positive integers by starting with a positive integer, a 1, and then applying the recursive formula an an1 3n 1 to generate a n for n =, 3, 4, and 5. If the value of a 5 was 407, what was the value of Karen s starting term, a 1? C 368 D What is the distance between y-intercepts of the graph of 4 6 C 11 D Which is a solution set to x { 1} { } C {, 1} D {, 1} 3x x? x 1 x 1 x 8 ( y 3 )? 6 Go to the next page.

8 P RECLCULUS F ORM 15 What is the range of the inverse of y = tan x? y y C 0 y D 0 y 16 James is standing 10 meters away from Samantha. bird is located in the sky at a point between where James and Samantha are standing. James is looking up at the bird at an angle of elevation of 74. Samantha is looking up at the bird at an angle of elevation of 47. pproximately how far is the bird from Samantha? 7.6 meters 8.5 meters C 11. meters D 13.1 meters 7 Go to the next page.

9 P RECLCULUS F ORM 17 What is the inverse function of f( x) log 5 (x 1)? f 1 x ( x) 5 1 f x 1 ( x) C f ( x) log (5x 1) 5x 1 1 D f ( x) log5 n lim 3 1 n n C 1 D r 8? 16 15sin circle ellipse C hyperbola D parabola 18 What is the value of the limit shown below? 19 What type of conic section is represented by 8 Go to the next page.

10 P RECLCULUS F ORM 0 James had a rectangular piece of cardboard that was four times as long as it was wide. He wanted to use the cardboard to make a box with no lid. To do this, he first cut a 3-by-3-inch square out of each of the four corners of the piece of cardboard, as shown in the picture below. Then James folded the cardboard along the four dotted lines shown in the picture. This created an open box with a volume of 336 cubic inches. What was the width of the sheet of cardboard that James started with? C D 10.5 inches 9.5 inches 8.5 inches 7.5 inches 1 Which expression is equivalent to cos sin sec sin? tan C D sin cot csc cos csc cot 9 Go to the next page.

11 P RECLCULUS F ORM Suppose that for each foot of land along the street, the annual tax is $5 per foot. The diagram below shows a plot of land ft 46 ft Street bout how much is the annual tax for the plot? $1,38 $1,93 C $1,31 D $1,411 3 The function Cx ( ).50x 1.00 models the cost per item for a company to x produce x items after the first item is made. What is the inverse function of C(x)? C D 1 C ( x) 1.00 x.50 1 C ( x) x C ( x) x C ( x).50 x Go to the next page.

12 P RECLCULUS F ORM 4 computer rental company charges $50 to rent a computer for one week. The table below shows the daily late fees the company charges if a computer is returned late. Days Late Daily Late Fee days 1 through 10 $5 days 11 through 0 $8 days 1 through 30 $10 What would be the total cost of renting a computer for one week and returning it 15 days late? $10 $15 C $140 D $170 5 From a point 100 feet from the base of a building, ngie looks up at a 40 angle to the top of a building. She walks 0 feet closer to the building. t approximately what angle must ngie now look up to see the top of the building? 3 46 C 60 D 77 This is the end of the multiple-choice portion of the test. 11 Go to the next page.

13 P RECLCULUS F ORM The questions you read next will require you to answer in writing. 1. Write your answers on separate paper.. e sure to write your name on each page. 1 The equation y 1 18 x represents the mirror inside a parabolic lamp. What is the focal width of the mirror? Use the equation to explain your answer t The function Pt () 1,440e models the number of cars a dealership sold t years after the first year it was open. y what percent is the number of cars being sold decreasing each year? How many cars did the dealership sell the year it opened? 3 Two parametric equations are shown below. x 3t y 4t 1 Convert the parametric equations into rectangular form. Determine what type of equation the rectangular form describes. 1 Go to the next page.

14 P RECLCULUS F ORM This is the end of the Precalculus test. 1. Look back over your answers.. Put all of your papers inside your test book and close the test book. 3. Place your calculator on top of the test book. 4. Stay quietly in your seat until your teacher tells you that testing is finished. 13

15 P RECLCULUS F ORM Precalculus Form Paper/Pencil Version Spring 013 nswer Key Item number Type Key Competency Goal(s) 1 MC D Relations and Functions MC D Relations and Functions 3 MC 1 Geometry and Measurement 4 MC D Relations and Functions 5 MC Relations and Functions 6 MC Relations and Functions 7 MC C Relations and Functions 8 MC Relations and Functions 9 MC C Relations and Functions 10 MC Relations and Functions 11 MC D Relations and Functions 1 MC D Relations and Functions 13 MC 1 Geometry and Measurement 14 MC Relations and Functions 15 MC Relations and Functions 16 MC C Relations and Functions 17 MC Relations and Functions 18 MC C Relations and Functions 19 MC C Relations and Functions 0 MC 1 Geometry and Measurement 1 MC D Relations and Functions MC Relations and Functions 3 MC Relations and Functions 1

16 P RECLCULUS F ORM Item number Type Key Competency Goal(s) 4 MC C Relations and Functions 5 MC Relations and Functions 6 CR Rubric 1 Geometry and Measurement 7 CR Rubric Relations and Functions 8 CR Rubric Relations and Functions Item Types: MC = multiple choice CR = constructed response