Tennessee Comprehensive Assessment Program TCAP TNReady Integrated Math II Part I PRACTICE TEST Student Name Teacher Name Tennessee Department of Education
Integrated Math II, Part I Directions This booklet contains constructed-response items and selectedresponse items in Integrated Math II. For constructed-response items, write your answer in the space provided. For selected-response items, circle the correct answer(s). You MAY use a calculator with all test items in this test booklet. Sample A: Constructed-Response The sum of two consecutive odd integers is 72. 1. Write an algebraic equation to determine the two integers. 2. What are the two integers? Write your answers in the spaces provided. 1. 2. Sample B: Selected-Response Factor the polynomial: s 2 + 12s + 32 A. (s + 4)(s 8) B. (s 2)(s + 16) C. (s + 4)(s + 8) D. (s + 16)(s + 2) Sample Answers A. B. 1. 2. x + x + 2 = 72 35, 37 1
Integrated Math II, Part I 32 1. Simplify the expression (3x 4 + 9x 3 7x + 15) + ( 6x 4 8x 2 + 5x 3). 734 2. Consider the function f (x) = x 2 2x. Graph the function f (x) on the coordinate plane. 2
Integrated Math II, Part I 1481 3. Consider the equation 3(x 5) 2 + 6 = 54. What value(s) of x makes the equation true? Enter one solution in each response box. If there is only one solution, leave one response box blank. 200 4. A quadratic equation has the following coefficients: a = 2, b = 3, and c = 3. Write the solution(s) of the equation. Enter one solution in each response box. If there is only one solution, leave one response box blank. 241 5. RST ~ UVW. The dilation that maps RST to UVW has a dilation factor of 2. The measure of angle R is 20 and the measure of angle S is 100. 3 What is the measure, in degrees, of angle W? 3
Integrated Math II, Part I 142 6. The length of one side of a shoebox is 8 cm more than twice the width. The base of the shoebox has an area of 72 cm 2. Write an equation to represent this situation with w representing the width. 187 7. A right triangle has leg lengths 0.3 centimeters and 0.4 centimeters. What is cosθ where θ is the smallest angle of the triangle? 526 8. A quadratic function is given as f (x) = 4x 2 + 8x + 10. Write an equivalent function by inserting the numerals 1 9 and operational signs (+, ) into the vertex form given. f (x) = (x ) 2 4
Integrated Math II, Part I 141 9. Each day, an investor deposits twice as much into the bank as she did the day before. Her initial investment is $3. Using the elements 1, 2, 3, 6, 9, and x, write an exponential equation to model her daily deposit, y, on day x. y = ( ) 481 10. The equation y = 2(x 1) 2 + 18 is used to determine the profit earned, y, from the sales of product, with x representing the price per unit sold. Plot the points representing the x-intercept(s), y-intercept(s), and maximum or minimum point, whichever one is appropriate, on the coordinate grid provided. 5
Integrated Math II, Part I 239 11. Chris is looking up at the top of a tree. He is standing 20 feet from the tree, and his line of sight is 35 from horizontal. His eyes are 5 feet above the ground. To the nearest foot, how tall is the tree? 1815 12. A quadratic function is given as f (x) = 3x 2 + 24x + 25. Write the vertex form of the given function. 6
Tennessee Comprehensive Assessment Program TCAP TNReady Integrated Math II Part II PRACTICE TEST Student Name Teacher Name Tennessee Department of Education
Integrated Math II, Part II, Subtest 1 Directions Subtest 1 of this booklet contains constructed-response items and selected-response items in Integrated Math II. For constructed-response items, write your answer in the space provided. For selected-response items, circle the correct answer(s). You MAY NOT use a calculator in Subtest 1 of this test booklet. Sample A: Constructed-Response The sum of two consecutive odd integers is 72. 1. Write an algebraic equation to determine the two integers. 2. What are the two integers? Write your answers in the spaces provided. 1. 2. Sample B: Selected-Response Factor the polynomial: s 2 + 12s + 32 A. (s + 4)(s 8) B. (s 2)(s + 16) C. (s + 4)(s + 8) D. (s + 16)(s + 2) Sample Answers A. B. 1. 2. x + x + 2 = 72 35, 37 1
Integrated Math II, Part II, Subtest 1 1284 1. What is the best first step in solving the equation 3x 2 + 8x = 5? A. adding 5 to both sides B. dividing both sides by 3 C. taking the square root of both sides D. factoring an x out of the left side of the equation 4 2. Fannie is making a rectangular blanket. The length of the blanket is 10 inches greater than its width, w, in inches. Write the function, f (w), that describes the area, in square inches, of Fannie s blanket as a function of the width, w. 555 3. Simplify the expression (2 3i)(4 + 2i). A. 14 B. 6i C. 2 8i D. 14 8i 2
Integrated Math II, Part II, Subtest 1 1288 4. The length of a rectangle is 7 inches longer than its width. The area of the rectangle is 260 square inches. What is the length, in inches, of the rectangle? 465 5. Determine which statement is true in regard to ABC and LMN. A. ABC ~ LMN by AA criterion. B. ABC ~ LMN by SAS criterion. C. ABC ~ LMN by SSS criterion. D. ABC and LMN are not similar. 3
Integrated Math II, Part II, Subtest 1 1696 6. Which expression is the correct factorization of x 6 y 6? A. (x + y) 3 (x y) 3 B. (x 2 y 2 )(x 4 + 2xy + y 4 ) C. (x y)(x + y)(x 2 + xy + y 2 )(x 2 xy + y 2 ) D. (x y)(x 2 + 2xy + y 2 )(x + y)(x 2 2xy + y 2 ) 691 7. A function is graphed on the coordinate plane. Select the function that is graphed on the coordinate plane. A. f( x) x 1 2 B. f( x) x 1 2 C. f( x) x 2 1 D. f( x) x 2 1 4
Integrated Math II, Part II, Subtest 1 5900 8. Let c represent any non-zero rational number. Select all values that, when added to c, will produce an irrational number. A. 5 13 B. 2 C. 36 D. 8.73 E. 95 694 9. The function f(x) = x 2 3x 4 is graphed on the coordinate plane. Consider f (x 3). Which option correctly describes the transformation to the graph? A. up 3 units B. down 3 units C. left 3 units D. right 3 units 5
Integrated Math II, Part II, Subtest 2 Directions Subtest 2 of this booklet contains constructed-response items and selected-response items in Integrated Math II. For constructed-response items, write your answer in the space provided. For selected-response items, circle the correct answer(s). You MAY use a calculator in Subtest 2 of this test booklet. 1255 10. Consider the equation x 2 12x + 49 = 22. Which equation has the same solution(s) as the given equation? A. (x 6) 2 = 9 B. (x 7) 2 = 22 C. (x + 7) 2 = 4.7 D. (x 12) 2 = 27 769 11. A support wire is attached to the top of an antenna. The support wire connects to the ground 15 feet from the bottom of the antenna. The support wire and the ground meet at an angle with measure 70, as shown. To the nearest foot, what is the height of the antenna? 6
Integrated Math II, Part II, Subtest 2 1537 12. A survey asked whether students would eat food served in the school cafeteria. The results are recorded in the table shown. Grade Yes No 9th 67 33 10th 63 47 11th 32 68 12th 12 88 What is the probability that a tenth-grade student will not eat food served in the school cafeteria, rounded to the nearest hundredth? 134 13. Calvin purchases a piece of heavy machinery for $32,300. The value of the machine depreciates at an annual rate of 8.3%. Which function represents the value of the machine with an approximate equivalent monthly depreciation rate? A. B. C. D. 1 12 f( t) = 32,300(0.917 t 1 12 f( t) = 32,300(1.083 t f( t) = 32,300(0.917 12 f( t) = 32,300(1.083 12 1 1 12t 12t 7
Integrated Math II, Part II, Subtest 2 946 14. The graph of a system of equations is shown. What are the x-values for the solutions to this system? 8
Integrated Math II, Part II, Subtest 2 243 15. RSV ~ UST Select all statements that are true. A. STU is a right triangle. B. RS is 4 x cm in length. 3 C. VRS STU D. The area of RSV is 9 8 x cm2. E. m RVS m UST 90 1538 16. A healthcare company surveys customers to determine whether each customer would be willing to pay an additional $35 monthly for extra coverage. The results of the survey are shown. Would you pay extra? Age Yes No Below 50 38 55 50 or older 45 22 What is the probability a customer below the age of 50 would be willing to pay an extra $35 monthly? 9
Integrated Math II, Part II, Subtest 2 1802 17. The chart gives the number of people owning cell phones as a function of years. Years Number (in millions) 1977 2.1 1978 2.4 1979 2.6 1980 3.0 1981 3.3 1982 3.7 1983 4.1 The number of people owning cell phones, N(t), is modeled by the equation N(t)=A 0 P t, where t represents the number of years since 1977. What is the value of A 0? A. 0.30 B. 2.0 C. 1.80 D. 2.1 229 18. In the figure shown, cos(w ) = 0.60. What is sin(x )? A. 0.36 B. 0.40 C. 0.60 D. 0.80 10