Algebra II. Administered May 2013 RELEASED

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1 STAAR State of Teas Assessments of Academic Readiness Algebra II Administered Ma 0 RELEASED Copright 0, Teas Education Agenc. All rights reserved. Reproduction of all or portions of this work is prohibited without epress written permission from the Teas Education Agenc.

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3 STAAR ALGEBRA II REFERENCE MATERIALS STAARTM State of Teas Assessments of Academic Readiness GENERAL FORMULAS Slope of a line m = Quadratic formula FACTORING b = b ac a Difference of squares a b = ( a b)( a + b) Difference of cubes a b = ( a b)( a + ab + b ) Sum of cubes a + b = ( a + b)( a ab + b LOGARITHMS ) Product log ( ) = log + log b b b Quotient log b = log log b Power log ( ) = r log CONIC SECTIONS b ( ) r b b General form A + B + C + D + E + F = 0 Circle ( h) + ( k) = r Parabola ( h) = p ( k) ( k) = p ( h) Ellipse ( h) ( k) + a b = ( k) ( h) + a b = Hperbola ( h) ( k) a b = ( k) ( h) a b = Page

4 STAAR ALGEBRA II REFERENCE MATERIALS CIRCUMFERENCE Circle C = πr or C = πd AREA Triangle A = h b Rectangle or parallelogram A = bh Rhombus A = dd Trapezoid A = (b + b ) h Regular polgon A ap = Circle A = πr SURFACE AREA Lateral Total Prism S = Ph S = Ph +B Pramid S = Pl S = Pl + B Clinder S = πrh S = πrh + πr Cone S = πrl S = πrl + πr Sphere S = πr VOLUME Prism or clinder V = Bh Pramid or cone V = Bh Sphere V = πr Page

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7 Page 7 Algebra II

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9 DIRECTIONS Read each question carefull. For a multiple-choice question, determine the best answer to the question from the four answer choices provided. For a griddable question, determine the best answer to the question. Then fill in the answer on our answer document. Some values for the function f() = log are given in Table. Table Table f() g() ,000,000 0,000 0,000 Which function can generate all the values in Table? A g() = 0 B g() = 0 C g() = 0 D g() = 0 For what value of c will the graphs of = 6 + c and = ( 9) 8 be the same? F 6 G 80 H 99 J Page 9

10 The rectangular patio shown in the diagram below is enclosed on three sides b a fence. l Patio w House The area of this patio is no more than 00 square feet. The total length of the three sides of this fence is no more than 60 feet. Which sstem of inequalities can be used to find values of l, the patio s length, and w, the patio s width, that will satisf these conditions? A l + w 60 C l + w 60 lw 00 lw 00 B l + w 60 D l + w 60 lw 00 lw 00 Page 0

11 The graph of the quadratic function f is shown on the grid below What does the solution set for f() = 0 appear to be? F {.} G {., } H {7., 7.} J {7.,., 7.} The cost of printing cookbooks is $.09 per book plus a one-time setup fee of $9. All taes are included. Which of the following functions models a(), the average cost per book of printing cookbooks? 9 A a() =.09 + B a() = C a() = D a() = Page

12 6 Which graph best represents the parent function of = ( +)? F H G J 7 There were 7 cell phones sold at an electronics store in Januar. Since then, cell phone sales at this store have increased at a rate of.7% per month. At this rate of growth, which function can be used to determine the monthl cell phone sales m months after Januar? A p(m) = 7(0.07) m B p(m) = 7(.07) m (m + ) C p(m) = 7(0.96) (m + ) D p(m) = 7(0.07) Page

13 8 The graph of the function f is shown on the grid below Based on the graph, for what values of is f() > 0? F All real numbers greater than 0 G All real numbers greater than H All real numbers less than or greater than J All real numbers greater than and less than 9 The sum of a number, n, and its square root can be represented b the equation = n + n. If = 0, which of the following is true? A n = 6 B n = C n = 6 and n = D n = and n = Page

14 0 The graph of the function h was obtained from the graph of the function g using a composite transformation, as shown below. g 7 6 h Which equation can be used to describe h() in terms of g()? F h() = g( + ) + G h() = g( + ) H h() = g( ) J h() = g( ) + Page

15 A craftsman wants to spend less than $00 on supplies for making bracelets and necklaces. Supplies for bracelet cost $, and supplies for necklace cost $9. This relationship is shown in the graph below. Jewelr Supplies Supplies for Necklaces Supplies for Bracelets The craftsman wants to make at least 0 more bracelets than necklaces. Which of the following is a reasonable solution? A bracelets and 0 necklaces B 0 bracelets and necklaces C 0 bracelets and 0 necklaces D bracelets and necklaces Page

16 Which function s graph has a verte at (, ) and contains the point (, )? F = ( + ) 0 G = ( ) 0 H = ( ) + J = ( + ) + What value of p makes the equation below true? 9 p = Record our answer and fill in the bubbles on our answer document. Page 6

17 An equation in the form + = is graphed below. a b If the values of a and b remain the same, which graph best represents + =? b a F H G J Page 7

18 An object is launched into the air. The table below shows the object s height above the ground at various times. Height vs. Time Elapsed Time (seconds) 6 Height Above the Ground (meters) Based on the data in the table, which of the following is closest to the object s height above the ground 9 seconds after being launched? A 0 m B m C 0 m D 9 m Page 8

19 6 A quadratic function is graphed on the grid below If this function is written in the form = a( h) + k, what is the value of a? F G 8 H J Page 9

20 7 Which two transformations can be used to obtain the graph of g() = c from the graph of f() = if c > 0? A A translation to the right c units followed b a reflection across the -ais B A translation to the left c units followed b a reflection across the -ais C A translation to the right c units followed b a reflection across the -ais D A translation to the left c units followed b a reflection across the -ais 8 Which of the following is a solution to 0 =? F G H J Page 0

21 9 What is the -value of the solution to the sstem of equations below? + + z = 8 + = 6 + z = Record our answer and fill in the bubbles on our answer document. 0 The function below can be used to model the area of a rectangle in square inches, A, if the rectangle has a perimeter of 7 inches and a width of w inches. A = 6w w In this situation, which of the following best describes the domain of the function? F 0 < w < 6 G 0 < w < 7 H 0 < w < 8 J 0 < w < 6 Page

22 What is the inverse of h() = log ()? A h Ầ() = () B h Ầ() = () C h Ầ() = (log ) D h Ầ() = log () Page

23 A table of values for the quadratic function g is shown below g() Which of the following statements about the graph of g are true? I. The graph has a line of smmetr at = 7. II. The graph has a -intercept at (0, Ѝ0). III. The graph has an -intercept at (, 0). IV. The graph has a verte at (6, 8). F I and II onl G III and IV onl H I, II, and III onl J I, II, III, and IV The product of consecutive odd integers is 8. If represents the smaller integer, which equation can be used to find both integers? A ( + ) = 8 B ( + ) = 8 C ( + ) = 8 D ( + )( + ) = 8 Page

24 7 If is an element in the domain of f() =, what is the corresponding element in the range? Record our answer and fill in the bubbles on our answer document. The roots of a quadratic equation are given b the epression below. Which of the following is an equivalent epression? A B C D Page

25 6 An antibiotic is introduced into a colon of,000 bacteria during a laborator eperiment. The function below can be used to model the number of bacteria in the colon after m minutes. m n(m) =,000(0.8) 0 Which value is closest to the amount of time needed for the population of the colon to drop to 8,000 bacteria? F min G min H 8 min J min 7 The table below shows values of a quadratic function g. 0 g() Based on the table, in which interval can a solution to g() = 0 be found? A < < B < < C < < D < < Page

26 8 The given function models the equivalent resistance in ohms, R, when a fied 9-ohm resistor is connected in parallel with a variable resistor of ohms. 9 R = 9 + Which value of is closest to the number of ohms needed in the variable resistor for there to be an equivalent resistance, R, of 6. ohms? F. G 7.6 H.7 J. Page 6

27 9 For the functions h and g, which statement is true if h() = g( + )? A The graph of h is the result of the graph of g being translated right units and down units. B The graph of h is the result of the graph of g being translated left units and down units. C The graph of h is the result of the graph of g being translated right units and up units. D The graph of h is the result of the graph of g being translated left units and up units. 0 The graph of the eponential function f is shown on the grid below For what values of is f() > 6? F > G > 0 H < < J < < Page 7

28 What value of n makes 0 n = 7 true? Record our answer and fill in the bubbles on our answer document. Which equation has the same graph as + = 0? F = ( ) + 9 G = ( ) + H = ( ) + 9 J = ( ) + Page 8

29 A sector of a circle is shown below. r r The area, A, of the sector is relationship? π times the square of the radius, r. Which graph represents this A A A Area C Area 0 Radius r 0 Radius r A A B Area D Area 0 Radius r 0 Radius r Page 9

30 The hpotenuse of a right triangle is 7 inches long. A leg of this triangle,, is inch less than twice the length of the other leg,. Which sstem of equations can be used to determine the lengths of the legs of this right triangle in inches? F + = 89 = G + = 89 + = H + = 7 = J + = 7 + = What is the solution set for + = 6? A { i } B { } C { i } D { } Page 0

31 6 A plane intersects a double cone as shown below. What conic section is created b this intersection? F Circle G Ellipse H Hperbola J Parabola 7 Each ear an architecture firm emplos senior interns and junior interns. Senior interns receive $00 per week, and junior interns receive $00 per week. This ear a minimum of 7 but no more than interns will be hired. The amount spent per week on interns cannot eceed $,000. Which statement about this situation is not true? A The architecture firm can emplo junior interns. B The architecture firm can emplo senior interns and 7 junior interns. C If both tpes of interns are hired, the firm will spend a minimum of $,00 per week on interns. D If both tpes of interns are hired, the firm will spend a maimum of $,800 per week on interns. Page

32 8 Which table contains onl values in the solution set for +? F 9 7 H G 8 6 J What is the solution set for the following equation? = 9 A, C { 8, 6} B, D { 8, 6} Page

33 0 For what value of b will f() = + b + 00 have 0 as its onl zero? Record our answer and fill in the bubbles on our answer document. Which function is equivalent to its inverse? A f() = B g() = C h() = 7 D j() = Page

34 Which of the following gives the equations for all the vertical asmptotes of the graph of + f() =? ( + 8)( ) F = G = and = 8 H = and = J = 8 and = What is the range of f() = +? A All real numbers B All real numbers greater than or equal to 0 C All real numbers greater than or equal to D All real numbers less than or equal to Page

35 Which of the following ordered pairs is a solution to the sstem of inequalities given below? + < + < 8 F (, ) G (, ) H (, ) J (, ) A rectangular parking lot measures 0 feet b 0 feet. The owner of the parking lot will epand the lot s size b adding feet and feet to its dimensions, as shown below. 0 ft 0 ft If the total area of the parking lot cannot eceed 0,000 square feet, which inequalit can be used to find all possible values of? A (0 + )(0 + ) 0,000 B (0 + )(0 + ) 0,000 C (0 + )(0 + ) 0,000 D (0 + )(0 + ) 0,000 Page

36 6 Which tpe of transformation can be used to obtain the graph of g() = ( ) from the graph of f() =? F Vertical shrink G Vertical shift down H Vertical shift up J Vertical stretch 7 What is the greatest value in the domain of the function graphed below? A B 6 C D 7 Page 6

37 8 A function is graphed below. Which function is best represented b this graph? F = ( + ) + G = ( ) + H = + + J = + 9 The average speed of sound in air at t degrees Celsius can be found using the function below. The speed, s, is measured in meters per second. s = 0.0 t + 7. If sound is traveling in air at an average speed of 6. meters per second, which temperature is closest to the value of t? A 76 C B 0 C C C D 09 C Page 7

38 0 Defective Parts Number of Defective Parts (per 0,000) Week A factor began producing new parts. Data were collected on the number of defective parts per 0,000 parts produced. The graph shown displas some of the data for the first 0 weeks of production. Based on the graph, during which week were approimatel 0 defective parts per 0,000 produced? F Week G Week H Week 6 J Week 8 Page 8 BE SURE YOU HAVE RECORDED ALL OF YOUR ANSWERS ON THE ANSWER DOCUMENT. STOP

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40 STAAR Algebra II Ma 0 TX69 A B C D E Printed in the USA DPSS/ISD69