Introduction - Algebra I

Transcription

1 LIFORNI STNRS TEST lgebra I Introduction - lgebra I The following released test questions are taken from the lgebra I Standards Test. This test is one of the alifornia Standards Tests administered as part of the Standardized Testing and Reporting (STR) Program under policies set b the State oard of Education. ll questions on the alifornia Standards Tests are evaluated b committees of content eperts, including teachers and administrators, to ensure their appropriateness for measuring the alifornia academic content standards in lgebra I. In addition to content, all items are reviewed and approved to ensure their adherence to the principles of fairness and to ensure no bias eists with respect to characteristics such as gender, ethnicit, and language. This document contains released test questions from the alifornia Standards Test forms in 00, 00, 00, 00, and 00. First on the pages that follow are lists of the standards assessed on the lgebra I Test. Net are released test questions. Following the questions is a table that gives the correct answer for each question, the content standard that each question is measuring, and the ear each question last appeared on the test. The following table lists each reporting cluster, the number of items that appear on the eam, and the number of released test questions that appear in this document. Some of the released test questions for lgebra I are the same test questions found in different combinations on the Integrated Mathematics and alifornia Standards Tests and the Summative High School Mathematics alifornia Standards Test. NUMER OF NUMER OF REPORTING QUESTIONS ON RELESE TEST LUSTER EXM QUESTIONS Number Properties, Operations, and Linear Equations Graphing and Sstems of Linear Equations Quadratics and Polnomials Functions and Rational Epressions TOTL 80 In selecting test questions for release, three criteria are used: () the questions adequatel cover a selection of the academic content standards assessed on the lgebra I Test; () the questions demonstrate a range of difficult; and () the questions present a variet of was standards can be assessed. These released test questions do not reflect all of the was the standards ma be assessed. Released test questions will not appear on future tests. For more information about the alifornia Standards Tests, visit the alifornia epartment of Education s Web site at This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opright 008 alifornia epartment of Education.

2 LIFORNI STNRS TEST lgebra I THE NUMER PROPERTIES, OPERTIONS, N LINER EQUTIONS REPORTING LUSTER The following alifornia content standards are included in the Number Properties, Operations, and Linear Equations reporting cluster and are represented in this booklet b test questions. These questions represent onl some was in which these standards ma be assessed on the lgebra I alifornia Mathematics Standards Test. LIFORNI ONTENT STNRS IN THIS REPORTING LUSTER lgebra I Standard Set.0 Students identif and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers, including closure properties for the four basic arithmetic operations where applicable:. Students use properties of numbers to demonstrate whether assertions are true or false..0* Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. The understand and use the rules of eponents..0 Students solve equations and inequalities involving absolute values..0* Students simplif epressions prior to solving linear equations and inequalities in one variable, such as ( ) + ( ) =..0* Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step. Standard Set.0 Students use and know simple aspects of a logical argument:. Students eplain the difference between inductive and deductive reasoning and identif and provide eamples of each.. Students identif the hpothesis and conclusion in logical deduction.. Students use countereamples to show that an assertion is false and recognize that a single countereample is sufficient to refute an assertion. Standard Set.0 Students use properties of the number sstem to judge the validit of results, to justif each step of a procedure, and to prove or disprove statements:. Students use properties of numbers to construct simple, valid arguments (direct and indirect) for, or formulate countereamples to, claimed assertions.. Students judge the validit of an argument according to whether the properties of the real number sstem and the order of operations have been applied correctl at each step.. Given a specific algebraic statement involving linear, quadratic, or absolute value epressions or equations or inequalities, students determine whether the statement is true sometimes, alwas, or never. * enotes ke standards This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opright 008 alifornia epartment of Education.

3 LIFORNI STNRS TEST lgebra I THE GRPHING N SYSTEMS OF LINER EQUTIONS REPORTING LUSTER The following four alifornia content standards are included in the Graphing and Sstems of Linear Equations reporting cluster and are represented in this booklet b test questions. These questions represent onl some was in which these standards ma be assessed on the lgebra I alifornia Mathematics Standards Test. LIFORNI ONTENT STNRS IN THIS REPORTING LUSTER lgebra I.0* Students graph a linear equation and compute the - and -intercepts (e.g., graph + = ). The are also able to sketch the region defined b linear inequalit (e.g., the sketch the region defined b + < )..0* Students verif that a point lies on a line, given an equation of the line. Students are able to derive linear equations using the point-slope formula. 8.0 Students understand the concepts of parallel lines and perpendicular lines and how those slopes are related. Students are able to find the equation of a line perpendicular to a given line that passes through a given point. 9.0* Students solve a sstem of two linear equations in two variables algebraicall and are able to interpret the answer graphicall. Students are able to solve a sstem of two linear inequalities in two variables and to sketch the solution sets. * enotes ke standards This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opright 008 alifornia epartment of Education.

4 LIFORNI STNRS TEST lgebra I THE QURTIS N POLYNOMILS REPORTING LUSTER The following eight alifornia content standards are included in the Quadratics and Polnomials reporting cluster and are represented in this booklet b test questions. These questions represent onl some was in which these standards ma be assessed on the lgebra I alifornia Mathematics Standards Test. LIFORNI ONTENT STNRS IN THIS REPORTING LUSTER lgebra I 0.0* Students add, subtract, multipl, and divide monomials and polnomials. Students solve multistep problems, including word problems, b using these techniques..0 Students appl basic factoring techniques to second- and simple third-degree polnomials. These techniques include finding a common factor for all terms in a polnomial, recognizing the difference of two squares, and recognizing perfect squares of binomials..0* Students solve a quadratic equation b factoring or completing the square. 9.0* Students know the quadratic formula and are familiar with its proof b completing the square. 0.0* Students use the quadratic formula to find the roots of a second-degree polnomial and to solve quadratic equations..0* Students graph quadratic functions and know that their roots are the -intercepts..0 Students use the quadratic formula or factoring techniques or both to determine whether the graph of a quadratic function will intersect the -ais in zero, one, or two points..0* Students appl quadratic equations to phsical problems, such as the motion of an object under the force of gravit. * enotes ke standards This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opright 008 alifornia epartment of Education.

5 LIFORNI STNRS TEST lgebra I THE FUNTIONS N RTIONL EXPRESSIONS REPORTING LUSTER The following si alifornia content standards are included in the Functions and Rational Epressions reporting cluster and are represented in this booklet b test questions. These questions represent onl some was in which these standards ma be assessed on the lgebra I alifornia Mathematics Standards Test. LIFORNI ONTENT STNRS IN THIS REPORTING LUSTER lgebra I.0* Students simplif fractions with polnomials in the numerator and denominator b factoring both and reducing them to the lowest terms..0* Students add, subtract, multipl, and divide rational epressions and functions. Students solve both computationall and conceptuall challenging problems b using these techniques..0* Students appl algebraic techniques to solve rate problems, work problems, and percent miture problems..0 Students understand the concepts of a relation and a function, determine whether a given relation defines a function, and give pertinent information about given relations and functions..0 Students determine the domain of independent variables and the range of dependent variables defined b a graph, a set of ordered pairs, or a smbolic epression. 8.0 Students determine whether a relation defined b a graph, a set of ordered pairs, or a smbolic epression is a function and justif the conclusion. * enotes ke standards This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opright 008 alifornia epartment of Education.

6 LIFORNI STNRS TEST lgebra I Is the equation ( ) = 8 equivalent to = 8? Yes, the equations are equivalent b the ssociative Propert of Multiplication. Yes, the equations are equivalent b the ommutative Propert of Multiplication. Yes, the equations are equivalent b the istributive Propert of Multiplication over ddition. No, the equations are not equivalent. S008 Which number does not have a reciprocal? S0 + 8 = What is the multiplicative inverse of? 9 0 S00 Which epression is equivalent to? S0 9 S0 What is the solution for this equation? = = or = = or = = or = = or = S00 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opright 008 alifornia epartment of Education.

7 LIFORNI STNRS TEST What is the solution set of the inequalit +? or or 8 Which equation is equivalent to ( + ) =? 9 = 9 + = 9 + = = S00 S000 lgebra I 0 The total cost (c) in dollars of renting a sailboat for n das is given b the equation c = 0 + 0n. If the total cost was $0, for how man das was the sailboat rented? 8 Solve: ( + ) = + Step : + = + Step : + = Step : = 0 Step : = S008 9 Which equation is equivalent to ( ) = ( )? 8 = 8 = 9 = 9 = S0009 Which is the first incorrect step in the solution shown above? Step Step Step Step S00 0-foot-long rope is cut into pieces. The first piece of rope is twice as long as the second piece of rope. The third piece of rope is three times as long as the second piece of rope. What is the length of the longest piece of rope? 0 feet 0 feet 0 feet 80 feet This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opright 008 alifornia epartment of Education. S00

8 LIFORNI STNRS TEST lgebra I The cost to rent a construction crane is $0 per da plus $0 per hour of use. What is the maimum number of hours the crane can be used each da if the rental cost is not to eceed $00 per da? Which number serves as a countereample to the statement below? ll positive integers are divisible b or S SG09 What is the solution to the inequalit >? > 9 >9 < 9 <9 S008 The lengths of the sides of a triangle are, +, and centimeters. If the perimeter is centimeters, what is the value of? What is the conclusion of the statement in the bo below? = = = If =, then = or =. = or = S00 S00 8 Which of the following is a valid conclusion to the statement If a student is a high school band member, then the student is a good musician? ll good musicians are high school band members. student is a high school band member. ll students are good musicians. ll high school band members are good musicians. S009 8 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opright 008 alifornia epartment of Education.

9 LIFORNI STNRS TEST 9 The chart below shows an epression evaluated for four different values of. + + Josiah concluded that for all positive values of, + + produces a prime number. Which value of serves as a countereample to prove Josiah s conclusion false? S00 0 John s solution to an equation is shown below. Given: + + = 0 Step : ( + )( + )= 0 Step : + = 0 or + = 0 Step : = or = Which propert of real numbers did John use for Step? multiplication propert of equalit zero product propert of multiplication commutative propert of multiplication distributive propert of multiplication over addition lgebra I Stan s solution to an equation is shown below. Given: n + 8( n + 0) = 0 Step : n + 8n + 0 = 0 Step : 9n + 0 = 0 Step : 9n = 0 0 Step : 9n = 90 Step : 9n 90 = 9 9 Step : n = 0 Which statement about Stan s solution is true? Stan s solution is correct. Stan made a mistake in Step. Stan made a mistake in Step. Stan made a mistake in Step. When is this statement true? S00 The opposite of a number is less than the original number. This statement is never true. This statement is alwas true. This statement is true for positive numbers. This statement is true for negative numbers. S0 S00 9 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opright 008 alifornia epartment of Education.

10 LIFORNI STNRS TEST lgebra I What is the -intercept of the graph of + =? S009 Which inequalit is shown on the graph below? Which best represents the graph of =? S0099 < > S00 0 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opright 008 alifornia epartment of Education.

11 LIFORNI STNRS TEST lgebra I Which inequalit does the shaded region of the graph represent? Which equation best represents the graph above? = = = + = + S0008 S00 8 Which point lies on the line defined b + =? (0, ) (0, ),, S00009 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opright 008 alifornia epartment of Education.

12 LIFORNI STNRS TEST lgebra I 9 What is the equation of the line that has a slope of and passes through the point (, 0)? Some ordered pairs for a linear function of are given in the table below. = = + = = + S The data in the table show the cost of renting a biccle b the hour, including a deposit. Hours (h) Renting a iccle ost in dollars (c) 0 8 If hours, h, were graphed on the horizontal ais and cost, c, were graphed on the vertical ais, what would be the equation of a line that fits the data? c = h c = h + Which of the following equations was used to generate the table above? = + = = = S08 The equation of line l is + =, and the equation of line q is = 0. Which statement about the two lines is true? Lines l and q have the same -intercept. Lines l and q are parallel. Lines l and q have the same -intercept. Lines l and q are perpendicular. S00 c = h + c = h S000 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opright 008 alifornia epartment of Education.

13 LIFORNI STNRS TEST Which equation represents a line that is parallel to = +? = + = + = + = + S0 lgebra I Which graph best represents the solution to this sstem of inequalities? S00 What is the solution to this sstem of equations? (, ) (, ) no solution = + = infinitel man solutions S000 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opright 008 alifornia epartment of Education.

14 LIFORNI STNRS TEST lgebra I Which ordered pair is the solution to the sstem of equations below?,, (, (, ) + = + = = S000 S0 Marc has a total of 00 dimes and quarters. If the total value of the coins is $.0, how man quarters does she have? 0 S008 8 Which of the following best describes the graph of this sstem of equations? = + = 0 + two identical lines two parallel lines two lines intersecting in onl one point two lines intersecting in onl two points 0 ( + 8) ( + )= S0008 The sum of two binomials is. If one of the binomials is, what is the other binomial? S00 S0009 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opright 008 alifornia epartment of Education.

15 LIFORNI STNRS TEST lgebra I Which of the following epressions is equal to ( + ) + ( )( + )? + Which is a factor of +? + + S000 + S09 volleball court is shaped like a rectangle. It has a width of meters and a length of meters. Which epression gives the area of the court in square meters? Which is the factored form of a ab + 8 b? S009 Which of the following shows 9t + + factored completel? (t + ) (t + )(t +) (9t + )(t +) 9t + t + t S00 What is the complete factorization of 8z? 8( + z )( z ) 8 ( + z)( z) 8( + z) 8 ( z) S00 (a 8b)( a b) (a b)( a b) (a b)( a b) (a 8b)( a 8b) S000 8 If is added to, the sum is. Which of the following could be the value of? S0 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opright 008 alifornia epartment of Education.

16 LIFORNI STNRS TEST lgebra I 9 What quantit should be added to both sides of this equation to complete the square? 8 = 0 What are the solutions for the quadratic equation + =?, 8, 8, 8 8, Leanne correctl solved the equation + = b completing the square. Which equation is part of her solution? ( +) = 8 ( + ) =0 ( +) =0 ( + ) = S008 S00 S09 arter is solving this equation b factoring. 0 + = 0 Which epression could be one of his correct factors? + + S00 Toni is solving this equation b completing the square. a + b + c = 0 (where a 0) Step : a + b = c Step : b c + = a a Step :? Which should be Step in the solution? c b = b a b c + = a a b b c b + + = + a a a a b b c b + + = + a a a a S000 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opright 008 alifornia epartment of Education.

17 LIFORNI STNRS TEST Four steps to derive the quadratic formula are shown below. lgebra I Which statement best eplains wh there is no real solution to the quadratic equation + + = 0? The value of ii is positive. The value of ii is equal to 0. The value of ii is negative. The value of ii is not a perfect square. S0 What is the correct order for these steps? I, IV, II, III I, III, IV, II II, IV, I, III II, III, I, IV What is the solution set of the quadratic equation = 0?, { +, } S00 Which is one of the solutions to the equation = 0? +, 8 8 no real solution S S00 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opright 008 alifornia epartment of Education.

18 LIFORNI STNRS TEST lgebra I 8 The graph of the equation = is shown below. 9 Which best represents the graph of = +? For what value or values of is = 0? = onl = onl = and = = and = S009 S00 0 Which quadratic function, when graphed, has -intercepts of and? =( )( + ) =( + )( 8) =( )( +) =( +)(8 ) S0 8 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opright 008 alifornia epartment of Education.

19 LIFORNI STNRS TEST How man times does the graph of = + intersect the -ais? none one two three S008 n object that is projected straight downward with initial velocit v feet per second travels a distance s= vt +t, where t = time in seconds. If Ramón is standing on a balcon 8 feet above the ground and throws a penn straight down with an initial velocit of 0 feet per second, in how man seconds will it reach the ground? seconds seconds seconds 8 seconds S008 The height of a triangle is inches greater than twice its base. The area of the triangle is 8 square inches. What is the base of the triangle? lgebra I + What is reduced to lowest terms? Simplif to lowest terms. ( +) ( + ) ( + ) ( ) ( + ) + S00 S00 in. 8 in. in. in. S000 9 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opright 008 alifornia epartment of Education.

20 LIFORNI STNRS TEST lgebra I What is + + reduced to lowest terms? (z ) (z +) (z + ) (z ) z( z+) (z + ) z( z ) (z + ) S000 0 What is a a a + 8a a S089 reduced to lowest terms? 9 Which fraction equals the product +? + + a a + + a + a a( a ) ( a +) S S009 0 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opright 008 alifornia epartment of Education.

21 LIFORNI STNRS TEST ( + ) ( )( + ) ( + )( ) + ( + )( ) ( + )( ) ( + ) + 8 = 9 S0 lgebra I pharmacist mied some 0%-saline solution with some %-saline solution to obtain 00 ml of a %-saline solution. How much of the 0%-saline solution did the pharmacist use in the miture? 0 ml ml 0 ml ml S00 nd s average driving speed for a -hour trip was miles per hour. uring the first hours he drove 0 miles per hour. What was his average speed for the last hour of his trip? Which fraction is equivalent to? + 0 miles per hour 0 miles per hour miles per hour 0 miles per hour S One pipe can fill a tank in 0 minutes, while another takes 0 minutes to fill the same tank. How long would it take the two pipes together to fill the tank? 0 min min min min S0 S00 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opright 008 alifornia epartment of Education.

22 LIFORNI STNRS TEST lgebra I Two airplanes left the same airport traveling in opposite directions. If one airplane averages 00 miles per hour and the other airplane averages 0 miles per hour, in how man hours will the distance between the two planes be miles?. 0.8 S00 8 For which equation graphed below are all the -values negative? Lisa will make punch that is % fruit juice b adding pure fruit juice to a -liter miture that is 0% pure fruit juice. How man liters of pure fruit juice does she need to add? 0. liter 0. liter liters 8 liters S Which relation is a function? {(, ), (, ), (0, 0), (, )} S00 {(, ), (0, 0), (, ), (, )} {(, 0), (, ), (, ), (, )} {(, ), (8, 8), (0, 8), (0, 0)} S000 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opright 008 alifornia epartment of Education.

23 LIFORNI STNRS TEST lgebra I 9 What is the domain of the function shown on the graph below? {,,, } {,,, } {,,, } {,,, } S00 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opright 008 alifornia epartment of Education.

24 LIFORNI STNRS TEST lgebra I 80 Which of the following graphs represents a relation that is not a function of? S000 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opright 008 alifornia epartment of Education.

25 LIFORNI STNRS TEST lgebra I Question Number orrect nswer Standard Year of Release This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opright 008 alifornia epartment of Education.

26 LIFORNI STNRS TEST lgebra I Question Number orrect nswer Standard Year of Release This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opright 008 alifornia epartment of Education.

27 LIFORNI STNRS TEST lgebra I Question Number orrect nswer Standard Year of Release This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opright 008 alifornia epartment of Education.