algebra ii honors semester 1 exam item specification sheet...

ALGEBRA II HONORS SEMESTER 1 EXAM ITEM SPECIFICATION SHEET & KEY

2008–2009 of 3 Revised: 8/18/08 Clark County School District

Constructed Response # Objective Syllabus Objective NV State Standard

1 Graph a polynomial function. Analyze graphs of polynomial functions to determine characteristics

6.1 6.8

1.12.7 2.12.4 4.12.9

2 Graph quadratic functions. Identify the domain and range of linear, quadratic, or polynomial functions.

2.2 5.1

2.12.3 2.12.4

3

Develop a mathematical model to solve real‐world problems.

Organize data using matrices. Simplify matrix expressions.

1.7 4.1 4.2

1.12.7 2.12.2

Multiple Choice # Objective Syllabus

Objective NV State Standard

Practice Key A / B

Final Key

1 Differentiate among subsets of real number systems. 1.1 1.12.8 C / 2 Evaluate algebraic expressions. 1.2 2.12.3 A / 3 Simplify algebraic expressions. 1.2 2.12.3 D / 4 Solve linear equations. 1.4 2.12.2 C /

5 Solve for a given variable in a given equation with more than one variable.

1.5 2.12.4 D /

6 Solve for a given variable in a given equation with more than one variable.

1.5 2.12.4 B /

7 Solve an absolute value equation or inequality. 1.6 2.12.2 C / 8 Solve a compound inequality. 1.6 2.12.2 A / 9 Applications of linear models. 1.7 2.12.2 B / 10 Differentiate between a relation and a function. 2.1 2.12.4 C / 11 Identify the domain and range of functions. 2.2 2.12.4 A / 12 Write the equation of a line. 2.5 4.12.5 C / 13 Write the equation of a line. 2.5 4.12.5 D / 14 Calculate the slope of a line. 2.6 4.12.5 D /

15 Recognize slope as a rate of change of one variable in terms of another.

2.7 4.12.5 C /

16 Use slopes to classify lines as parallel, perpendicular, or neither.

2.8 4.12.5 A /

17 Graph linear and absolute value equations and inequalities. 2.10 4.12.5 D /

18 Solve application problems using linear models and applying direct variation

2.12 2.12.6 A /

19 Define, graph, or evaluate piecewise functions. 2.13 4.12.5 B /

20 Solve system of equations. 3.1 2.12.5 4.12.5

D /


C /


B /

23 Graph solution set of a system of inequalities. 3.2 4.12.5 A /

24 Solve application problems involving systems of equations or inequalities.

3.3 2.12.6 B /

25 Solve application problems using linear programming. 3.4 5.12.1 C / 26 Organize data using matrices. 4.1 1.12.7 B /





Practice Key A / B

Final Key

27 Simplify matrix expressions. 4.2 1.12.7 A /

28 Simplify matrix expressions. 4.2 2.12.2 2.12.5 4.12.5

B /

29 Find the determinant of a matrix. 4.3 2.12.6 C /

30 Solve systems using matrices. 4.5 2.12.2 2.12.5 4.12.5

D /

31 Graph quadratic functions. 5.1 2.12.3 2.12.4

D /

32 Solve quadratic equations. 5.2 1.12.6 1.12.7 2.12.3

C /


D /


C /


D /

36 Analyze the nature of the roots of a quadratic equation. 5.3 1.12.6 1.12.7 2.12.4

B /

37 Solve quadratic equation with complex solutions. 5.4 1.12.7 A /

38 Perform operations with complex numbers. 5.5 2.12.3 2.12.4

B /

39 Graph and solve quadratic inequalities. 5.6

1.12.6 1.12.7 2.12.3 4.12.5

D /

40 Develop models involving quadratic equations to solve real‐world problems.

5.9 1.12.7 B /

41 Graph a polynomial function. 6.1 2.12.4 D / 42 Graph a polynomial function. 6.1 2.12.4 A /

43 Simplify polynomial expressions. 6.2 1.12.7 2.12.4

B /

44 Solve polynomial equations by factoring and graphing. 6.3 1.12.7 2.12.3 2.12.4

C /

45 Solve polynomial equations by factoring and graphing. 6.3 1.12.7 2.12.3 2.12.4

C /

46 Find rational zeros of a polynomial. 6.4 2.12.3 2.12.4

A /





Practice Key A / B

Final Key

47 Use the Fundamental Theorem of Algebra to determine the number of zeros.

6.5 1.12.7 D /

48 Divide polynomials. 6.6 1.12.7 A /

49 Analyze graphs of polynomial functions to determine characteristics.

6.8 1.12.7 4.12.9

B /

50 Analyze graphs of polynomial functions to determine characteristics.

6.8 1.12.7 4.12.9

B /

51 Solve an absolute value equation or inequality. 1.4 2.12.2 A / 52 Solve a compound inequality. 1.6 2.12.2 A / 53 Graph linear and absolute value equations and inequalities. 2.10 4.12.5 B / 54 Explore relationships among families of lines. 2.11 4.12.5 D /

55 Solve application problems involving systems of equations or inequalities.

3.3 3.12.3 A /

56 Find the inverse matrix (2x2) and use it to solve matrix equations.

4.4 2.12.2 2.12.5 4.12.5

A /

57 Solve systems using matrices. 4.5 2.12.2 2.12.5 4.12.5

B /

58 Write a quadratic function from characteristics of its graph. 5.8 4.12.5 B / 59 Use the factor theorem. 6.6 1.12.7 C /

60 Identify all possible rational zeros of a polynomial function by using the Rational Root Theorem.

6.7 2.12.3 2.12.4

A /

Algebra II H Semester 1 Practice Exam A

2008–2009 1 GO ON Clark County School District Revised 8/18/08

1. To which sets of numbers does –5 belong?

I. integers

II. natural numbers

III. rational numbers

IV. real numbers

V. whole numbers

A. II and IV only

B. III and IV only

C. I, III, and IV only

D. III, IV, and V only

2. Evaluate 2 4b ac− for 3a = − , b = 1, and 2c = − .

A. 23−

B. 17−

C. 17

D. 25

3. Which is a simplified form of the

expression ( ) ( )212 1 6 183

x x− − − ?

A. 16 24x −

B. 8 24x −

C. 6 6x +

D. 8x

4. What is the value of n if 9 2 57 3 14

n + = ?

A. 6742

n = −

B. 3998

n = −

C. 1354

n = −

D. 4354

n =

5. Below is the formula for the surface area of a right circular cylinder.

22 2A rh rπ π= +

Which is a correct formula for the height, h, expressed in terms of radius, r, and surface area, A?

A. 22

2r Ah

rππ−

=

B. 2 22

Ah rr

ππ

= −

C. 22 2h A r rπ π= − −

D. 2

Ah rrπ

= −

6. Which represents y in terms of x for the equation 3 2 5 6x y x y+ = − + ?

A. 2 6y x= − +

B. 2 6y x= −

C. 8 6y x= −

D. 8 6y x= +



7. Rewrite the absolute value inequality as a compound inequality: 6 7x + > .

A. 13 1x− < <

B. 13x > − or 1x <

C. 13x < − or 1x >

D. no solution

8. Which expresses all of the solutions for the compound inequality below?

( )2 4 2z + ≥ and 15 9 3z≥ − +

A. 3 8z− ≤ ≤

B. z = –3 and z = 8

C. 3z ≤ − and 8z ≥

D. no solution

9. In 2000 the average price of a home in West County was $95,000. By 2007 the average price of a home was $123,000. Which of the following is a linear model for the price of a home, P, in West County in terms of the year, t? Let t = 0 correspond to 2000.

A. 123,000 4,000P t= −

B. 95,000 4,000P t= +

C. 123,000 28,000P t= −

D. 28,000 95,000P t= +

10. Which relation is a function?

A. 2 4x y= +

B. 2 23 6 5 1x y+ − =

C. {(–1, 6), (3, 6), (–5, 6)}

D. {(6, –5), (6, 2), (2, –1)}

11. What is the range of the following relation?

{( 2,0),(1, 3),(5, 2)}?− − −

A. {–3, –2, 0}

B. {–2, 1, 5}

C. {0, 2, 3}

D. {–5, –1, 2}

12. Write the standard form of the equation of the line that passes through the point ( )2,2− and is parallel to the line 5 2 1x y+ = − .

A. 2 5 8x y− =

B. 2 5 12x y− =

C. 5 2 6x y+ = −

D. 5 2 1x y+ = −



13. Which equation describes the pattern in the table?

x 1 2 3 4 5 y 7 11 15 19 23

A. 3 4y x= −

B. 3 4y x= +

C. 4 3y x= −

D. 4 3y x= +

14. Use the graph below.

What is the slope of the line?

A. 51

B. 15

C. 51

−

D. 15

−

15. William is hiking in the hills. He began the hike at 10:00 a.m. at an elevation of 2,000 ft. He reached a peak of 4,000 ft. at 2:00 p.m. What is the average rate of change in Bill’s elevation?

A. 200 ft. per hour

B. 250 ft. per hour

C. 500 ft. per hour

D. 1000 ft. per hour

16. Write an equation in standard form that is perpendicular to 5 2y x= − and goes through ( )10,3− .

A. x + 5y = 5

B. x – 5y = –25

C. 5x – y = 2

D. 5x + 5y = –42



17. Graph the linear equation 9 7 63x y− = .

A.

x

y

B.

x

y

C.

x

y

D.

x

y

18. Joe’s pay (P) varies directly with the square of the number of widgets (w) he produces. When he produces 2 widgets, he is paid $16. How many widgets would he have to produce to make $144?

A. 6

B. 8

C. 12

D. 36

19. Evaluate ( 3)f − for the piecewise function

2

, 0( )

3 , 0x x

f xx x x

≤⎧= ⎨ − >⎩

.

A. ( 3) 18f − = −

B. ( 3) 3f − = −

C. ( 3) 0f − =

D. ( 3) 18f − =

20. Solve the following linear system.

5 2 85 32

x y

y x

− =

= +

A. (0, –4)

B. (2, 8)

C. infinitely many solutions

D. no solution



21. Find the y-coordinate of the solution to the linear system.

3 4 15

x yx y

− = −+ = −

A. –5

B. –3

C. –2

D. no solution

22. What is the x-coordinate of the solution to the following system of equations?

2 53 14

2 3 2 2

x y zx zx y z

+ − =+ =

− − + =

A. 14 B. 5

C. 1−

D. 2−

23. Graph the system of inequalities.

2 13

y xy x≤ +≥ − +

A.

x

y

−10 10

−10

10

B.

x

y

−10 10

−10

10

C.

x

y

−10 10

−10

10

D.

x

y

−10 10

−10

10



24. For one month of internet access, Southern Nevada Web charges $4.00 per hour with a base fee of $20.00. Silver State Internet does not charge a base fee, but charges $6.00 per hour for internet access. How many hours of use will the costs for the two companies be the same?

A. 2 hours

B. 10 hours

C. 16 hours

D. 24 hours

25. Using linear programming procedures, the equation 4 7C x y= + is to be maximized subject to the following constraints:

00

23 4 8

2 5 10

xyx y

x yy x

≥≥+ ≥

− + ≤≥ −

The grid may be used to sketch the feasible region.

x

y

What is the minimum value for the objective function?

A. 51

B. 14

C. 8

D. 0



26. A school fundraiser sells different sizes of gift baskets with a varying assortment of books and pencils. A basic basket contains 3 books and 4 pencils. A big basket contains 7 books and 8 pencils. Books cost $5, and pencils cost $2.

Which of the following shows the use of matrices to find the total cost for each size of basket?

A. 3 4 2 26

7 8 5 54⎡ ⎤ ⎡ ⎤ ⎡ ⎤

=⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦

B. 3 4 5 23

7 8 2 51⎡ ⎤ ⎡ ⎤ ⎡ ⎤

=⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦

C. 3 7 2 41

4 8 5 48⎡ ⎤ ⎡ ⎤ ⎡ ⎤

=⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦

D. 3 7 5 29

4 8 2 36⎡ ⎤ ⎡ ⎤ ⎡ ⎤

=⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦

27. Which is the sum A + B, given that 9 2 31 5 8

A− −⎡ ⎤

= ⎢ ⎥⎣ ⎦

and

5 4 04 3 7

B−⎡ ⎤

= ⎢ ⎥− − −⎣ ⎦?

A. 14 6 3

3 2 1− −⎡ ⎤⎢ ⎥−⎣ ⎦

B. 14 6 3

3 2 1− −⎡ ⎤⎢ ⎥− −⎣ ⎦

C. 4 6 33 8 1

− −⎡ ⎤⎢ ⎥− − −⎣ ⎦

D. 14 6 3

5 8 15⎡ ⎤⎢ ⎥⎣ ⎦

28. Given 0 2 15 1 0

A⎡ ⎤

= ⎢ ⎥− −⎣ ⎦and

1 40 15 1

B−⎡ ⎤

⎢ ⎥= ⎢ ⎥⎢ ⎥−⎣ ⎦

,

find the product AB.

A. 0 85 1

−⎡ ⎤⎢ ⎥−⎣ ⎦

B. 5 15 19

⎡ ⎤⎢ ⎥−⎣ ⎦

C. 7 31 22

−⎡ ⎤⎢ ⎥−⎣ ⎦

D. not possible

29. Calculate the determinant 2 3 04 1 30 5 2

−.

A. 50−

B. –30

C. –2

D. 0

30. Solve for x and y: 2 5 113 7 5

xy

− −⎡ ⎤ ⎡ ⎤ ⎡ ⎤=⎢ ⎥ ⎢ ⎥ ⎢ ⎥−⎣ ⎦ ⎣ ⎦ ⎣ ⎦

A. ( )8,1−

B. 23,3

⎛ ⎞−⎜ ⎟⎝ ⎠

C. 11 5,3 4

⎛ ⎞⎜ ⎟⎝ ⎠

D. ( )52,23



31. Which graph from a graphing calculator represents the function

24( 8 15)y x x= − + + ? (Assume the scale on each graph is one unit per tick mark.)

A.

B.

C.

D.

32. Solve the equation 2 18 81 0x x− + = by factoring.

A. 9x = ±

B. 9x = −

C. 9x =

D. no solution

33. Which is the solution set for 22 7 1 0x x+ + = , using the quadratic

formula?

A. 7 41 7 41,4 4

⎧ ⎫+ −⎪ ⎪⎨ ⎬⎪ ⎪⎩ ⎭

B. 7 57 7 57,4 4

⎧ ⎫+ −⎪ ⎪⎨ ⎬⎪ ⎪⎩ ⎭

C. 7 57 7 57,4 4

⎧ ⎫− + − −⎪ ⎪⎨ ⎬⎪ ⎪⎩ ⎭

D. 7 41 7 41,4 4

⎧ ⎫− + − −⎪ ⎪⎨ ⎬⎪ ⎪⎩ ⎭

34. Which are solutions for 2 6 40 0x x+ − = when solved by completing the square?

A. x = 10 or x = 4

B. x = 10 or x = –4

C. x = –10 or x = 4

D. x = –10 or x = –4



35. Which is the solution set of ( )26 4 77x + = ?

A. 4 77 4 77,12 12

⎧ ⎫− +⎪ ⎪⎨ ⎬⎪ ⎪⎩ ⎭

B. 4 77 4 77,6 6

⎧ ⎫− +⎪ ⎪⎨ ⎬⎪ ⎪⎩ ⎭

C. 4 77 4 77,12 12

⎧ ⎫− − − +⎪ ⎪⎨ ⎬⎪ ⎪⎩ ⎭

D. 4 77 4 77,6 6

⎧ ⎫− − − +⎪ ⎪⎨ ⎬⎪ ⎪⎩ ⎭

36. Use the discriminant to determine the number and types of solutions of the equation 29 30 25 0x x− + = .

A. no real solutions, 2 imaginary solutions

B. 1 real solution, no imaginary solutions

C. 1 real solution, 1 imaginary solution

D. 2 real solutions

37. What are the solutions of the quadratic equation 23 5 4x x+ = − ?

A. 5 236ix − +

= , 5 236ix − −

=

B. 5 736ix − +

= , 5 736ix − −

=

C. 5 236ix +

= , 5 236ix −

=

D. 5 736ix +

= , 5 736ix −

=

38. Write the expression 7 33 9

ii

++

as a complex

number in standard form.

A. 1 312 4

i−

B. 8 315 5

i−

C. 8 415 5

i+

D. 112

i+



39. Which of the following screens from a graphing calculator represents

2 4y x x≤ − ? (Assume the scale on each graph is one unit per tick mark.)

A.

B.

C.

D.

40. For the scenario below, use the model 2

0 016h t v t h= − + + , where h = height (in feet), h0 = initial height (in feet), v0 = initial velocity (in feet per second), and t = time (in seconds).

A cheerleading squad performs a stunt called a “basket toss” where a team member is thrown into the air and is caught moments later. During one performance, a cheerleader is thrown upward leaving her teammates’ hands 6 feet above the ground with an initial vertical velocity of 15 feet per second.

When the girl falls back, the team catches her at a height of 5 feet. How long was the cheerleader in the air?

A. 116

second

B. 1 second

C. 9116

seconds

D. 2 seconds



41. Which graph represents the factored function ( ) ( )( )3 2f x x x x= − + ? (Assume the scale on each graph is one unit per tick mark.)

A.

B.

C.

D.

42. Graph the polynomial function: 4 2( ) 2 1f x x x= − + − .

A.

x

y

B.

x

y

C.

x

y

D.

x

y



43. Multiply the following polynomials.

( )( )24 4x x x+ + +

A. x x3 2 16+ +

B. x x x3 25 8 16+ + +

C. x x x3 23 8 16+ + +

D. x x3 25 16+ +

44. Factor the polynomial 4 28 9x x− − completely.

A. 2( 1)( 1)( 9)x x x− + +

B. 2 2( 8) 9x x − −

C. 2( 3)( 3)( 1)x x x− + +

D. ( ) ( )( )21 3 3x x x+ − +

45. Factor the polynomial equation 38 27x +

A. ( )32 3x +

B. ( )( )22 3 2 3x x− +

C. ( )( )22 3 4 6 9x x x+ − +

D. ( )( )22 3 4 6 9x x x− + +

46. Which of the following represents the solution set of the polynomial equation below?

3 2( ) 4 8 2f x x x x= − − +

A. 1 1, , 22 2

⎧ ⎫−⎨ ⎬⎩ ⎭

B. 11, , 22

⎧ ⎫−⎨ ⎬⎩ ⎭

C. { }0, 1, 2

D. 12, , 22

⎧ ⎫−⎨ ⎬⎩ ⎭

47. According to the Fundamental Theorem of Algebra, how many solutions does the polynomial ( ) 3 510 3 2 4f x x x x= − + + − have?

A. 2

B. 3

C. 4

D. 5

48. What is 3 23 6x x− − divided by 5x − ?

A. 2 442 105

x xx

+ + +−

B. 2 2068 405

x xx

− + −−

C. 2 4685

x xx

− −−

D. 2 425

x xx

+ +−



49. State the end behavior of the graph of ( ) 3 7 4f x x x= − + + as x → −∞ .

A. ( )f x →−∞

B. ( )f x →+∞

C. ( ) 4f x →

D. ( ) 0f x →

50. Which best represents the polynomial function 4 3 25y x x x= − − ? (Assume the scale on each graph is one unit per tick mark.)

A.

B.

C.

D.

51. Which is a solution of 5 6 21x− + ≤ ?

A. 2735

x− ≤ ≤

B. 27 35

x≤ ≤ −

C. 27 35

x− ≤ ≤

D. 3x ≥ −

52. Find the solution to 27 5 35

y− < − <

A. –5 < y < 20

B. y < –5 and y > 20

C. 4 165 5

y< <

D. 45

y < and 165

y >



53. Graph the following function: 2 5y x= − − +

A.

x

y

B.

x

y

C.

x

y

D.

x

y

54. Which linear equation has the steepest slope?

A. 2 5y x= +

B. 1 52

y x= − +

C. 1 54

y x= +

D. 4 5y x= − +

55. Prom tickets are sold in advance for $60 each and on the day of the dance for $75 each. For the dance to occur at least 200 of the 800 tickets must be sold in advance. Let t represent the number of advanced tickets sold and p represent the number sold on the day of the dance. Which of the following systems of inequalities represents the number of tickets sold?

A. 2000

800

tpt p

≥≥+ ≤

B. 00

800

tpt p

≥≥+ ≤

C. 00

200

tpt p

≥≥+ ≤

D. 6075

200

tpt p

≤≤+ ≤



56. Which product would be used to solve the

matrix equation 3 4 62 1 7

ab

−⎡ ⎤ ⎡ ⎤ ⎡ ⎤⋅ =⎢ ⎥ ⎢ ⎥ ⎢ ⎥

⎣ ⎦ ⎣ ⎦ ⎣ ⎦ by

using inverse matrices?

A. 1 4 612 3 711

⎡ ⎤ ⎡ ⎤⋅⎢ ⎥ ⎢ ⎥−⎣ ⎦ ⎣ ⎦

B. 3 4 612 1 711

−⎡ ⎤ ⎡ ⎤⋅⎢ ⎥ ⎢ ⎥

⎣ ⎦ ⎣ ⎦

C. 1 4 62 3 7

⎡ ⎤ ⎡ ⎤⋅⎢ ⎥ ⎢ ⎥−⎣ ⎦ ⎣ ⎦

D. 3 4 62 1 7

−⎡ ⎤ ⎡ ⎤⋅⎢ ⎥ ⎢ ⎥

⎣ ⎦ ⎣ ⎦

57. Cramer’s Rule is used to solve the system of equations:

3 2 174 2 3 102 5 9 6

x y zx y zx y z

− + =+ − =+ − = −

Which determinant represents the numerator for z?

A. 3 1 24 2 32 5 9

−−−

B. 3 1 174 2 102 5 6

−

−

C. 17 3 110 4 2

6 2 5

−

−

D. 3 17 24 10 32 6 9

−− −

58. Write an equation for the parabola whose vertex is at ( 5,7)− and passes through ( 3, 1)− − .

A. 21 ( 5) 711

y x= − + +

B. 22( 5) 7y x= − + +

C. 21 ( 5) 72

y x= − + +

D. 21 ( 5) 72

y x= − − +


2008–2009 16 Clark County School District Revised 8/18/08

59. One factor of 3 22 11 12x x x+ − − is x + 4. What are the remaining factors?

A. x + 1 and x + 3

B. x – 1 and x + 3

C. x + 1 and x – 3

D. x – 1 and x – 3

60. List all of the possible rational zeros of ( ) 3 22 6 7 6p x x x x= − + − .

A. 1 31, 2, 3, 6, ,2 2

± ± ± ± ± ±

B. 1, 2, 3, 6± ± ± ±

C. 1 1 1 21, 2, , , ,6 3 2 3

± ± ± ± ± ±

D. 1 1 21, 2, 3, 6, , ,3 2 3

± ± ± ± ± ± ±

Algebra II H Semester 1 Practice Exam A Free Response


1. Let ( ) ( ) ( )23 1p x x x x= − + .

A. Sketch the graph of ( )p x . Label all intercepts.

B. Find another polynomial function, ( )q x , that has the same zeros as ( )p x and goes through the

point ( )1,16− .

C. Explain how to determine the end behaviors of a polynomial function.



2. Let ( ) 2 2 15f x x x= + − .

A. Find the vertex and the axis of symmetry.

B. ( )0, 15− is a point on ( )y f x= . Explain how you can use the symmetric properties of a

parabola to find another point on ( )y f x= .

C. Sketch the graph of ( )y f x= . Include and label at least 5 points on your graph including the vertex and intercepts.

D. Find the domain and range of ( )f x .


2008–2009 19 Clark County School District Revised 8/18/08

3. A bakery chain displays prices in a 1 3× matrix and daily sales at its three stores in a 3 3× matrix as shown below:

Prices Number of Items Sold

[ ]Cupcakes Cookies Cakes

$2 $1 $10

Store A Store B Store CCupcakes 12 10 20Cookies 25 40 80Cakes 6 4 12

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

A. Find the product of the two matrices. Explain what the product represents.

B. How would you find the total gross revenue from all three stores?

algebra ii honors semester 1 exam item specification sheet...

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