Alg 1, Practice Test #2

Multiple Choice Identify the choice that best completes the statement or answers the question.

Simplify the expression.

____ 1.

a. b. c. d.

____ 2.

a. b. c. d.

____ 3. a. b. c. d.

____ 4. a. b. c. d.

____ 5. a. b.

c. d.

____ 6. Write as a decimal. a. 0.4 b. 0.004 c. –120 d. 4,000

Write the number in standard notation.

____ 7.

a. 0.0907 b. 0.907 c. 0.00907 d. –181.4

____ 8. Which list shows the numbers in order from least to greatest? a. c. b. d.

Complete the equation, by supplying the missing exponent.

____ 9. 3 a. –8 b. –3 c. 8 d. 4

____ 10. Find the next three terms of the sequence 3, 9, 27, 81, . . . a. –243, –729, –2187 c. 81, 243, 729 b. 243, 729, 2187 d. 87, 249, 87

(k2)4

k6

2k8

k16

k8

37

35

335

312 1

39

9

−(6)−1

6 − 1

−16

1

6

− 1

6

6 ⋅ 6t − 2

⋅ 6t

182t − 2

2162t − 1

62t − 1

62t − 2

(−5g5h6)2(g4h2)4

25g26h20 g26h20

25

−25g26h20 25g15h14

4 ⋅ 10−3

9.07 × 10−2

5.4 × 104, 5.4 × 10

3, 4.5 × 10

45.4 × 10

3, 5.4 × 10

4, 4.5 × 10

4

5.4 × 103, 4.5 × 10

4, 5.4 × 10

44.5 × 10

4, 5.4 × 10

3, 5.4 × 10

4

⋅ 3−6= 3

2

Determine whether the sequence is arithmetic or geometric.

____ 11. –2, 10, –50, 250, . . .

a. arithmetic b. geometric

____ 12. Suppose a population of 250 crickets doubles in size every 6 months. How many crickets will there be after 2 years? a. 4,000 crickets c. 2,000 crickets b. 6,000 crickets d. 1,000 crickets

Match the table with the function that models the data.

____ 13.

x y

1 4

2 16

3 64

4 256 a. b. c.

Match the function rule with the graph of the function.

____ 14.

a. c.

y = x4 y = 4x y = 4

x

y = 10 ⋅ 4x

b. d.

Find the balance in the account.

____ 15. $2,400 principal earning 2%, compounded annually, after 7 years

a. $2,756.85 c. $17,136.00 b. $307,200.00 d. $2,736.00

____ 16. A boat costs $11,850 and decreases in value by 10% per year. How much will the boat be worth after 8 years? a. $5,101.04 b. $11,770.00 c. $4,590.93 d. $25,401.53

Simplify the product.

____ 17. 5a2(3a4 + 3b)

a. 8a4 + 8ab c. 15a6 + 15a2b b. 15a8 + 3b d. 8a6 + 15a2b

Simplify the product using FOIL.

____ 18.

a. c. b. d.

____ 19. Find the missing coefficient.

a. 65 b. 5 c. –5 d. –65

Find the product.

____ 20. (2n + 2)(2n – 2)

a. 4n2 – 4 c. 4n2 + 2n – 4 b. 4n2 – 4n – 4 d. 4n2 + 4n – 4

Factor the expression.

(4x + 3)(2x + 5)

8x2+ 14x − 15 8x

2+ 26x + 15

8x2− 14x − 15 8x

2− 26x + 15

(5d − 7)(5d − 6) = 25d2+ +42

____ 21. x2 – 10xy + 24y2

a. (x + 6y)(x + 4y) c. (x + 2y)(x – 12y) b. (x – 2y)(x + 12y) d. (x – 6y)(x – 4y)

____ 22. 6x2 + 5x + 1 a. (3x – 1)(2x – 1) c. (3x – 1)(2x + 1) b. (3x + 1)(2x – 1) d. (3x + 1)(2x + 1)

____ 23. 16m2 – 24mn + 9n2

a. (4m – 3n)(4m + 3n) c. (4m – 3n)2

b. (16m – 3n)(m + 3n) d. (4m + 3n)2

____ 24. 50k3 – 40k2 + 75k – 60 a. 5(2k2 – 3)(5k + 4) c. (2k2 + 15)(5k – 20) b. (10k2 – 3)(25k + 4) d. 5(2k2 + 3)(5k – 4)

____ 25. Find the GCF of the first two terms and the GCF of the last two terms of the polynomial. 5h3 + 20h2 + 4h + 16 a. 5h2, 16 b. 5h3, 4 c. 5h2, 4 d. h2, h

Factor by grouping.

____ 26. 21m2 – 29m – 10

a. (7m – 2)(3m – 5) c. (7m + 2)(3m – 5) b. (7m + 2)(3m + 5) d. (7m – 2)(3m + 5)

____ 27. Identify the vertex of the graph. Tell whether it is a minimum or maximum.

a. (0, –1); minimum c. (0, –1); maximum b. (–1, 0); maximum d. (–1, 0); minimum

____ 28. Which of the quadratic functions has the narrowest graph? a. b. c. d.

y = −x2

y =1

4x2 y = 4x

2

y =1

9x2

____ 29. A ball is thrown into the air with an upward velocity of 36 ft/s. Its height h in feet after t seconds is given by the function . a. In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary. b. What is the ball’s maximum height? a. 1.13 s; 69.75 ft b. 1.13 s; 29.25 ft c. 1.13 s; 31.5 ft d. 2.25 s; 9 ft

Solve the equation using the zero-product property.

____ 30.

a. n = or n = c. n = 0 or n =

b. n = 0 or n = d. n = or n =

Solve the equation by factoring.

____ 31.

a. z = 3 or z = 9 c. z = –3 or z = 9 b. z = 3 or z = –9 d. z = –3 or z = –9

____ 32. a. z = or z = –2 c. z = 3 or z = –2 b. z = or z = 2 d. z = 3 or z = 2

____ 33. The expression ________ has the solution x = 0. a. always b. sometimes c. never

Solve the equation by completing the square. Round to the nearest hundredth if necessary.

____ 34.

a. 5, –1 b. 11, –7 c. 1.73, –1.73 d. 1, 3

____ 35. a. 4.66, 5.12 b. 3.62, –6.62 c. 3.55, –6.55 d. 24.75, –27.75

Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.

____ 36. A rocket is launched from atop a 101-foot cliff with an initial velocity of 116 ft/s.

a. Substitute the values into the vertical motion formula . Let h = 0. b. Use the quadratic formula find out how long the rocket will take to hit the ground after it is launched.

Round to the nearest tenth of a second. a. ; 0.8 s c. ; 0.8 s b. ; 8 s d. ; 8 s

____ 37. For which discriminant is the graph possible?

h = −16t2+ 36t + 9

−8n(10n − 1) = 0

−1

8−1

10−1

10

1

10−1

8

1

10

z2− 6z − 27 = 0

3z2+ 3z − 6 = 0

1

1

ax2− bx = 0

x2− 4x = 5

x2+ 3x = 24

h = −16t2+ vt + c

0 = −16t2+ 101t + 116 0 = −16t

2+ 116t + 101

0 = −16t2+ 116t + 101 0 = −16t

2+ 101t + 116

a. b. c.

Find the number of real number solutions for the equation.

____ 38.

a. 0 b. 1 c. 2

____ 39. Which kind of function best models the data in the table? Graph the data and write an equation to model the data.

x y 0 –1 1 –2 2 –3 3 –4 4 –5

a.

exponential; y = 3x – 1

c.

linear; y = –x – 1

b2− 4ac = −4 b

2− 4ac = 3 b

2− 4ac = 0

x2+ 0x − 1 = 0

b.

quadratic; y = x2 – 1

d.

linear; y = x – 1

Short Answer

40. Write with only one exponent. Use parentheses.

41. Factor the following expression.

198q3r2 – 184q2r2 + 18qr2

42. The formula models the height of a model rocket, where h is the height in meters, t is the time

in seconds and v is the initial vertical velocity in meters per second. If the model rocket is fired at an initial vertical velocity of 80 meters per second, will the rocket ever reach a height of 88 meters? Justify your answer.

43. Graph the data in the table below. Which kind of function best models the data? Write an equation to model

the data.

x y 0 30 1 6 2 1.2 3 0.24 4 0.048

32x5y5

h = −16t2+ vt

44. Graph the data in the table below. Which kind of function best models the data? Write an equation to model

the data.

x y 0 –3 1 –2 2 –3 3 –6 4 –11

Essay

45. Find the area of the shaded region. Show all your work.

46. The perimeter of a rectangular concrete slab is 114 feet and its area is 702 square feet. Find the dimensions of

the rectangle. a. Using l for the length of the rectangle, write an expression for the width of the rectangle in terms of l.

(Hint: Solve the formula for w.) Show your work. b. Write a quadratic equation using l, the expression you found in part (a), and the area of the slab. c. Solve the quadratic equation. Use the two solutions to find the dimensions of the rectangle.

Other

Which method(s) would you choose to solve the equation? Justify your reasoning.

47.

P = 2l + 2w

3x2− 27 = 0

Alg 1, Practice Test #2 Answer Section

MULTIPLE CHOICE

1. ANS: D PTS: 1 DIF: L2

REF: 8-4 More Multiplication Properties of Exponents OBJ: 8-4.1 Raising a Power to a Power NAT: ADP I.1.5 | ADP J.1.1 STA: PA M11.A.1.1.2 | PA M11.A.2.2.2 TOP: 8-4 Example 1 KEY: raising a power to a power | exponential expression | simplifying an exponential expression

2. ANS: D PTS: 1 DIF: L2 REF: 8-5 Division Properties of Exponents OBJ: 8-5.1 Dividing Powers With the Same Base NAT: ADP I.1.5 | ADP I.2.2 | ADP J.1.1 STA: PA M11.A.1.1.2 TOP: 8-5 Example 1 KEY: dividing powers with the same base | exponential expression

3. ANS: D PTS: 1 DIF: L2 REF: 8-1 Zero and Negative Exponents OBJ: 8-1.1 Zero and Negative Exponents NAT: ADP J.1.1 | ADP J.1.6 TOP: 8-1 Example 1 KEY: zero as an exponent | negative exponent | simplfying a power

4. ANS: C PTS: 1 DIF: L4 REF: 8-3 Mulitplication Properties of Exponents OBJ: 8-3.1 Multiplying Powers NAT: ADP I.1.5 | ADP J.1.1 STA: PA M11.A.1.1.2 | PA M11.A.2.2.2 TOP: 8-3 Example 2 KEY: exponential expression | multiplying powers with the same base | simplifying an exponential expression

5. ANS: A PTS: 1 DIF: L3 REF: 8-4 More Multiplication Properties of Exponents OBJ: 8-4.2 Raising a Product to a Power NAT: ADP I.1.5 | ADP J.1.1 STA: PA M11.A.1.1.2 | PA M11.A.2.2.2 TOP: 8-4 Example 4 KEY: exponential expression | raising a product to a power | simplifying an exponential expression

6. ANS: B PTS: 1 DIF: L3 REF: 8-1 Zero and Negative Exponents OBJ: 8-1.1 Zero and Negative Exponents NAT: ADP J.1.1 | ADP J.1.6 TOP: 8-1 Example 1 KEY: simplifying an exponential expression | negative exponent

7. ANS: A PTS: 1 DIF: L2 REF: 8-2 Scientific Notation OBJ: 8-2.1 Writing Numbers in Scientific and Standard Notations NAT: NAEP 2005 N1d | NAEP 2005 N1f | ADP I.1.5 | ADP I.2.2 STA: PA M11.A.1.1.2 TOP: 8-2 Example 3 KEY: scientific notation | standard notation

8. ANS: B PTS: 1 DIF: L2 REF: 8-2 Scientific Notation OBJ: 8-2.2 Using Scientific Notation NAT: NAEP 2005 N1d | NAEP 2005 N1f | ADP I.1.5 | ADP I.2.2 STA: PA M11.A.1.1.2 TOP: 8-2 Example 5 KEY: standard notation | scientific notation | ordering

9. ANS: C PTS: 1 DIF: L3 REF: 8-3 Mulitplication Properties of Exponents OBJ: 8-3.1 Multiplying Powers NAT: ADP I.1.5 | ADP J.1.1 STA: PA M11.A.1.1.2 | PA M11.A.2.2.2 KEY: multiplying powers with the same base | simplifying an exponential expression | exponential expression

10. ANS: B PTS: 1 DIF: L2 REF: 8-6 Geometric Sequences OBJ: 8-6.1 Geometric Sequences NAT: NAEP 2005 A1a | NAEP 2005 A1i | ADP I.1.2 TOP: 8-6 Example 2 KEY: geometric sequence | common ratio

11. ANS: B PTS: 1 DIF: L2 REF: 8-6 Geometric Sequences OBJ: 8-6.1 Geometric Sequences NAT: NAEP 2005 A1a | NAEP 2005 A1i | ADP I.1.2 TOP: 8-6 Example 3 KEY: arithmetic sequence | geometric sequence | common ratio | common difference

12. ANS: A PTS: 1 DIF: L3 REF: 8-7 Exponential Functions OBJ: 8-7.1 Evaluating Exponential Functions NAT: NAEP 2005 A1e | ADP J.2.3 | ADP J.4.7 | ADP J.5.4 TOP: 8-7 Example 2 KEY: exponential function | function | problem solving | word problem

13. ANS: C PTS: 1 DIF: L2 REF: 8-7 Exponential Functions OBJ: 8-7.2 Graphing Exponential Functions NAT: NAEP 2005 A1e | ADP J.2.3 | ADP J.4.7 | ADP J.5.4 TOP: 8-7 Example 3 KEY: exponential function | graphing

14. ANS: B PTS: 1 DIF: L2 REF: 8-7 Exponential Functions OBJ: 8-7.2 Graphing Exponential Functions NAT: NAEP 2005 A1e | ADP J.2.3 | ADP J.4.7 | ADP J.5.4 TOP: 8-7 Example 3 KEY: exponential function | graphing | arithmetic sequence

15. ANS: A PTS: 1 DIF: L2 REF: 8-8 Exponential Growth and Decay OBJ: 8-8.1 Exponential Growth NAT: NAEP 2005 A2h | ADP I.4.1 | ADP J.2.3 | ADP J.4.7 | ADP J.5.4 | ADP J.5.6 TOP: 8-8 Example 2 KEY: exponential growth | growth factor | problem solving | word problem | compound interest

16. ANS: A PTS: 1 DIF: L3 REF: 8-8 Exponential Growth and Decay OBJ: 8-8.2 Exponential Decay NAT: NAEP 2005 A2h | ADP I.4.1 | ADP J.2.3 | ADP J.4.7 | ADP J.5.4 | ADP J.5.6 TOP: 8-8 Example 5 KEY: exponential function | problem solving | word problem | exponential decay | decay factor

17. ANS: C PTS: 1 DIF: L2 REF: 9-2 Multiplying and Factoring OBJ: 9-2.1 Distributing a Monomial NAT: NAEP 2005 N5b | NAEP 2005 A3b | NAEP 2005 A3c | ADP J.1.3 | ADP J.1.4 STA: PA M11.D.2.2.2 | PA M11.D.2.2.1 TOP: 9-2 Example 1 KEY: polynomial | multiplying a monomial and a trinomial

18. ANS: C PTS: 1 DIF: L3 REF: 9-3 Multiplying Binomials OBJ: 9-3.1 Multiplying Two Binomials NAT: NAEP 2005 M1h | NAEP 2005 A3c | ADP J.1.3 | ADP K.8.2 STA: PA M11.D.2.2.1 TOP: 9-3 Example 2 KEY: polynomial | FOIL

19. ANS: D PTS: 1 DIF: L2 REF: 9-3 Multiplying Binomials OBJ: 9-3.1 Multiplying Two Binomials NAT: NAEP 2005 M1h | NAEP 2005 A3c | ADP J.1.3 | ADP K.8.2 STA: PA M11.D.2.2.1 TOP: 9-3 Example 2 KEY: polynomial | FOIL

20. ANS: A PTS: 1 DIF: L3 REF: 9-4 Multiplying Special Cases OBJ: 9-4.2 Difference of Squares NAT: NAEP 2005 A3c | ADP J.1.3 STA: PA M11.D.2.2.1 TOP: 9-4 Example 4 KEY: polynomial | difference of squares

21. ANS: D PTS: 1 DIF: L3 REF: 9-5 Factoring Trinomials of the Type x^2 + bx + c OBJ: 9-5.1 Factoring Trinomials

NAT: NAEP 2005 A3c | ADP J.1.4 STA: PA M11.D.2.2.2 TOP: 9-5 Example 2 KEY: polynomial | factoring trinomials

22. ANS: D PTS: 1 DIF: L2 REF: 9-6 Factoring Trinomials of the Type ax^2 + bx + c OBJ: 9-6.1 Factoring ax^2 + bx + c NAT: NAEP 2005 A3c | ADP J.1.4 STA: PA M11.D.2.2.2 TOP: 9-6 Example 1 KEY: polynomial | factoring trinomials

23. ANS: C PTS: 1 DIF: L3 REF: 9-7 Factoring Special Cases OBJ: 9-7.1 Factoring Perfect-Square Trinomials NAT: ADP J.1.4 STA: PA M11.D.2.2.2 TOP: 9-7 Example 2 KEY: polynomial | factoring trinomials | perfect-square trinomial

24. ANS: D PTS: 1 DIF: L3 REF: 9-8 Factoring by Grouping OBJ: 9-8.1 Factoring Polynomials With Four Terms NAT: NAEP 2005 A3c | ADP J.1.4 STA: PA M11.D.2.2.2 TOP: 9-8 Example 2 KEY: polynomial | factoring a polynomial

25. ANS: C PTS: 1 DIF: L2 REF: 9-8 Factoring by Grouping OBJ: 9-8.1 Factoring Polynomials With Four Terms NAT: NAEP 2005 A3c | ADP J.1.4 STA: PA M11.D.2.2.2 TOP: 9-8 Example 1 KEY: polynomial | factoring a polynomial

26. ANS: C PTS: 1 DIF: L3 REF: 9-8 Factoring by Grouping OBJ: 9-8.2 Factoring Trinomials by Grouping NAT: NAEP 2005 A3c | ADP J.1.4 STA: PA M11.D.2.2.2 TOP: 9-8 Example 3 KEY: polynomial | factoring trinomials | factoring by grouping

27. ANS: C PTS: 1 DIF: L2 REF: 10-1 Exploring Quadratic Graphs OBJ: 10-1.1 Graphing y = ax^2 NAT: NAEP 2005 A1e | ADP J.2.3 | ADP J.4.5 | ADP J.5.3 TOP: 10-1 Example 1 KEY: quadratic function | parabola | maximum | minimum | vertex

28. ANS: C PTS: 1 DIF: L2 REF: 10-1 Exploring Quadratic Graphs OBJ: 10-1.1 Graphing y = ax^2 NAT: NAEP 2005 A1e | ADP J.2.3 | ADP J.4.5 | ADP J.5.3 TOP: 10-1 Example 3 KEY: quadratic function | parabola

29. ANS: B PTS: 1 DIF: L2 REF: 10-2 Quadratic Functions OBJ: 10-2.1 Graphing y = ax^2 + bx + c NAT: NAEP 2005 A4a | NAEP 2005 A4c | ADP J.1.6 | ADP J.4.5 | ADP J.5.3 TOP: 10-2 Example 2 KEY: quadratic function | maximum | vertex | problem solving | word problem | multi-part question

30. ANS: B PTS: 1 DIF: L2 REF: 10-4 Factoring to Solve Quadratic Equations OBJ: 10-4.1 Solving Quadratic Equations NAT: NAEP 2005 A4a | NAEP 2005 A4c | ADP J.3.5 | ADP J.5.3 STA: PA M11.D.2.1.5 TOP: 10-4 Example 1 KEY: zero-product property | solving quadratic equations

31. ANS: C PTS: 1 DIF: L2 REF: 10-4 Factoring to Solve Quadratic Equations OBJ: 10-4.1 Solving Quadratic Equations NAT: NAEP 2005 A4a | NAEP 2005 A4c | ADP J.3.5 | ADP J.5.3 STA: PA M11.D.2.1.5 TOP: 10-4 Example 2 KEY: factoring | solving quadratic equations

32. ANS: A PTS: 1 DIF: L2 REF: 10-4 Factoring to Solve Quadratic Equations OBJ: 10-4.1 Solving Quadratic Equations NAT: NAEP 2005 A4a | NAEP 2005 A4c | ADP J.3.5 | ADP J.5.3

STA: PA M11.D.2.1.5 TOP: 10-4 Example 2 KEY: factoring | solving quadratic equations

33. ANS: A PTS: 1 DIF: L3 REF: 10-4 Factoring to Solve Quadratic Equations OBJ: 10-4.1 Solving Quadratic Equations NAT: NAEP 2005 A4a | NAEP 2005 A4c | ADP J.3.5 | ADP J.5.3 STA: PA M11.D.2.1.5 KEY: solving quadratic equations | factoring | reasoning

34. ANS: A PTS: 1 DIF: L2 REF: 10-5 Completing the Square OBJ: 10-5.1 Solving by Completing the Square NAT: NAEP 2005 A4a | ADP J.3.5 | ADP J.5.3 TOP: 10-5 Example 2 KEY: solving quadratic equations | completing the square

35. ANS: B PTS: 1 DIF: L2 REF: 10-5 Completing the Square OBJ: 10-5.1 Solving by Completing the Square NAT: NAEP 2005 A4a | ADP J.3.5 | ADP J.5.3 TOP: 10-5 Example 2 KEY: solving quadratic equations | completing the square

36. ANS: B PTS: 1 DIF: L2 REF: 10-6 Using the Quadratic Formula OBJ: 10-6.1 Using the Quadratic Formula NAT: ADP I.4.1 | ADP J.3.5 | ADP J.5.3 TOP: 10-6 Example 3 KEY: quadratic formula | solving quadratic equations | word problem | problem solving | multi-part question

37. ANS: C PTS: 1 DIF: L2 REF: 10-7 Using the Discriminant OBJ: 10-7.1 Number of Real Solutions of a Quadratic Equation NAT: NAEP 2005 D1e | NAEP 2005 A2g | ADP J.4.5 | ADP J.5.3 TOP: 10-7 Example 1 KEY: discriminant | solving quadratic equations

38. ANS: C PTS: 1 DIF: L2 REF: 10-7 Using the Discriminant OBJ: 10-7.1 Number of Real Solutions of a Quadratic Equation NAT: NAEP 2005 D1e | NAEP 2005 A2g | ADP J.4.5 | ADP J.5.3 TOP: 10-7 Example 1 KEY: solving quadratic equations | one solution | two solutions | discriminant

39. ANS: C PTS: 1 DIF: L2 REF: 10-8 Choosing a Linear, Quadratic, or Exponential Model OBJ: 10-8.1 Choosing a Linear, Quadratic, or Exponential Model NAT: NAEP 2005 A1e | NAEP 2005 A2d | ADP J.4.8 | ADP J.5.3 | ADP J.5.4 TOP: 10-8 Example 2 KEY: linear function | graphing

SHORT ANSWER

40. ANS:

PTS: 1 DIF: L3 REF: 8-4 More Multiplication Properties of Exponents OBJ: 8-4.2 Raising a Product to a Power NAT: ADP I.1.5 | ADP J.1.1 STA: PA M11.A.1.1.2 | PA M11.A.2.2.2 KEY: raising a product to a power | multiplying powers with the same base | raising a power to a power

41. ANS: 2qr2(9q – 1)(11q – 9)

PTS: 1 DIF: L4 REF: 9-6 Factoring Trinomials of the Type ax^2 + bx + c OBJ: 9-6.1 Factoring ax^2 + bx + c NAT: NAEP 2005 A3c | ADP J.1.4 STA: PA M11.D.2.2.2 TOP: 9-6 Example 3

(2xy)5

KEY: polynomial | factoring trinomials

42. ANS: Yes; the discriminant is greater than or equal to 0, so there is at least one solution to the quadratic equation.

PTS: 1 DIF: L3 REF: 10-7 Using the Discriminant OBJ: 10-7.1 Number of Real Solutions of a Quadratic Equation NAT: NAEP 2005 D1e | NAEP 2005 A2g | ADP J.4.5 | ADP J.5.3 TOP: 10-7 Example 2 KEY: solving quadratic equations | discriminant | word problem | problem solving | reasoning

43. ANS:

exponential;

PTS: 1 DIF: L3 REF: 10-8 Choosing a Linear, Quadratic, or Exponential Model OBJ: 10-8.1 Choosing a Linear, Quadratic, or Exponential Model NAT: NAEP 2005 A1e | NAEP 2005 A2d | ADP J.4.8 | ADP J.5.3 | ADP J.5.4 TOP: 10-8 Example 3 KEY: exponential function | graphing

44. ANS:

y = 30 ⋅ 0.2x

quadratic;

PTS: 1 DIF: L4 REF: 10-8 Choosing a Linear, Quadratic, or Exponential Model OBJ: 10-8.1 Choosing a Linear, Quadratic, or Exponential Model NAT: NAEP 2005 A1e | NAEP 2005 A2d | ADP J.4.8 | ADP J.5.3 | ADP J.5.4 TOP: 10-8 Example 3 KEY: quadratic function | graphing

ESSAY

45. ANS:

[4] (2x + 2)(3x – 4) – (x – 3)(x – 6) = (6x2 –8x + 6x – 8) – (x2 –6x – 3x + 18) = (6x2 – 2x – 8) – (x2 – 9x + 18) = 5x2 + 7x – 26 [3] one minor computational error [2] error in formula with correct computation [1] correct answer without work shown

PTS: 1 DIF: L3 REF: 9-3 Multiplying Binomials OBJ: 9-3.1 Multiplying Two Binomials NAT: NAEP 2005 M1h | NAEP 2005 A3c | ADP J.1.3 | ADP K.8.2 STA: PA M11.D.2.2.1 TOP: 9-3 Example 3 KEY: rubric-based question | extended response | polynomial | Distributive Property

46. ANS: [4] a.

b.

c. Methods may vary. Check student’s work. Solutions are 18 and 39. [3] parts (a) and (b) correct with minor computational error in (c) [2] incorrect equation in (b), but appropriate method used in (c) [1] part (a) correct

PTS: 1 DIF: L4 REF: 10-6 Using the Quadratic Formula OBJ: 10-6.2 Choosing an Appropriate Method for Solving NAT: ADP I.4.1 | ADP J.3.5 | ADP J.5.3 KEY: solving quadratic equations | rubric-based question | word problem | problem solving

OTHER

y = −x2+ 2x − 3

P = 2l + 2w

114 = 2l + 2w

114 − 2l = 2w

114

2−2l

2=2

w

57 − l = w

l(57 − l) = 702

57l − l2= 702

l2− 57l = −702

l2− 57l + 702 = 0

47. ANS: Square roots; there is no x term.

PTS: 1 DIF: L3 REF: 10-6 Using the Quadratic Formula OBJ: 10-6.2 Choosing an Appropriate Method for Solving NAT: ADP I.4.1 | ADP J.3.5 | ADP J.5.3 TOP: 10-6 Example 4 KEY: solving quadratic equations | reasoning