Algebra 2

Benchmark ReviewMs. Cheung

Standard 1.0

1)

The absolute value of any number will always be positive, thus the equation |5 – 6m| > - 7 will always be true!!

Standard 1.0

2)

627510 x 55510 x

55510 x 55510 x

9

455

x

x13

655

x

x

Standard 2.03. Which order pair is the solution to the system of equations below?

207 yx

1642074 yy

1648028 yy168032 y

6432 y2y

Solve for xSubstitute for xDistributeCombine Like Term

Combine Like termSolve for y

6

2014

20)2(7

207

x

x

x

yx

Standard 2.04. Which order pair is the solution to the system of equations below?

242

2028

yx

yx

Multiply 2 to equation 2

Add the two equations1

44

264

24

x

x

x

yx

428

2028

yx

yx

244 y 6y

5) Ms. Cheung’s current phone plan is about to be expired. She has been offered two promotions from two different phone providers. AT&T provides a 500 minute plan at $30 with 40 cents per text message. T-Mobile provides a 500 minute plan at $40 with 30 cents per text message. If x represents the number of text sent and y is the total amount charge for both plans, how do you write a system of equations that model this situation?

Standard 2.0

xy

xy

3.040

4.030

6) Gerardo wrote a matrix equation.

What is the solution to Gerardo’s equation?

Standard 2.0

6

20

21

34

y

x

62

2034

6

20

21

34

yx

yx

y

x

4 ,262

2034

yx

yx

7) Jackie wrote a matrix equation.

What is the solution to Gerardo’s equation?

Standard 2.0

6

3

23

12

y

x

623

32

6

3

23

12

yx

yx

y

x

3 ,0623

32

yx

yx

Standard 3.0

8)

234

234

723

835

nnn

nnn

234 152 nnn

Standard 3.0

1414a

66 2

aa

14206 2 aa

Standard 3.0

105

126 2

k

kk

10176 2 kk

Standard 3.0

342486 3434 xxxx

11)

48x 312x 1

Given a polynomial expression such that it has two factors of

A)B) C)D)

24503510 234 xxxx

).4( and )1( xx

).2( and )1( xx

).3( and )1( xx

).3( and )2( xx

).4( and )3( xx

441

6424 632

Standard 3.012)

13) Which of the following represent the graph of ?23 i

Standard 5.0

A

D

C

B

14. Kevin knows that . What will he get if he simplifies

A)B) C)D)

i 1

4 and 4

Standard 5.0

?16

4

i4

ii 4 and 4

15. Jocelyn knows that . What will he get if he simplifies

A)B) C)D)

i 1

8 and 8

Standard 5.0

?64

8

i8

ii 8 and 8

16. Jocelyn knows that . What will she get if he simplifies

A)B) C)D)

i 1

Standard 6.0

?252

i10

i5

i10

i5

Standard 6.017)

2339

)3)(3(

iii

ii

)1(9

10

Standard 6.018)

i

ii

32

523

Standard 6.019)

ii

ii

43512

)43(512

i9

Standard 8.0

20)

042 p 4 ,0 ,1 cba

)1(2

)4)(1(400 2 x 216 2

4 2or 2 xx

Standard 8.0

21)

02556 2 xx 25 ,5 ,6 cba

)6(2

)25)(6(455 2 x 12600255 12

6255

12255

12255 or xx

12255

35

35 or xx

22. Given the graph f(x)=ax2+bx+c. If a is negative, what would my graph look like?

A) A linear graph going upB) A linear graph going upC) A quadratic graph going upD) A quadratic graph going down

Standard 9.0

f(x)=ax2+bx+c is a Quadratic Equation since it has a power of 2.

Since a is negative, the graph will be going downward.

23)

Standard 9.0

Vertex(-3, -2)

Vertex(2, 2)

From (-3, -2) to (2, 2)We get

)2 ,3(

)2 ,2(

2)2 3,(2

4) (5,

Positive 5, so it’s 5 unit to the right.

Positive 4, 4 units UP!!

24)

Standard 9.0

Vertex(5, 1)

Vertex(-5, 1)

Both functions have the same coefficient: 3, both have the same shape.

Both functions are positive, so both vertices are minimum.

Both functions are positive, so their vertices are minimums.

25) What is the minimum value of the function f(x)=x2 – 9?

A) – 9 B) – 3 C) 0D) 9

Standard 10.0

Minimum The lowest Point!Find the vertex!

X= - b/2aX = 0/2 = 0

y = 0 – 9= -9

The lowest Point!

Standard 10.0

26)

X= - b/2aX = -6/2 = - 3

y=(-3)2+6(-3)+5= 9 – 18 + 5 = - 4

Vertex: ( - 3, - 4)

Standard 24.0

27)𝐅𝐢𝐧𝐝 𝐟 (𝟐 )𝐛𝐲 𝐬𝐮𝐛𝐬𝐭𝐢𝐭𝐮𝐭𝐢𝐧𝐠𝐱=𝟐𝐢𝐧𝐭𝐨𝐟 (𝐱)

𝑔 ( 𝑓 (2 ))¿𝑔 (3 (2 )2−4)

¿𝑔 (12−4)

¿𝑔 (8)

-6

¿10

Standard 24.0

28)

𝐒𝐮𝐛𝐬𝐭𝐢𝐭𝐮𝐭𝐢𝐧𝐠𝐠 (𝐱)𝐢𝐧𝐭𝐨𝐟 (𝐱)

𝑓 (𝑔 (𝑥 ))¿ 𝑓 (𝑥+3) S

¿ (𝑥+3)2−1

¿ 𝑥2+6 𝑥+9−1

¿ 𝑥2+6 𝑥+8

Standard 24.029) Which of the following functions is the

inverse of f(x) = 3x – 2?

321

321

231

231

)(

)(

)(

)(

x

x

x

x

xf

xf

xf

xfA)

B)

C)

D)

𝐒𝐭𝐞𝐩𝟐 :𝐒𝐰𝐢𝐭𝐜𝐡 𝐱𝐚𝐧𝐝 𝐲 .𝐒𝐭𝐞𝐩𝟑 :𝐒𝐨𝐥𝐯𝐞𝐟𝐨𝐫 𝐲 .

𝐒𝐭𝐞𝐩𝟏 :𝐒𝐮𝐛𝐬𝐭𝐢𝐭𝐮𝐭𝐞𝐲 𝐟𝐨𝐫 𝐟 (𝐱 ) .

𝑓 (𝑥 )=3 x−2𝐒𝐭𝐞𝐩𝟏 :𝐒𝐮𝐛𝐬𝐭𝐢𝐭𝐮𝐭𝐞𝐲 𝐟𝐨𝐫 𝐟 (𝐱 ) .y=3 x−2𝐒𝐭𝐞𝐩𝟐 :𝐒𝐰𝐢𝐭𝐜𝐡 𝐱𝐚𝐧𝐝 𝐲 .x=3 y−2𝐒𝐭𝐞𝐩𝟑 :𝐒𝐨𝐥𝐯𝐞𝐟𝐨𝐫 𝐲 .+𝟐 +𝟐

x+2=3 y𝟑 𝟑𝑥+2

3=𝑦

Standard 7.030) Rewrite the following exponents to positive

exponents.

24

52

3

2

)(

)(

yx

yxxf

y

xxfA)

B)

𝑓 (𝑥 )= 1

𝑥2 𝑦3

𝑓 (𝑥 )=𝑥2 𝑦2

𝑥4 𝑦5𝑥2 𝑦 3

𝑓 (𝑥 )= 1

𝑥2 𝑦3

Standard 7.031) 𝐒𝐭𝐞𝐩𝟐 :𝐍𝐞𝐠𝐚𝐭𝐢𝐯𝐞𝐄𝐱𝐩𝐨𝐧𝐞𝐧𝐭

𝐒𝐭𝐞𝐩𝟑 :𝐒𝐢𝐦𝐩𝐥𝐢𝐟𝐲

𝐒𝐭𝐞𝐩𝟏 :𝐃𝐢𝐬𝐭𝐫𝐢𝐛𝐮𝐭𝐞𝐞𝐱𝐩𝐨𝐧𝐞𝐧𝐭

¿ 3𝑎2𝑏3𝑐− 2

𝑎− 3𝑏6𝑐3

¿ 3𝑎2𝑏3𝑎3

𝑏6𝑐3𝑐2

¿ 3𝑎5𝑏3

𝑏6𝑐5 𝐒𝐭𝐞𝐩𝟑 :𝐒𝐢𝐦𝐩𝐥𝐢𝐟𝐲

¿ 3 𝑎5

𝑏3𝑐5

Standard 7.032) 𝐒𝐭𝐞𝐩𝟐 :𝐒𝐢𝐦𝐩𝐥𝐢𝐟𝐲

𝐒𝐭𝐞𝐩𝟏 :𝐅𝐚𝐜𝐭𝐨𝐫𝐢𝐳𝐞

¿𝑥(𝑥+4)𝑥+3

∙(𝑥+3)(𝑥−3)(𝑥+4)(𝑥−3)

¿ 𝑥

Standard 7.033) 𝐒𝐭𝐞𝐩𝟐 :𝐍𝐞𝐠𝐚𝐭𝐢𝐯𝐞𝐄𝐱𝐩𝐨𝐧𝐞𝐧𝐭

𝐒𝐭𝐞𝐩𝟑 :𝐒𝐢𝐦𝐩𝐥𝐢𝐟𝐲

𝐒𝐭𝐞𝐩𝟏 :𝐃𝐢𝐯𝐢𝐝𝐞𝐬𝐰𝐢𝐭𝐜𝐡𝐭𝐨𝐌𝐮𝐥𝐭𝐢𝐩𝐥𝐲

¿ 20 𝑥− 4

27 𝑦2 ×15 𝑦−5

8 𝑥− 3𝐒𝐭𝐞𝐩𝟏 :𝐃𝐢𝐯𝐢𝐝𝐞𝐬𝐰𝐢𝐭𝐜𝐡𝐭𝐨𝐌𝐮𝐥𝐭𝐢𝐩𝐥𝐲

¿ 2027 𝑦 2𝑥4×

15 𝑥3

8 𝑦5𝐒𝐭𝐞𝐩𝟐 :𝐍𝐞𝐠𝐚𝐭𝐢𝐯𝐞𝐄𝐱𝐩𝐨𝐧𝐞𝐧𝐭

¿5

9 𝑦 2𝑥×

5

2 𝑦5

𝑥

5

2

59

𝐒𝐭𝐞𝐩𝟑 :𝐒𝐢𝐦𝐩𝐥𝐢𝐟𝐲

¿25

18𝑥 𝑦7

Standard 7.034)

𝐒𝐭𝐞𝐩𝟐 :𝐒𝐢𝐦𝐩𝐥𝐢𝐟𝐲𝐒𝐭𝐞𝐩𝟏 :𝐅𝐚𝐜𝐭𝐨𝐫𝐢𝐳𝐞

¿4 (𝑥2−4)

2−𝑥

¿4 (𝑥+2)(𝑥−2)

2−𝑥-1

¿−4 (𝑥+2)

Standard 22.035)

Strategy: Convert to decimal

=0.5 + 0.25+ 0.125 + 0.625 + …

=0.5 + 0.25+ 0.125 + 0.0625 + …

=0.9375

Closest to 1

How about

=

= =

Standard 22.036)

Strategy:Substitute n=1, 2, 3, 4, 5 into the answer choice to see if the term generated is the same as the question= 4(1) = 4 ≠3 (first term)

1st term 2nd term3rd term 4th term5th term

n=1 n=2 n=3 n=5n=4

= 3+4(1) = 7 ≠3 (first term)

= 2(1)+1 = 3 ¿3 (first term)= 2(2)+1 = 5 ≠7 (second term)

= 4(1)-1 = 3 (first term) = 4(2)-1 = 7 (second term)= 4(3)-1 = 11 (third term) = 4(4)-1 = 15 (fourth term)= 4(5)-1 = 19 (fifth term)

¿1525

Standard PS 1.0

37)Strategy: Identify Keywords

P(cm label & no labels)=P(cm label) P(no labels)

¿28

×1024

Multiply

No. of rulers with cm labels

Total No. of Rulers

No. of rulers without labels

One less ruler

5

3

1

21

8

14¿

14

38)

Standard PS 1.0

Strategy: Identify Keywords

Not raining in San Francisco and not raining in Sydney

Multiply

P(not raining in SF & not raining in Sydney)=P(not raining in SF) P(not raining in Sydney)

¿ (1−80 % )×(1−30 % )¿20 %×70 %¿14 %

39)

Standard PS 1.0Strategy: Identify Keywords

Green and green Multiply

P(green & green)=P(green) P(green)

¿26×

34

No. of green marble in 1st

bag

Total No. of Marbles in

1st bag

No. of green marbles in 2nd bag

Total No. of marbles in 2nd

bag

12

1

2

¿14

40)

Standard PS 2.0

41) Standard PS 2.0