Algebra 2: Extended Review

Factoring

100

b²+2b-24

(b+6)(b-4)

200

10m² + 89m − 9

(m + 9)(10m − 1)

300

9p²r + 73pr + 70r

r(p + 7)(9p + 10)

400

14m² +1=6m² +7m

7 + (17)^1/2 /16, 7 - (17)^1/2 /16

500

b² −4b−14=−2

-2, 6

600

30n²b − 87nb + 30b

3b(2n − 5)(5n − 2)

700

3a² = 6a − 3

1

800

10x² +9 = x

1 + i(359)^1/2 / 20, 1 - i(359)^1/2 / 20

900

9x² −11=6x

(1 + 2 (3)^1/2 )/ 3, (1 - 2 (3)^1/2 )/ 3

1000

8a² +6a=−5

-3 + i(31)^1/2 / 8, -3 - i(31)^1/2 / 8

Expressions/Equations

100

Write the expression in its simplest form:

2 / v² − 12v + 27 ⋅ v²−12v+27 / 3

2/3

200

Solve for n.

5 |9−5n| − 7 = 38

0, 18/5

300

Write the expression in its simplest form:

x² −2x−15 / x² −6x+5

x+3 / x+1

400

Write the expression in its simplest form:

1 / n+9 ÷ 6−n/ 3n-18

-3 / n+9

500

Solve for n.

5 − 8 |−2n| = −75

-5, 5

600

Solve for n.

3 − |8x−6| = 3

3/4

700

Write the expression in its simplest form:

[x² - 16/ 9-x ]⋅ [x² +x-90 / x² +14x+40]

-(x-4)

800

Solve for x.

4(2x - 1)^1/3 - 5 = 3

2x - 1 = 8

x=9/2

900

Simplify.

(108 m⁶ p⁵ q⁴)^1/3

3m²pq (4p²q)^1/3

1000

Simplify.

−8 (405 p ³q ⁸r ⁶ )^1/4

−24q²r  (5p ³ r ² )^1/4

Exponents

100

w⁵w⁻⁸w⁶

w³

200

Find the cubic root.

1000 / 27

10 / 3

300

Simplify.

(x² / 3y)^1/3

(9x²y²)^1/3 /3y

400

Solve for x.

3^2x-2 =9

x = 2

500

Simplify.

2k^-1 × 3k³

6k²

600

Simplify.

(4m^-1 n² )³

(64n⁶)/m³

700

Simplify.

((2a³b^-2)/b³)²

4a⁶ / b¹⁰

800

DOUBLE JEOPARDY!!

Simplify.

(m⁴n^-3 × mn)/(n²)^-1

m⁵

900

Simplify.

4x⁰y^-2 / 4xy^-4

y² / x

1000

Simplify.

(3x^-3y² × x^-4 y^-4 ) / (3xy² × 3yx^-1)

1/3x⁷y⁵

Sequence/Series

100

Find the next three terms.

−34, −134, −234, −334, ...

−434, −534, −634

200

−21, −16, −11, −6, ...

−1, 4, 9

300

Write the explicit formula.

35, 31, 27, 23, ...

a_n =39−4n

400

Evaluate the arithmetic series.

7+9+11+13..., n=10

S₁₀ = 160

500

Evaluate the arithmetic series.

a₁ =42, a_n =146, n=14

S₁₄ = 1316

600

Determine the value of n.

a₁ =−2, r=5, S_n =−62

n = 3

700

1, 5, 25, 125, ... Find a₉

a₉ = 390625

800

Find the number of terms for this geometric series:

−4+16−64+256..., S_n =52428

n = 8

900

TRIPLE JEOPARDY!!!

Evaluate the geometric series

a₁ =4, a_n =8748, r=3

S_n = 13120

1000

DOUBLE JEOPARDY!!

Find the summation of 4 - 10x as x goes from 1 to 12.

−732

Logarithm

100

Condense.

4log3 − 4log8

log (3⁴ / 8⁴)

200

Condense.

log 2 + log 11 + log 7

log 154

300

Condense.

20 log₆ u + 5 log₆ v

log₆ (u²⁰v⁵)

400

Write the change of base formula.

log_b(a) = log a / log b

500

Use a calculator to approximate each to the nearest thousandth.

log₆ 22

1.725

600

Use a calculator to approximate each to the nearest thousandth.

log₁₄ 2.6

0.362

700

Rewrite the equation in exponential form.

log ₁₁ 121 = 2

11²=121

800

Rewrite the equation in exponential form.

log₅ x =19

5¹⁹ =x

900

DOUBLE JEOPARDY!!

log  (x + 6) − log  x = log  2

x=6

1000

log x + log 8 = 2  

25/2