Algebra 2 Review

Simplifying Rational Expressions

100

Simplify: (2a² +10a) / (3a² + 15a)

2/3 where a ≠ 0, -5

200

(x²+x−6) / (x² +8x+15)

(x-2) / (x+5) where x ≠ -3, -5

300

(2(x²+6x+5) / (x(x+5 )

2(x+1) / x where x ≠ 0, -5

400

(3x² - 13x - 30) / (18x² - 50)

(x-6) / 2(3x-5) where x ≠ 5/3, -5/3

500

(8x² - 46x + 45) / (4x² - 17x + 15)

(2x-9) / (x-3) where x ≠ 5/4, 3

Multiplying and Dividing

100

(7x / (2x - 10)) divided by (x² - 6x) / (x² - 11x + 30)

7/2 where x ≠ 5, 6, 0

200

(6x² + x - 15) / 4x² divided by (3x² + 5x)

(2x-3) / 4x³ where x ≠ 0, -5/3

 

300

(x² - 3x) / (x - 2) TIMES (x² + x - 6) / x

x²-9 where x ≠ 2, 0

400

(3x² + 13x + 4) / (4x² - 16) Divided by (8x + 32) / (4x + 8)

(3x + 1) / (8(x - 2)) where x ≠ -2, 2, -4

500

(4x² + 20x) / (x³ + 4x²) TIMES (x² + 8x + 16) / (8x² + 36x - 20)

(x+4)  / (x(2x-1)) where x ≠ 0, -4, -5, 1/2 

Addition and Subtraction

100

(5x / (x + 3)) + (15 / (x + 3))

5 where x ≠ -3

200

(6n / (n - 5)) - (5 / (n - 2))

(6n² - 17n +25) / ((n - 5)(n - 2)). where n ≠ 5, 2

300

((k + 1) / (k - 2)) - (2 / 3)

(k + 7) / (3(k - 2)) where k ≠ 2

400

(4 / (p + 1)) + ((4p) / (2p - 2))

(2p² + 6p - 4) / ((p + 1)(p - 1)) where p ≠ 1, -1

500

(3 / (m - 5)) + ((m - 2) / (10m + 20))

(m² + 23m + 70) / (10(m + 2)(m - 5)) where m ≠ -2, 5 

Arithmetic Sequences & Series

100

What is the 9th term of this series: -19, -13, -7. -1...  

29

200

What is the sum for the first 20 terms of the following series: 4+7+10+13...

680

300

Clarissa is buying a prom dress on layaway. She agrees to make a $15 payment and increase the payment by $5 each week. How much money in total will Clarissa have paid after 9 weeks?

$315

400

Find the sum of the first 16 terms of the series 7.5+7+6.5+...

60

500

The Louvre pyramid in Paris, France, is built of glass panes. There are 4 panes in the top row, and each additional row has 4 more panes than the previous row. If the pyramid were made of 18 complete rows, how many panes would it have?

684 panes

Geometic Sequences & Series

100

Is the following series geometric? (yes or no) 8, 24, 70, 210...

no

200

What is the sum of the first 6 terms of the geometric series: 2+1+1/2+1/4...

3.9375

300

What is the sum of the first 8 terms of the series: 10+1+1/10+1/100+...

11.111111

400

Write a possible explicit rule for the nth term of the sequence: 54, 18, 6, 2, 2/3...

a_n=54(1/3)^(n-1) or a_n=162(1/3)^n

500

Write a possible explicit rule for the nth term of the sequence: 2, 5, 12.5, 31.25

a_n=2(5/2)^(n-1) or a_n=0.8(5/2)^n