Deck 14: Additional Topics in Algebra

Question 1

Find the right part of the equality.

A)
B)
C)
D)
E)

Answer 1

Question 2

Carry out the expansion. (2a + b) ⁹

A) 2a ⁹ + 2,304a ⁸ b + 4,608a ⁷ b ² + 5,376a ⁶ b ³ + 4,032a ⁵ b ⁴ + 2,016a ⁴ b ⁵ + 672a ³ b ⁶ + 144a ² b ⁷ + 18ab ⁸ + b ⁹
B) 512 a ⁹ + 2,304a ⁸ b - 4,608a ⁷ b ² + 5,376a ⁶ b ³ - 4,032a ⁵ b ⁴ + 2,016a ⁴ b ⁵ - 672a ³ b ⁶ + 144a ² b ⁷ - 18ab ⁸ + b ⁹
C) 512a ⁹ + 2,304a ⁸ b + 4,610a ⁷ b ² + 5,376a ⁶ b ³ + 4,032a ⁵ b ⁴ + 2,016a ⁴ b ⁵ + 672a ³ b ⁶ + 144a ² b ⁷ + 18ab ⁸ + b ⁹
D) 512a ⁹ + 2,304a ⁸ b - 4,608a ⁷ b ² + 5,376a ⁶ b ³ - 4,032a ⁵ b ⁴ + 2,016a ⁴ b ⁵ - 672a ³ b ⁶ + 144a ² b ⁷ - 18ab ⁸ + b ⁹
E) 512a ⁹ + 2,304a ⁸ b + 4,608a ⁷ b ² + 5,376a ⁶ b ³ + 4,032a ⁵ b ⁴ + 2,016a ⁴ b ⁵ + 672a ³ b ⁶ + 144a ² b ⁷ + 18ab ⁸ + b ⁹

Answer 2

512a ⁹ + 2,304a ⁸ b + 4,608a ⁷ b ² + 5,376a ⁶ b ³ + 4,032a ⁵ b ⁴ + 2,016a ⁴ b ⁵ + 672a ³ b ⁶ + 144a ² b ⁷ + 18ab ⁸ + b ⁹

Question 3

Find the indicated term.

A) 101
B) 110
C) 220
D) 55
E) 111

Answer 3

110

Question 4

Evaluate the sum.

A)
B)
C)
D)
E)

Question 5

Evaluate and simplify.

A) 0
B) 4
C) 14
D) 9
E) 1

Question 6

Find the indicated term.

A)
B)
C)
D)
E)

Question 7

Carry out the expansion. (2 - 2x) ⁶

A) 64 - 387x - 957x ² - 1,280x ³ - 960x ⁴ - 384x ⁵ - 64x ⁶
B) 64 + 384x + 960x ² - 1,280x ³ + 960x ⁴ - 384x ⁵ + 64x ⁶
C) 64 - 384x - 960x ² - 1,280x ³ - 960x ⁴ - 384x ⁵ - 64x ⁶
D) 64 - 384x + 960x ² - 1,280x ³ + 960x ⁴ - 384x ⁵ + 64x ⁶
E) 64 - 387x + 960x ² - 1,280x ³ + 960x ⁴ - 384x ⁵ + 64x ⁶

Question 8

Find for and .

A)
B) limit does not exist
C)
D)
E)

Question 9

Use the graph to find

A) 24
B) 
C) 0
D) 12
E) limit does not exist

Question 10

Find the sum of the first 50 terms in an arithmetic series that has first term - 18 and 50th term 129.

A)
B)
C)
D)
E)

Question 11

For what natural numbers is the following inequality true?

A)
B)
C)
D)
E)

Question 12

For what natural numbers is the following inequality true?

A)
B)
C)
D)
E)

Question 13

The sequence is defined recursively. Compute the first five terms of the sequence.

A)
B)
C)
D)
E)

Question 14

Find the coefficient of the term containing a ⁴ in the expansion of .

A) 12,870
B) 495
C) 12,871
D) 25,740
E) 1,839

Question 15

Find the right part of the equality.

A)
B)
C)
D)

Question 16

Find the third term in the expansion of (a - b) ²⁷ .

A) - 17,550a ⁴ b ²³
B) 17,550a ²³ b ⁴
C) - 17,550a ²³ b ⁴
D) 17,551a ²³ b ⁴
E) - 17,551a ²³ b ⁴

Question 17

The sum of three consecutive terms in an arithmetic sequence is 30, and their product is 750. Find the three terms. (Suggestion: Let x denote the middle term and d the common difference.)

A) 5, 9, 13
B) 4, 9, 14
C) 5, 10, 15
D) 1, 10, 15
E) 6, 10, 14

Question 18

Express as a fraction.

A)
B)
C)
D)
E)

Question 19

Find the common difference d for the following arithmetic sequence. 12, 7, 2, - 3, ...

A) 5
B) - 5
C) 3
D) - 3
E) - 6

Question 20

Find the right part of the equality.

A)
B)
C)
D)
E) none of the above

Question 21

Use the position function to find the velocity in feet/second at time seconds. The velocity at time seconds is given by

A) limit does not exist
B) 32 feet/second
C) 64 feet/second
D) 0 feet/second
E) -64 feet/second

Question 22

Find .

A)
B) limit does not exist
C)
D)
E) 0

Question 23

Find by direct substitution.

A)
B)
C)
D)
E)

Question 24

Use the graph to determine (if it exists).

A) 0
B) 3
C) -3
D) limit does not exist
E) 6

Question 25

Find .

A) limit does not exist
B) 5
C) 50
D) 75
E) 15