Question 1

For what natural numbers is the following inequality true? $n ^ { 3 } > ( n + 10 ) ^ { 2 }$

Accepted Answer

A)  $n \leq 7$ 
B)  $n \geq 8$ 
C)  $25 \leq n \leq 25$ 
D)  $9 \leq n \leq 25$ 
E)  $n \geq 7$ 
A)  $n \leq 7$ 
B)  $n \geq 8$ 
C)  $25 \leq n \leq 25$ 
D)  $9 \leq n \leq 25$ 
E)  $n \geq 7$

Question 2

Find $\lim _ { t \rightarrow 5 } \frac { t ^ { 3 } - 125 } { t - 5 }$ .

Accepted Answer

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

Question 3

Carry out the expansion. (2 - 2x) 6

Accepted Answer

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  
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 4

Find the coefficient of the term containing a 4  in the expansion of $( \sqrt { a } - \sqrt { x } ) ^ { 16 }$ .

Accepted Answer

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

Question 5

The sequence is defined recursively. Compute the first five terms of the sequence. $a _ { 1 } = - 2 ; a _ { n } = \sqrt { a _ { 2 } ^ { n - 1 } + 1 } , n \geq 2$

Accepted Answer

A)  $- 2 , \sqrt { 5 } , \sqrt { 6 } , \sqrt { 5 } , \sqrt { 2 }$ 
B)  $- 2 , \sqrt { 10 } , \sqrt { 6 } , \sqrt { 7 } , 4 \sqrt { 2 }$ 
C)  $- 2 , \sqrt { 5 } , \sqrt { 6 } , \sqrt { 7 } , 2 \sqrt { 2 }$ 
D)  $- 2 , \sqrt { 5 } , \sqrt { 3 } , \sqrt { 7 } , 2 \sqrt { 8 }$ 
E)  $- 2 , \sqrt { 5 } , \sqrt { 3 } , \sqrt { 7 } , \sqrt { 2 }$ 
A)  $- 2 , \sqrt { 5 } , \sqrt { 6 } , \sqrt { 5 } , \sqrt { 2 }$ 
B)  $- 2 , \sqrt { 10 } , \sqrt { 6 } , \sqrt { 7 } , 4 \sqrt { 2 }$ 
C)  $- 2 , \sqrt { 5 } , \sqrt { 6 } , \sqrt { 7 } , 2 \sqrt { 2 }$ 
D)  $- 2 , \sqrt { 5 } , \sqrt { 3 } , \sqrt { 7 } , 2 \sqrt { 8 }$ 
E)  $- 2 , \sqrt { 5 } , \sqrt { 3 } , \sqrt { 7 } , \sqrt { 2 }$

For what natural numbers is the following inequality true? $n ^ { 3 } > ( n + 10 ) ^ { 2 }$

Find $\lim _ { t \rightarrow 5 } \frac { t ^ { 3 } - 125 } { t - 5 }$ .

Carry out the expansion. (2 - 2x)⁶

Find the coefficient of the term containing a⁴ in the expansion of $( \sqrt { a } - \sqrt { x } ) ^ { 16 }$ .

The sequence is defined recursively. Compute the first five terms of the sequence. $a _ { 1 } = - 2 ; a _ { n } = \sqrt { a _ { 2 } ^ { n - 1 } + 1 } , n \geq 2$

Fundamentals

Equations and Inequalities

Functions

Polynomial and Rational Functions Applications to Optimization

Exponential and Logarithmic Functions

An Introduction to Trigonometry Via Right Triangles

The Trigonometric Functions

Graphs of the Trigonometric Functions

Analytical Trigonometry

Additional Topics in Trigonometry

Systems of Equations

The Conic Sections

Roots of Polynomial Equations

Filters

Exam 14: Additional Topics in Algebra

For what natural numbers is the following inequality true? n3>(n+10)2n ^ { 3 } > ( n + 10 ) ^ { 2 }n3>(n+10)2

Find lim⁡t→5t3−125t−5\lim _ { t \rightarrow 5 } \frac { t ^ { 3 } - 125 } { t - 5 }limt→5​t−5t3−125​ .

Carry out the expansion. (2 - 2x) 6

Find the coefficient of the term containing a 4 in the expansion of (a−x)16( \sqrt { a } - \sqrt { x } ) ^ { 16 }(a​−x​)16 .

The sequence is defined recursively. Compute the first five terms of the sequence. a1=−2;an=a2n−1+1,n≥2a _ { 1 } = - 2 ; a _ { n } = \sqrt { a _ { 2 } ^ { n - 1 } + 1 } , n \geq 2a1​=−2;an​=a2n−1​+1​,n≥2

Fundamentals

Equations and Inequalities

Functions

Polynomial and Rational Functions Applications to Optimization

Exponential and Logarithmic Functions

An Introduction to Trigonometry Via Right Triangles

The Trigonometric Functions

Graphs of the Trigonometric Functions

Analytical Trigonometry

Additional Topics in Trigonometry

Systems of Equations

The Conic Sections

Roots of Polynomial Equations

Filters

For what natural numbers is the following inequality true? $n ^ { 3 } > ( n + 10 ) ^ { 2 }$

Find $\lim _ { t \rightarrow 5 } \frac { t ^ { 3 } - 125 } { t - 5 }$ .

Carry out the expansion. (2 - 2x)⁶

Find the coefficient of the term containing a⁴ in the expansion of $( \sqrt { a } - \sqrt { x } ) ^ { 16 }$ .

The sequence is defined recursively. Compute the first five terms of the sequence. $a _ { 1 } = - 2 ; a _ { n } = \sqrt { a _ { 2 } ^ { n - 1 } + 1 } , n \geq 2$