A+ Answers

Question 1          
If three people are selected at random, find the probability that at least two of them have the same birthday.
A. ≈ 0.07              
B. ≈ 0.02              
C. ≈ 0.01              
D. ≈ 0.001            
Question 2          
Find the indicated term of the arithmetic sequence with first term, a₁, and common difference, d. 
Find a₂₀₀ when a₁ = -40, d = 5
A. 865    
B. 955    
C. 678   
D. 895   
Question 3          
Write the first six terms of the following arithmetic sequence.
a_n = a_n-1 - 0.4, a₁ = 1.6
A. 1.6, 1.2, 0.8, 0.4, 0, -0.4              
B. 1.6, 1.4, 0.9, 0.3, 0, -0.3              
C. 1.6, 2.2, 1.8, 1.4, 0, -1.4              
D. 1.3, 1.5, 0.8, 0.6, 0, -0.6              
Question 4          
To win at LOTTO in the state of Florida, one must correctly select 6 numbers from a collection of 53 numbers (1 through 53). The order in which the selection is made does not matter. How many different selections are possible?
A. 32,957,326 selections 
B. 22,957,480 selections 
C. 28,957,680 selections 
D. 225,857,480 selections              
Question 5          
If two people are selected at random, the probability that they do not have the same birthday (day and month) is 365/365 * 364/365. (Ignore leap years and assume 365 days in a year.)
A. The first person can have any birthday in the year. The second person can have all but one birthday.               
B. The second person can have any birthday in the year. The first person can have all but one birthday.               
C. The first person cannot a birthday in the year. The second person can have all but one birthday.    
D. The first person can have any birthday in the year. The second cannot have all but one birthday.   
Question 6          
Write the first four terms of the following sequence whose general term is given.
a_n = (-3)ⁿ
A. -4, 9, -25, 31   
B. -5, 9, -27, 41   
C. -2, 8, -17, 81   
D. -3, 9, -27, 81   
Question 7          
If three people are selected at random, find the probability that they all have different birthdays.
A. 365/365 * 365/364 * 363/365 ≈ 0.98        
B. 365/364 * 364/365 * 363/364 ≈ 0.99        
C. 365/365 * 365/363 * 363/365 ≈ 0.99        
D. 365/365 * 364/365 * 363/365 ≈ 0.99        
Question 8          
Write the first six terms of the following arithmetic sequence. 
a_n = a_n-1 + 6, a₁ = -9
A. -9, -3, 3, 9, 15, 21          
B. -11, -4, 3, 9, 17, 21        
C. -8, -3, 3, 9, 16, 22          
D. -9, -5, 3, 11, 15, 27       
Question 9          
Use the Binomial Theorem to expand the following binomial and express the result in simplified form.
(x² + 2y)⁴
A. x⁸ + 8x⁶ y + 24x⁴ y² + 32x² y³ + 16y⁴        
B. x⁸ + 8x⁶ y + 20x⁴ y² + 30x² y³ + 15y⁴        
C. x⁸ + 18x⁶ y + 34x⁴ y² + 42x² y³ + 16y⁴      
D. x⁸ + 8x⁶ y + 14x⁴ y² + 22x² y³ + 26y⁴        
Question 10        
Use the formula for the sum of the first n terms of a geometric sequence to solve the following.
Find the sum of the first 11 terms of the geometric sequence: 3, -6, 12, -24 . . .
A. 1045 
B. 2108 
C. 10478              
D. 2049 
Question 11        
If 20 people are selected at random, find the probability that at least 2 of them have the same birthday.
A. ≈ 0.31              
B. ≈ 0.42              
C. ≈ 0.45              
D. ≈ 0.41              
Question 12        
Find the indicated term of the arithmetic sequence with first term, a₁, and common difference, d. 
Find a₆ when a₁ = 13, d = 4
A. 36      
B. 63      
C. 43      
D. 33      
Question 13        
Write the first four terms of the following sequence whose general term is given.
a_n = 3ⁿ
A. 3, 9, 27, 81      
B. 4, 10, 23, 91    
C. 5, 9, 17, 31      
D. 4, 10, 22, 41   
Question 14        
You volunteer to help drive children at a charity event to the zoo, but you can fit only 8 of the 17 children present in your van. How many different groups of 8 children can you drive?
A. 32,317 groups               
B. 23,330 groups               
C. 24,310 groups              
D. 25,410 groups              
Question 15        
Write a formula for the general term (the n^th term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for a_n to find a₂₀, the 20^th term of the sequence. 
a_n = a_n-1 - 10, a₁ = 30
A. a_n = 60 - 10n; a = -260 
B. a_n = 70 - 10n; a = -50   
C. a_n = 40 - 10n; a = -160 
D. a_n = 10 - 10n; a = -70   
Question 16        
The following are defined using recursion formulas. Write the first four terms of each sequence.
 
a₁ = 4 and a_n = 2a_n-1 + 3 for n ≥ 2
A. 4, 15, 35, 453 
B. 4, 11, 15, 13    
C. 4, 11, 25, 53   
D. 3, 19, 22, 53   
Question 17        
Consider the statement "2 is a factor of n² + 3n."
If n = 1, the statement is "2 is a factor of __________."
If n = 2, the statement is "2 is a factor of __________."
If n = 3, the statement is "2 is a factor of __________."
If n = k + 1, the statement before the algebra is simplified is "2 is a factor of __________."
If n = k + 1, the statement after the algebra is simplified is "2 is a factor of __________."
A. 
4; 15; 28; (k + 1)² + 3(k + 1); k² + 5k + 8       
`
B. 
4; 20; 28; (k + 1)² + 3(k + 1); k² + 5k + 7       
C. 
4; 10; 18; (k + 1)² + 3(k + 1); k² + 5k + 4       
D. 
4; 15; 18; (k + 1)² + 3(k + 1); k² + 5k + 6       
Question 18        
Find the indicated term of the arithmetic sequence with first term, a₁, and common difference, d. 
Find a₅₀ when a₁ = 7, d = 5
A. 192    
B. 252    
C. 272   
D. 287   
Question 19        
Use the formula for the sum of the first n terms of a geometric sequence to solve the following.
Find the sum of the first 12 terms of the geometric sequence: 2, 6, 18, 54 . . .
A. 531,440           
B. 535,450           
C. 535,445           
D. 431,440           
Question 20        
Write the first four terms of the following sequence whose general term is given.
a_n = 3n + 2
A. 4, 6, 10, 14      
B. 6, 9, 12, 15      
C. 5, 8, 11, 14      
D. 7, 8, 12, 15      
Question 21        
 Locate the foci and find the equations of the asymptotes.
 
x²/100 - y²/64 = 1
A. Foci: ({= ±2√21, 0); asymptotes: y = ±2/5x             
B. Foci: ({= ±2√31, 0); asymptotes: y = ±4/7x             
C. Foci: ({= ±2√41, 0); asymptotes: y = ±4/7x             
D. Foci: ({= ±2√41, 0); asymptotes: y = ±4/5x             
Question 22        
Find the vertex, focus, and directrix of each parabola with the given equation.
(x + 1)² = -8(y + 1)
A. Vertex: (-1, -2); focus: (-1, -2); directrix: y = 1        
B. Vertex: (-1, -1); focus: (-1, -3); directrix: y = 1        
C. Vertex: (-3, -1); focus: (-2, -3); directrix: y = 1        
D. Vertex: (-4, -1); focus: (-2, -3); directrix: y = 1        
Question 23        
Find the standard form of the equation of each hyperbola satisfying the given conditions.
Endpoints of transverse axis: (0, -6), (0, 6)
Asymptote: y = 2x
A. y²/6 - x²/9 = 1  
B. y²/36 - x²/9 = 1               
C. y²/37 - x²/27 = 1            
D. y²/9 - x²/6 = 1  
Question 24        
Locate the foci of the ellipse of the following equation.
 
7x² = 35 - 5y²
A. Foci at (0, -√2) and (0, √2)          
B. Foci at (0, -√1) and (0, √1)          
C. Foci at (0, -√7) and (0, √7)         
D. Foci at (0, -√5) and (0, √5)         
Question 25        
Find the standard form of the equation of the following ellipse satisfying the given conditions. 
Foci: (-2, 0), (2, 0)
Y-intercepts: -3 and 3
A. x²/23 + y²/6 = 1              
B. x²/24 + y²/2 = 1              
C. x²/13 + y²/9 = 1              
D. x²/28 + y²/19 = 1           
Question 26        
Find the vertex, focus, and directrix of each parabola with the given equation.
(x - 2)² = 8(y - 1)
A. Vertex: (3, 1); focus: (1, 3); directrix: y = -1            
B. Vertex: (2, 1); focus: (2, 3); directrix: y = -1            
C. Vertex: (1, 1); focus: (2, 4); directrix: y = -1            
D. Vertex: (2, 3); focus: (4, 3); directrix: y = -1            
Question 27        
Find the vertices and locate the foci of each hyperbola with the given equation.
x²/4 - y²/1 =1
A. 
Vertices at (2, 0) and (-2, 0); foci at (√5, 0) and (-√5, 0)           
B. 
Vertices at (3, 0) and (-3 0); foci at (12, 0) and (-12, 0)            
C. Vertices at (4, 0) and (-4, 0); foci at (16, 0) and (-16, 0)      
D. Vertices at (5, 0) and (-5, 0); foci at (11, 0) and (-11, 0)      
Question 28        
Convert each equation to standard form by completing the square on x and y.
4x² + y² + 16x - 6y - 39 = 0
A. (x + 2)²/4 + (y - 3)²/39 = 1            
B. (x + 2)²/39 + (y - 4)²/64 = 1          
C. (x + 2)²/16 + (y - 3)²/64 = 1         
D. (x + 2)²/6 + (y - 3)²/4 = 1              
Question 29        
Convert each equation to standard form by completing the square on x or y. Then find the vertex, focus, and directrix of the parabola.
y² - 2y + 12x - 35 = 0
A. (y - 2)² = -10(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 9           
B. (y - 1)² = -12(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 6           
C. (y - 5)² = -14(x - 3); vertex: (2, 1); focus: (0, 1); directrix: x = 6          
D. (y - 2)² = -12(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 8          
Question 30        
Find the standard form of the equation of the ellipse satisfying the given conditions.
Major axis vertical with length = 10
Length of minor axis = 4
Center: (-2, 3)
A. (x + 2)²/4 + (y - 3)²/25 = 1            
B. (x + 4)²/4 + (y - 2)²/25 = 1            
C. (x + 3)²/4 + (y - 2)²/25 = 1            
D. (x + 5)²/4 + (y - 2)²/25 = 1            
Question 31        
Locate the foci and find the equations of the asymptotes.
 
4y² – x² = 1
A. (0, ±√4/2); asymptotes: y = ±1/3x             
B. (0, ±√5/2); asymptotes: y = ±1/2x             
C. (0, ±√5/4); asymptotes: y = ±1/3x             
D. (0, ±√5/3); asymptotes: y = ±1/2x             
Question 32        
Find the focus and directrix of the parabola with the given equation.
8x² + 4y = 0
A. Focus: (0, -1/4); directrix: y = 1/4              
B. Focus: (0, -1/6); directrix: y = 1/6              
C. Focus: (0, -1/8); directrix: y = 1/8              
D. Focus: (0, -1/2); directrix: y = 1/2              
Question 33        
Find the standard form of the equation of each hyperbola satisfying the given conditions.
Foci: (0, -3), (0, 3)
Vertices: (0, -1), (0, 1)
A. y² - x²/4 = 0     
B. y² - x²/8 = 1     
C. y² - x²/3 = 1     
D. y² - x²/2 = 0     
Question 34        
Find the vertex, focus, and directrix of each parabola with the given equation.
(y + 3)² = 12(x + 1)
A. Vertex: (-1, -3); focus: (1, -3); directrix: x = -3        
B. Vertex: (-1, -1); focus: (4, -3); directrix: x = -5        
C. Vertex: (-2, -3); focus: (2, -4); directrix: x = -7        
D. Vertex: (-1, -3); focus: (2, -3); directrix: x = -4        
Question 35        
Find the vertex, focus, and directrix of each parabola with the given equation.
(y + 1)² = -8x
A. Vertex: (0, -1); focus: (-2, -1); directrix: x = 2          
B. Vertex: (0, -1); focus: (-3, -1); directrix: x = 3          
C. Vertex: (0, -1); focus: (2, -1); directrix: x = 1           
D. Vertex: (0, -3); focus: (-2, -1); directrix: x = 5         
Question 36        
Convert each equation to standard form by completing the square on x and y.
9x² + 16y² - 18x + 64y - 71 = 0
A. (x - 1)²/9 + (y + 2)²/18 = 1            
B. (x - 1)²/18 + (y + 2)²/71 = 1          
C. (x - 1)²/16 + (y + 2)²/9 = 1            
D. (x - 1)²/64 + (y + 2)²/9 = 1            
Question 37        
Find the focus and directrix of each parabola with the given equation.
x² = -4y
A. Focus: (0, -1), directrix: y = 1     
B. Focus: (0, -2), directrix: y = 1     
C. Focus: (0, -4), directrix: y = 1     
D. Focus: (0, -1), directrix: y = 2     
Question 38        
Find the standard form of the equation of each hyperbola satisfying the given conditions.
Foci: (-4, 0), (4, 0)
Vertices: (-3, 0), (3, 0)
A. x²/4 - y²/6 = 1  
B. x²/6 - y²/7 = 1  
C. x²/6 - y²/7 = 1  
D. x²/9 - y²/7 = 1  
Question 39        
Find the vertices and locate the foci of each hyperbola with the given equation.
y²/4 - x²/1 = 1
A. Vertices at (0, 5) and (0, -5); foci at (0, 14) and (0, -14)      
B. Vertices at (0, 6) and (0, -6); foci at (0, 13) and (0, -13)      
C. 
Vertices at (0, 2) and (0, -2); foci at (0, √5) and (0, -√5)           
D. Vertices at (0, 1) and (0, -1); foci at (0, 12) and (0, -12)      
Question 40        
Find the standard form of the equation of the ellipse satisfying the given conditions.
Endpoints of major axis: (7, 9) and (7, 3) 
Endpoints of minor axis: (5, 6) and (9, 6)
A. (x - 7)²/6 + (y - 6)²/7 = 1               
B. (x - 7)²/5 + (y - 6)²/6 = 1               
C. (x - 7)²/4 + (y - 6)²/9 = 1               
D. (x - 5)²/4 + (y - 4)²/9 = 1