Q. Which of the following distributions is used to model the number of successes in a fixed number of trials?
A.
Normal
B.
Binomial
C.
Poisson
D.
Exponential
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Solution
The binomial distribution models the number of successes in a fixed number of trials.
Correct Answer:
B
— Binomial
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Q. Which of the following inequalities represents the solution to 2x + 3 > 7?
A.
x > 2
B.
x < 2
C.
x > 3
D.
x < 3
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Solution
Step 1: Subtract 3 from both sides: 2x > 4. Step 2: Divide by 2: x > 2.
Correct Answer:
A
— x > 2
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Q. Which of the following inequalities represents the solution to 3x + 2 > 11?
A.
x > 3
B.
x < 3
C.
x > 4
D.
x < 4
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Solution
Subtracting 2 from both sides gives 3x > 9. Dividing by 3 results in x > 3.
Correct Answer:
C
— x > 4
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Q. Which of the following inequalities represents the solution to x + 4 > 2?
A.
x > -2
B.
x < -2
C.
x > -6
D.
x < -6
Show solution
Solution
Subtract 4 from both sides: x > -2.
Correct Answer:
A
— x > -2
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Q. Which of the following is a composite number? 2, 3, 4, 5
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Solution
4 is a composite number.
Correct Answer:
C
— 4
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Q. Which of the following is a factor of the polynomial x^2 + 4x + 4?
A.
x + 2
B.
x - 2
C.
x + 4
D.
x - 4
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Solution
The polynomial can be factored as (x + 2)(x + 2) or (x + 2)^2. Therefore, x + 2 is a factor.
Correct Answer:
A
— x + 2
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Q. Which of the following is a factor of the polynomial x^2 - 4?
A.
x - 2
B.
x + 2
C.
x^2 + 4
D.
x - 1
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Solution
The polynomial x^2 - 4 can be factored as (x - 2)(x + 2). Therefore, x - 2 is a factor.
Correct Answer:
A
— x - 2
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Q. Which of the following is a factor of the polynomial x^2 - 5x + 6?
A.
(x - 2)
B.
(x - 3)
C.
(x + 2)
D.
(x + 3)
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Solution
Step 1: Factor the polynomial: (x - 2)(x - 3). Step 2: The factors are (x - 2) and (x - 3).
Correct Answer:
A
— (x - 2)
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Q. Which of the following is a factor of the polynomial x^3 - 3x^2 - 4x + 12?
A.
x - 2
B.
x + 2
C.
x - 3
D.
x + 3
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Solution
Using synthetic division or the factor theorem, we can test x = 2. Substituting gives us 2^3 - 3(2^2) - 4(2) + 12 = 0, confirming that x - 2 is a factor.
Correct Answer:
A
— x - 2
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Q. Which of the following is a factor of the polynomial x^3 - 4x^2 + 4x?
A.
x - 2
B.
x + 2
C.
x
D.
x - 4
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Solution
We can factor out x from the polynomial: x^3 - 4x^2 + 4x = x(x^2 - 4x + 4) = x(x - 2)^2. Thus, x is a factor.
Correct Answer:
C
— x
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Q. Which of the following is a factor of x^2 - 9?
A.
(x - 3)
B.
(x + 3)
C.
(x - 3)(x + 3)
D.
(x^2 + 9)
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Solution
x^2 - 9 is a difference of squares and can be factored as (x - 3)(x + 3).
Correct Answer:
C
— (x - 3)(x + 3)
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Q. Which of the following is a polynomial?
A.
3x^2 + 2x - 1
B.
1/x + 2
C.
sqrt(x) + 3
D.
ln(x)
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Solution
A polynomial is a sum of terms with non-negative integer exponents. 3x^2 + 2x - 1 fits this definition.
Correct Answer:
A
— 3x^2 + 2x - 1
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Q. Which of the following is a prime number? 4, 5, 6, 8
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Solution
5 is a prime number.
Correct Answer:
B
— 5
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Q. Which of the following is a Pythagorean identity?
A.
sin²x + cos²x = 1
B.
tanx = sinx/cosx
C.
secx = 1/cosx
D.
cscx = 1/sinx
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Solution
The Pythagorean identity is sin²x + cos²x = 1.
Correct Answer:
A
— sin²x + cos²x = 1
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Q. Which of the following is a root of the polynomial x^2 + 3x - 10?
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Solution
Factoring gives (x + 5)(x - 2) = 0. The roots are x = -5 and x = 2, so 2 is a root.
Correct Answer:
B
— 2
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Q. Which of the following is a root of the polynomial x^2 - 4?
A.
-2
B.
0
C.
2
D.
Both -2 and 2
Show solution
Solution
Step 1: Factor the polynomial: (x - 2)(x + 2). Step 2: Set each factor to zero: x - 2 = 0 or x + 2 = 0. Roots are x = 2 and x = -2.
Correct Answer:
D
— Both -2 and 2
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Q. Which of the following is a root of the polynomial x^2 - 7x + 10?
Show solution
Solution
The polynomial can be factored as (x - 2)(x - 5). Setting each factor to zero gives us x = 2 and x = 5, so 2 is a root.
Correct Answer:
B
— 2
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Q. Which of the following is a root of the polynomial x^3 - 6x^2 + 11x - 6?
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Solution
Using the Rational Root Theorem, we can test x = 1, 2, and 3. Testing x = 3 gives 3^3 - 6(3^2) + 11(3) - 6 = 0, so x = 3 is a root.
Correct Answer:
C
— 3
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Q. Which of the following is a solution to the equation 2x^2 - 8 = 0?
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Solution
First, add 8 to both sides: 2x^2 = 8. Then divide by 2: x^2 = 4. Taking the square root gives x = ±2. Thus, 2 is a solution.
Correct Answer:
B
— 2
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Q. Which of the following is a solution to the equation 3x + 7 = 16?
A.
x = 3
B.
x = 2
C.
x = 1
D.
x = 0
Show solution
Solution
Step 1: Subtract 7 from both sides: 3x = 9. Step 2: Divide both sides by 3: x = 3.
Correct Answer:
B
— x = 2
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Q. Which of the following is a solution to the equation 4x + 1 = 13?
A.
x = 2
B.
x = 3
C.
x = 4
D.
x = 5
Show solution
Solution
Subtract 1 from both sides: 4x = 12. Then divide by 4: x = 3.
Correct Answer:
A
— x = 2
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Q. Which of the following is a solution to the equation 4x + 1 = 17?
A.
x = 4
B.
x = 3
C.
x = 2
D.
x = 5
Show solution
Solution
Step 1: Subtract 1 from both sides: 4x = 16. Step 2: Divide by 4: x = 4.
Correct Answer:
C
— x = 2
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Q. Which of the following is a solution to the equation 4x - 7 = 5?
A.
x = 1
B.
x = 2
C.
x = 3
D.
x = 4
Show solution
Solution
Add 7 to both sides: 4x = 12. Then divide by 4: x = 3.
Correct Answer:
A
— x = 1
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Q. Which of the following is a solution to the equation x^2 + 2x - 8 = 0?
Show solution
Solution
Factor the equation: (x + 4)(x - 2) = 0. The solutions are x = -4 and x = 2.
Correct Answer:
A
— -4
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Q. Which of the following is a solution to the equation x^2 + 6x + 9 = 0?
A.
x = -3
B.
x = 3
C.
x = 0
D.
x = -6
Show solution
Solution
The equation can be factored as (x + 3)(x + 3) = 0. Thus, the solution is x = -3.
Correct Answer:
A
— x = -3
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Q. Which of the following is a solution to the equation x^2 - 7x + 10 = 0?
Show solution
Solution
Factoring gives (x - 5)(x - 2) = 0, so the solutions are x = 5 and x = 2.
Correct Answer:
C
— 5
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Q. Which of the following is a solution to the inequality 2x + 3 > 7?
Show solution
Solution
Step 1: Subtract 3 from both sides: 2x > 4. Step 2: Divide by 2: x > 2. The solution includes all values greater than 2.
Correct Answer:
B
— 2
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Q. Which of the following is a solution to the inequality 3x - 4 < 5?
A.
x < 3
B.
x > 3
C.
x < 2
D.
x > 2
Show solution
Solution
Add 4 to both sides: 3x < 9. Then divide by 3: x < 3.
Correct Answer:
A
— x < 3
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Q. Which of the following is a solution to the inequality 3x - 5 < 4?
A.
x < 3
B.
x > 3
C.
x < 2
D.
x > 2
Show solution
Solution
Add 5 to both sides: 3x < 9. Then divide by 3: x < 3.
Correct Answer:
A
— x < 3
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Q. Which of the following is a solution to the inequality 5x - 7 < 8?
A.
x < 3
B.
x > 3
C.
x < 2
D.
x > 2
Show solution
Solution
Add 7 to both sides: 5x < 15. Divide by 5: x < 3.
Correct Answer:
A
— x < 3
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