Cloze Test
Q. If 5x + 2 = 17, what is the value of x?
Solution
Subtract 2 from both sides to get 5x = 15, then divide by 5 to find x = 3.
Correct Answer: B — 3
Q. If a number is even, which of the following must also be even?
-
A.
Its square
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B.
Its cube
-
C.
The sum of it and 2
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D.
All of the above
Solution
All options result in even numbers when an even number is used.
Correct Answer: D — All of the above
Q. If a number is even, which of the following must be true?
-
A.
It is divisible by 2
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B.
It is divisible by 3
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C.
It is odd
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D.
It is prime
Solution
An even number is defined as being divisible by 2.
Correct Answer: A — It is divisible by 2
Q. If a number n is odd, what can we say about n^2?
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A.
n^2 is even
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B.
n^2 is odd
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C.
n^2 is prime
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D.
n^2 is composite
Solution
The square of an odd number is always odd.
Correct Answer: B — n^2 is odd
Q. If a polynomial f(x) = x^2 - 4, what are its roots?
-
A.
-2, 2
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B.
0, 4
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C.
1, -1
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D.
2, 2
Solution
Setting f(x) = 0 gives x^2 - 4 = 0, so x = ±2.
Correct Answer: A — -2, 2
Q. If a sequence is defined by a_n = 3n + 1, what is a_4?
Solution
Substituting n = 4 gives a_4 = 3(4) + 1 = 12 + 1 = 13.
Correct Answer: B — 11
Q. If a sequence is defined by a_n = 3n + 1, what is a_5?
Solution
a_5 = 3(5) + 1 = 15 + 1 = 16.
Correct Answer: A — 14
Q. If n is an odd integer, which of the following is always even?
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A.
n + 1
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B.
n - 1
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C.
2n
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D.
All of the above
Solution
Both n + 1 and n - 1 are even, and 2n is always even.
Correct Answer: D — All of the above
Solution
7 divided by 3 gives a remainder of 1.
Correct Answer: B — 2
Q. What is the 5th term in the arithmetic sequence 2, 5, 8, ...?
Solution
The common difference is 3. The 5th term is 2 + 4*3 = 14.
Correct Answer: A — 14
Q. What is the 5th term of the arithmetic sequence 3, 7, 11, ...?
Solution
The common difference is 4; thus, the 5th term is 3 + 4*4 = 19.
Correct Answer: B — 19
Q. What is the greatest common divisor (GCD) of 12 and 15?
Solution
The GCD of 12 and 15 is 3, as it is the largest number that divides both.
Correct Answer: B — 3
Q. What is the product of the roots of the polynomial x^2 - 5x + 6?
Solution
The product of the roots is given by c/a = 6/1 = 6.
Correct Answer: A — 6
Q. What is the remainder when 25 is divided by 4?
Solution
25 divided by 4 gives a quotient of 6 and a remainder of 1.
Correct Answer: C — 3
Q. What is the remainder when 37 is divided by 5?
Solution
37 divided by 5 gives a quotient of 7 and a remainder of 2.
Correct Answer: C — 2
Q. What is the sum of the first five positive integers?
Solution
The sum is 1 + 2 + 3 + 4 + 5 = 15.
Correct Answer: B — 15
Q. What is the value of 10 mod 3?
Solution
10 divided by 3 gives a remainder of 1.
Correct Answer: B — 2
Q. What is the value of 2x if x = 4?
Solution
2x = 2 * 4 = 8.
Correct Answer: C — 8
Q. What is the value of 3^2 + 4^2?
Solution
3^2 = 9 and 4^2 = 16, so 9 + 16 = 25.
Correct Answer: A — 25
Q. What is the value of 3^3?
Solution
3^3 = 3 * 3 * 3 = 27.
Correct Answer: C — 27
Q. What is the value of 5! (5 factorial)?
-
A.
20
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B.
60
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C.
120
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D.
240
Solution
5! = 5 * 4 * 3 * 2 * 1 = 120.
Correct Answer: C — 120
Q. What is the value of 7 mod 4?
Solution
7 divided by 4 gives a remainder of 3.
Correct Answer: A — 1
Q. What is the value of x in the equation 2x - 4 = 10?
Solution
Adding 4 to both sides gives 2x = 14, so x = 14/2 = 7.
Correct Answer: B — 7
Q. Which of the following is a factor of 36?
Solution
6 is a factor of 36 since 36 ÷ 6 = 6.
Correct Answer: B — 6
Q. Which of the following is a solution to the equation x^2 - 4 = 0?
-
A.
-2
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B.
0
-
C.
2
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D.
Both -2 and 2
Solution
The equation factors to (x - 2)(x + 2) = 0, giving solutions x = -2 and x = 2.
Correct Answer: D — Both -2 and 2
Q. Which of the following is a solution to the equation x^2 - 5x + 6 = 0?
Solution
Factoring gives (x-2)(x-3)=0, so x=2 or x=3.
Correct Answer: B — 2
Q. Which of the following is an even integer?
Solution
8 is an even integer as it is divisible by 2.
Correct Answer: C — 8
Q. Which of the following numbers is prime?
Solution
11 is only divisible by 1 and itself, making it prime.
Correct Answer: C — 11
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