Q. For the quadratic equation x^2 + 2x + k = 0 to have real roots, what must be the minimum value of k? (2020)
Solution
The discriminant must be non-negative: 2^2 - 4*1*k >= 0, thus k <= 1.
Correct Answer: A — -1
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Q. For the quadratic equation x^2 + 4x + k = 0 to have equal roots, what must be the value of k? (2022)
Solution
For equal roots, the discriminant must be zero: 4^2 - 4*1*k = 0, thus k = 4.
Correct Answer: B — 8
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Q. If 2y - 7 = 13, what is the value of y? (2023)
Solution
2y - 7 = 13 => 2y = 20 => y = 10.
Correct Answer: A — 10
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Q. If 4z + 8 = 32, what is the value of z? (2023)
Solution
4z + 8 = 32 => 4z = 24 => z = 6.
Correct Answer: B — 5
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Q. If 5m + 15 = 45, what is the value of m? (2023)
Solution
5m + 15 = 45 => 5m = 30 => m = 6.
Correct Answer: A — 5
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Q. If 6a + 4 = 28, what is the value of a? (2023)
Solution
6a + 4 = 28 => 6a = 24 => a = 4.
Correct Answer: B — 4
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Q. If 8b + 16 = 48, what is the value of b? (2023)
Solution
8b + 16 = 48 => 8b = 32 => b = 4.
Correct Answer: A — 4
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Q. If A > B and B > C, which of the following is true?
-
A.
A > C
-
B.
C > A
-
C.
B < A
-
D.
C < B
Solution
If A > B and B > C, then by transitive property, A > C is true.
Correct Answer: A — A > C
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Q. If A < B and B ≤ C, which of the following is true?
-
A.
A < C
-
B.
C < A
-
C.
B < A
-
D.
C = B
Solution
Since A < B and B ≤ C, it follows that A < C.
Correct Answer: A — A < C
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Q. If A ≤ B and B < C, which of the following is true?
-
A.
A < C
-
B.
C < A
-
C.
B = A
-
D.
C < B
Solution
From A ≤ B and B < C, we can conclude A < C.
Correct Answer: A — A < C
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Q. If D = E and E > F, which of the following is true?
-
A.
D > F
-
B.
F < D
-
C.
E < D
-
D.
D < E
Solution
Since D = E and E > F, it follows that D > F.
Correct Answer: A — D > F
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Q. If M ≥ N and N > O, which of the following is true?
-
A.
M > O
-
B.
M < O
-
C.
N < M
-
D.
O = N
Solution
From M ≥ N and N > O, we can conclude M > O.
Correct Answer: A — M > O
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Q. If P > Q and Q = R, which of the following is true?
-
A.
P > R
-
B.
R < P
-
C.
Q < P
-
D.
P = Q
Solution
Since Q = R and P > Q, it follows that P > R.
Correct Answer: A — P > R
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Q. If P ≤ Q and Q < R, which of the following is true?
-
A.
P < R
-
B.
P = R
-
C.
Q = P
-
D.
R < P
Solution
Since P ≤ Q and Q < R, it follows that P < R.
Correct Answer: A — P < R
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Q. If the roots of the equation x^2 + 3x + 2 = 0 are a and b, what is the value of a + b? (2022)
Solution
The sum of the roots is -b/a = -3/1 = -3.
Correct Answer: A — -3
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Q. If the roots of the equation x^2 + 6x + 9 = 0 are equal, what is the value of the root? (2023)
Solution
The equation can be factored as (x+3)(x+3)=0, hence the root is -3.
Correct Answer: A — -3
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Q. If X > Y and Y = Z, which of the following is true?
-
A.
X > Z
-
B.
Z > X
-
C.
Y < Z
-
D.
X = Y
Solution
Since Y = Z and X > Y, it follows that X > Z.
Correct Answer: A — X > Z
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Q. If X < Y and Y = Z, which of the following is true?
-
A.
X < Z
-
B.
Z < X
-
C.
Y < X
-
D.
X = Y
Solution
Since Y = Z, and X < Y, it follows that X < Z.
Correct Answer: A — X < Z
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Q. Solve for x: 10x - 10 = 0. (2023)
Solution
10x - 10 = 0 => 10x = 10 => x = 1.
Correct Answer: B — 1
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Q. Solve for x: 7x - 3 = 18. (2023)
Solution
7x - 3 = 18 => 7x = 21 => x = 3.
Correct Answer: C — 5
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Q. The equation x^2 - 9 = 0 has roots that are: (2019)
-
A.
-3 and 3
-
B.
0 and 9
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C.
3 and 9
-
D.
1 and -1
Solution
Factoring gives (x-3)(x+3)=0, hence the roots are -3 and 3.
Correct Answer: A — -3 and 3
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Q. The roots of the equation x^2 - 7x + 10 = 0 are: (2019)
-
A.
1 and 10
-
B.
2 and 5
-
C.
3 and 4
-
D.
5 and 2
Solution
Factoring gives (x-2)(x-5)=0, hence the roots are 2 and 5.
Correct Answer: C — 3 and 4
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Q. What is the value of x in the equation 5x + 2 = 17? (2023)
Solution
5x + 2 = 17 => 5x = 15 => x = 3.
Correct Answer: B — 3
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Q. What is the value of y in the equation 9y - 5 = 22? (2023)
Solution
9y - 5 = 22 => 9y = 27 => y = 3.
Correct Answer: B — 3
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