Algebra & Number Theory
Q. What is the value of x in the equation 7x - 2 = 5x + 10?
Solution
Subtract 5x from both sides: 2x - 2 = 10. Add 2: 2x = 12. Divide by 2: x = 6.
Correct Answer: A — 4
Q. What is the value of x in the equation x^2 - 2x - 8 = 0?
Solution
Factoring gives (x - 4)(x + 2) = 0, so x = 4 or x = -2.
Correct Answer: C — 4
Q. What is the value of √(16) + √(9)?
Solution
√(16) = 4 and √(9) = 3, so 4 + 3 = 7.
Correct Answer: B — 7
Q. What is the value of √(25) - √(16)?
Solution
√(25) = 5 and √(16) = 4, so 5 - 4 = 1.
Correct Answer: B — 3
Q. Which of the following is equal to 5^(2/3)?
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A.
√(25)
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B.
5√(5)
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C.
25
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D.
√(125)
Solution
5^(2/3) = (5^(1/3))^2 = 5√(5).
Correct Answer: B — 5√(5)
Q. Which of the following is equivalent to (x^(1/2))^4?
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A.
x^(2)
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B.
x^(1)
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C.
x^(1/4)
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D.
x^(1/8)
Solution
Using the power of a power property, (x^(1/2))^4 = x^(1/2 * 4) = x^(2).
Correct Answer: A — x^(2)
Q. Which of the following is equivalent to 2^(3) * 2^(2)?
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A.
2^(5)
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B.
2^(6)
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C.
2^(7)
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D.
2^(8)
Solution
Using the property a^m * a^n = a^(m+n), we have 2^(3+2) = 2^(5).
Correct Answer: A — 2^(5)
Q. Which of the following is equivalent to 2^(3/2)?
Solution
2^(3/2) = √(2^3) = √8.
Correct Answer: A — √8
Q. Which of the following is equivalent to log10(0.01)?
Solution
log10(0.01) = log10(10^-2) = -2.
Correct Answer: B — -2
Q. Which of the following is equivalent to log5(25)?
Solution
log5(25) = log5(5^2) = 2.
Correct Answer: B — 2
Q. Which of the following is true for the expression 3^(2x) = 27?
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A.
x = 1
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B.
x = 2
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C.
x = 3
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D.
x = 0
Solution
27 = 3^(3), so 2x = 3, thus x = 3/2.
Correct Answer: A — x = 1
Q. Which of the following is true for the expression 4^(x) = 16?
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A.
x = 1
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B.
x = 2
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C.
x = 3
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D.
x = 4
Solution
16 = 4^(2), thus x = 2.
Correct Answer: B — x = 2
Q. Which of the following is true for the expression 5^(x) = 25?
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A.
x = 1
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B.
x = 2
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C.
x = 3
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D.
x = 4
Solution
25 = 5^(2), thus x = 2.
Correct Answer: B — x = 2
Q. Which of the following is true for √(x^2)?
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A.
x
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B.
-x
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C.
-
D.
x
-
.
-
.
x^2
Solution
√(x^2) = |x|.
Correct Answer: C —
Q. Which of the following pairs of numbers has an HCF of 10?
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A.
20 and 30
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B.
25 and 35
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C.
40 and 50
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D.
15 and 25
Solution
The HCF of 40 and 50 is 10, as it is the largest number that divides both.
Correct Answer: C — 40 and 50
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