Algebraic expression of word expression "2 times number a increased by 3" is
Answer: B
"2 times number \( a \)" is \( 2a \), and "increased by 3" adds 3 to it.
\[ 2a + 3 \]
The order matters: \( 3a + 2 \) would be three times the number increased by two.
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Simplify 15ax² ⁄ 5x
Answer: B
Divide the coefficients and subtract the exponents.
\[ \frac{15ax^{2}}{5x} = \frac{15}{5} \cdot a \cdot x^{2-1} = 3ax \]
The \( x \) in the denominator lowers the power by one; leaving it as \( x^{2} \) is the usual slip.
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Simplify (1 ⁄ s) - (1 ⁄ t)
Answer: B
Put both fractions over the common denominator \( st \).
\[ \frac{1}{s} - \frac{1}{t} = \frac{t}{st} - \frac{s}{st} = \frac{t-s}{st} \]
The order matters: subtracting \( \tfrac{1}{t} \) leaves \( t \) first in the numerator, so \( \tfrac{s-t}{st} \) is the negative of the answer.
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Sum of 2a + b + 5c and -5a - 2b + 3c is
Answer: C
Add the like terms.
\[ a: \ 2 - 5 = -3 \]
\[ b: \ 1 - 2 = -1 \]
\[ c: \ 5 + 3 = 8 \]
\[ \therefore\ -3a - b + 8c \]
The \( c \) terms are both positive, so that coefficient grows while the other two turn negative.
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Factorization of p(4q + 3) +4(4q+3) leads to
Answer: C
Both terms share the bracket \( (4q + 3) \).
\[ p(4q+3) + 4(4q+3) = (p + 4)(4q + 3) \]
Checking: \( 4pq + 3p + 16q + 12 \), which is what the original expands to.
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By solving expression 4[3s - 2(6s - 8)], answer will be
Answer: C
Work from the inside out.
\[ 2(6s - 8) = 12s - 16 \]
\[ 3s - (12s - 16) = 3s - 12s + 16 = -9s + 16 \]
\[ 4(-9s + 16) = -36s + 64 \]
The minus in front of the inner bracket flips both its terms, turning \( -16 \) into \( +16 \).
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Sum of 2s + 4t -3u + 5v, -s + 2t + 9u - 11v and 3s - 4t + 2u - 3v is
Answer: D
Collect each variable across the three expressions.
\[ s: \ 2 - 1 + 3 = 4 \]
\[ t: \ 4 + 2 - 4 = 2 \]
\[ u: \ -3 + 9 + 2 = 8 \]
\[ v: \ 5 - 11 - 3 = -9 \]
\[ \therefore\ 4s + 2t + 8u - 9v \]
The options differ only in the signs of the \( t \) and \( u \) terms, so those two columns decide the answer.
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Simplify (2 ⁄ tanA) + (4 ⁄ tanB)
Answer: A
The common denominator is \( \tan A \tan B \).
\[ \frac{2}{\tan A} + \frac{4}{\tan B} = \frac{2\tan B}{\tan A \tan B} + \frac{4\tan A}{\tan A \tan B} \]
\[ = \frac{2\tan B + 4\tan A}{\tan A \tan B} \]
Each numerator picks up the other denominator - swapping them is the error the second option represents.
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Which of the following is the numerical coefficient of -5xy?
Answer: C
\[ -5xy = (-5) \cdot xy \]
The numerical coefficient is −5 - the sign belongs with it. Dropping the minus gives 5, which is the magnitude of the coefficient rather than the coefficient itself.
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Simplify 5⁄2 ÷ 1⁄x
Answer: A
Dividing by a fraction means multiplying by its reciprocal.
\[ \frac{5}{2} \div \frac{1}{x} = \frac{5}{2} \times \frac{x}{1} = \frac{5x}{2} \]
The reciprocal of \( \tfrac{1}{x} \) is \( x \), so the \( x \) moves to the numerator.
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