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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By factorizing algebraic expression 4px - 8qx - 3py + 6qy, answer will be
Answer: D
Group in pairs and factor each.
\[ 4px - 8qx - 3py + 6qy = 4x(p - 2q) - 3y(p - 2q) \]
\[ = (4x - 3y)(p - 2q) \]
Taking out \( -3y \) rather than \( 3y \) from the second pair is what makes both brackets read \( (p - 2q) \).
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