1. A
   for all real numbers $a$, $b$ and $c$
2. B
   only when $a eq 0$
3. C
   only when $b eq 0$
4. D
   only when at least one of $a$ and $b$ is non-zero

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1. A
   $\beta - \alpha$
2. B
   $\pi + \beta - \alpha$
3. C
   $\dfrac{\pi + 2\beta + 2\alpha}{2}$
4. D
   $\dfrac{\pi - 2\beta + 2\alpha}{2}$

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1. A
   $|2m\sin(\alpha-\beta)|$
2. B
   $|2m\cos(\alpha-\beta)|$
3. C
   $|m\sin(2\alpha-2\beta)|$
4. D
   $|m\sin(2\alpha-2\beta)|$

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1. A
   $\left(-\sqrt{2}, \sqrt{2}\right)$
2. B
   $\left(\sqrt{2}, -\sqrt{2}\right)$
3. C
   (1, 1)
4. D
   (1, -1)

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1. A
   $\dfrac{1}{2}$
2. B
   $\dfrac{1}{\sqrt{2}}$
3. C
   $\dfrac{\sqrt{3}}{2}$
4. D
   $\dfrac{1}{2\sqrt{2}}$

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1. A
   $\dfrac{1}{2},\, \dfrac{1}{2},\, \dfrac{1}{\sqrt{2}}$
2. B
   $\dfrac{1}{\sqrt{2}},\, \dfrac{1}{2},\, \dfrac{1}{2}$
3. C
   $\dfrac{1}{\sqrt{2}},\, \dfrac{1}{2},\, -\dfrac{1}{2}$
4. D
   Cannot be determined due to insufficient data

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1. A
   (3, 5, 4)
2. B
   (2, 5, 5)
3. C
   (-1, -1, 5)
4. D
   (2, -1, 0)

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1. A
   2
2. B
   3
3. C
   5
4. D
   7

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1. A
   90°
2. B
   60°
3. C
   45°
4. D
   30°

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1. A
   1, -1
2. B
   -1, 1
3. C
   0, 2
4. D
   3, 4

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1. A
   $(a+b)^{2}$
2. B
   $(a-b)^{2}$
3. C
   $a^{2}+b^{2}$
4. D
   $|a^{2}+b^{2}|$

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1. A
   30°
2. B
   45°
3. C
   60°
4. D
   75°

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1. A
   $\dfrac{1}{x} + \dfrac{1}{y}$
2. B
   $\dfrac{1}{y} - \dfrac{1}{x}$
3. C
   $\dfrac{xy}{x+y}$
4. D
   $1 + \dfrac{1}{xy}$

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1. A
   0
2. B
   $2\sin\alpha$
3. C
   $2\sin\beta$
4. D
   $\sin\alpha + \sin\beta$

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1. A
   $\dfrac{1}{5}$
2. B
   $\dfrac{1}{6}$
3. C
   $\dfrac{1}{7}$
4. D
   $\dfrac{1}{9}$

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1. A
   2
2. B
   1
3. C
   0
4. D
   -19

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1. A
   $\dfrac{a^{2}-b^{2}}{ab}$
2. B
   $\dfrac{a^{2}}{bc}$
3. C
   $\dfrac{b^{2}}{ca}$
4. D
   $\dfrac{c^{2}}{ab}$

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1. A
   $\tan A$
2. B
   $\cot A$
3. C
   $2\tan A$
4. D
   $2\cot A$

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1. A
   $\tan\left(\dfrac{A}{2}\right)$
2. B
   $\cot\left(\dfrac{A}{2}\right)$
3. C
   $2\tan\left(\dfrac{A}{2}\right)$
4. D
   $2\cot\left(\dfrac{A}{2}\right)$

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1. A
   0
2. B
   1
3. C
   2
4. D
   4

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1. A
   40 square units
2. B
   80 square units
3. C
   120 square units
4. D
   160 square units

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1. A
   1 only
2. B
   2 only
3. C
   Both 1 and 2
4. D
   Neither 1 nor 2

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1. A
   $\dfrac{1}{4}$
2. B
   $\dfrac{1}{3}$
3. C
   $\dfrac{1}{2}$
4. D
   1

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1. A
   1
2. B
   2
3. C
   3
4. D
   4

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1. A
   $5x^{2} - 2x + 5$
2. B
   $3x^{2} - 2x - 5$
3. C
   $3x^{2} - 2x + 5$
4. D
   $3x^{2} - 10x + 5$

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