Practice every past-year question.

1. A
   142
2. B
   68
3. C
   136
4. D
   102

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1. A
   $\frac{41}{8}e + \frac{19}{8}e^{- 1} - 10$
2. B
   $- \frac{41}{8}e + \frac{19}{8}e^{- 1} - 10$
3. C
   $\frac{41}{8}e - \frac{19}{8}e^{- 1} - 10$
4. D
   $\frac{41}{8}e + \frac{19}{8}e^{- 1} + 10$

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1. A
   $2a + 4$
2. B
   $2a - 4$
3. C
   $4 - 2a$
4. D
   $a + 4$

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1. A
   a parabola
2. B
   a straight line
3. C
   a hyperbola
4. D
   an ellipse

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

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1. A
   $- \frac{18}{11}$
2. B
   $- \frac{18}{19}$
3. C
   $- \frac{4}{3}$
4. D
   $\frac{18}{35}$

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1. A
   $A_{1} = A_{2}$ and $A_{1} + A_{2} = \sqrt{2}$
2. B
   $A_{1}:A_{2} = 1:2$ and $A_{1} + A_{2} = 1$
3. C
   $2A_{1} = A_{2}$ and $A_{1} + A_{2} = 1 + \sqrt{2}$
4. D
   $A_{1}:A_{2} = 1:\sqrt{2}$ and $A_{1} + A_{2} = 1$

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1. A
   $\log_{e}2$
2. B
   $\log_{e}\left( \frac{e}{2} \right)$
3. C
   e
4. D
   $e^{2} - 1$

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1. A
   $F_{1}$ is not a tautology but $F_{2}$ is a tautology
2. B
   $F_{1}$ is a tautology but $F_{2}$ is not a tautology
3. C
   $F_{1}$ and $F_{2}$ both area tautologies
4. D
   Both $F_{1}$ and $F_{2}$ are not tautologies

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1. A
   has a unique solution when $5a = 2b + c$
2. B
   has infinite number of solutions when $5a = 2b + c$
3. C
   has no solution for all $a,b$ and $c$
4. D
   has a unique solution for all $a,b$ and $c$

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1. A
   $\frac{6}{7}$
2. B
   $\frac{4}{7}$
3. C
   $\frac{3}{7}$
4. D
   $\frac{1}{7}$

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1. A
   $\frac{1}{\sqrt{2}}( - \widehat{j} + \widehat{k})$
2. B
   $\frac{1}{\sqrt{2}}(\widehat{i} - \widehat{j})$
3. C
   $\frac{1}{\sqrt{3}}(\widehat{i} - \widehat{j} + \widehat{k})$
4. D
   $\frac{1}{\sqrt{3}}(\widehat{i} + \widehat{j} - \widehat{k})$

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1. A
   $\frac{1}{2}$
2. B
   -1
3. C
   1
4. D
   0

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

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1. A
   $10^{5}$
2. B
   $\ ^{10}C_{5}$
3. C
   $5^{5}$
4. D
   5!

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1. A
   11
2. B
   $6x$
3. C
   12
4. D
   6

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1. A
   $( - \infty, - 2\rbrack \cup \left\lbrack - \frac{4}{3},\infty \right)$
2. B
   $( - \infty, - 1\rbrack \cup \lbrack 2,\infty)$
3. C
   $( - \infty, - 2\rbrack \cup \lbrack - 1,\infty)$
4. D
   $( - \infty, - 2\rbrack \cup \left\lbrack - \frac{3}{2},\infty \right)$

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1. A
   47
2. B
   39
3. C
   43
4. D
   41

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1. A
   $2e^{\left( e^{x} - 1 \right)} - 1$
2. B
   $e^{\left( e^{x} - 1 \right)}$
3. C
   $2e^{e^{x}} - 1$
4. D
   $e^{e^{x}} - 1$

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1. A
   A right-angle triangle having two of its sides of length $2r$ and $r$.
2. B
   An equilateral triangle of height $\frac{2r}{3}$.
3. C
   An isosceles triangle with base equal to $2r$.
4. D
   An equilateral triangle having each of its side of length $\sqrt{3}r$.

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1. A
   77
2. B
   42
3. C
   35
4. D
   82

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1. A
   $\frac{10!}{\sqrt{3}(5!)^{2}}$
2. B
   $\frac{2.10!}{3(5!)^{2}}$
3. C
   $\frac{10!}{3(5!)^{2}}$
4. D
   $\frac{2.10!}{3\sqrt{3}(5!)^{2}}$

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1. A
   $100(e - 1)$
2. B
   $100e$
3. C
   $100(1 - e)$
4. D
   $100(1 + e)$

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1. A
   4
2. B
   2
3. C
   16
4. D
   8

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1. A
   $\frac{1}{2}|\overrightarrow{a}|^{4}\overrightarrow{b}$
2. B
   $\overrightarrow{a} \times \overrightarrow{b}$
3. C
   $|\overrightarrow{a}|^{4}\overrightarrow{b}$
4. D
   $\overrightarrow{0}$

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