Q1 & Q2 & Q3 & Q4 & Q5 & Q6 & Q7 & Total \hline & & & & & & & & & & & & & & \hline \end{tabular}
1. For ALL APPLICANTS.
For each part of the question on pages $3 - 7$ you will be given four possible answers, just one of which is correct. Indicate for each part $\mathbf { A } - \mathbf { J }$ which answer (a), (b), (c), or (d) you think is correct with a tick ( ✓ ) in the corresponding column in the table below. Please show any rough working in the space provided between the parts.
A. The area of the region bounded by the curves $y = x ^ { 2 }$ and $y = x + 2$ equals
(a) $\frac { 7 } { 3 }$
(b) $\frac { 7 } { 2 }$
(c) $\frac { 9 } { 2 }$
(d) $\frac { 11 } { 2 }$
B. The smallest value of the function
$$f ( x ) = 2 x ^ { 3 } - 9 x ^ { 2 } + 12 x + 3$$
in the range $0 \leq x \leq 2$ is
(a) 1
(b) 3
(c) 5
(d) 7
C. What is the reflection of the point $( 3,4 )$ in the line $3 x + 4 y = 50$ ?
(a) $( 9,12 )$
(b) $( 6,8 )$
(c) $( 12,16 )$
(d) $( 16,12 )$
D. The equation $x ^ { 3 } - 30 x ^ { 2 } + 108 x - 104 = 0$
(a) no real roots;
(b) exactly one real root;
(c) three distinct real roots;
(d) a repeated root.
E. The fact that
$$6 \times 7 = 42$$
is a counter-example to which of the following statements?
(a) the product of any two odd integers is odd;
(b) if the product of two integers is not a multiple of 4 then the integers are not consecutive;
(c) if the product of two integers is a multiple of 4 then the integers are not consecutive;
(d) any even integer can be written as the product of two even integers. F. How many values of $x$ satisfy the equation
$$2 \cos ^ { 2 } x + 5 \sin x = 4$$
in the range $0 \leqslant x < 2 \pi$ ?
(a) 2
(b) 4
(c) 6
(d) 8 G. The inequalities $x ^ { 2 } + 3 x + 2 > 0$ and $x ^ { 2 } + x < 2$, are met by all $x$ in the region:
(a) $x < - 2$;
(b) $- 1 < x < 1$;
(c) $x > - 1$;
(d) $x > - 2$. H. Given that
$$\log _ { 10 } 2 = 0.3010 \text { to } 4 \text { d.p. and that } 10 ^ { 0.2 } < 2$$
it is possible to deduce that
(a) $2 ^ { 100 }$ begins in a 1 and is 30 digits long;
(b) $2 ^ { 100 }$ begins in a 2 and is 30 digits long;
(c) $2 ^ { 100 }$ begins in a 1 and is 31 digits long;
(d) $2 ^ { 100 }$ begins in a 2 and is 31 digits long. I. The power of $x$ which has the greatest coefficient in the expansion of $\left( 1 + \frac { 1 } { 2 } x \right) ^ { 10 }$ is
(a) $x ^ { 2 }$
(b) $x ^ { 3 }$
(c) $x ^ { 5 }$
(d) $x ^ { 10 }$ J. A sketch of the curve with equation $x ^ { 2 } y ^ { 2 } ( x + y ) = 1$ is drawn in which of the following diagrams?
[Figure](a)
[Figure](c)
[Figure](b)
[Figure](d)