CSEC Additional Mathematics Paper 2 May/June 2008 - Free CXC Past Paper with Answers

$A \cap B = \emptyset$,

In the diagram, set notation, the set represented by the shaded region.

$(C \cup D) \subseteq E$.

Sketch, on the same diagram, the graphs of $y = x - 3$ and $y = |2x - 9|$.

Solve the equation $|2x - 9| = x - 3$.

$(1 + 3x)^8$,

$(1 - 4x)(1 + 3x)^8$.

Given that $\sin x = p$, find an expression, in terms of $p$, for $\sec^2 x$.

Prove that $\sec A \operatorname{cosec} A - \cot A = \tan A$.

Write down an expression, in terms of $x$, for $(OP)^2$.

Denoting $(OP)^2$ by $S$, find an expression for $\frac{dS}{dx}$.

Find the value of $x$ for which $S$ has a stationary value and the corresponding value of $OP$.

$2^{2x+1} = 20$,

$\frac{5^{4y-1}}{25^{2-y}} = \frac{1}{125^{y+3}}$.

$AB$,

$BC$,

the matrix $X$ such that $AX = B$.

Find

$\int \frac{12}{(2x-1)^4} dx$,

$\int x(x-1)^2 dx$.

Given that $y = 2(x-5)\sqrt{x+4}$, show that .

Given that $y = 2(x-5)\sqrt{x+4}$, show that .

Hence find $\int \frac{(x+1)}{\sqrt{x+4}} dx$.

the range of f,

$f^2(1)$,

an expression for $f^{-1}(x)$.

The function g is defined by $g(x) = \frac{20}{x+1}$ for . Find

$g^{-1}(2)$,

the value of $x$ for which $fg(x) = 38$.

Find the coordinates of $A$ and of $B$.

Find the area of the shaded region.

OR

Solutions to this question by accurate drawing will not be accepted.

The points $A(-2, 2)$, $B(4, 4)$ and $C(5, 2)$ are the vertices of a triangle. The perpendicular bisector of and the line through parallel to intersect at the point . Find the area of the quadrilateral .