CSEC Additional Mathematics Paper 1 May/June 2012 - Free CXC Past Paper with Answers

The expression $ab + 3c - 3b - ac$ is equal to

Which of the following graphs BEST represents $f(x) = x(1-x)$?

The number of visas, $V(x)$, issued by an embassy annually is given by $V(x)=7x^2-42x+72$. The LEAST number of visas issued in a particular year, $x$, is

The roots of the equation $5x^2 + 6x - 2 = 0$ are

The set of values of $x$ for which $5x+7 > 10x - 13$ is

The range of values of $x$ for which $5x+6 \leq x^2$ is

If $f(x) = 3x-4$ and $fg(x) = x$, then $g(x)$ is

The value of $g^{-1}[f(3)]$ is

A function $h$ is defined by $h: x \to 5x + 2$. Expressed in terms of $a$, $h (2a+3)$ is

A function $f$ is defined by $f: x \to 2x-1$. The function $f^2$ is defined as

$\sqrt[3]{3 \times 27^m}$ is equal to

$(8+\sqrt{5})(2-\sqrt{5})$ can be expressed as

The value of $2^z$ where $z = 5 + \log_2 3$ is

The expression $\frac{\sqrt{5}-1}{1+\sqrt{5}}$ when simplified is equal to

$\frac{2^{-1}}{8^3}$ simplifies to

In a geometric progression, each of whose terms is positive, the fifth term is 45 and the seventh term is 5. The SIXTH term is

The sum of the ODD integers between 10 and 50 is

The first four terms of a convergent geometric progression (GP) is given by 500, 200, 80, 32. The sum to infinity of this GP is

A long-distance runner runs the first kilometre of a race in 3 minutes 45 seconds but finds that his speed drops steadily so that each kilometre takes him 12 seconds more than the preceding one. The time taken to cover the first 12 kilometres is

The lines $7x-4y+25=0$ and $3x-y-5=0$ intersect at the point P, where

The line through the points P(k, 2) and Q(6, 8) is parallel to the line with equation $3x+y-21=0$. The value of k is

The point (2, 3) is at one end of a diameter of the circle whose equation is $x^2+y^2 - 10x + 2y + 1 = 0$. The coordinates of the other end of the diameter are

The vector a is given as $5i + 12j$. A unit vector parallel to a is

Given that $\vec{OA} = \begin{pmatrix} -17 \\ 25 \end{pmatrix}$ and $\vec{OB} = \begin{pmatrix} 4 \\ 5 \end{pmatrix}$, the vector $\vec{AB}=$

The acute angle AOB is given by

If $\sin \theta = \frac{5}{13}$ and $\theta$ is obtuse, then $\tan \theta =$

$\cos (A + B) + \cos (A - B) =$

The SMALLEST positive angle for which the equation sin θ – cos θ = 0 for 0 ≤ θ ≤ 2π, is

sin (α + 45°) is equal to

Convert $\frac{4\pi}{5}$ radians into degrees.

The exact value of tan 150° is given by

The trigonometrical expression $\frac{\sin x}{1-\cos x} + \frac{\sin x}{1+\cos x}$ is identical to

Given that $y = (5-2x)^5$, then $\frac{dy}{dx}$ =

The gradient at $x = \frac{\pi}{6}$ on the curve $y = \sin x$ is

The equation of a curve is given by $y = (x^2+2) (x - 1)^3$. The gradient function, $\frac{dy}{dx}$, is given by

Given $y = 5 \sin 2x$, then $\frac{dy}{dx}$ =

The curve C is given by the equation $y=x^2 + \frac{16}{x}$. The second derivative, $\frac{d^2 y}{dx^2}$ is given by

The value of $a$ for which $\int_{0}^{a} (x^2-5) dx = \frac{50}{3}$ is

$\int (3x-5)^4 dx =$

The region in the first quadrant enclosed by the curve $y=x-\frac{1}{2}x^2$, the lines $x=0$ and $x=2$ is rotated completely about the x-axis. The volume in units$^3$ of the solid generated is

The region R is enclosed by the x-axis, the curve $y = x^2 + 2x - 1$, the lines $x = 2$ and $x = 3$. The area in units$^2$ of R is

$\int (\sin x + 2\cos x) dx =$

Given that $\frac{d}{dx} \left( \frac{x}{1+x} \right) = \frac{1}{(1+x)^2}$, then $\int_0^2 \frac{3}{(1+x)^2} dx$ is equal to