CSEC Additional Mathematics Paper 1 May/June 2015 - Free CXC Past Paper with Answers

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

If $x^2 - 6x + 13 = a(x+h)^2 + k$ then

The roots of the equation $3x^2 - 6x - 5 = 0$ are

The values of $x$ for which $(x+15)^2 = 64x$ are

The range of values for which $x^2 - 7x + 10 < 0$ is

The set of values of $x$ for which $3x + 2 > x - 2$ is

Functions $f$ and $g$ are defined by $f: x \to 2x - 5$ and $g: x \to 4 + \frac{3}{2x}$, $x \neq 0$. The composite function $gf$ is defined by

Given that $f(x) = x^2 + 4x - 21$, the range of $f(x)$ is

If function m: x → 5 + 2x, then m(4 - 2a) is

If $f:x \to 2\left(\frac{x}{3}+5\right)$, then $f^{-1}(x)$ is equal to

Given that $3 \times 27^{2x} = 9^x$, the value of x is

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

The value of x for which $4^{x+1} = 2$ is

Given that $\log_2 x^3 = 6$, then the value of x is

Given that $\alpha$ and $\beta$ are the roots of the equation $x^2 + 3x + 4 = 0$, what is the value of $(\alpha + \beta)^2$?

The common ratio of the geometric sequence 8, 12, 18, ... is

The sum of the ODD integers between 10 and 50 is

For the arithmetic progression -12, -7, -2, 3, 8... the nth term is given by

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 line L passes through the point (6, 5) and is perpendicular to the line whose equation is $3x+4y-7=0$. The equation of L is

The line $y = 2x - 7$ and the line $x + 3y = 7$ intersect at the point

A circle C has centre (3, -2) and radius 4. The equation of C is

Two vectors are equal if they

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

The position vector of the point P relative to an origin O is given as p = 5i + 2j and the position vector of Q relative to an origin O is given as q = -4i + 10j.

Which of the following statements is TRUE?

The EXACT value of $\frac{\sin 150^\circ}{\cos 150^\circ}$ is given as

The size of angle X, measured in radians, is

Which of the following graphs represents $y = \sin x$?

The smallest positive angle within the range $0 \le \theta \le 2\pi$ that satisfies the equation $(2 \cos \theta - 1)(\cos \theta - 2) = 0$ is

sin ($\alpha - 45^\circ$) is equal to

$\frac{4\pi}{5}$ radians converted to degrees is

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

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

$\frac{d}{dx}\sqrt{(7x^2 + 4)}=$

At the point (7, 4) on the curve $y = f(x)$, $\frac{dy}{dx} = 0$ and $\frac{d^2y}{dx^2} = -5$. The point (7, 4) is

Given that $y = \cos 2x$, then $\frac{dy}{dx} =$

If $y = \frac{x^2}{x+3}$ then $\frac{dy}{dx}$ is

The curve C with equation $y = f(x)$ has a stationary point at $(-2, 5)$. If $f''(x) = x^4 - 15$, then $(-2, 5)$ is

If $\int_{2}^{a} (6+3x) dx = 72$, where $a > 2$, then $a =$

The region bounded by the curve $y = x^2$, the x-axis and the lines $x = 0$ and $x = 1$ is rotated $360^\circ$ about the x- axis. The volume of the solid generated can be found from:

$\int (2x-5)^3 dx = $

If $y = 3x^2 + \cos x$ then $\int y dx =$

$\int_{1}^{2}(1+x+x^2)dx=$

The region R is enclosed by the x-axis, the curve $y = -x^2 + 2$, the lines $x = 0$ and $x = 1$. The area of R is