CSEC Additional Mathematics Paper 1 May/June 2018 - Free CXC Past Paper with Answers

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

The linear factor of $x^3 - 3x^2 - 3x - 4$ is

Given that $f(x) = \frac{6-x}{x}-x-2x^2$ is less than or equal to $k$ , where $k \in \mathbb{R}$ , then $k$ is equal to

Given that $f(x) = 1 - 4x - 2x^2$ , then $f(x)$ can be expressed in the form

A quadratic equation is such that the sum of its roots is $\frac{2}{3}$ and the product of its roots is $\frac{3}{4}$ . The quadratic equation is

$12x^2 + 8x + 9 = 0$

$12x^2 - 8x - 9 = 0$

Given that $x > 0$ , the set of values of $x$ for which $x-2 < \frac{15}{x}$ is

$\{x: x>0 \cup x>5\}$

Given that $f(x) = 13x - 6 - 2x^2$ , the values of $x$ for which $f(x) < 0$ are

$x > \frac{1}{2}$ and $x > 6$

If $f(x) = \frac{1}{8}x^3$ , $x \in \mathbb{R}$ and $-2 \le x \le 4$ , then

$-8 \le f(x) \le 64$

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

$3\left(\frac{x}{2}-5\right)$

$3\left(\frac{x}{2}+5\right)$

If $f(x) = \frac{4x+1}{x-2}$ , $x \neq 2$ , $x \in \mathbb{R}$ , then $ff(x)=$

$\frac{2x-1}{-3-x}$ , $x \neq -3$ ,

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

The value of $x$ for which $9^{x+1} = 3$ is

Given that $\log_x 2^6 = 6$ , then the value of $x$ is

The value of $\sqrt{18} + \sqrt{50}$ is

The value of $x$ for which $3^{x+1} + 3^{x-1} = 90$ is

$\frac{1}{2} \left( \frac{\log 90}{\log 3} - 2 \right)$

$\frac{\log 10}{\log 3}$

The series $-2 + \frac{4}{3} - \frac{8}{9} + \dots$ converges to the limit

What is the sum of the ODD integers between 10 and 50?

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

A sequence of positive integers {U_n} is defined by $U_n = 3\left(\frac{1}{2}\right)^{n-1}$ . The 10th term of the sequence is given by

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

The line through the points Q(h, 2) and R(4, 8) is parallel to the line with equation $2x + y - 10 = 0$ . The value of h is

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

The vectors $\mathbf{i}$ and $\mathbf{j}$ represent 1 km/h east and north respectively. A man sails a boat on a lake such that the velocity is $-1 + 2\mathbf{j}$ when there is no current. If there is a current of $3\mathbf{i}$ , then the resultant velocity, $\mathbf{v}$ , is given by

$2\mathbf{i} + 2\mathbf{j}$ km/h

$4\mathbf{i} - 2\mathbf{j}$ km/h

$-4\mathbf{i} + 2\mathbf{j}$ km/h

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

$15\mathbf{i} + 36\mathbf{j}$

$195\mathbf{i} + 468\mathbf{j}$

$\frac{1}{13}(5\mathbf{i} + 12\mathbf{j})$

$\frac{3}{13}(5\mathbf{i} + 12\mathbf{j})$

The position vector of two points A and B relative to an origin O are given by $\vec{OA} = \begin{pmatrix} 3 \\ 0 \end{pmatrix}$ and $\vec{OB} = \begin{pmatrix} 8 \\ 5 \end{pmatrix}$ respectively. The modulus of $\vec{AB}$ and the angle $\vec{AB}$ makes with the x-axis respectively are

modulus = 10, angle = 45°

modulus = 10, angle = 30°

modulus = $\sqrt{50}$ , angle = 45°

modulus = $\sqrt{50}$ , angle = 90°

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

What is the arc length, $x$ , in metres, along the outer edge of the protractor?

The graph of $y = \sin 2x$ is

If $\sin (x+20^\circ) = \cos x$ , then the value of $x$ is

d/dx ( (2x-1)/(5-x) ) =

Given y = 2x² + 3 cos x, then dy/dx =

The curve C with equation y = f(x) has a stationary point at (-2, 5). If f''(x) = x⁴ - 15, then (-2, 5) is

a minimum turning point

a maximum turning point

∫₀² (3x+4)³ dx =

The solution to ∫₅¹ (1/(5x-2)²) dx is

A curve C passes through the point (2, -5). The gradient of the curve at the point (x, y) is given by $\frac{dy}{dx} = 7 - x^2$ . The equation of the curve is

$y=7x-\frac{1}{4}x^4-15$

If $\int_0^1 f(x)dx = 6$ , then $\int_0^1 4f(x)dx+5=$

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

\cos x - 2 \sin x + c

2 \cos x + \sin x + c

$12x^2 - 8x + 9 = 0$

$12x^2 + 8x - 9 = 0$

$x < -\frac{1}{2}$ and $x > 6$

$x > \frac{1}{2}$ and $x < 6$

$\frac{1}{3}\left(\frac{x}{2}-5\right)$

$\frac{2x-1}{5-x}$ , $x \neq 5$ , $x \in \mathbb{R}$

$\left(\frac{x+2}{x-2}\right)^2$ , $x \neq 2$ , $x \in \mathbb{R}$

$\frac{2x-1}{3x+5}$ , $x \neq -\frac{5}{3}$ , $x \in \mathbb{R}$

$-4\mathbf{i} - 2\mathbf{j}$ km/h

CSEC Additional Mathematics Paper 1 May/June 2018 - Free CXC Past Paper with Answers

CSEC Additional Mathematics Paper 1 May/June 2018 Questions