CSEC Additional Mathematics Paper 1 May/June 2020 - Free CXC Past Paper with Answers

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

$\frac{1}{x+3} + \frac{3}{x^2-9}$ expressed as a single fraction is

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

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

$a=1 \quad h=3 \quad k=4$

$a=1 \quad h=-3 \quad k=4$

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

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

The values of $x$ for which $\frac{3x-2}{2x+1} \le 0$ are

$-\frac{1}{2} < x \le \frac{2}{3}$

$x \le -\frac{1}{2}$ or $x \ge \frac{2}{3}$

If $f(x) = -\frac{2}{9}x^3$ , $-3 \le x \le 3$ , $x \in \mathbb{R}$ , then

A function is defined by $f:x \to \frac{1}{x+1}$ , $x \neq -1$ . The value of $f^{-1}(1)$ is

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

$gf:x \to \frac{6}{x} - 5$ , $x \neq 0$

Which of the following graphs depicts a function?

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

$\frac{1}{3}(3-\sqrt{5})$

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

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

Which of the following mathematical statements are true? I. $\log_b PQ = \log_b P \times \log_b Q$ II. $\log_b \frac{P}{Q} = \log_b P - \log_b Q$ III. $\log_b P^3 = b \log_b P$

Given that $3 \times 27^x = 9^4$ , the value of $x$ is

The sum of the first $n$ terms of a geometric series is $S_n = 4^n - 1$ . For this series I. the common ratio is $-1$ II. the first 3 terms are 3, 12 and 48 III. $S_n = 2^{2n} - 1$

The sum of $\sum_{k=1}^{3} \frac{1}{k}$ is

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

The sum of the odd integers between 10 and 50 is

The coordinates of the centre of a circle with equation $(x-1)^2 + (y+3)^2 = 36$ is

The points of intersection of the line with equation $y-x-2=0$ and the circle with equation $x^2+y^2=10$ are

$(3, 1)$ and $(-1, -3)$

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 $-\mathbf{i} + 2\mathbf{j}$ 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

Two vectors are equal if they

have the same magnitude and different directions

have the same magnitude and same direction

are parallel and are in different directions

have different magnitudes and are in the same direction

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

The figure MON below shows a quarter circle with radius 4 cm. The perimeter of the figure, in cm, is

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

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

The exact value of $\cos\left(\frac{5\pi}{12}\right)$ is

$\frac{1}{4}(\sqrt{6}+\sqrt{2})$

$\frac{1}{4}(\sqrt{6}-\sqrt{2})$

$\frac{1}{2}(\sqrt{6}+\sqrt{2})$

$\frac{1}{2}(\sqrt{6}-\sqrt{2})$

Item 32 refers to the figure below.

The size of angle x, measured in radians, is

If $\sin x = s$ , then $\cos 2x$

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

$\frac{1}{\sqrt{2}}(\sin \alpha - \cos \alpha)$

$\frac{1}{\sqrt{2}}(\cos \alpha - \sin \alpha)$

$\frac{1}{2}(\sin \alpha - \cos \alpha)$

$\frac{1}{2}(\cos \alpha - \sin \alpha)$

If $f'(x) = \sin 3x - \cos 4x$ , then $f''(x)$ =

$3 \cos 3x + 4 \sin 4x$

$9 \sin 3x - 16 \cos 4x$

The curve C has the equation $y = f(x)$ . C has a stationary point at $(-2, 5)$ . If $f''(x) = x^3 - 15$ , then $(-2, 5)$ is

a minimum turning point

a maximum turning point

$\frac{-9-4x}{(5-x)^2}$

$-\frac{9}{(5-x)^2}$

$\frac{9-4x}{(5-x)^2}$

The point P(1,1) lies on the curve $y=\frac{3x-2}{2x-1}$ . The value of the gradient of the curve at P is

Given $y=2x^2+3 \sin x$ , then $\frac{dy}{dx}=$

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

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

$\frac{(2x-4)^4}{2} + k$

$\frac{(2x-4)^4}{8} + k$

The region bounded by the curve $y=2 \sin x$ , the x-axis and the lines $x=0$ and $x=\pi$ is revolved about the x-axis to form a solid of revolution. The volume of the solid generated can be found from

$\pi \int_0^\pi 4 \sin^2 x dx$

$\pi \int_0^\pi 2 \sin^2 x dx$

$2\pi \int_0^\pi 4 \sin^2 x dx$

$4\pi \int_0^\pi 2 \sin^2 x dx$

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

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

$-\sin x + \cos x + c$

$\sin x - 2 \cos x + c$

$\sin x - \cos x + c$

$\sin x + 2 \cos x + c$

$\frac{x^2-6}{(x^2-9)(x+3)}$

$a=1 \quad h=-4 \quad k=3$

$a=-1 \quad h=4 \quad k=3$

$gf:x \to 3 + \frac{6}{x}$ , $x \neq 0$

$gf:x \to \frac{8x-17}{2x-5}$ , $x \neq \frac{5}{2}$

$gf:x \to \frac{8x-20}{2x-5}$ , $x \neq \frac{5}{2}$

$\frac{1}{2}(\sqrt{5}-3)$

$\frac{1}{3}(\sqrt{5}-3)$

$\frac{1}{2}(3-\sqrt{5})$

$(-3, -1)$ and $(-1, -3)$

$(-3, -1)$ and $(1, 3)$

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

$9 \sin 3x + 16 \cos 4x$

$-9 \sin 3x + 16 \cos 4x$

CSEC Additional Mathematics Paper 1 May/June 2020 - Free CXC Past Paper with Answers

CSEC Additional Mathematics Paper 1 May/June 2020 Questions