CSEC Additional Mathematics Paper 1 May/June 2021 - Free CXC Past Paper with Answers

When $x^3 - 7x^2 + 2x - 1$ is divided by $x + 2$, the quotient is

Given that $f(x) = ax^2 + bx + c$, then $f(x)$ can be expressed in the form

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

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

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

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

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

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

Given that $\log_p X = 6$ and $\log_p Y = 4$, the value of $\log_p \left(\frac{X}{Y}\right)$ is

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

The value of $x$ such that $\log_2 (5x + 1) - \log_2 (3x - 5) = 2$ is

The common ratio of the geometric sequence $8, 12, 18, \dots$ is

The sum of the first $n$ terms of a series is given by $\sum_{r=1}^{n}(5-3r)$. The sum of the first $10$ terms is

The sum of $\sum_{k=1}^{3}\frac{1}{k}$ 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 point on the other end of the diameter are

The lines $7x - 4y + 25 = 0$ and $3x - y - 5 = 0$ intersect at the point $P$. The coordinates of $P$ are

The points of intersection of the line with equation $x + y = 7$ and the circle with equation $x^2 + y^2 = 25$ are $P$ and $Q$. The coordinates of $P$ and $Q$ respectively are

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

The triangle $OAB$ has vertices given by $\begin{pmatrix} 0 \\ 0 \end{pmatrix}$, $\begin{pmatrix} -3 \\ a \end{pmatrix}$, $\begin{pmatrix} 6 \\ 2 \end{pmatrix}$ respectively. Given that the angle $A\hat{O}B$ is $\frac{\pi}{2}$, then $a =$

The position vectors of $A$ and $B$ relative to an origin $O$ are $\begin{pmatrix} 2 \\ 5 \end{pmatrix}$ and $\begin{pmatrix} 3 \\ -1 \end{pmatrix}$ respectively. The acute angle $AOB$ is given by

The exact value of $\cos(\frac{5\pi}{12}) =$

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

$\sin(\frac{\pi}{2}-x) + \cos(x+\frac{\pi}{2}) =$

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

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

The size of the missing angle, $X$, measured in radians, is

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

For $0^\circ < x < 360^\circ$, the equation $3 \sin^2 x = 8 \cos x$ has only one real solution given by

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

Which of the following statements is true?

$\frac{d}{dx} \left( \frac{2x-1}{5-x} \right) =$

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

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

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

$\int_{0}^{3} (3x + 4)^3 \, dx =$

A car and a delivery truck both start from rest and accelerate at the same rate. However, the car accelerates for twice the amount of time as the truck. What is the travelled distance of the car compared to the truck?

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

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

If winning the car or the cruise vacation are equally likely, what is the probability of winning the car?

In a regular deck of 52 cards where there are 26 red and 26 black cards, if a single card is selected at random, what is the probability of getting a red card?

A fair 6-sided die is rolled. Given that an odd number has turned up, what is the probability that it is a prime number?

Which of the following statements is true regarding the shape of the distribution of the weights of the girls compared to the boys?

Joseph collects data on the colour of cars passing his yard. The data can be described as