CSEC Additional Mathematics Paper 1 May/June 2026 - Free CXC Past Paper with Answers

The expression $x - 3$ is a factor of

$2x^3 + 6x^2 + x + 3$

$x^3 - 3x^2 - 5x + 15$

$3x^4 - 8x^3 - 3x^2 + 1$

Given that $x + 2$ is a factor of $f(x) = 2x^3 - 3x^2 - 5x + p$ , then $p$ is equal to

The minimum value of the expression $4x^2 - 8x - 5$ is

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

If the roots of the equation $4x^2 - 16x + 11 = 0$ are $\alpha$ and $\beta$ , then the value of $\alpha + \beta$ is

Which of the following graphs represents $f(x) = x(2 + x)$ ?

The set of values of $x$ for which $\frac{2x-1}{x-1} \geq 0$ is

$x \geq -\frac{1}{2}$

$x \leq \frac{1}{2}$ or $x > 1$

$x \geq -\frac{1}{2}$ and $x \geq 1$

The set of values of $x$ for which $3x^2 + 5x < 2$ is

$-\frac{3}{5} < x < 0$

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

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

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

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

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

If $8^{2x-1} = 32^{x+1}$ , then $x =$

In a geometric progression, the fifth term is $45$ and the seventh term is $5$ . The SIXTH term is

The $n$ th term of the series $128 + 64 + 32 + \dots$ is

The expression $\sum_{r=1}^{5} (-1)^r (3)^{r+1} =$

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 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 point on the other end of the diameter are

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

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

The vector $a$ is given as $8i + 15j$ . A unit vector parallel to vector $a$ is

$\frac{1}{17}(8i + 15j)$

$\frac{7}{17}(8i + 15j)$

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

$\cos^{-1} \left( \frac{1}{\sqrt{290}} \right)$

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?

$p$ and $q$ are parallel.

$p$ and $q$ are perpendicular.

The acute angle between $p$ and is .

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

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

If the area of the semi-circle is $32\pi$ , what is the length of the arc connecting Points A and B?

The graph shown above represents the function

$\frac{1}{2} \cos x$

$\cos (\frac{1}{2} x)$

If $\pi < \theta < 2\pi$ and $2\cos \theta = \sqrt{3}$ , then $\theta$ is

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

The roots of the equation $6 \sin^2 x + 7 \sin x - 5 = 0$ are

$\frac{\pi}{6}, \frac{5\pi}{6}$

$\frac{\pi}{6}, \frac{7\pi}{6}$

$\frac{\pi}{6}, \frac{9\pi}{6}$

$\frac{\pi}{6}, \frac{11\pi}{6}$

$\frac{2 \sin x \cos x}{\cos^2 x - \sin^2 x} =$

$\frac{2}{\cos x - \sin x}$

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

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

$\frac{d}{dx} x \sin 2x =$

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

$-\cos 2x - 2 \sin 2x$

$\sin 2x - 2x \cos 2x$

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

The area of a square increases at a rate of $10 \text{ cm}^2 \text{s}^{-1}$ . The rate of increase of its side when it has a length of $2 \text{ cm}$ is

$0.2 \text{ cm s}^{-1}$

$2.0 \text{ cm s}^{-1}$

$2.5 \text{ cm s}^{-1}$

$5.0 \text{ cm s}^{-1}$

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

The curve $C$ has the equation $y = f(x)$ . $C$ has a stationary point at $(-1, 2)$ . If $f''(x) = \frac{6}{x^4} + 2$ , then $(-1, 2)$ is

a point of inflexion

a minimum turning point

a maximum turning point

During the journey there is a stage when the boy accelerates. The value of the acceleration is

$-10.0 \text{ ms}^{-2}$

$2.5 \text{ ms}^{-2}$

$3.5 \text{ ms}^{-2}$

$20.0 \text{ ms}^{-2}$

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

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

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

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 value of the interquartile range is

A survey was conducted among 20 doctors and the following information was collected: $\bar{x} = 6$ and $\sum f(x - \bar{x})^2 = 115$ . The variance of the data is

What is the value of X?

A bag contains 15 balls numbered 1 through 15. What is the probability of selecting a ball that has an odd number and is divisible by 5?

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

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

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

$\frac{1}{\sqrt{2}}$

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

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

$\cos^{-1} \left( \frac{11}{\sqrt{290}} \right)$

$\cos^{-1} \left( \frac{\sqrt{11}}{\sqrt{290}} \right)$

$\cos^{-1} \left( \frac{-1}{\sqrt{290}} \right)$

The acute angle between $p$ and $q$ is $45^\circ$ .

$1 - \sin x - \cos x$

CSEC Additional Mathematics Paper 1 May/June 2026 - Free CXC Past Paper with Answers

CSEC Additional Mathematics Paper 1 May/June 2026 Questions