CSEC Additional Mathematics Paper 1 May/June 2023 - Free CXC Past Paper with Answers

The expression $pq + 5r - 5q - pr$ is equal to

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

If $x^2 - 8x + 19 = a(x+h)^2 + k$ , then

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

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

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

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

distinct and not real

real and not distinct

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

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

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

The set of values of $x$ for which $\frac{5x-2}{2-3x} \ge 0$ , $x \ne \frac{2}{3}$ , is given by

$\{x:x \ge \frac{2}{5} \cup x > \frac{2}{3}\}$

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

$x < -5$ and $x > -5$

(8+√5)(2-√5) can be expressed as

$\frac{5^{-1}}{125^3}$ simplifies to

$\frac{1}{\sqrt{5}}$

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

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

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

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

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

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

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 $y - x - 3 = 0$ and the circle with equation $x^2 + y^2 = 17$ are

$(4, 1)$ and $(-1, -4)$

Given that $OA = \begin{pmatrix} -17 \\ 25 \end{pmatrix}$ and $OB = \begin{pmatrix} 4 \\ 5 \end{pmatrix}$ , then the vector $AB =$

$\begin{pmatrix} -13 \\ 30 \end{pmatrix}$

$\begin{pmatrix} -13 \\ -20 \end{pmatrix}$

The vector $a$ is given as $8i + 15j$ . A unit vector parallel to $a$ 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 $A\hat{O}B$ is given by

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

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

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

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

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

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

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

$-\frac{1}{\sqrt{3}}$

Item 24 refers to the following protractor which represents half of a circle. The protractor has a radius of 1.5 metres and the angle AOB measures 30°.

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

If $\tan \theta = \frac{5}{12}$ and $\theta$ is reflex, then $\sin \theta =$

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

Given that $\cos x = \frac{3}{5}$ and $x$ is acute, then the value of $\sin 2x$ is

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

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

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

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

$\sin x = -\frac{1}{3}$

$\cos x = \frac{1}{3}$

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

$-\frac{\sqrt{3}}{2}$

$\frac{\sqrt{3}}{2}$

Which of the following statements about the object's motion is true?

The object covers the same distance during M and R.

The object moves with uniform velocity during F.

The object does not accelerate during T.

The object is at rest during M.

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

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

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

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

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

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

a point of inflexion

a minimum turning point

a maximum turning point

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

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

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

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

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

$\int (3x-5)^4 dx = $

$\frac{(3x-5)^5}{5} + k$

$\frac{(3x-5)^5}{3} + k$

$\frac{(3x-5)^5}{15} + k$

$\frac{(3x-5)^3}{15} + k$

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

$\int_1^2 (1+x+x^2)dx = $

The gradient of the tangent to the curve C at $(x, y)$ is given by $\frac{dy}{dx} = 9x^2 - 4$ . The equation of the curve that passes through the point $(-1, 2)$ is

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

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

Which of the following is an advantage of a stem and leaf diagram over a box and whisker plot?

It easily handles large amount of data.

The median and quartiles are immediately visible.

Several data sets can be compared on the same plot.

It immediately shows any gaps that might exist in the data.

The 50th percentile is defined as the

If a team loses a match, what is the probability that the team is NOT Parrot Catchers Club?

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?

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

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

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

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

$\{x:x \le \frac{2}{5} \cup x > \frac{2}{3}\}$

$\{x: \frac{2}{5} \le x < \frac{2}{3}\}$

$\{x: \frac{2}{3} < x \le \frac{2}{5}\}$

$(-4, -1)$ and $(-1, -4)$

$(-4, -1)$ and $(1, 4)$

$\begin{pmatrix} -21 \\ 20 \end{pmatrix}$

$\begin{pmatrix} 21 \\ -20 \end{pmatrix}$

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

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

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

$\frac{1}{\sqrt{3}}$

$\sin x = \frac{1}{3}$

$\cos x = -\frac{1}{3}$

$y = 18x^2 + 4x - 1$

$y = 18x^2 - 4x + 1$

CSEC Additional Mathematics Paper 1 May/June 2023 - Free CXC Past Paper with Answers

CSEC Additional Mathematics Paper 1 May/June 2023 Questions