CSEC Additional Mathematics Paper 1 May/June 2024 - Free CXC Past Paper with Answers

The expression x - 3 is a factor of

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

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

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

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

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

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

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

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

The roots of the equation $3x^2 - 7x + 3 = 0$ are

What values of y simultaneously satisfy the equations $y = x^2 - 3x + 4$ and $y - x = 1$ ?

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

$x \leq \frac{2}{3}$

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

$x \leq -\frac{1}{2}$ or $x \geq \frac{2}{3}$

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

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

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

$\frac{4}{\sqrt{6}-2}$ is equal to

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

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

$\frac{\log_p 6}{\log_p 4}$

The value of $x$ for which $3^{x+2} + 3^x = 90$ is

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

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

Which of the following is NOT an arithmetic sequence?

-7, -9, -11, -13, ...

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_{2n} = 2^{4n} - 1

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 coordinates of the centre of a circle with equation (x-1)² + (y + 3)² = 36 are

The line x + y = 1 and the circle x² + y² = 5 intersect at the points

(-1,-2) and (-2, -1)

The triangle OAB has vertices given by (0, 0), (a, 0) and (0, -4) respectively. Given that the area of the triangle is 6, then a =

The vector a is given as 5i + 12j. A unit vector parallel to a is

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

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

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 q is 60°.

The acute angle between p and q is 45°.

If cos 2x = 1-2s², then sin x =

The EXACT value of cos $\frac{5\pi}{12}$ =

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

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

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

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

Item 24 refers to the following diagram.

If the area of the semicircle is 32π, what is the length of the arc connecting points A and B?

Item 25 refers to the following graph.

The graph shown above represents the function

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

If $\sin (90° - x) = \cos x$ , then the value of x is

sin 50° cos 40° - cos 50° sin 40° =

The size of angle x, measured in radians, is

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

Given that $y = \sqrt{5-x}$ , then $\frac{dy}{dx}$ is

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

At the 10 m stopping point on a runway, an airplane is stationary before takeoff. If the airplane travels 120 m from this point in 4 seconds, what is its speed at the point of takeoff?

The gradient function $\frac{dy}{dx}$ of the curve $y = \sin (2x^2 + 1)$ is

$4x \cos (2x^2 + 1)$

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

Item 36 refers to the following graph which shows the journey of a boy, where time is given in seconds and velocity in ms⁻¹

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

If c is a constant, then $\int(2x - 5)^3 dx = $

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

$\frac{(2x-5)^2}{8} + c$

$\frac{(2x-5)^4}{8} + c$

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

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

If c is a constant, then $\int (\sin x + 2 \cos x) dx = $

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

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

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

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

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

There are 108 cards in a deck of UNO playing cards. Of these, 4 are "Wild", 4 are "Wild Draw Four" and each of 4 colours (red, yellow, green, blue) is represented by 25 cards. If a player needs to select 1 card, what is the probability of NOT drawing a "Wild Draw Four"?

One advantage of using a box and whisker plot is that

the variance can be identified

all data values can be identified

the mean value can be identified

the spread of the distribution can be identified

What is the value of X?

Item 45 refers to the following diagram.

The tree diagram above shows the probability of Events A and B occurring. Based on the diagram, the value of P(A|B) =

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

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

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

$3^{\frac{3m+1}{n}}$

$1 - \sin x - \cos x$

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

$\frac{1}{2\sqrt{5-x}}$

$-\frac{1}{2\sqrt{5-x}}$

$\frac{1}{4x} \cos (2x^2 + 1)$

$- 4x \cos (2x^2 + 1)$

CSEC Additional Mathematics Paper 1 May/June 2024 - Free CXC Past Paper with Answers

CSEC Additional Mathematics Paper 1 May/June 2024 Questions