CSEC Additional Mathematics Paper 2 May/June 2025 - Free CXC Past Paper with Answers

The relationship between two variables, $x$ and $y$, is $10^{2x} \times 10^y = 3$. Express the relationship in the form $y = \log b + ax$, where $a, b \in \mathbb{R}$.

Hence, state the value of the $y$-intercept of a graph of $y$ versus $x$.

Determine whether the series $2 + 6 + 18 + 54 + 162 + \dots$ is arithmetic or geometric. Justify your response.

In a geometric progression, the 3rd term is 25 and the sum of the 1st and 2nd terms is 500. Find the common ratio where $r > 0$.

A kitchen garden has an area, $A$, $(10 - 3\sqrt{5})\ \text{m}^2$. The length of the garden is . Determine the value of , if the width of the garden, in metres, is in the form , where is a real number.

Using the grid on page 11, draw the graphs of $\sin 2x$ and $\cos 2x$, for $0 \le x \le \pi$.

Hence or otherwise, solve the equation $\sin 2x = \cos 2x$ for $0 \le x \le \pi$.

Using an appropriate double-angle formula, derive the identity for $\sin 2x$.

Hence, prove the identity $\frac{1 + \sin 2x}{\sin x + \cos x} = \sin x + \cos x$.

The position vectors of two points, $A$ and $B$, whose coordinates are $(2, 3)$ and $(-3, 2)$ respectively are relative to an origin, $O$.

Express the unit vector $\vec{AB}$ in terms of $x\mathbf{i} + y\mathbf{j}$.

Find the angle $A\hat{O}B$, in degrees.

Hence, state the relationship between the vectors $\vec{OA}$ and $\vec{OB}$.

Differentiate the following expression with respect to $x$, simplifying your answer.

$y = \sin 4x + \frac{3}{x^2}$

Determine the coordinates of all the stationary points of the curve $y = \frac{1}{3}x^3 - \frac{5}{2}x^2 + 4x - \frac{1}{2}$.

Hence, determine the nature of EACH of the stationary points found in (b) (i).

The length of each edge of a cube is increasing at a rate of $0.25 \text{ cm s}^{-1}$. Calculate the rate of change of the volume of the cube at the instant when the length is $8 \text{ cm}$.

Determine

Determine $\int \sqrt{2x + 1} \text{ } dx$

$\int \sin 2x + 5 \cos x \text{ } dx$.

Figure 1 shows the region enclosed between the $x$-axis, the $y$-axis, the curve $y = x^2 + 2$ and the line $x = 3$.

Figure 2 shows the shaded region enclosed between the $x$-axis, the $y$-axis and the curve $y = 4 - x^2$.

Figure 2. Region bounded by a curve, the x-axis and y-axis

If the region is rotated about the $x$-axis through one complete revolution, calculate the volume of the solid formed.

ALL working MUST be clearly shown.

If $P(A) = 0.8$, $P(B) = 0.5$ and $P(A \cup B) = 0.9$, calculate $P(B|A)$.

A fair, blue dice has each of the numbers 1, 3, 5, 7, 9 and 11 on its faces. A second, fair, red dice has each of the numbers 2, 4, 6, 8, 10 and 12 on its faces. The dice are rolled simultaneously and the sum of the numbers on their faces is recorded.

Complete the possibility space table below by inserting the sum of the two dice on each roll. The first sum and the last sum have been inserted for you.

Complete the possibility space table below by inserting the sum of the two dice on each roll. The first sum and the last sum have been inserted for you.

State the probability that the sum of the scores from throwing the dice at (b) (i) is

• prime
• even

Calculate the interquartile range of the data set represented in the stem-and-leaf diagram below.

Key: 3|0 means 30

Figure 3 shows a box-and-whisker plot which represents a set of numerical data.

State the median of the data set.

Determine the range of the data set.

Describe the shape of the distribution.

Five out of 30 students in a class were randomly selected and their heights recorded in centimetres as shown below.

Calculate the variance of their heights, in square centimetres.