CSEC Additional Mathematics Paper 2 May/June 2024 - Free CXC Past Paper with Answers

Write the expression $2\log_x x + 2 - \log_x y$ as a single term.

By using logarithms, express the relationship $Y = 7 \times 5^t$ in linear form.

Hence, state the value of the gradient of the line which represents the relationship in (b) (i).

Rationalize the denominator of the expression $\frac{1+\sqrt{2}}{3-\sqrt{2}}$.

Evaluate $\sum_{i=0}^{4} 5^{i-2}$.

Determine whether the following sequence is divergent or convergent. Justify your response.

$1, -\frac{2}{3}, \frac{4}{9}, -\frac{8}{27}, \dots$

Determine the points of intersection of the circle $x^2 + y^2 - 4x + 6y + 8 = 0$ and the line $y = x - 6$.

Given that the coordinates of the points $A$ and $B$ are $(7, -3)$ and $(2, 1)$ respectively, state the position vectors corresponding to the points $A$ and in the form .

Given that the coordinates of the points $A$ and $B$ are $(7, -3)$ and $(2, 1)$ respectively, state the position vectors corresponding to the points $A$ and in the form .

Determine $\vec{AB}$.

Calculate the value of the scalar product $\vec{OA} \cdot \vec{OB}$.

Using the letters $p$, $q$ or $r$, write an expression for EACH of the following trigonometric ratios. (i) sin $\theta =$ cos $\theta =$

(ii) Using your answers in (c) (i), determine the value of $$. Recall that .

Using the letters $p$, $q$ or $r$, write an expression for EACH of the following trigonometric ratios. sin $\theta =$ cos $\theta =$

Using your answers in (c) (i), determine the value of $\sin^2 \theta + \cos^2 \theta$. Recall that $\sin^2 \theta = (\sin \theta)^2$.

Prove the identity $\tan A + \frac{1}{\tan A} = \frac{1}{\sin A \cos A}$.

Use the definition of the derivative as a limit to find $f'(x)$ for the function $f(x) = x^2 - 3$.

Use the definition of the derivative as a limit to find $f'(x)$ for the function $f(x) = x^2 - 3$.

Hence, determine the value of $f'(5)$.

Given that $y = \frac{\sin x}{\cos x}$, show that $\frac{dy}{dx}=\frac{1}{{}^{}}$.

The equation of a curve is given by $y = (5x^2 - 7)^4$. Determine the equation of the gradient of the curve.

The region enclosed between the curve $y = x^2 + 1$, the $x$-axis, the $y$-axis and the line $x = 2$ is rotated about the $x$-axis through an angle of $360^\circ$.

Calculate the volume of the solid of revolution that is formed.

As a particle moves along a straight line, its displacement is measured from a fixed point, O, on the line. At time $t$ seconds, the acceleration, $a$, is given by $a = 24t - 14$.

(i) Find the expression for the velocity, $v$, of the particle, given that when $$, .

Find the expression for the velocity, $v$, of the particle, given that when $t = 1$, $v = 3 \text{ ms}^{-1}$.

Using your answer in (b) (i), find an expression for the displacement, $s$, of the particle, given that when $t = 1$, $s = 10 \text{ m}$.

The gradient function of the curve $C$ is given by $7 - 2x$. If the curve passes through the point $(3, 8)$, find the equation of the curve.

The heights of 35 children at a nursery were recorded to the nearest centimetre. The data is shown below.

61  118  79   90   83   70   80
95   75  76   92   62  115   79
71  103  109   84   65   86   92
111   78   94   74   99   81  108
108   67  109   92   79  116   62

Display the data shown above on a stem-and-leaf diagram.

From the stem-and-leaf diagram in (a) (i), determine the value of the

• median
• lower quartile
• upper quartile.

At another nearby nursery, the heights of children of the same age were recorded. The median height was 79 cm and the interquartile range was 24 cm.

Compare the characteristics of the two groups of children at the two nurseries and describe ONE distinct observation about the distributions.

A bag contains 6 red marbles and 5 black marbles. During 2 rounds of a marble game, a student is required to randomly draw 1 marble without replacement for each round.

Construct a probability tree diagram to represent this information.

Using your answer in (b) (i), find the probability that the marbles drawn are ALL the SAME colour.

Given two events, $A$ and $B$, $P(A \cup B) = 0.7$, $P(A) = 0.3$ and .

Calculate $P(A \cap B)$.

What is the relationship between Events $A$ and $B$?