CSEC Additional Mathematics Paper 2 May/June 2023 - Free CXC Past Paper with Answers

Given that $f(x) = 3x^2 - 9x + 1$, (i) express $f(x)$ in the form , where , and are real numbers (ii) state the coordinates of the minimum point of .

express $f(x)$ in the form $a(x+b)^2 + c$, where $a$, and are real numbers

state the coordinates of the minimum point of $f(x)$.

The equation $3x^2 - 6x - 2 = 0$ has roots $\alpha$ and $\beta$. Find the value of .

John's grandparents started a university fund for him at a bank, with $4000. The bank offered two options for interest.

• Option 1 — $240 per annum
• Option 2 — 5% of the current balance per annum Determine the sum of money in the university fund at the beginning of the ninth year for both options.

The equation of a circle is $x^2 + y^2 - 8x - 18y + 93 = 0$. (i) Determine the coordinates of the centre of the circle.

Find the length of the radius.

Find the equation of the normal to the circle at the point $(2, 8)$.

The position vectors of two points, $A$ and $B$, relative to an origin $O$, are such that $\vec{OA} = 3\mathbf{i} - \mathbf{j}$ and . Determine (i) the unit vector

the acute angle $A\hat{O}B$, in degrees, to 1 decimal place.

Solve the equation $2 \sin^2 \theta = 3 \cos \theta$ where $0^\circ < \theta < 180^\circ$.

Prove the identity $\frac{1}{1 - \sin x} + \frac{1}{1 + \sin x} = \frac{2 \tan x}{\cos x}$.

A function given by $y = ax^2 + bx + c$ has a gradient of $9 - \frac{1}{2}x$ at a stationary value of 5. Determine the values of $a$, $b$ and $c$ in the function.

Determine the values of $a$, $b$ and $c$ in the function.

Determine the nature of the stationary point.

A drone tracks the movement of an object in motion on the ground. The following movements are recorded.

• It moves at a constant velocity of 4 m/s for 5 seconds.
• Its velocity increases uniformly for 3 seconds to 10 m/s.
• It moves at that velocity for 7 seconds.
• It slows uniformly until it comes to rest after 4 seconds.

Sketch the graph of the movement of the object.

Sketch the graph of the movement of the object.

Calculate the distance travelled by the object in the second part of the journey.

Determine the object's acceleration in the final part of the journey.

Consider a toy truck moving along a miniaturized racing course with an acceleration of $a(t) = 9t^2 + 2t - 1$, where $t$ is the time in seconds. Assume that the speed of the toy truck is measured in cm/second.

Outline how an equation for the speed of the truck would be found, using the given equation for the acceleration.

Find the speed of the truck at $t = 10$ seconds.

Find the distance covered by the truck between 5 and 10 seconds. Express your answer to the nearest whole number.

Find

$\int (2x+3)^2 dx$

$\int 5 \cos 2x dx$.

If $\frac{dy}{dx} = 6x - 10$ and $y = 12$ when , find the equation for in terms of .

Write the raw data set that was used to construct the diagram above.

Determine the following measures for the data set.

The median exam score

The mean exam score

The modal score(s)

Given that for the data set $\sum x^2 = 48999$ and $\sum x = 885$, find the standard deviation of the data set using the formula $S = \sqrt{\frac{\sum x^2 - \frac{(\sum x)^2}{n}}{n-1}}$

If a student needed to score at least half the total marks possible to pass the exam, determine the probability of a student failing the exam. Give your answer to 2 decimal places.

Given that a randomly selected student has passed the exam, what is the probability that the student scored over 60? Give your answer to 2 decimal places.

Based on the given stem and leaf diagram, describe the distribution of the data set.

Your friend suggested that a bar graph or histogram could be used to represent the data. Advise your friend on which graph is the better option giving ONE reason to support your answer.