CSEC Additional Mathematics Paper 2 May/June 2016 - Free CXC Past Paper with Answers

Determine the nature of the roots of the quadratic equation $2x^2 + 3x - 9 = 0$.

Given that $f(x) = 2x^2 + 3x - 9$, sketch the graph of the quadratic function, clearly indicating the minimum value.

Evaluate $\sum_{r=1}^{2x} 3^r$.

A man invested $Sx$ in a company in January 2010, on which he earns quarterly dividends. At the end of the second, third and fourth quarter in 2011, he earned $100, $115 and $130 respectively. Calculate the total dividends on his investment by the end of 2016.

The points $M(3, 2)$ and $N(-1, 4)$ are the ends of a diameter of circle $C$. Determine the equation of circle $C$.

The points $M(3, 2)$ and $N(-1, 4)$ are the ends of a diameter of circle $C$. Determine the equation of circle $C$.

Find the equation of the tangent to the circle $C$ at the point $P(-1, 6)$.

The position vector of two points $A$ and $B$, relative to a fixed origin, $O$, are $\vec{a}$ and respectively, where , and . lies on such that .

The following diagram (not drawn to scale) shows two sectors, $AOB$ and $DOC$. $OB$ and $OC$ are $x$ cm and $(x + 2)$ cm respectively and angle $AOB = \theta$.

If $\theta = \frac{2\pi}{9}$ radians, calculate the area of the shaded region in terms of $x$.

Given that $\cos 30^\circ = \frac{\sqrt{3}}{2}$ and , without the use of a calculator, evaluate , in surd form, giving your answer in the simplest terms.

Prove that the identity $\frac{\sin (\theta + \alpha)}{\cos \theta \cos \alpha} = \tan \theta + \tan \alpha$.

Find $\frac{dy}{dx}$ given that $y = \sqrt{5x^2 - 4}$, simplifying your answer.

The point $P(1, 8)$ lies on the curve with equation $y = 2x (x + 1)^2$. Determine the equation of the normal to the curve at the point $$.

Obtain the equation for EACH of the two tangents drawn to the curve $y = x^2$ at the points where $y = 16$.

Find $\int (3 \cos \theta - 5 \sin \theta) d\theta$.

Evaluate $\int_{1}^{3} \left[ \frac{2}{x^3} - 3 + 2x^2 \right] dx$.

The following figure shows the finite region $R$ bounded by the lines $x = 1$, $x = 2$ and the arc of the curve $y = (x - 2)^2 + 5$.

The point $P(1, 2)$ lies on the curve which has a gradient function given by $\frac{dy}{dx} = 3x^2 - 6x$. Find the equation of the curve.

Use the data set provided below to answer the questions which follow.

Construct a stem-and-leaf diagram to represent the given data.

State an advantage of using the stem-and-leaf diagram to represent the given data.

Determine the mode.

Determine the median.

Determine the interquartile range.

Two events, $A$ and $B$, are such that $P(A) = 0.5$, $P(B) = 0.8$ and $P(A \cup B) = 0.9$.

Determine $P(A \cap B)$.

Determine $P(A \mid B)$.

State, giving a reason, whether or not $A$ and $B$ are independent events.

A bag contains 3 red balls, 4 black balls and 3 yellow balls. Three balls are drawn at random with replacement from the bag. Find the probability that the balls drawn are all of the same colour.

A motorist starts from a point, $X$, and travels 100 m due North to a point, $Y$, at a constant speed of 5 m $s^{-1}$. He stays at $Y$ for 40 seconds and then travels at a constant speed of 10 m $s^{-1}$ for 200 m due South to a point, $Z$.

On the following grid, draw a displacement–time graph to display this information.

Calculate the average speed for the whole journey.

Calculate the average velocity of the whole journey.

A particle starting from rest, travels in a straight line with an acceleration, $a$, given by $a = \cos t$ where $t$ is the time in seconds.

Find the velocity of the particle in terms of $t$.

Calculate the displacement of the particle in the interval of time $t = \pi$ to $t = 2\pi$.