CSEC Mathematics Paper 2 May/June 2014 - Free CXC Past Paper with Answers

Write as a single fraction in its LOWEST terms $\frac{x - 2}{3} + \frac{x + 1}{4}$

Write an equation in $x$ to represent EACH statement below. Do NOT solve the equation.

When 4 is added to a certain number the result is the same as halving the number and adding 10.

Squaring a number and subtracting 6 gives the same result as doubling the number and adding 9.

John drew the diagram below to show what he was thinking. Input $x$ -> Multiply by 3 -> Add 5 -> Output $y$

Use information from the diagram to write a formula for $y$ in terms of $x$.

If the number 4 is the input, what number would be the output?

If the number 8 was the output, what number was the input?

Reverse the formula written at (c) (i) above to write $x$ in terms of $y$.

Solve the following simultaneous equations: $2x + 3y = 9$ $3x - y = 8$

The universal set, $U$, is defined as the set of integers between 11 and 26. $A$ and $B$ are subsets of $U$ such that: $A = \{\text{even numbers}\}$ $B = \{\text{multiples of 3}\}$

How many members are in the universal set, $U$?

List the members of the subset $A$.

List the members of the subset $B$.

Draw a Venn diagram to represent the relationships among $A$, $B$ and $U$.

Using a ruler, a pencil and a pair of compasses, construct a) a triangle $PQR$ in which $PQ = 8$ cm, $PR = 6$ cm and angle $P = 60^\circ$ b) the line segment which is perpendicular to and meets at . [Note: Credit will be given for clearly drawn construction lines.]

Measure and state the size of angle $QRX$.

Copy and complete EACH of the following sentences:

1 cm on the map represents ___________ cm on the island.

An area of 1 cm$^2$ on the map represents an area of ___________ cm$^2$ on the island.

Given that 1 km = 100 000 cm, a distance of 1 cm on the map represents a distance of ___________ km on the island.

L and M are two tracking stations.

State, in centimetres, the distance LM on the map.

Calculate the ACTUAL distance, in kilometres, from L to M on the island.

The area shaded on the map is a forest reserve.

Estimate the area of the forest reserve as shown on the map, in cm$^2$, by counting squares.

Calculate, in km$^2$, the ACTUAL area of the forest reserve.

Triangle $ABC$ has coordinates $A(1,2)$, $B(4,2)$ and $C(1,0)$.

On the answer sheet provided, draw triangle $A'B'C'$, the image of triangle $ABC$, under an enlargement, centre $$ and scale factor 2.

Triangle $A''B''C''$ is the image of triangle $ABC$, under a transformation, . Describe the transformation, .

The diagram below, not drawn to scale, shows the positions of two ships, $P$ and $Q$, at anchor. $FT$ is the vertical face of a cliff jutting out to the water. $P$ and $Q$ are 118 m apart. $FT = 80$ m and .

the angle of elevation of $T$ from $P$

the length of $FP$

the angle of elevation of $T$ from $Q$.

Determine the value of The coordinates of the points M and N are M $(-1, y)$ and N $(x, 9)$ respectively.

$y$

$x$

Determine

the gradient of the line MN

the equation of the line MN

the equation of the line parallel to MN, and passing through the origin.

On the answer sheet provided, carefully draw the tangent line to the graph $y = x^2$ at the point $(2, 4)$.

Estimate the gradient of the tangent to the curve at $(2, 4)$.

Copy and complete the frequency table for the data shown above.

State the modal number of books in the bags of the sample of students.

Using the table in (a) above, or otherwise, calculate

the TOTAL number of books

the mean number of books per bag.

Determine the probability that a student chosen at random has LESS THAN 4 books in his/her bag.

Draw Figure 4, the next figure in the sequence above.

Complete the table below by inserting the missing information at the rows numbered (i) and (ii).

Write an expression in $f$ for the number ($n$) of dots used in drawing the $f^{th}$ figure.

Which figure in the sequence contains 145 dots?

Two functions are defined as follows: $g(x) = 4x + 3$ $f(x) = \frac{2x + 7}{x + 1}$

State the value of $x$ for which $f(x)$ is undefined.

Calculate the value of $gf(5)$.

Find $f^{-1}(x)$.

A ball is thrown vertically upwards. Its height, $h$ metres, above the ground after $t$ seconds is shown in the table below.

Using 2 cm to represent 1 second on the $x$-axis and 1 cm to represent 10 metres on the $y$-axis, plot a graph to show the height of the ball during the first 6 seconds.

the average speed of the ball during the first 2 seconds

The diagram below, not drawn to scale, shows a circle, centre $O$. The line $BC$ is a tangent to the circle at $B$. Angle $CBD = 42^\circ$ and angle $OBE = 20^\circ$.

Calculate, giving a reason for EACH step of your answer, the measure of:

$\angle BOE$

$\angle OED$

$\angle BFE$

The diagram below, not drawn to scale, shows the positions of three ports, $P$, $Q$ and $R$.

$Q$ is 80 km from $P$. $R$ is 100 km from on a bearing of . .

the bearing of $P$ from $Q$

the distance $PR$ correct to 2 decimal places

the measure of $\angle QPR$ to the nearest degree.

The matrix $M$ is defined as

$M = \begin{pmatrix} 7 & 2 \\ p & -1 \end{pmatrix}$

Determine the value of $p$ for which the matrix $M$ does NOT have an inverse.

Express the equations

$4x - 2y = 0$ $2x + 3y = 4$

in the form $AX = B$, where , and are matrices.

In the diagram below, the coordinates of $P$ and $Q$ are $(2, 4)$ and $(8, 2)$ respectively. The line segment joining the origin $(0,0)$ to the point may be written as .

What term is used to describe $\vec{OP}$?

Write EACH of the following in the form $\begin{pmatrix} a \\ b \end{pmatrix}$

Given that $\vec{OP} = \vec{RQ}$, determine the coordinates of the point, .

State the type of quadrilateral formed by $PQR O$. Justify your answer.