CSEC Mathematics Paper 2 May/June 2018 - Free CXC Past Paper with Answers

Factorize, completely, EACH of the following expressions.

$1 - 4h^2$

$pq - q^2 - 3p + 3q$

Solve EACH of the following equations.

$\frac{3}{2}y = 12$

$2x^2 + 5x - 3 = 0$

The quantities $F$, $m$, $u$, $v$ and $t$ are related according to the formula $F = \frac{m(v - u)}{t}$.

Find the value of $F$ when $m = 3$, $u = -1$, $v = 2$ and .

Make $v$ the subject of the formula.

Using a ruler, a pencil and a pair of compasses, construct the triangle $ABC$, such that $AB = 8$ cm, $\angle BAC = 30^\circ$ and $AC = 10$ cm.

The diagram below shows the triangle $OPQ$.

State the coordinates of the point $Q$.

The line $PQ$ is mapped to $P'Q'$ by an enlargement, centre $O$ and scale factor 3. On the diagram above, draw the line $P^{\mathrm{\prime }}$.

The $\triangle OPQ$ undergoes a reflection in the line $y = 0$ to produce the image $O''P''Q''$. On the diagram above, draw the .

The function $f$ with domain, $A = \{1, 2, 3\}$ is given by $f(x) = \frac{1}{2}x - 3$.

What is the value of $f(1)$?

Find the value of $x$ for which $f(x) = -2$.

An ordered pair for the function is expressed in the form $(a, b)$. Using your answers to (a) (i) and (a) (ii), or otherwise, list the ordered pairs for the function, $f$.

Explain why $f(x) \ne 5$ for the function specified on page 13.

Solve the inequalities a) $3x - 1 < 11$ b) $2 \le 3x - 1$

Represent the solution to $2 \le 3x - 1 < 11$ on the number line shown below.

Students in a group were asked to name their favourite sport. Their responses are shown on the pie chart below.

Calculate the value of $x$.

What percentage of the students chose cricket?

Given that 40 students chose tennis, calculate the TOTAL number of students in the group.

The diagram below shows a frequency polygon of the number of goals scored by a football team in 25 matches.

Complete the following table using the information in the diagram.

What is the modal number of goals scored by the team?

Determine the median number of goals scored by the team.

Calculate the mean number of goals scored by the team.

In this question, take the value of $\pi$ to be $\frac{22}{7}$.

The diagram below, not drawn to scale, shows the cross-section of a circular metal disc of radius 21 mm. A square hole with sides 6 mm is located at the centre of the disc.

Calculate

the circumference of the disc

the area, in $\text{mm}^2$, of the cross-section of the disc.

Given that the thickness of the disc is 2 mm, calculate the maximum number of discs that can be constructed from $1\ 000\ \text{cm}^3$ of available metal.

($1\ \text{cm}^3 = 1\ 000\ \text{mm}^3$)

A globe is a scaled spherical representation of the earth. The actual length of the equator (LL) is 40 000 km and is represented on the globe by a piece of string of length 160 cm. (i) What length of string would represent an actual distance of 500 km on the globe? (ii) The distance between Palmyra $(P)$ and Quintec $(Q)$ is represented on the globe by a string of length 25 cm. Calculate the value of $PQ$, the actual distance, in km, between $P$ and $Q$.

What length of string would represent an actual distance of 500 km on the globe?

The distance between Palmyra $(P)$ and Quintec $(Q)$ is represented on the globe by a string of length 25 cm. Calculate the value of $PQ$, the actual distance, in km, between $P$ and $Q$.

Draw Figure 4 of the sequence.

Study the pattern of numbers in each row of the table below. Each row relates to one of the figures in the sequence of figures on page 22. Some rows have not been included in the table. Complete the rows numbered (i), (ii) and (iii).

Complete the rows numbered (i), (ii) and (iii). (i) Figure 4: Number of Squares ($S$) and Perimeter ($P$).

Complete the rows numbered (i), (ii) and (iii). (ii) Number of Squares ($S$) when Perimeter ($P$) is 43.

Complete the rows numbered (i), (ii) and (iii). (iii) Figure $n$: Number of Squares ($S$) and Perimeter ($P$).

Determine the relationship between the number of squares, $S$, and the perimeter, $P$, of a figure.

The diagram on page 25 shows six points of the function $y = 3x + \frac{1}{x}$. The coordinates of these six points are given in the table below.

Complete the table above by calculating and inserting the missing values of $y$.

On the diagram on page 25, the ordered pairs shown in the table have been plotted except for the missing ones. Using your answers in (a) (i), plot the missing points and connect all the points with a smooth curve.

By drawing an appropriate straight line on the diagram on page 25, find approximate solutions to the equation $3x + \frac{1}{x} = 6$.

The diagram below, not drawn to scale, shows the relative positions of three reservoirs $B$, $F$ and $G$, all on level ground. The distance $BF = 32 \text{ km}$, $FG = 55 \text{ km}$, $\angle BFG$ is $103^\circ$ and $F$ is on a bearing of $042^\circ$ from $B$.

Determine the bearing of $B$ from $F$.

Calculate the distance $BG$, giving your answer to one decimal place.

Calculate, to the nearest degree, the bearing of $G$ from $B$.

The diagram below, not drawn to scale, shows a circle, with centre $O$. The points $A$, $B$, $C$ and $M$ are on the circumference. The straight line $CN$ is a tangent to the circle at the point and is perpendicular to .

Calculate the acceleration, in $\text{m s}^{-2}$, of the car during Stage B.

Calculate the average speed of the car during Stage B.

At time $t = 60$ seconds, the car starts to slow down with a uniform deceleration of $2.5 \text{ ms}^{-2}$. Determine how long it will take the car to come to rest.

VECTORS AND MATRICES

(a) A transformation, $T$, is defined by the matrix $T = \begin{pmatrix} 2 & -1 \\ 2 & 0 \end{pmatrix}$

The point $A(-2, 3)$ is mapped on to the point $A'(a, b)$ under $T$. (i) Find the value of $a$ and of .

Determine the transformation matrix that maps $A'$ to $A$.

Another transformation, $P$, is defined by the matrix $P = \begin{pmatrix} 0 & 1 \\ 1 & -2 \end{pmatrix}$.

< ![CDATA[The diagram below, not drawn to scale, shows a quadrilateral $ABCD$ in which $\vec{AB} = m$, $$ and .

Complete the statement below on the geometric properties of the following vectors.

$\vec{AB}$ and $\vec{DC}$ are .................................................................... and

Express $\vec{BC}$ in terms of $m$ and $n$.

$L$ is the midpoint of $\vec{CD}$. Find $\vec{BL}$ in terms of and .