CSEC Mathematics Paper 2 May/June 2008 - Free CXC Past Paper with Answers

Find the value of EACH of the following when $a = 2$, $b = -1$, $c = 3$ (i) $a(b+c)$ (ii) $\frac{4b^2 - 2ac}{a+b+c}$

$a(b+c)$

$\frac{4b^2 - 2ac}{a+b+c}$

Change the following statements into algebraic expressions: (i) Four times the sum of $x$ and $5$ (ii) $16$ larger than the product of $a$ and $b$

Four times the sum of $x$ and $5$

$16$ larger than the product of $a$ and $b$

Solve the equation $15 - 4x = 2(3x+1)$.

Factorise completely (i) $6a^2b^3 + 12a^3b$ (ii) $2m^2 + 9m - 5$.

$6a^2b^3 + 12a^3b$

$2m^2 + 9m - 5$.

Calculate the value of $t$, the number of students who were interested in becoming doctors.

The data above are to be represented on a pie chart. Calculate the size of the angle in each sector of the pie chart. Using a circle of radius $4$ cm, construct the pie chart to represent the data.

The data above are to be represented on a pie chart. Calculate the size of the angle in each sector of the pie chart.

Using a circle of radius $4$ cm, construct the pie chart to represent the data.

A Universal set, U, is defined as $U = \{15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25\}$.

Sets M and N are subsets of U such that M = {Prime Numbers} and N = {Even Numbers}. (i) Draw a Venn diagram to represent the sets M, N and U. (ii) List the elements of the set $(M \cup N)'$.

Draw a Venn diagram to represent the sets M, N and U.

List the elements of the set $(M \cup N)'$.

Using only a pair of compasses, a ruler and a pencil, construct parallelogram $ABCD$ in which $AB = AD = 7$ cm and the angle $BAD$ is $60^\circ$. Measure and write down the length of the diagonal .

Using only a pair of compasses, a ruler and a pencil, construct parallelogram $ABCD$ in which $AB = AD = 7$ cm and the angle $BAD$ is $60^\circ$.

Measure and write down the length of the diagonal $AC$.

Calculate the length of $RS$.

Calculate the perimeter of the entire floor.

Calculate the area of the entire floor.

Section A of the floor is to be covered with flooring boards measuring $1$ m by $20$ cm. How many flooring boards are needed for covering Section A?

In the diagram below, not drawn to scale, GH is a vertical pole standing on a horizontal plane and H, J and K are points on the horizontal plane.

$GH = 12$ metres and the angles of elevation of the top of the pole G from J and K are $32^\circ$ and $27^\circ$ respectively. (i) Copy the diagram and insert the angles of elevation. (ii) Calculate to one decimal place a) the length of HJ b) the length of JK.

Copy the diagram and insert the angles of elevation.

Calculate to one decimal place a) the length of HJ b) the length of JK.

An answer sheet is provided for this question. (i) The figure labelled $P$ undergoes a transformation, such that its image is $Q$. Describe this transformation completely. (ii) On the answer sheet provided, draw and label a) the line $y = x$ b) $S$, the image of $P$ under a reflection in the line .

The figure labelled $P$ undergoes a transformation, such that its image is $Q$. Describe this transformation completely.

On the answer sheet provided, draw and label a) the line $y = x$ b) $S$, the image of $P$ under a reflection in the line $y = x$.

The equation of the line above is $y = mx + c$.

State the value of $c$.

Determine the value of $m$.

Determine the coordinates of the mid-point of the line segment $AB$.

The point $(-2, k)$ lies on the line. Determine the value of $k$.

Determine the coordinates of the point of intersection of the line $y = x - 2$ and the line shown above.

What was the TOTAL cost of the stamps?

She had to post a parcel and the total cost of postage was $25.70. What stamps can she select from the collection, to make up this amount if she must use

as many $4.00 stamps as possible?

all her $1.00 stamps?

What is the LARGEST number of stamps that she can use from the collection to post the parcel?

What is the LARGEST number of stamps that she can use from the collection to post the parcel?

List the selection of stamps she can use.

Simplify

$x^2 \times x^3 \div x^4$

$a^{\frac{2}{3}} b^2 \times \sqrt{ab^3}$

If $f(x) = 2x - 3$, find the value of

$f(2)$

$f^{-1}(0)$

$f^{-1}f(2)$

The temperature, $K$, of a liquid $t$ minutes after heating is given in the table below.

Using a scale of 2 cm to represent 10 minutes on the horizontal axis and a scale of 2 cm to represent 10 degrees on the vertical axis, construct a temperature-time graph to show how the liquid cools in the 60 minute interval.

Draw a smooth curve through all the plotted points.

Use your graph to estimate a) the temperature of the liquid after 15 minutes b) the rate of cooling of the liquid at $t = 30$ minutes.

Solve the following pair of equations for $x$ and $y$: $y + 4x = 27$ $xy + x = 40$

The shaded area in the diagram below shows the solution of a set of inequalities in $x$ and $y$. The variable $x$ represents the number of boys in a cricket club and $y$ represents the number of girls in the cricket club.

Use the graph above to answer the questions which follow.

State, using arguments based on the graph, whether the cricket club can have as members: a) 10 boys and 5 girls b) 6 boys and 6 girls.

Write down the set of THREE inequalities that define the shaded region.

A company sells uniforms for the club and makes a profit of $3.00 on a boy's uniform and $5.00 on a girl's uniform. a) Write an expression in $x$ and $y$ that represents the total profit made by the company on the sale of uniforms. b) Calculate the minimum profit the company can make.

In the diagram below, not drawn to scale, $PQ$ is a tangent to the circle, centre $O$. $PR$ is parallel to $OS$ and angle $SPR = 26^\circ$.

Calculate, giving reasons for your answer, the size of

angle $PTS$

angle $RPQ$.

In the diagram below, not drawn to scale, $O$ is the centre of the circle of radius 8.5 cm and $AB$ is a chord of length 14.5 cm.

Calculate the value of $\theta$ to the nearest degree.

Calculate the area of triangle $AOB$.

Hence, calculate the area of the shaded region. [Use $\pi = 3.14$].

Calculate the length of the major arc $AB$.

Draw a diagram showing the journey of the ship from $R$ to $S$ to $T$. Show on your diagram

the North direction

the bearings $112^\circ$ and $033^\circ$

the points $R$, $S$ and $T$

the distances 75 km and 56 km.

Calculate

the size of angle $RST$

the size of angle $RTS$

the bearing of $R$ from $T$.

The ship leaves Port $T$ and travels due west to a point $X$ which is due north of $R$.

Show on your diagram the journey from $T$ to $X$.

Calculate the distance $TX$.

Copy the diagram and complete it to show the points of $P$ and $M$.

$OB$ is produced to $N$ such that $OB = BN$.

Show the position of $N$ on your diagram.

Express in terms of $\mathbf{a}$ and $\mathbf{b}$ the vectors $\vec{AB}$, $\stackrel{}{}$ and .

Use a vector method to prove that $P$, $M$ and $N$ are collinear.

Calculate the length of $AN$ if $\mathbf{a} = \begin{pmatrix} 6 \\ 2 \end{pmatrix}$ and $\mathbf{b}=($.

$X$ and $Y$ are two matrices where $X = \begin{pmatrix} -2 & 0 \\ 5 & 1 \end{pmatrix}$ and $Y = \begin{pmatrix} 4 & -1 \\ 3 & 7 \end{pmatrix}$.

Evaluate $X^2 + Y$.

The matrix $\begin{pmatrix} 1 & 2 \\ 1 & 3 \end{pmatrix}$ maps $Q(1,$ to .

The vertices of triangle $DEF$ are $D(5, 12)$, $E(2, 7)$ and $F(8, 4)$.

Triangle $DEF$ undergoes an enlargement with centre, $O$, and scale factor, $k$. Its image is $D'E'F'$ where . a) Determine the value of . b) Hence write down the coordinates of and .

$D'E'F'$ undergoes a clockwise rotation of $90^\circ$ about the origin. a) Determine the matrix that represents a clockwise rotation of about the origin. b) Determine the coordinates of , the image of , under this rotation. c) Determine the matrix that maps triangle onto triangle .