CSEC Mathematics Paper 2 May/June 1982 - Free CXC Past Paper with Answers

Estimate in cm$^2$ the area of the scale drawing

Calculate the actual area of the island in square kilometres giving your answer to 2 significant figures

State the area of the island in hectares, giving your answer to 2 significant figures.

the length of $BD$

the area of $ABCD$

The trapezium $ABCD$ above (not drawn to scale) is a diagram of a plot of land such that $AB$ is parallel to $DC$. $DC = 40 \text{ m}$, , and angle .

$OQRS$ is a quadrilateral such that $OQ = \begin{pmatrix} 6 \\ 3 \end{pmatrix}$, $OR = \begin{pmatrix} -3 \\ 7 \end{pmatrix}$ and $OS = \begin{pmatrix} 1 \\ 5 \end{pmatrix}$. $T$ is the point on $OQ$ such that $OT:TQ = 1:2$

Prove that $QRST$ is a parallelogram.

Use your Venn diagram to determine whether the following conclusions are true (T), false (F) or inconclusive (I). Justify your answers. V. Kevin is a member of Plymouth School. VI. Martin swims well.

Draw a Venn diagram to illustrate the following propositions I. All students are members of Plymouth School. II. Students who study hard swim well. III. Kevin, Lise and Martin are Fifth Form students. IV. Martin studies hard.

Simplify $(x^{\frac{1}{3}})^3 \times \sqrt{x^9}$

Find the value of $x^0$ when $y = 16^{-\frac{1}{3}}$

The area of a rectangle is $270 \text{ cm}^2$. If the shorter side was reduced by $2 \text{ cm}$ and the longer side was increased by $4 \text{ cm}$ then the area would be increased by $16 \text{ cm}^2$. Find the lengths of the sides of the original rectangle.

Draw up a frequency table to represent this information

Determine the mode size, median size and mean size of this sample

The store manager wishes to replenish his stock. Which of the three measures should he use to determine what size to order in the largest quantity?

State a reason for your choice.

Estimate the probability that a pair of shoes chosen at random from the sample of 100 pairs is a size 6.

Using a scale of $2 \text{ cm}$ to represent 1 unit on each axis draw the graph of the function for the given range of values of $x$.

Draw the tangent to the curve at the point $P$ where $x = +1$.

From your graph estimate the gradient of the curve at $P$.

Draw an accurate full size diagram of the net.

Measure and write down the length of $EA$.

Sketch the cross section $VDH$ of the pyramid indicating clearly on your sketch the lengths of $VD$ and $DH$.

By calculation, determine $VX$ the height of the pyramid, [$X$ is the centre of the base]

The net is assembled as a pyramid with apex $V$ and base $BDFH$.

A ball is dropped into a pool of water and after $t$ seconds its depth $d \text{ cm}$ below the surface is given by the equation $d = 5t^2 - 30t$.

What is the minimum value of $d$?

What does this minimum value of $d$ imply physically?

Interpret these two values of $t$.

By completing the square express this equation in the form $d = 5 [(t - m)^2 - k]$ where $m$ and $k$ are constants.

For what value of $t$ is $d$ a minimum?

For what two values of $t$ is $d = 0$?

Calculate its speed when $t = 0$. After $2$ hours the train reaches a speed of $w \text{ kmh}^{-1}$ and maintains that speed for $1$ hour.

Calculate the value of $w$. The train accelerates again and its speed is now given by the equation $v = 5t + 1$, when $t \ge 3$.

Draw the speed - time graph of the journey for $0 \le t \le 8$ using $2 \text{ cm}$ to represent $1 \text{ hour}$ along the horizontal axis and $2 \text{ cm}$ to represent along the vertical axis.

Use your graph to calculate the distance travelled after $8 \text{ hours}$.

At a certain time hurricane Betty was situated at Latitude $10.3^\circ N$, Longitude $62.0^\circ W$. Calculate in km correct to two significant figures how far it had travelled when it was situated at $P$ ($15.7^\circ N, 62.0^\circ W$).

At the point $P$ the hurricane changes course and veers directly west along the same parallel of latitude $15.7^\circ N$ at a constant speed of $40 \text{ kilometres per hour}$. Determine its location $18 \text{ hours}$ after its change of course.

Draw a sketch of triangle $FPQ$ indicating on your diagram the bearings of $F$ from $P$ and $Q$. Calculate

the distance $PF$

the height of the pole $TF$

Determine the images of $(0, 1)$ and $(1, 0)$ under $T$.

Describe the geometrical transformation $T$.

In the figure, not drawn to scale, $A$ is $(4, 3)$ and $B$ is $(-3, 12.6)$. The images of $A$ and under are and respectively. Calculate the gradients of and .

State the size of angle $OAB$.

Calculate the length of $AB$. Hence write down the length of $A'B'$.

Calculate the area of triangle $OAB$. Hence write down the area of triangle $OA'B'$.