CSEC Mathematics Paper 2 May/June 1983 - Free CXC Past Paper with Answers

A bus is scheduled to depart at 15:40 for a journey which is scheduled to take $3\frac{1}{2}$ hours. It left at 16:45 and arrived at its destination 48 minutes later than scheduled. How long did this journey take?

The sides of a rectangular plate are measured as 7.3 cm and 2.8 cm correct to the nearest mm. Calculate from these measurements correct to 1 decimal place the area $A$ cm$^2$.

the greatest possible value of the area.

Write down the possible area of the plate in the form $(A \pm b)$ cm$^2$ where $b$ is the error correct to 1 decimal place.

Given that $f(x) = \frac{x+1}{2x-5}$ and $g(x) = \frac{2x-5}{x+1}$ and $h(x) = \frac{5x+1}{2x-1}$. Evaluate $f(3)$ and $g(4)$.

Show that $hf(3) = 3$.

Write down the expression for $f^{-1}(x)$.

The dimensions of a plot of land $ABC$ are such that angle $BAC = 45^\circ$, angle $ACB = 70^\circ$ and $BC = 200$ m. Calculate to 2 significant figures the length of $AB$.

Calculate in terms of $\vec{k}$ and $\vec{l}$, the position vector of .

Show that $\vec{LJ} = \vec{k} - 2\vec{l}$.

Express $\vec{LM}$ in terms of $\vec{k}$ and .

A rhombus $OJKL$ is such that $OK$ and $LJ$ intersect at $M$, $\vec{k}$ and are position vectors of and referred to the origin .

The weights of pupils in a school are shown in the table below:

Draw a cumulative frequency curve to represent the data. (USE GRAPH PAPER)

Determine the interquartile range of this distribution.

Estimate the probability that if a boy in this grade/class is chosen at random he weighs 41 kg or less.

A man in Honduras deposited H$10 000 in a fixed deposit account for 2 years at 12% per annum Simple Interest. At the time he deposited his money, H$1.00 = US$1.20, and at the end of the two years when he withdrew his deposit, H$1.00 = US$1.00. (The US$ did not change in value during this period.) Calculate, in H$, the interest he received,

Determine, in US$, the equivalent value of his initial deposit,

Express the amount (in US$) he received at the end of the two years as a percentage of the initial deposit (in US$).

If he converts the total amount he received at the end of the two years, would he get more $US now than for his initial deposit two years earlier? Justify your answer.

Let $\mu = \{ \text{persons} \}$ $N = \{ \text{numerate persons} \}$ $M = \{ \text{mathematicians} \}$ $P = \{ \text{poets} \}$

Examine EACH of the Venn diagrams below and state whether each statement satisfies the following 3 statements. Justify your answers in each case.

"All mathematicians are numerate." "Some poets are mathematicians." "Krishna Naipaul (K) is a poet."

Construct a triangle $ABC$ such that $AB = 6$ cm, $BC = 4.5$ cm and $CA = 3$ cm.

Construct the image of triangle $ABC$ found by reflecting triangle $ABC$ in side $AB$. Label the image of $C$ as $C'$.

Measure and state the length of $CC'$.

If $AB$ intersects $CC'$ at $N$, write down two statements about $NC'$.

State the type of polygon formed by the composite figure $ABC$ and its image.

The transformation $M$ maps $(a, b)$ onto $(-b, a)$. The transformation $L$ maps $(a,b$ onto . is a line segment where is the point and is the origin. Calculate the coordinates of and where is the image of the line segment under the transformation where and .

The area of a parallelogram $ABCD = 69.0$ m$^2$. $AB = 9.2$ m and $AD = 8.7$ m. Calculate the size of angle $BAD$.

Given that $\sin \theta = \frac{7}{25}$, calculate, without using tables: the value of $\tan \theta$ if $\theta$ is acute.

the value of $\cos \theta$ if $\theta$ is obtuse.

A BWIA Tri-star jet travels 80 km/h faster than a 747 jet liner. The Tri-star takes one hour less than the 747 jet to travel a journey of 6 280 km. Denoting the speed of the 747 jet liner by $x$ km/h. Write down in terms of $x$ expressions for the time taken by the 747 jet liner

the Tri-star jet.

Form an equation to connect these times and show that it simplifies to $x^2 + 80x - 502\,400 = 0$.

Hence find the speed of both aircrafts to the nearest km/hr.

Two types of crates A and B are available for shipping agricultural machinery. The capacity and shipping charge per trip for both types of crates are shown in the table below:

A firm wants to use the crates for shipping an order containing at least 120 brush cutters, 60 rotivators and 120 farmals. Using $x$ to represent the number of crates A and $y$ as the number of crates B, write down a set of inequalities which satisfy the above conditions.

Find graphically the minimum cost for shipping the order using both types of crates.

A chord $PQ$ of a circle of radius 10 cm is 3.16 cm from $O$ the centre of the circle. Calculate (a) the size of the angle, in radians, subtended by the arc $PQ$ at $O$.

the length, in centimetres, of the arc $PQ$.

the area, in cm$^2$, of the minor sector $OPQ$.

Write down the inverse of $B$.

Show that $BB^{-1}$ is the identity matrix.

Find the values of $x$ and $y$ which satisfy the equation $(AB)B^{-1} \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} 0 \\ 8 \end{pmatrix}$.

Calculate: (a) the mean score

(b) the standard deviation, giving your answer correct to one decimal place.

(c) Eight other students in a parallel form 6D completed the same quiz. The mean of their scores was 74 and the standard deviation was 2.88. Comment on the performance of the two forms.

Calculate the probability that, if two applicants are selected at random, at least one of them is a man.

If the man and his wife are selected, in how many ways can two other persons also be selected from the remaining applicants.

Calculate the probability that, if four applicants are selected at random, the man and his wife are selected.

Construct truth tables for $\sim q \lor p$ and $\sim p \land q$.

What conclusion, if any, can you draw about the compound statements $\sim q \lor p$ and $\sim p \land q$?

Let $p$ represent "All primes greater than 2 are odd." Let $q$ represent "All odd numbers are not even."

Translate the compound statements $\sim q \lor p$ and $\sim p \land q$ into words and state whether they are true or false. Justify your answers.

$M$ and $N$ are both multiples of 3 where $M$ and $N$ are natural numbers. By writing $M = 3x$ and $$ prove that is also a multiple of 3.

$t$ and $u$ are the tens and units digit respectively of a natural number between 10 and 100. If $t + u$ is a multiple of 3 prove that this natural number is always a multiple of 3.