CSEC Mathematics Paper 2 May/June 1979 - Free CXC Past Paper with Answers

After a 15 per cent increase, a teacher's monthly salary was $977.50. Calculate the teacher's salary if a 20 per cent increase had been given instead.

In a circle, centre O, AB is a chord of length 12 cm. Given that $\angle BOA = 80^\circ$, calculate to 3 significant figures, the area of the minor segment cut off by AB. [Take $\pi$ to be $\frac{22}{7}$].

Determine the length of QP, stating reasons.

Calculate the radius of the larger circle.

Write down the value of $\tan \angle OML$.

the equation of the line $\ell$,

the image of $(2, 3)$,

the matrix which describes T.

A transformation T maps $(1,1)$ onto $(-1,1)$. If this transformation is a rotation through two right angles about the origin, followed by a reflection in a line $\ell$, determine

Construct a cumulative frequency table with intervals "less than or equal to 4", "less than or equal to 8", etc.

What percentage of students obtained scores less than or equal to 12?

Using (i), draw the cumulative frequency curve and estimate the pass mark if 60 per cent of the students passed.

What is the probability of selecting at random, from the Maths class, a student whose score $x$ is such that $17 < x < 24$?

Calculate the lengths of OP and OQ.

If OP, OQ are adjacent sides of a parallelogram, whose area is given by $\begin{vmatrix} 12 & 4 \\ 5 & 3 \end{vmatrix}$, find , where is the angle between OP and OQ. Leave your answer in fractional form.

the equation of the axis of symmetry,

whether the function has a maximum or minimum value and state this value,

which members of the range are negative.

From the graph, determine

the latitude of P, if the length of the parallel of latitude through P is 24 000 km,

the distance of X, a place 750 km due South of Spanish Town ($18^\circ N, 77^\circ W$),

the longitude of Y, a place 750 km due East of Spanish Town.

the distance of A from the base of the building,

the height of the building,

the length of the flagstaff.

Draw graphs on the same grid to show these conditions.

If he charges $24 per night for a double room and $16 per night for a single room, which arrangement gives the owner maximum income?

Find also the maximum number of empty rooms the owner can have in the extension so that his income for a night will be at least $248.

the aircraft's course,

the ground speed,

the time taken by the aircraft to reach its destination which is located 1030 km away.

Do either Part A or Part B

PART A A random sample of 50 electric light bulbs is tested to find out how many hours each would stay alight. The results are recorded in the table below:

PART B In an experiment the following values of the quantity X were obtained

Calculate the mean and standard deviation for this distribution.

Within how many standard deviations from the mean is the quantity X equal to 8?

Estimate what percentage of the X values is within one standard deviation of the mean.

Calculate the mean number of hours and standard deviation of the sample.

Suppose the quality is maintained at the current level when the sample mean is greater than 72 hours and the standard deviation is less than one hour. Does the sample given above meet with the quality requirement? Give reasons for your answer.

How many light bulbs lie within 2 standard deviations of the mean?

State which pair(s) of the events X, Y, Z will be mutually exclusive.

Find the probability of outcomes in which

X or Y will occur,

Y or Z will occur,

Y only will occur,

Suppose the coin is now weighted so that 'heads' is twice as likely to appear as 'tails', determine the probability of 'heads' and 'six' appearing.

In each of the following, state whether the statements p $\land$ q, and p $\lor$ q, are true or false, giving reasons for your answers: (a) p: Every quadrilateral has four sides. q: Two is an even number. (b) p: If $x = 5$ then $x^2 = 25$. q: All dogs are black. (c) p: All triangles are circles. q: January is the last month of the year.

Write the converse, inverse and contrapositive of each of the following statements, stating in each case, whether it is true or false: (a) If a triangle is equilateral then it is isosceles. (b) If an integer is even, then its cube is even.

'If $x = 0$ then $xy = 0$'. Which of the following statements is equivalent to the above? (a) if $xy = 0$, then $x = 0$. (b) if $x \ne 0$, then $xy \ne 0$. (c) if $xy \ne 0$, then $x \ne 0$. State the reason for your choice.

Construct a truth table to determine if the two statements below are logically equivalent. (a) People must work hard or they will not succeed in life. (b) If people succeed in life, then they must work hard.

(a) All regular polygons are polygons whose sides are equal in length. (b) PQRS is a regular polygon, (c) Therefore PQRS a polygon whose sides are equal in length. Using, $L = \{ x : x \text{ is a regular polygon} \}$ $M = \{ x : x \text{ is a polygon whose sides are equal in length} \}$ Express the statements (a), (b), (c) above in the language of sets.

Draw Venn diagrams to show that the reasoning in each of the following sets of statements is faulty: (a) All students hate homework. No fireman is a student. Therefore no fireman hates homework. (b) All good swimmers are athletes. West Indian cricketers are athletes. Therefore West Indian cricketers are good swimmers.