CSEC Mathematics Paper 2 May/June 1985 - Free CXC Past Paper with Answers

Given that $\begin{pmatrix} 3 & -2 \\ 2 & 1 \end{pmatrix} \begin{pmatrix} a \\ b \end{pmatrix} = \begin{pmatrix} 5 \\ 5 \end{pmatrix}$, determine the values of $a$ and $b$.

Find the values of $x$ to 2 significant figures in the equation $2x^2 + 5x = 9$.

$5 000 was put in a fixed deposit account on 1st January, 1984 for 6 months. The rate of interest was 12.5% per annum. On 1st July, 1984 the total amount received was reinvested for a further 6 months at 12.0% per annum. Calculate the final amount received at the end of the year.

Of the 100 candidates who wrote the examinations in Computer Science, Statistics and Accounts, 48 candidates passed Computer Science, 14 passed Computer Science and Accounts only, and 14 passed Statistics and Accounts only.

Three times as many passed in both Statistics and Computer Science as passed all three subjects.

Assume that:

• $x$ candidates passed Statistics only
• $a$ candidates passed Accounts only
• $y$ candidates passed Computer Science only
• $y$ candidates passed all three subjects

Represent the information given above on a suitable Venn diagram and hence write down TWO equations in $x$ and $y$ which can be used to solve for $x$ and $y$.

ABCDE is a regular pentagon inscribed in a circle centre O, radius 12 cm, as shown in the diagram above. M is the mid-point of DC.

(i) Calculate the angle DOC (in degrees). (ii) Calculate DM. (iii) Hence, find the perimeter of the pentagon.

In the diagram above the triangle ABC undergoes a shear so that A is mapped onto D and DC is parallel to AB, B and C remaining fixed. EF is the image of DC under translation and DE is equal to BC.

Describe (i) a single transformation that will map triangle EFC onto triangle DAB. (ii) a single transformation that will map triangle BMC onto triangle BDF.

a single transformation that will map triangle EFC onto triangle DAB.

a single transformation that will map triangle BMC onto triangle BDF.

Complete the column for the cumulative frequency on the answer sheet provided.

Using a scale of 1 cm to represent 7 days on the $x$-axis and 1 cm to represent 20 boxes on the $y$-axis, draw a cumulative frequency curve.

Use the curve to determine (i) the number of boxes of oranges collected in the last 30 days (ii) the number of days before a target of 360 boxes was reached.

the number of boxes of oranges collected in the last 30 days

the number of days before a target of 360 boxes was reached.

A box contains 10 similar balls, 4 of which are yellow. The first ball taken out at random is yellow. It is not replaced. Calculate the probability that a second ball taken out at random is yellow.

A cylindrical object of height 21 cm has an outer diameter of 28 cm and an inner diameter of 24 cm. The material of which it is made has a density of 6 g/cm$^3$. Calculate, to the nearest kilogram, the mass of the object.

The points A, B, and C have position vectors $4\vec{x} - 5\vec{y}$, $3\vec{x} + 4\vec{y}$ and $\vec{x} + 9\vec{y}$ respectively where $\vec{x}$ and $\vec{y}$ are unit vectors along $Ox$ and $Oy$ as shown in the diagram above.

(i) Find the length of vector $\vec{AB}$. (ii) Find the values of $p$ and $q$ if $OACB$ is a parallelogram.

Find the length of vector $\vec{AB}$.

Find the values of $p$ and $q$ if $OACB$ is a parallelogram.

Calculate the value of $y$ when $x = 0$.

Draw a graph of the recorded observations using a scale of 2 cm to 1 unit on the $x$-axis and 1 cm to 2 units on the $y$-axis, clearly indicating the incorrect value.

Estimate the correct value of $y$ for the incorrect one given.

Find the values of $B$ and $C$ in the formula.

Copy and complete the table below for values of $s$ and $t$ for $0 \le t \le 9$.

Draw the graph of the relation $s = 9 + 8t - t^2$ using a scale of 2 cm to represent 1 second and 2 cm to represent 10 metres.

Using the graph, find (i) the greatest distance of the object from A (ii) the time when the object returns to A (iii) the speed after it has travelled 5 seconds.

the greatest distance of the object from A

the time when the object returns to A

the speed after it has travelled 5 seconds.

Denoting the width of the first plot by $x$ metres and the width of the second plot by $y$ metres, derive a relation between $x$ and $y$.

If $y = x + 1$, calculate the values of $x$ and $y$.

Calculate the length of AC.

Show that BD is perpendicular to AC.

Prove that ABCD is a trapezium.

Estimate the mean income per hour of the families in Sample A.

Using a scale of 2 cm to represent $5 and 2 cm to represent 5 families draw a frequency polygon to illustrate the incomes of the families in Sample B.

How would you determine which sample had a more equitable distribution of income? Give reasons to support any statements you make.

Brian and David play each other in the 2nd Round.

Either Frank or George (or both) will reach the 2nd Round.

PF

MP.

$\vec{MN} = \frac{1}{3}\vec{QR}$.

MN is parallel to QR.

Copy and complete the truth table below for the compound statement $p \land (p \to q)$.

If p represents the statement "I like cricket", and q represents the statement "I play basketball well", what conclusion can be drawn from the statement $p \land (p \to q)$?

Consider the following TWO arguments: (i) $x < 5$ $y < 50$ Therefore $x < y$

Prove that the sum of any three consecutive integers is divisible by 3.

Any even number may be written as $2n$ where $n$ can be a negative or positive integer or zero.

Prove that

If the product of any two integers is odd then the sum of the integers is even.

Prove that $\frac{a^2 + b^2}{c^2 + d^2} = \frac{ab}{cd}$.