CSEC Mathematics Paper 2 May/June 2015 - Free CXC Past Paper with Answers

Answer ALL questions in this section. All working must be clearly shown.

Using a calculator, or otherwise, determine the EXACT value of:

$2 \frac{2}{5} - 1 \frac{1}{3} + \frac{1}{2}$

$(4.14 \div 5.75) + (1.62)^2$

$2 \times 3.142 \times 1.25$

$\sqrt{2.89} \times \tan 45^\circ$

The table below shows a shopping bill prepared for Mrs Rowe. The prices of some items are missing.

Item	Unit Cost Price	Total Cost Price
3 kg sugar	X	$10.80
4 kg rice	Y	Z
2 kg flour	$1.60	$3.20

Calculate the value of X, the cost of 1 kg of sugar.

If the cost price of 1 kg of rice is 80 cents MORE than for 1 kg of flour, calculate the values of Y and Z.

A tax of 10% of the total cost price of the three items is added to Mrs Rowe's bill. What is Mrs Rowe's TOTAL bill including the tax?

Given that $a = 4$ , $b = 2$ and $c = -1$ , find the value of:

A bottle contains 500 ml of orange juice. Write an expression for EACH of the following. The amount of juice left in the bottle after pouring out

$q$ glasses each containing $r$ ml.

Write as a single fraction, as simply as possible $\frac{2k}{3} + \frac{2 - k}{5}$

Four mangoes and two pears cost $24.00, while two mangoes and three pears cost $16.00.

Write a pair of simultaneous equations in $x$ and $y$ to represent the information given above.

State clearly what $x$ and $y$ represent.

Factorize completely:

The Venn diagram below shows the number of students who play the guitar (G) or the violin (V) in a class of 40 students.

How many students play neither the guitar nor the violin?

Write an expression, in terms of $x$ , which represents the TOTAL number of students in the class.

Write an equation which may be used to determine the total number of students in the class.

How many students play the guitar?

Using a ruler, a pencil and a pair of compasses, construct triangle ABC with AB = 9 cm, angle ABC = $90^\circ$ and BC = 6 cm.

Measure and state the size of angle BAC.

On the diagram, show the point D such that ABCD is a parallelogram.

A graph sheet is provided for this question.

The table below is designed to show values of $x$ and $y$ for the function $y = x^2 - 2x - 3$ for integer values of $x$ from -2 to 4.

$x$	-2	-1	0	1	2	3	4
$y$	5		-3		-3		5

Complete the table for the function $y = x^2 - 2x - 3$ .

On the graph page 13, plot the graph of $y = x^2 - 2x - 3$ using a scale of 2 cm to represent 1 unit on the $x$ -axis and 1 cm to represent 1 unit on the $y$ -axis.

On the graph on page 13, draw a smooth curve passing through the points on your graph.

Complete the following sentences using information from your graph.

The values of $x$ for which $x^2 - 2x - 3 = 0$ are ................................. and .................................

The minimum value of $x^2 - 2x - 3$ is .................................

The equation of the line of symmetry of the graph of $y = x^2 - 2x - 3$ is .................................

A car is travelling at a constant speed of 54 km/h.

Calculate the distance it travels in $2\frac{1}{4}$ hours.

Calculate the time, in seconds, it takes to travel 315 metres, given that $1 \text{ km/h} = \frac{5}{18} \text{ m/s}$ .

Write the following scales in the form $1 : x$ .

1 millimetre = 1 metre

The map shown below is drawn on a grid of 1 cm squares. $P, Q, R$ and $S$ are four tracking stations. The scale of the map is $1 : 2 \ 000$ .

Determine, in centimetres, the distance from $Q$ to $R$ on the map. $QR = \text{......................................... cm}$

Determine, by counting, the area in square centimetres of the plane $PQRS$ on the map.

Calculate the ACTUAL distance, in kilometres, between $Q$ and $R$ .

Calculate the ACTUAL area, in square metres, of the plane $PQRS$ .

The diagram below, not drawn to scale, shows two cylindrical water tanks, A and B. Tank B has base diameter $8 \text{ m}$ and height $5 \text{ m}$ . Both tanks are filled with water.

Take $\pi = 3.14$ . (i) Calculate the volume of water in Tank B. (2 marks) (ii) If the area of the base of A is $314 \text{ m}^2$ , calculate the length of the radius of Tank A. (1 mark)

The diagram below, not drawn to scale, shows two cylindrical water tanks, A and B. Tank B has base diameter $8 \text{ m}$ and height $5 \text{ m}$ . Both tanks are filled with water.

Take $\pi = 3.14$ . (i) Calculate the volume of water in Tank B. (2 marks) (ii) If the area of the base of A is $314 \text{ m}^2$ , calculate the length of the radius of Tank A. (1 mark)

Calculate the volume of water in Tank B.

If the area of the base of A is $314 \text{ m}^2$ , calculate the length of the radius of Tank A.

Tank A holds 8 times as much water as Tank B. Calculate the height, $h$ , of Tank A.

The diagram below shows triangle $PQR$ and its image, triangle $P'Q'R'$ , after an enlargement centred at the point C on the diagram.

Use the information from the diagram to complete the statements below.

The size of the scale factor is ................................... .

The scale factor is negative because 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The length of $PQ$ is $\sqrt{13}$ units, therefore, the length of $P'Q'$ is .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... units.

The area of triangle $PQR$ is ........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................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square units.

The area of $P'Q'R'$ is .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................- times the area of triangle which is 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square units.

The line graph below shows the monthly sales, in thousands of dollars, at a car dealership for the period July to November 2014.

Complete the table below to show the sales for EACH month.

Month	July	August	September	October	November
Sales in $ Thousands	13		36

Between which TWO consecutive months was there the GREATEST increase in sales?

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and 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.........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................'s

Calculate the mean monthly sales for the period July to November 2014.

The TOTAL sales for the period July to December was $130 000.

Calculate the sales, in dollars, for the month of December.

Complete the line graph to show the sales for December.

A sequence of figures is made up of equilateral triangles, called unit triangles. The first three figures in the sequence are shown below.

Draw Figure 4 of the sequence.

Study the patterns of numbers in each row of the table below. Each row relates to one of the figures in the sequence of figures. Some rows have not been included in the table.

Complete the rows numbered (i), (ii), (iii) and (iv).

Figure	Number of Unit Triangles	Number of Unit Sides
1	1	$\frac{(3 \times 1)(1 + 1)}{2} = 3$
2	4	$\frac{(3 \times 2)(2 + 1)}{2} = 9$
3	9	$\frac{(3 \times 3)(3 + 1)}{2} = 18$
(i) 4
(ii)	144
(iii) 25
(iv) $n$

SECTION II

Answer TWO questions in this section.

ALGEBRA AND RELATIONS, FUNCTIONS AND GRAPHS

A graph sheet is provided for this question.

A teacher marks an examination out of a maximum of 120 marks. The marks are then converted to percentages.

Calculate the percentage for a student who scores

60 marks
120 marks.

On the graph sheet on page 27, plot a graph to show the information in (i).

A candidate is awarded 95 marks on the examination. Use the graph drawn at (ii) to determine the candidate's percentage.

Draw lines on your graph to show how the percentage was obtained.

A candidate is awarded a Grade A if her percentage is 85% or more. Use the graph drawn at (ii) to determine the minimum mark the candidate needs to be awarded a Grade A.

Draw lines on your graph to show how the percentage was obtained.

The functions $f(x)$ and $g(x)$ are defined as $f(x) = 3x + 2$ $g(x) = \frac{x^2 - 1}{3}$

Write an expression in terms of $x$ for $f^{-1}(x)$ .

Write an expression for $g f(x)$ , in the form $(x + a)(x + b)$ , where $a$ and .

MEASUREMENT, GEOMETRY AND TRIGONOMETRY

The diagram below, not drawn to scale, shows a vertical tower, $BT$ , with a flagpole, $TP$ , mounted on it. A point $R$ is on the same horizontal ground as $B$ , such that $RB = 60$ m, and the angles of elevation of $T$ and $P$ from $R$ are $35^\circ$ and $42^\circ$ , respectively.

Label the diagram to show

the distance 60 m
the angles of $35^\circ$ and $42^\circ$
any right angle(s).

Calculate the length of the flagpole, giving your answer to the nearest metre.

The diagram below, not drawn to scale, shows the relative positions of three fishing boats, $K$ , $L$ and $M$ . $L$ is on a bearing of $040^\circ$ from and is due south of . km and km.

On the diagram show the bearing of $040^\circ$ .

Calculate the measure of $\angle KLM$ .

Calculate the length, to the nearest kilometre, of $KM$ .

Calculate the measure of $\angle LKM$ to the nearest degree.

Calculate the bearing of $M$ from $K$ .

VECTORS AND MATRICES

Calculate the matrix product $AB$ where $A = \begin{pmatrix} 1 & 1 \\ 2 & 3 \end{pmatrix}$ and $B = \begin{pmatrix} 1 & 2 \\ 0 & 1 \end{pmatrix}$ .

Show that the matrix product of $A$ and $B$ is NOT commutative, that is, $AB \neq BA$ .

Find $A^{-1}$ , the inverse of $A$ .

Given that $M = \begin{pmatrix} 2x & 2 \\ 9 & 3 \end{pmatrix}$ , calculate the value(s) of for which .

The position vectors of the points $R, S$ and $T$ , relative to an origin, $O$ , are $\begin{pmatrix} -3 \\ 4 \end{pmatrix}$ , and respectively.

Calculate the value of $|\vec{OR}|$ .

Express in the form $\begin{pmatrix} x \\ y \end{pmatrix}$ , the vectors $\vec{RS}$ and .

Using the results of combining the vectors in (b) (ii) on page 33, justify that RS is parallel to ST and that RST is a straight line.

CSEC Mathematics Paper 2 May/June 2015 Questions

Question 1 (12 marks)

Question 2 (12 marks)

Question 3 (12 marks)

Question 4 (10 marks)

Question 5 (12 marks)

Question 6 (11 marks)

Question 7 (8 marks)

Question 8 (10 marks)

Question 9 (15 marks)

Question 10 (15 marks)

Question 11 (15 marks)