CSEC Mathematics January 2012 Past Paper

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TEST CODE OI234O2O
JANUARY 2012FORM TP 2012017
CARIBBEAN EXAMINATIONS COUNCIL
SECONDARY EDUCATION CERTIFICATE
EXAMINATION
MATHEMATICS
Paper 02 - General Proficiency
2 hours 40 minutes
04 JANUARY 2012 (a.m.)
Reouired Examination Materials
Electronic calculator
Geometry set
Graph paper (provided)
-
T
-
DO NOT TURN THIS PAGE UNTILYOU ARE TOLD TO DO SO.
READ THE FOLLOWING INSTRUCTIONS CAREFULLY.
1. This paper consists of TWO sections.
2. There are EIGHT questions in Section I and THREE questions in Section II.
3. Answer ALL questions in Section I, and any TWO questions from Section II.
4. Write your answers in the booklet provided.
5. All working must be clearly shown.
6. A list of formulae is provided on page 2 of this booklet.
: Copyight O 2009 Caribbean Examinations Council
:: All rights reserved.
=
ot234ozotJANUARY/r'2012
:=

v
LIST OF F'ORMULAE
Volume of a prism
Volume of cylinder
Volume of a right pyramid
Circumference
Arc length
Area of a circle
Area of a sector
Area of trapezium
Roots of quadratic equations
V
Trigonometric ratios
Area of triangle
Sine rule
Cosine rule
0 1 234020/JANUARYiF 20 I 2
+bx+c:0,
-b+"16'i;
2a
opposite side
: aypotenuse
Page 2
V : Ah where I is the area of a cross-section and h is the perpendicular
length.
Y: nf h where r is the radius of the base and & is the perpendicular height.
V : ! m where A is the area of the base and h is theperpendicular height.3
C:2nr where r is the radius of the circle.
S: * x2nr where 0 is the angle subtended by the arc, measured in
degrees.
A: nf where r is the radius of the circle.
e
A: 360
x nl where 0 is the angle of the sector, measured in degrees.
A : + @ + b) ft where a and b are the lengths of the parallel sides and ft is
the perpendicular distance between the parallel sides.
If ax2
then x
sin 0
^ adjacent side
cos u : -l-------;-
nypotenuse
^ oDDosite side
tan 0 : -++-.::adlacent srde
Area of A :
I U, where b is the length of the base and ft is
the perpendicular height.
I
Area of L,ABC : ; ab sin C
Areaof MBC :
, a+b+cwnere
2
abc
sinA sinB sin C
a2 : b2 * c2 - 2bccosA
Opposite
*b
Adjacent
s(s-a)(s-b)(s-c)
GO ON TO THE NEXT PAGE

SECTION I
AnswerALL the questions in this section.
All working must be clearly shown.
1. (a) Using a calculator, or otherwise, calculate the EXACT value of
Page 3
( 3 marks)
( 3 marks)
/ t2
^l(i)
[t;,,)
-- 31 ' expressing vour answer as a fraction
(ii) Jaos29 + 0.216, expressing your answer in standard form.
(b) A typist is paid a basic wage of $22.50 per hour for a 4O-hour week.
(i) Calculate the typist's basic weekly wage.
Overtime is paid at one and a half times the basic hourly rate.
( l mark)
(iD Calculate the overtime wage for ONE hour of overtime work. ( l mark)
To earn some extra money, the typist decided to work overtime.
Calculate
(iiD the wage she would earn for overtime if she worked for a TOTAL of 52 hours
during agivenweek. ( 2marks)
(i") the number of overtime hours she must work during a given week to eam a
TOTALwage of $1440. ( 2marks)
Total 12 marks
0 123 4020/ IANUARY/p 20 I 2

./
Solve the pair of simultaneous equations
3x + 2Y: 13
x - 2Y: -1.
Factorise completely
(i) x2 - 16
(ii) 2x2 - 3x + 8x - 12.
A universal set, U, is defined as:
U : { 51, 52, 53, 54, 55, 56, 57,58, 59 }
A andB are subsets of U, such that:
I : { odd numbers }
.B: { prime numbers }
(i) List the members of the setl.
(ii) List the members of the set B.
(iiD Draw a Venn diagram to represent the sets A, B and U.
(i) Using a pair of compasses, a ruler and a pencil
(a)
Page 4
( 3 marks)
(1mark)
( 2 marks)
( lmark )
( lmark )
( lmark )
(lmark)
( lmark )
( 3 marks)
(b)
3.
(c) Tickets for a football match are sold at $30 for EACH adult and $15 for EACH child.
A company bought 28 tickets.
(i) Ifx of these tickets were for adults, write in terms ofx,
a) the number of tickets for children
b) the amount spent on tickets for adults
c) the amount spent on tickets for children.
(iD Show that the TOTAL amount spent on the 28 tickets is $(15x + 420).
( lmark )
(iiD Given that the cost of the 28 tickets was $660, calculate the number of adult
tickets bought by the company. ( 2 marks)
Total12 marks
(a)
(b)
a) construct a triangle CDE in which DE : 10 cm, DC : 8 cm and
Z CDE:45". ( 4 marks)
b) construct a line, CF, perpendicular to DE such that F lies on DE.
( 2 marks)
(ii) Using a protractor, measure and state the size of I DCE. ( 1 mark )
Total 12 marks
0 1 234020/JANU ARY E 2012

4.
Page 5
(a) The following is an extract from a bus schedule. The bus begins its journey at Belleview,
travels to Chagville and ends its journey at St. Andrews.
Town Arrive Depart
Belleview 6:40 a.m.
Chagville 7:35 a.m. 7:45 a.m.
St. Andrews 8:00 a.m.
(i)
(ii)
(iiD
(i)
(ii)
(iiD
Water is poured into a cylindrical
water was poured into the bucket,
bucket with a base area of 300 cm2. If 4.8 litres of
what is the height of the water in the bucket?
( 3 marks)
How long did the bus spend at Chagville? ( 1 mark )
How long did the bus take to travel from Belleview to Chagville?
( lmark )
The bus travelled at an average speed of 54 km/hour from Belleview to Chagville.
Calculate, in kilometres, the distance from Belleview to Chagville.
( 2 marks)
(b)
(c) The diagram below, not drawn to scale, shows a cuboid with length 13 cm, width 4 cm
and height ft cm.
thcm
ryl.
State, in terms of ft, the area of the shaded face of the cuboid. ( 1 mark )
Write an expression, in terms of h, for the volume of the cuboid. ( 1 mark )
If the volume of the cuboid is 286 cm3 calculate the height, h, of the cuboid.
( 2 marks)
Total ll marks
I
I
t_
O 1 23 4O2O I JANUARY/F 20 I 2

v
5. (a) The diagram below, not drawn
JK parallel to ML. LM: MP,
LMP:36.
to scale, shows TWO triangles, JKL and,
KLP is a straight line, angle JLM: 22"
Page 6
MLP,with
and angle
Calculate, giving reasons for your answers, the measure of EACH of the following:
(i) z MLP
(iD t rJK
(iiD z JKL
(iv) z KLJ
(b) The diagrambelow shows atriangle, PQR,andits image, P'e,R,.
( 4 marks)
State the coordinates of P and, Q. ( 2 marks)
Desciibe fully the transformation that maps triangle PQRonto triangle P,Q,R,.
( 2 marks)
images of P and Qunder the translation
(D
(ii)
(iiD Write down the coordinates of the
I ',l.
[-6]
( 2 marks)
Total 10 marks
v
0 l 234020/JANUARY/r' 20 1 2

6.
Page 7
Thetablebelowshowscorrespondingvaluesofxandyforthefunctiony:f-2x-3,for
integer values ofx from -2to 4.
Copy and complete the table. ( 2marks)
(c)
(d)
Using a scale of 2 cm to represent I unit on thex-axis, and 1 cm to represent L unit
on they-axis, plot the points whose x andy values are recorded in your table, and draw
a smooth curve through your points. ( 4 marks)
Using your graph, estimate the value ofy when x:3.5. Show on your graph how the
value was obtained. ( 2 marks)
Without further calculations,
(D write the equation of the axis of symmetry of the graph ( 1 mark )
(iD estimate the minimum value of the functiony ( I mark )
(iiD state the values of the solutions of the equation: x2 - 2x - 3 : 0. ( I mark )
Total ll marks
(a)
(b)
(
(
x .|
-1 0 I 2
a
J 4
v 5 -J -4 0 5
0 1 234020IJANUARY/F 20 1 2

l,
7. The histogram below shows the distribution of heights of seedlings in a sample.
(a) copy and complete the frequency table for the data in the sample.
Determine
(i) the modal class interval
(ii) the number of seedlings in the sample
(iiD the mean height of the seedlings
(iv) the probability that a seedling chosen at random has a height that is GREATER
than3o"-''
- (2marks)
Total 12 marks
(b)
Page 8
( 3 marks)
( lmark )
( 2 marks)
( 4 marks)
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Height in cm Mid-point tr'requency
1-10 5.5 18
11 - 20 15.5 25
2t-30
31 -40
41-50
o r23 4020I JANUARY/F 20 I 2

!/
8. An answer sheet is proyided for this question.
Sarah is making a pattern of squares using straws. She
longer straws for the diagonals. The first three figures
below:
Page 9
uses four straws for the sides and two
in her sequence of shapes are shown
(a)
(b)
Figure 1 Figure 2 Figure 3
On your answer sheet, draw Figure 4,the FOURTH shape in the pattern.
( 2 marks)
On your answer sheet, complete the TWO rows in the table for
(D Figure 4
(ii) Figure 10.
( 4 marks)
Which figure in the sequence uses 106 straws? ( 2 marks)
Obtain an expressi on in n, for the total number of straws used in the nth pattern.
( 2marks)
Total l0 marks
(i)
tll
ttt
F------+ +---
ttt
ltt
(ii)
I
(c)
(d)
Total Number of Straws
tr'igure Formula Number
1(6) - 0 6
2 2(6) - r 1l
J 3(6) - 2 16
4
0 t23 4020I JANUARY/p 20 I 2

t
9.
SECTION II
Answer TWO questions in this section.
ALGEBRAAND RELATIONS, FUNCTIONS AND GRAPHS
(a) (D Make I the subject of the formula
2x +3
' -r-4
(ii) Hence,determinetheinverseof f(x =
2x+3
" where x*4.
x-4'
(iii) Find the value ofx for which/(:r) : 0.
(b)
Page 10
( 2 marks)
( 2 marks)
( 2 marks)
The diagram below shows the graphs of three lines and a shaded region defined by three
inequalities associated with these lines.
The inequality associated with the line 3y: * is 3y > _r.
lY'
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_
1"1" f- t
i i::i...i:
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ffi ffifi>rfr
'.1...i .:.i.''.i, N
i;-* fr Ilni-';'
N10 30 40 -x
(D State the other TWO inequalities which define the shaded region.
The function p : 4x + 3y satisfies the solution
( 2 marks)
set represented by the closed triangular
Identi$' the three pairs of (x, y) values for whichp has a maximum or a minimum
value. ( 3 marks)
Which pair of (x, y) values makesp a maximum? Justify your answer.
( 4 marks)
Total 15 marks
20
regron.
(ii)
(iii)
0 123 4020I JANUARY/p 20 1 2

t
(a)10.
Page 1l
MEASUREMENT, GEOMETRY AND TRIGONOMETRY
The diagram below, not drawn to scale, shows a regular hexagon with centre, O, and
AO: 5 cm.
(b)
(i) Determine the size of angle AOB.
(iD Calculate, to the nearest whole number, the area of the hexagon.
The diagram below, not drawn to scale, shows a vertical pole, PL,
a hoizontal plane, KLM. The angle of elevation of P from K is 28",
LM:19mand ZKLM:115".
P
( 2 marks)
( 3 marks)
standing on
KL: 15 M,
a)
b)
c)
PL
KM
the angle of elevation of P from M.
M
ONE right angle.
( 2 marks)
( 2 marks)
( 3 marks)
( 3 marks)
Total 15 marks
(iD
(D Copy the diagram. Show the angle of elevation ,28" and
Calculate, giving your answer to 2 significant figures, the measure of
O 1234O2O / JANUARYIF 20 1 2

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Page 12
11. (a) The diagram below shows two position vectors & una dg.
(i) Write as a column vector, ln tn" for- [t] .
a) dt
Y)
( lmark )
b) ota ( l mark )
c) 3A ( 2 marks) !
(iD Given that G is the mid-point of the line AB, write as a column vector in the
/x
forml l:
v)
a) ic (lmark)
b) ic (lmark)
(b) L and M are two matrices where
(t 2 (-t 3)
':[' 4) anaM:[o 2)
Evaluate
(i) L+2M (2marks)
(iD LM (2marks)
(+ 2)
(c) The matrix, Q, is such that O :
[l t)
(i) FindQ-1. (2marks)
(iD Using a matrix method, find the values of x andy in the equation
(+ 2 /x /s
[' ')l;: [,J ( 3 marks)
Total 15 marks
END OF'TEST
IF YOU FINISH BEFORE TIME IS CALLED, CHECK YOUR WORK ON THIS TEST.
I

CSEC Mathematics January 2012 Past Paper

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