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FORM TP 2018017
qtu
rESr coDE 01234020
-l
JANUARY 2OI8
CARIBBEAN EXAMINATIONS COUNCIL
CARIBBEAN SECONDARY EDUCATION CERTIFICATE@
EXAMINATION
MATHEMATICS
Paper 02 - General Prcficiency
2 hours 40 minutes
READ THE FOLLOWING INSTRUCTIONS CAREFULLY.
1.
This paper consists of TWO sections: I and II.
2.
Section I has EIGHT questions and Section II has THREE questions.
3.
AnswerALL questions in Section I and any TWO questions from Section II.
4.
Write your answers in the booklet provided.
5.
Do NOT write in the margins.
6.
All working MUST be clearly shown.
7.
A list of formulae is provided on page 4 of this booklet.
8.
If you need to rewrite any answer and there is not enough space to do so on the
original page, you must use the extra page(s) provided at the back of this booklet.
Remember to draw a line through your original answer.
9.
If you use the extra page(s) you MUST write the question number clearly in the
box provided at the top of the extra page(s) and, where relevant, include the
question part beside the answer.
Required Examination Materials
Electronic calculator
Geometry set
DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO.
Copyright @ 2017 Caribbean Examinations Council
All rights reserved'
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LIST OF FORMULAE
Volume of a prism
V
: Ah where I is the area of a cross-section and ft is the perpendicular
length.
nf hwhere r is the radius of the base and & is the perpendicular height.
Volume of a cylinder
V=
Volume of a right pyramid
f : ]-,lhwttere ,,{ is the area of the base and & is the perpendicular height.
Circumference
C = Znr where r is the radius of the circle.
Arc length
t: *-
I
x 2nr where 0 is the angle subtended by the arc, measured in
degrees.
Area of a circle
Area of a
sector
Areaof atrapezium
A : nf where r is the radius of the circle.
n: #x
nl where 0 is the angle of the sector, measured in degtees.
A=+@+ b)ft where aandbare the lengths of theparallel sides and ft
is the perpendicular distance between the parallel sides.
Roots of quadratic equations lf axz + bx -r
c: 0,
+,{b? 4a;
then l- = -b
----u-
Trigonometric ratios
stn 0
length of opposite side
: I#gtfm$Foienuse
cos0 =
length ofadjacent side
length ofhypotenuse
tanO:
side
length of
length ofadjacent side
Opposite
0
Area of a triangle
Adjacent
Areaof A= ) bhwhereb is the length of the base and ft is the perpendicular
height.
Area of A ABC =
|- ab sin C
Area of A ABC :
where s -
a_b-c
a+b*c
2
silT
sm7
Cosine rule
a2 = b2. i c2 - 2bc cos A
silU
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Sine rule
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s(s-a)(s-b)(s-c)
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A
b
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SECTION I
Answer ALL questions in this section.
All working must be clearly shown.
1.
(a)
Using a calculator, or otherwise, calculate
(i) t* * ,1 * tf , eivinc your answer as a fraction in its lowest terms
(2 marks)
(ii)
165 x 0.382, giving your answer as an EXACT value.
(1 mark)
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(b)
Write your answer in (a) (ii) correct to
(i)
two decimal places
(1 mark)
(iD three significant figures
(1 mark)
(iii)
the nearest whole number.
(1 mark)
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(c)
MrAdams invested $5 000 at the credit union and received S5 810, inclusive of simple
interest, after 3 years.
Determine
(i)
the simple interest earned
(1 mark)
(ii)
the annual interest rate paid by the credit union
(2 marks)
(iii)
the length of time it will take for MrAdams' investment to be doubled, at the same
rate of interest.
(2 marks)
Total l1 marks
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PaseTl
(a)
Given that a * b means J;4b
(i)
, where the positive root is taken, determine
the value of I * 2
(2 marks)
(ii)
whether the operation denoted by * is commutative. Justifu your answer.
(3 marks)
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(b)
(D
Solve the inequality 3 -Zx> 5
(2 marks)
(ii)
Represent your answer in (b) (i) on the number line shown below.
-4 -3 -2 -1 0 1 2 3
4
(l mark)
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(c)
{
Statement one: Two adult tickets and three children tickets cost $43.00.
Statement two: One adult ticket and one ticket for a child cost $18.50.
(i)
Let x represent the cost of an adult ticket andy the cost of a ticket for a child. Write
TWO equations in x andy to represent the information above.
(2 marks)
(iD
Solve the equations to determine the cost of an adult ticket.
(2 marks)
Total 12 marks
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3.
eaee
(a)
{
The universal set U: {b, d, e,f, g, i, k, s, t,v, w}. The Venn diagram below shows U and
three sets, M, P and R, which are subsets of U.
t
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(i)
State the value of n(Pt-rR)
(1 mark)
(ii)
List the members of
a) MnP
(2 marks)
b)
MwR'
(2 marks)
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(b)
(i)
{
Using a ruler, a pencil and a pair of compasses, construct triangle PQR with
PQ:8 cm, angle PQR:120" and QR:5 cm.
(4 marks)
(ii)
Measure and state the length of the side PR.
(1 mark)
(iii)
On your diagram in (b) (i), construct the point S, such that PQRS forms a
(2 marks)
parallelogram.
Total 12 marks
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(a)
The equation of a straight line, l, is given as 3x - 4y
(i)
{
: 5.
Write the equation of the line, /, in the formy : mx * c
(2 marks)
(ii)
Hence, determine the gradient of the line, /.
(l mark)
(iii)
The point P with coordinates (r, 2) lies on the line /. Determine the value of r.
(2 marks)
(iv) Find the equation of the straight line passing through the point (6, 0) which is
perpendicular to l.
(2 marks)
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(b)
(i)
Draw the straight lines x * y: l0 andy: x on the grid below.
irl
(2 marks)
(iD On the same grid, shade the region which satisfies the FOUR inequalities
x>0
vZ0
x+y<10 and
x) v.
'-l
(2 marks)
Total ll marks
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(a)
{
The regular polygon EFGHIJ, shown below, has centre O. Triangle OEF is equilateral
and EF: 5 cm.
Scm F
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What is the name of the polygon shown above?
(1 mark)
(iD Calculate the perimeter of the polygon EFGHIJ.
(1 mark)
(iii)
Determine the size of each interior angle of the polygon.
(2 marks)
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(iv)
{
Show, by calculation, that the area of the polygon, to the nearest whole number,
is 65 cm2.
(3 marks)
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(b)
{
A tank has a cross section with dimensions identical to the polygon EFGHIJ in 5 (a).
Water is poured into the tank at a rate of 75 cm3 per second. After 52 seconds the tank is
2
5
full
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(i)
Determine the capacity of the tank, in litres.
(3 marks)
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(ii)
{
Calculate the height, ft, in metres, of the tank.
(2 marks)
Total 12 marks
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The diagram below shows triangle PQR.
l,
(a)
State the coordinates of R.
(1 mark)
(b)
On the diagram above, draw
(i)
L P'Q'R' , a reflection of L, PQR in the line y : I
(2 marks)
(ii)
L P" Q" R" , a reflection of L P'Q'R' in the line x : 0
(2 marks)
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(c)
Describe, fully, the single transformation that maps A P" Q't Rtt onto A PpR
(3 marks)
(d)
Triangle PQRundergoes an enlargement of scale factor 2. Calculate the area of its image.
(2 marks)
Total 10 marks
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(a)
,
I
The marks obtained by 10 students in a test, scored out of 60, are shown below.
29 38 26 42
45 35 37 38
38
3r
For the data above, determine
(i)
the range
(1 mark)
(iD the median
(1 mark)
(iii)
the interquartile range
(2 marks)
(iv) the probability that a student chosen at random scores less than half the total marks
in the test.
(2 marks)
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(b)
The frequency distribution below shows the masses, in kg, of 50 adults prior to the start
of a fitness programme.
Mass (kg)
Midpoint
Frequency
6044
62
8
65-69
67
11
70-74
72
15
75-79
77
9
80-84
82
5
85-89
87
2
On the grid on page23, using a scale of 2 cm to represent 5 units on the x-axis and I cm
to represent 1 unit on the y-axis, draw a frequency polygon to represent the information
in the table.
(6 marks)
Total 12 marks
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A sequence of figures is made from toothpicks of unit length. The first three figures in the sequence
are shown below.
/\ AZ N/N
Frgure 1
(a)
Figure 2
Figure 3
Draw Figure 4 of the sequence.
(2 marks)
(b)
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 above. Some rows have not been included in the
table.
Complete the rows numbered (i), (ii), (iii) and (iv).
Figure
Number of Toothpicks
in Pattern
Perimeter of Figure
1
a
J
0+l+2:3
2
7
I +2+2:5
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2+3 +2:7
(0
(2 marks)
4
19+20+2:41
(ii)
(iii)
(iv)
t27
n
(2 marks)
(2 marks)
(2 marks)
Total 10 marks
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SECTION II
Answer TWO questions in this section.
ALGEBRAAI\D RELATIONS, FUNCTIONS AND GRAPHS
9.
(a)
(i)
Show, by calculation, that the EXACT roots of the quadratic equation
*+2x-5:0are-1 +./6.
(3 marks)
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(ii)
{
Hence, or otherwise, solve the simultaneous equations
2+ x=y
xy: 5.
(4 marks)
(b)
The incomplete table below shows values of x andy for the function !:2,
values ofx from -l to 4.
x
1
v
0
1
1
2
J
for integer
4
8
(D
Complete the table for the functiony:2'
(ii)
On the grid provided on page 27, draw the graph of y:2', using a scale of 2 cm
to represent 1 unit on the x-axis and I cm to represent 1 unit on they-axis.
(2 marks)
(4 marks)
(iii)
Drawing appropriate lines on your graph, determine the value of x for which
2': lI.
(2 marks)
Total 15 marks
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i'.','',.f.,
1,.
l,r,.
L.
1,,
.1'.,,i,[,
'.1,..
l,
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,,j.i''Ji
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,1.
i
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ll''
1..
1.,.
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MEASUREMENT, GEOMETRY AND TRIGONOMETRY
10.
(a)
The diagram below, not drawn to scale, shows a circle with centre O. The points A, B,
C and D are on the circumference of the circle. EAF and EDG arc tangents to the circle
at A andD respectiv ely.,a6O : ll4o and CbC: 18o.
1
E
Calculate, giving reasons for EACH step of your answer, the measure of
(i)
n
ACD
(2 marks)
(ii)
AED
(2 marks)
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(iiD o^c
(2 marks)
(iv) ebc
(2 marks)
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(b)
{
The diagram below shows a cuboid
60cm.-----------._ R
V
c$
t
20 cm
+
T
W
Give your answer correct to one decimal place.
O
A straight adjustable wire connects R to P along the top of the cuboid. Calculate
the length of the wire.ttP.
(1 mark)
(ii)
The connection at P is now adjusted and moved to Z.
Calculate the length of the wire RZ.
(2 marks)
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(iiD Calculate the angle TRV.
(2 marks)
(iv)
Complete the following statements
The size of the angle through which the wire moves from i?P to RZ is
An angle which is the same in size as RTVis
(2 marks)
Total 15 marks
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VECTORS AND MATRICES
11.
(a)
:[iJ ,fr:[-N,.or:[l]'
Given the vectors O?
(i)
--)
determine the vector 0p
(2 marks)
(iD show that dr"parallel to RS]giving a reason for your answer,
(1 mark)
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(b)
{
XYZis a triangle and Mis the midpointof XZ.
---)
YZ:b.
XY:t and--)
Express the following vectors in terms of a and b, simplifying your answers where possible:
---)
(i) xz
(1 mark)
(ii)
---)
MY
(3 marks)
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(c)
The matrices
(i)
I and .B are given ,., :
iil
:
f-l | '""0 , l+
[-i ?1
6J
Determine A-t,the inverse ofl.
(2 marks)
(ii)
Show that A tA = I, the identity matrix.
(2 marks)
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(iii)
{
Determine the ma1u.ixA2
(2 marks)
(iv) a)
Explain why the matrix ptoduct AB is NOT possible
(1 mark)
b)
Without calculating, state the order of the matrix product BA.
(l mark)
Total 15 marks
END OF TEST
IF YOU FINISH BEFORE TIME IS CALLED, CHECK YOUR WORI( ON THIS TEST.
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TEST CODE
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Page 2
FORM TP 2004101
MA Y/JUNE 2004
CARIBBEAN
EXAMINATIONS
SECONDARY
COUNCIL
EDUCATION CERTIFICATE
EXAMINATION
MATHEMATICS
Paper 02
- General Proficiency
2 hours 40 minutes
( 1.7~Y2~i*.m.)
LIST OF FORMULAE
)
Volume of a prism
v Ah where A is the area of a cross-section and h is the perpendicular
length.
Volume of a right pyramid
v = 13Ah where A is the area of the base and h is the perpendicular
Circumference
C
Area of a circle
A = nr where r is the radius of the circle.
Area of trapezium
A = (a + b) h where a and b are the lengths of the parallel sides and h is
=
height.
= 2nr where r is the radius of the circle.
i
the perpendicular
distance between the parallel sides.
Roots of quadratic equations IfaX + bx + c = 0,
thenx=-
INSTRUCTIONS TO CANDIDATES
1.
Answer ALL questions in Section I, and ANY TWO in Section II.
2.
Write your answers in the booklet provided.
3.
All working must be shown clearly.
4.
Examination
Trigonometric
ratios
-b :t .Jb2 - 4ac
2a
sin a = opposite side
-~~
hypotenuse
~OPPOSite
Adjacent
adjacent side
cos a = hypotenuse
A list of fonnulae is provided on page 2 of this booklet.
tan a = opposite side
adjacent side
Materials
Electronic calculator (non-programmable)
Geometry set
Mathematical tables (provided)
Graph paper (provided)
Area of triangle
Area
of ~ = 12 bh where
b is the length
of the base and h is the
~
1
Area of MBC""""",ili~IMh.gh'
= 'J!lbsin C
Area of MBC
<
2
Copyright @ 2003 Caribbean Examinations
All rights reserved.
Council.
Sine rule
--L_~-~
sin A -
Cosine rule
a2 = b2 + C2 - 2bc cos A
0 I234020/F 2004
b
)
= .js(s - a) (s - b) (s - c)
where s = a + b + c
DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO
'h
I
sinB -
sinC
C
~
b
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0 I 234020/F
2004
A
Page 3
SECTION
Answer ALL the questions
,i
Page 4
3.
I
(a)
A club has 160 members, some of whom play tennis (T) or cricket (C) or both. 97 play
tennis, 86 play cricket and 10 play neither, x play both tennis and cricket.
in this section.
I"
All working must be clearly shown.
I.
(a)
(b)
Using a calculator, or otherwise, detennine the exact value of
(i)
Draw a Venn diagram to represent this information.
(ii)
How many members play both tennis and cricket?
In a beauty contest, the scores awarded by eight judges were:
5.9
(i)
(i)
(c)
6.8
6.5
6.7
8.2
6.1
6.3
Using the eight scores, detennine:
M
a)
the mean
the median
(iii)
31. - 21~
21.
5
b)
c)
the mode
(i)
Write your answer in Part (a) (i) correct to one significant figure.
(ii)
Write your answer in Part (a) (ii) in standard form.
(i)
Mr Mitchell deposited $40 000 in a bank and earned simple interest at 7% per
annum for two years.
(6 marks)
(ii)
(b)
6.7
2.32 + 4.12
. 0.18 - 0.003
(ii)
(5 marks)
Only six scores are to be used. Which two scores may be omitted to leave the
value of the median the same?
(6 marks)
(2 marks)
Total 11 marks
4.
(i)
(a)
Using the formula
.[Iii!
Calculate the amount he will receive at the end of the two-year period.
t ='V12n
(ii)
Mr Williams bought a plot of land for $40 000. The value of the land
appreciated by 7% each year.
Calculate the value of the land after a period of two years.
(a)
(b)
(ii)
(4 marks)
Total 12 marks
2.
calculate the value of t when m
(b)
'~I
'1['11
,
Express m as subject of the formula in (a) (i) above.
In the diagram below, not drawn to scale, EFGH is a rectangle.
1\
0
such that ED = DG = 12 cm and GDF = 43 .
(i)
x2
x-I- I
(ii)
4ab2 + 2a2b
ab
Express as a single fraction:
3p
q
2'
+p'
The point D on HG is
(4 marks)
H
D~
(2 marks)
=0
12cm ---
G
Calculate correct to one decimal place
Solve for x, given
3x2 - 7x + 2
(5 marks)
F
Simplify:
(i)
(c)
=20 and n =48.
(4 marks)
the length of GF
(ii)
the length of HD
(iii)
the size of the angle HDE.
(7 marks)
1
Total 10 marks
I~
Tota112 marks
1:111
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1"':
",'ii,'
01234020/F 2004
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Page 5
5.
An answer sheet is provided
(a)
(b)
Page 6
6.
for this question.
On the section of the answer sheet provided for 5 (a):
The amount a plumber charges for services depends on the time taken to complete the repairs
plus a fixed charge.
.
The graph below shows the charges in dollars (ti) for repairs in terms of the number of
minutes (t) taken to complete the repairs.
(i)
write down the coordinates of the point P
(ii)
draw a line segment PQ through the point, P, such that the gradient of PQ is
-3 .
(3 marks)
2
d
"
On the section of the answer sheet provided for 5 (b):
(i)
draw the reflection of quadrilateral A in the mirror line, labelled MI,
Label its image B.
(ii)
draw the reflection of quadrilateral B in the mirror line, labelled M2.
Label its image C.
(c)
30
(4 marks)
Complete the sentence in part (c) on your answer sheet, describing FULLY the single
geometric transformation which maps quadrilateral A onto quadrilateral C.
(3 marks)
70
Total 10 marks
(a)
What was the charge for a plumbing job which took 20 minutes?
(b)
How many minutes were spent completing repairs that cost:
(i)
$38.00
(ii)
$20.oo?
(1 mark)
(2 marks)
(c)
What is the amount of the fixed charge?
(1 mark)
(d)
Calculate the gradient of the line.
(2 marks)
(e)
Write down the equation of the line in terms of d and t.
(2 marks)
(f)
Detennine the length of time taken to complete a job for which the charge was $78.00.
(3 marks)
Total 11 marks
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Ol2340201F
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Page 7
7.
(a)
Page 8
8.
A piece of wire is bent in the fonn of a circle and it encloses an area of 154 cm2.
(i)
Calculate:
Cups of chocolate
the radius of the circle
Recipe A
3
2
b)
the circumference
Recipe B
2
1
of the circle.
The same piece of wire is then bent in the fonn of a square.
(b)
CUps of Milk
a)
(Use 1t = 22)
7
(ii)
Two recipes for making chocolate drinks are shown in the table below.
:1
(6 marks)
Calculate the area enclosed by the square.
The diagram below shows a map of Bay time drawn on a grid of 1 cm squares. The scale
of the map is 1:100 000.
.
II
. What percent of the mixture using Recipe A is chocolate?
(b)
By showing suitable calculations, determine which of the two recipes, A or B, is richer
in ch~colate.
(2 marks)
(c)
If the mixtures from Recipe A and Recipe B are combined,
chocolate in the new mixture?
(d)
A vendor makes chocolate drink using Recipe A. 3 cups of milk and 2 cups of chocolate
can make 6 bottles of chocolate drink. A cup of milk costs $0.70 and a cup of chocolate
costs $1.15.
';1
II
II
(i)
What is the cost of making 150 bottles of chocolate drink?
(ii)
What should be the selling price of each bottle of chocolate drink to make an
overall profit of 20%?
(6 marks)
Tota112 marks
i
Find to the nearest lan, the shortest distance between Rose Hall and South Port.
(ii)
Determine the bearing of South Port from Spring Hall.
what is the percent of
(2 marks)
,
iJ
(i)
(2 marks)
(a)
(6 marks)
Total 12 marks
i
,
J
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0 12340201F
012340201F 2004
2004
.r
'II
Page 9
SECTION
Answer TWO questions
ALGEBRA
AND RELATIONS,
II
Page 10
10.
in this section
FUNCTIONS
A vendor buys x kg of peanuts and y kg of cashew nuts.
(a)
(i)
AND GRAPHS
To get a good bargain, she must buy a minimum of 10 kg of peanuts and a
minimum of 5 kg of cashew nuts.
Write TWO inequalities which satisfy these conditions.
9.
(a)
The table below shows COITesponding values for P and r.
E8
m
4
62.5
0.2
2
n
(ii)
She buys no more than 60 kg of nuts. Peanuts cost $4.00 per kg and cashew
cost $8.00 per kg and she spends at least $200.
nuts
Write TWO inequalities which satisfy these conditions.
(S marks)
(b)
Given that P varies directly as r3, calculate the values of m and n.
Using a scale of 2 cm to represent 10 kg on each axis, draw the graph of the FOUR
inequalities in (a) (i) and (a) (ii).
(6 marks)
On your graph, shade ONLY the region which satisfies all four inequalities.
(b)
In the diagram below, not drawn to scale, AKLM and ASTJ are both rectangles.
A
3.r
S
(6 marks)
(c)
3
The profit on the sale of 1 kg of peanuts is $2.00 and on 1 kg of cashew nuts is $5.00.
K
~
J
T
Given that AS
(i)
(ii)
Using your graph, determine the number of kilograms of each type of nut the
vendor must sell in order to make the maximum profit.
(ii)
Calculate the maximum profit.
(4 marks)
Total IS marks
5
M
(i)
L
= 3x cm, AJ = 2xcm, SK = 3 cm andJM = 5cm
Obtain an expression, in terms of x, for the area of rectangle AKLM.
Given that the area of rectangle AKLM is 60 cm2, show that
2x2 + 7x - 15 = 0
(iii)
Hence, calculate the value of x and state the length of AK and AM.
(9 marks)
Total IS marks
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Page 11
GEOMETRY
11.
(a)
Page 12
12.
AND TRIGONOMETRY
(a)
In the diagram below, VWZ and WXYZ are two circles inter~ting at Wand -';; SVT is a
tangent to the circle at V, VWX and vzy are straight lines, TVY = 78° and SVX = 51°.
Given that sin e = -{3
2
,0° ~ e ~ 90°.
(i)
Express in fractional or surd form the value of cos e.
(ii)
Show
that the area of tria~gle
CDE is 150 -{3 square
units,
where
CD = 30 units
and DE = 20 units.
c
D
E
(i)
(iii)
Calculate the size of EACH of the following angles, giving reasons for your
answers.
1\
a)
(b)
VZW
(7 marks)
Calculate the length of the side EC.
In this question, use 1t = 3.14 and assume the earth to be a sphere of radius
6 370km.
1\
b)
(b)
(i)
Xyz
(4 marks)
The diagram below shows a sketch of the earth with the Greenwich Meridian and the
Equator labelled.
Draw a diagram to represent the information given below.
N
Show clearly the north line in your diagram.
Town F is 50 kIn east of town G.
Town H is on a bearing of 040° from town F.
Equator
The distance from F to H is 65 km.
Greenwich
Meridian
(ii)
Calculate, to the nearest
(iii)
Calculate, to the nearest degree, the bearing of H from G.
kilometre,
the actual distance GH.
S
(11 marks)
The towns A and B are both on the circle of latitude 24° N. The longitude of A is
108° E and the longitude of B is 75° E.
Total 15 marks
(i)
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0 1234V20/F
2004
Copy the sketch above of the earth and in~ert the points A and B on your
diagram.
012340201F
2004
,
Page 13
(ii)
Calculate, correct to the nearest
a)
b)
Page 14
kilometre,
/
the radius of the circle of latitude 24° N
6.
An answer sheet is provided
(a)
the shortest distance between A and B, measured along the circle of
latitude 24° N.
(8 marks)
for this question.
On the answer sheet provided, perform the following transformations:
(i)
Reflect triangle P in the y-axis.
Label its image Q.
Total IS marks
(ii)
VECTORS AND MATRICES
13.
Draw
the line y
=x and reflect triangle Q in this line.
(S marks)
Label its image R.
The vertices of a quadrilateral, OABC, are (0, 0), (4, 2), (6, 10) and (2, 8) respectively.
Use a vector method to answer the questions which follow.
(a)
Write as~olumn
(i)
OA
vector, in the form [;],
the vector
(iii)
Describe, in words, the single geometric transformation
onto triangle R.
(iv)
Reflect triangle Q in the x-axis.
-7
(ii)
(b)
Label its image S.
CB
(3 marks)
Calculate loX/ ' the magnitude of oX.
(i)
(ii)
State two geometrical relationships
(v)
Write down the 2 x 2 matrix for the transformation
onto triangle S.
(i)
Write down the 2 x 2 matrices for
(1 mark)
(b)
(c)
which maps triangle P
(3 marks)
between the line segments OA and CB.
Explain why OABC is a parallelogram.
(4 marks)
a)
a reflection
b)
a reflection in the line y
which maps triangle P
(3 marks)
in the y-axis
= x.
(d)
If M is the midpoint of the diagonal DB, and N is the midpoint of the diagonal AC,
determine the position vector
(i),
(ii)
-7
OM
-7
ON
(ii)
Using the two matrices in b (i) above, obtain a SINGLE matrix for a reflection
(4 marks)
in the y-axis followed by a reflection in the line y x.
=
Total IS marks
Hence, state one conclusion which can be made about the diagonals of the parallelogram
OABC.
(7 marks)
Total IS marks
01 2340201F
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2004
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END OF TEST
012340201F
2004