Csec maths paper2_2010-2016

TEST CODE OI234O2O
JANUARY 2O1OFORM TP 2010015
CARIBBEAN EXAMINATIONS COUNCIL
SECONDARY ED UCATION CERTIFICATE
EXAMINATION
MATHEMATICS
Paper 02 - General Proficiency
2 hours 40 minutes
05 JANUARY 2010 (a.m.)
INSTRUCTIONS TO CANDIDATES
AnswerALL questions in Section I, andANY TWO in Section II.
Write your answers in the booklet provided.
All rvorking must be clearly shown.
A list of formulae is provided on page 2 of this booklet.
Bxamination Materials
Electronic calculator (non-programmable)
Geometry set
Mathemati cal tables (provided)
Graph paper (provided)
DO NOT TURN TIIIS PAGE UNTIL YOU ARE TOLD TO DO SO.
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Copyright O 2009 Caribbean Examinations Council@.
All rishts reserved.
0 t23 4020/ I ANUARYiF 20 1 0

I
(a)
SECTION I
AnswerALL the questions in this section.
All working must be clearly shown.
Using a calculator, or otherwise, calculate the exact value of
(i) his fixedsalary for the year
(ii) the amount he received in commission for the year
(iii) his TOTAL income for the year.
(c) The ingredients for making pancakes are shown in the diagram below.
l.
Page 3
( 3 marks)
( l mark)
( l mark)
( l mark)
(b)
2.76
0s + 8'72
In a certain company, a salesman is paid a fixed salary of $3 140 per month plus an
annual commission of 2o/oon the TOTAL value of cars stld for the year. If the ,u-l"r-u1
sold cars valued at$720 000 in 2009, calculate
Ingredients for making 8 pancakes
2 cups pancake mix
1
15 cups milk
Ryan wishes to make 12 pancakes using the instructions given above. Calculate
the number of cups of pancake mix he must use. ( 2 marks)
Neisha used 5 cups of milk to make pancakes using the same instructions. How
many pancakes did she make? ( 3 marks)
(i)
(ii)
Total ll marks
0 1 234020/JANUARY/F 20 1 0
GO ON TO THE NEXT PAGE

2. (a) Given that a: 6, b : - 4 and c : 8, calculate the value of
ctz+b
c-b
Simplify the expression:
(i) 3(x - y) + 4(x + 2v)
(ii) 4x2 x 3xa
6x3
(a) T and E are subsets of a universal set, U, such that:
U : {7,2,3,4,5,6;7,8,9,10, 11, 12 }
T: {multiplesof3 I
E : { even numbers }
(i) Draw a Venn diagram to represent this information.
(ii) List the members of the set
a) TaE
b) (TwD'.
Page 4
( 3 marks)
1 2 marks)
( 3 marks)
( 4 marks)
( l mark)
( l mark)
(b)
(c) (D Solve the inequality
x-3 ( 3 marks)
(ii) Ifx is an integer, determine the SMALLEST value of-r that satisfies the inequality
in (c) (i) above. ( l mark)
Total 12 marks
3.
o 1 23 4020I JANUARY/F 20 1 0

(b) Using a pencil, a ruler, and a pair of compasses only:
(i) Construct, accurately, the triangle IBC shown below, where,
AC: 6cm
Z ACB : 60o
ICAB: 60"
Complete the diagram to shon' the kite, ABCD, in which lD
Measure and state the size of I DAC.
(ii)
(iiD
Page 5
( 3 marks)
:5cm.
( 2 marks)
( l mark)
Total12 marks
6cm
0 123 4020I IAN UARY/F 20 1 0

4.
Page 6
(a) The diagram below, not drawn to scale, shows a triangle LMN with LN : 12 cm,
NM :x cm and I NLM : 0 o. The point K on LM is such that i/K is perpendicular to
LM, NK:6 cm, and KM: 8 cm.
(b)
Calculate the value of
(Dx
(iD e.
The diagram below shows a map of a playing field drawn on a grid of I
The scale of the map is I : 1 250.
( 2 merks)
( 3 merks)
cm squar€s.
(D
(ii)
Measure and state, in centimetres, the distance from S to F on the map.
( lmark )
Calculate the distance, in metres, from ,S to F on the ACTUAL playing field.
( 2 marks)
o t234020 / JANUARY/F 20 I 0

(iii) Daniel ran the distance from
^Sto
F in9.72 seconds.
in
a) m/s
b) km/h
giving your answer correct to 3 significant figures.
A straight line passes through the point T (4,1) and has a gradient of
the equation of this line.
Page 7
Calculate his average speed
( 3 marks)
Total ll marks
Determine
( 3 marks)
( 3 marks)
J
Ts. (a)
(b)
(iD
(iii)
(iv)
(v)
(i) Using a scale of 1 cm to represent I unit on both axes, draw thetriangle ABC
with vertices A (2;3), B (5,3) and C (3,6).
On the same axes used in (b) (D, draw and label the line y : 2.
( l mark)
Draw the image of triangle ABC vnder a reflection in the line y : 2. Label the
imageA'B'C'. ( 2marks)
Draw a new triangle A"B"C'with vertices A,, (-7,4),8,,(-4,4) and
e'e6,7). ( lmark)
Name and describe the single ffansformation that maps triangle ABC onto
triangleA"B"C". ( 2marks)
Total12 marks
0 1 234020/JANUARY tF 2010

6.
Page 8
A class of 26 students each recorded the distance travelled to schooi. The distance. to the nearest
km, is recorded below:
6
t2
30
21
26
39
l1
l6
11
J
l7
22
22
'34
24
32
25
l6
22
8
13
18 28
19 14
23
(a) Copy and complete the frequency table to represent this data.
Distance in kilometres Frequency
I -5 1
6- 10 2
lt - l5 4
t6-20 61
2t -25
26-30
31 - 35
36-40
( 2 marks)
(c)
(d)
Using a scale of 2 cm to represent 5 km on the horizontal axis and a scale of I cm to
represent 1 student on the vertical axis, draw a histogram to represent the data.
( 5 marks)
Calculate the probability that a student chosen at random from this class recorded the
distance travelled to school as 26 km or more. ( 2 marks)
The P.T.A. plans to set up a transportation service for the school. Which average, mean,
mode or median, is MOST appropriate for estimating the cost of the service? Give a
reason fbr your answer. ( 2 marks)
Total 11 marks
(b)
o 1 23 4020 I JANUARY/F 20 1 0

7. The graph shown below represents a function of the form: f(x): ax2 * bx + c.
Using the graph above, deterrrine
(D the value off(x) when x: 0
(ii) the values of x whenf(x) : 0
(iii) the coordinates of the maximum point
(iv) the equation of the axis of symmetry
(v) thevalues of xwhen.f(x):5
(vi) theintervalwithinwhichrlieswhenfx) > 5.
Page 9
' ( lmark)
( 2 marks)
( 2 marks)
( 2 marks)
( 2 marks)
Write your answer in the forrn a < x < b.
( 2 marks)
Total 11 marks
.-r- i- f-1-
:i.'j
'i-'i-r
-|I
.i....i....i...i
i....i-..;...i.
-i-i-i.-i
i-t +l.+-i.-i.f -i.--i...i...i.
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..1...i...r....1
..t...+...i....i.
iiit
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iiii
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I i- r-j.-it
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':i..'i...i...1
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o 123 4020/ JANUARY/F 20 1 0

8.
Page 10
Bianca makes hexagons using sticks of equal length. She then creates patterns by joining the
hexagons together. Pattems 1,2 and 3 are shown below:
Pattem2 Pattern 3Pattern 1
Ol Hexagon
The table below shows the
sticks used to make EACH
2 Hexagons
number of hexagons in
pattern.
3 Hexagons
EACH pattem created and the number of
(a) Determine the values of
(i) x
(ii) v
(iii) z.
Write down an expression for S in terms of n. where S represents
used to make a pattern of n hexagons.
Bianca used a total of 76 sticks to make a pattern of ft hexagons.
of h.
(b)
(c)
( 2 marks)
( 2 marks)
( 2 marks)
the number of sticks
( 2 marks)
Determine the value
( 2 marks)
Total 10 marks
Number
of
hexagons
in the
pattern
I 2 -t 4 5 20 n
Number
of sticks
used for
the
pattern
6 ll T6 x v ^s
01234A20 I JANUARY/F 20 1 0

-T
(a)9.
Page 11
SECTION II
Answer TWO questions in this secfion.
RELATIONS, FUNCTIONS AID GRAPHS
The relationship between kinetic energy, E,mass, m, and velociry v, for a moving particle
is
(b)
l"E::l|lV .
2
(i) Express v in terms of E and m. ( 3
(ii) Determinethevalueofywhen E:45and,m:13. ( 2
Given S6) : 3*-Bx+2,
(i) witeg(x) intheform a(x+b)2 *c,where a,bandc e R ( 3
(iD solve the equation S(x):0, writing your answer(s) correct to 2 decimal
(4
(iii) A sketch of the graph of g(x) is shown below.
Copy the sketch and state
marks)
marks)
marks)
places.
marks)
a)
b)
c)
they-coordinate of A
the x-coordinate of C
the x andy-coordinates ofB. ( 3 marks)
Totel 15 marks
0 1 234020IJANUARYiT 20 1 0

10. (a)
Page 12
The manager of apizza shop wishes'to makex smallpizzas and_r,large pizzas. His oven
holds no more than 20 pizzas.
(D Write an inequality to represent the given condition. ( 2 marks)
The ingredients for each small pizza cost $ 15 and for each large pizza S30. The
manager plans to spend no more than $450 on ingredients.
(ii)
(i)
Write an inequality to represent this condition. ( 2 marks)
Using a scale of 2 cm on the x-axis to represent 5 small pizzas and 2 cm on
they-axis to represent 5 large pizzas, draw the graphs ofthe lines associated
with the inequalities at (a) (i) and (a) (ii) above. ( 4 marks)
(iD Shade the region which is defined byALL of the following combined:
the inequalities written at (a) (i) and (a) (ii)
the inequalities x > 0 andy > 0 ( I mark)
(iii) Using your graph, state the coordinates of the vertices of the shaded region.
( 2 marks)
(c) The pizza shop makes a profit of $8 on the sale of EACH small pizza and S20 on the
sale of EACH large pizza. All the pizzas that were made were sold.
(i) Write an expression in r and y for the TOTAL profit made on the sale of the
pflzas. ( lmark)
(iD Use the coordinates ofthe vertices given at (b) (iii) to determine the MAXIMUM
profit. ( 3 marks)
Total 15 marks
(b)
0123 4020I JANUARY/F' 20 I 0

T
(a)11.
Page 13
GBOMETRY AND TRIGONOMETRY
The diagram below, not drawn to scale, shows three stations P, Q and R, such that the
bearing of Q from R is 116" and the bearing of P from R is 242". The vertical line at R
shows the North direction.
(i)
(i i)
Show that angle PR.Q: 126". ( 2 marks)
Given that PR: 38 metres and QR : 102 metres, calculate the distance PQ,
giving your answer to the nearest metre. ( 3 marks)
(b) K, L and M are points along a straight line on a horizontal plane, as shown below.
KLM
A vertical pole, ,S1(, is positioned such that the angles of elevation of the top of the pole
,S from L and M are 2I" and 14o respectively.
The height of the pole,,S1(, is 10 metres.
(i) Copy and complete the diagram to show the pole SK and the angles of elevation
of ,S from L and M.
Calculate, correct to ONE decimal place,
( 4 marks)
(ii)
a)
b)
the length of KL
the length of LM. ( 6 marks)
Total 15 marks
0 I 23 4020I JANUARY/F 20 1 0

t2. (a)
Calculate, giving reasons for your answer, the measure of angle
(D GFH
(iD GDE
(iii) DEF.
(b) Use r :3.14 in this part of the question.
Given that GC:4 cm,calculate the area of
-,(1)
ttiangle GCH
(ii) the minor sector bounded by arc GH andradli GC and HC
*(iD the shaded segment.
Page 14
The diagram below not drawn to scale, shows two circles. C is the centre ofthe smaller
circle, GH is a common chord and DEF is a triangle.
Angle GCH:88" and angle GHE : 126".
( 2 marks)
( 3 marks)
( 2 marks)
( 3 marks)
( 3 marks)
( 2 marks)
Total 15 marks
0 1 23 4020/ TANUARY/F 20 1 0

(a)
Page 15
VECTORS AND MATRICES
The figure beloq not drawn to scale, shows the points O (0,0), A (5,0) and B (-1,4)
which are the vertices of atriangle OAB.
o (0,0)
(i) Express in the ar- lfl the vectors
lbt
-)
a) OB
-) -+
A (5,0)
b) OA+OB (3marks)
(ii) If M (xy) is the midpoint of AB, determine the values of x and y.
( 2 marks)
In the figure below, not drawn to scale, OE, EF and MF are straight lines. The point
FI is such that EF : 3EH. The point G is such that Mtr : 5 MG. M is the midpoint of
oE.
-+ ->
The vector OM: v and EH: tt.
(b)
(i) Write in terms of a and/or y, an expression for:
_>
a) HF
-+
b) MF
-)
c) OH
Showthat i": I (z,*r
5 /
Hence, prove that O, G and lllie on a straight line.
( l mark)
( 2 marks)
( 2 marks)
( 2 marks)
( 3 marks)
Total 15 marks
(iD
(iii)
B (-1,4)
ot23 4020/ JANUARY/F 20 1 0

14. (a) L andNare two matrices where
L:lz 2l and.^/: lr 3l
l.r 4) l.0 2
Evaluate L - N2.
END OF TEST
Page 16
( 3 marks)
( 4 marks)
Total 15 marks
(b)
(c)
The matrix, M, isgiven as M :'I 12
]
. Cut.olate the values ofx for which Mis
singular. t3 x) (2marks)
A geometric transformation, R, maps the point (2,1) onto (-1,2).
Giventhat n : [0 {l ,"ul"rrtutethevaluesofpandq. ( 3marks)
lq ol'
[ .']
A translation, T --l'_l maps the point (5,3) onto (1,1). Determine the values of r and. l.s
s. ."1
( 3 marks)
Determine the coordinates of the image of (8,5) under the combined transformation,
(d)
(e)
R followed by 7.
ot23 4020I JANUARYiF 20 I 0

b?
FORM TP 2010087
TEST CODE OI234O2O
MAY/JLINE 2O1O
ILCARIBBEAN EXAMINATIONS COUNC
SECONDARY EDUCATION CERTIFICATE
EXAMINATION
MATHEMATICS
Paper 02 - General Proficiency
2 hours 40 minutes
19 MAY 2010 (a.m.)
INSTRUCTIONS TO CANDIDATES
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.
Required Examination Materials
Electronic calculator
Geometry set
Graph paper (provided)
DO NOT TURN THrS IGE UNTTLYOU ARA TOLD TO DO SO.
-
-
E
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--
-
--
Copyright O 2008 Caribbean Examinations Council@.
All rights reserved.
0r234020tF 2010

Vt
LIST OF FORMULAE
Volume of a prism
Volume of cylinder
Volume of a right pyramid
Circumference
Area of a circle
Area of trapezitm
Roots of quadratic equations If qx2 + bx
then x :
Trigonometric ratios sin0 =
cosO =
tanO =
Area of triangle
Sine rule
Cosine rule
Page 2
V : Ah where A is the area of a cross-section and ft is the perpendicular
length.
V: nf h where r is the radius of the base and ft is the perpendicular height.
f :
! n where Ais the area ofthe base and h isthe perpendicular height.
C:2nr where r is the radius of the circle.
A: nf where r is the radius of the circle.
A :
+@
+ b) h where a and b are the lengths of the parallel sides and ft is
the perpendicular distance between the parallel sides.
*c
-b+
:0,
Jb' 4t"
2a
opposite side
hypotenuse
adjacent side
hypotenuse
opposite side
Opposite
adjacent side
Area of A :
lUrwhere b is the length of the base and ft is the
perpendicular height
Area of LABC : ab sin C
Areaof a,ABC: @-c;
. a+b+cwnere -s :
2
ab-c
sinA sinB sin C
Adjacent
(- b -----------__?-
012340201F 2010
a2 : b2 + c2 - 2bccosA
l

v.
(a)1.
SECTION I
Answer ALL the questions in this section.
All working must be clearly shown.
Determine the EXACT value of:
(i) 1r 2
,2- 5
o1 "7
(ii) 2.s2 - +
giving your answer correct to 2 significant figures
Page 3
( 3 marks)
( 3 marks)
(b) Mrs. Jack bought 150 T-shirts for $1 920 from a factory.
(D Calculate the cost of ONE T:shirt. ( l mark)
The T-shirts are sold at $19.99 each.
Calculate
(ii) the amount of money Mrs. Jack received after selling ALL of the T-shirts
( l mark)
(iii) the TOTAL profit made ( I mark )
(iv) the profit made as a percentage of the cost price, giving your answer correct to
( 2 marks)
Total ll marks
01234020/F 2010
the nearest whole number.

(a))
(b)
(c)
(ii) the product of TWO consecutive numbers when the smaller number isy
( l mark)
Given that a: -1, b :2 and c : -3, find the value of:
(i) a*b+c
(ii) b2 * c2
Write the following phrases as algebraic expressions:
(i) seven times the sum of r andy
Solve the pair of simultaneous equations:
2x + y:7
x -2y: 1
Factorise completely:
(i) b?-*
(ii) 2ax - 2ay - bx + by
(iii) 3xz + 10x - 8
survey.
Calculate the value of x.
Page 4
( lmark)
( l mark)
( l mark)
( 3 marks)
( l mark)
( 2 marks)
( 2 marks)
Totall2 marks
( 2 marks)
( 2 marks)
3.
(d)
(a) A survey was conducted among 40 tourists. The results were:
28 visitedAntigua (A)
30 visited Barbados (B)
3x visited both Antigua and Barbados
r visited neither Antigua nor Barbados
(D Copy and complete the Venn diagram below to represent the given information
above.
( 2 marks)
(ii) Write an expression, in x, to represent the TOTAL number of tourists in the
(iii)
012340201F 20t0

t
(b)
Page 5
The diagram below, not drawn to scale, shows a wooden toy in the shape of a prism,
with cross section ABCDE. F is the midpoint of EC, and ZBAE: ZCBA:90o.
(a)4.
Calculate
(D the length of EF
(ii) the length of DF
(iiD the area of the face ABCDE.
(i) Given that y :50 when x : 10, find the value of ft.
(ii) Calculate the value ofy when x : 30.
Wheny varies directly as the square ofx, the variation equation is writteny : ld,where
k is a constant.
( l mark)
( 2 marks)
( 3 marks)
Total12 marks
( 2 marks)
( 2 marks)
(b) (i) Using a ruler, a pencil and a pair of compasses, construct triangle EFG with
EG:6 cm
ZFEG:60"
and ZEGF:90".
(ii) Measure and state
a) the length of EF
b) the size of ZEFG.
( 5 marks)
( 2 marks)
Total ll marks
---r---F
012340201F 2010

t.-
5- (a) The functions/and g are defined as/(-r) :2x - 5 and g(x) : xz + 3.
(i) Calculate the value ol
a) JV)
b) sfl4).
Find/-'(x).
Use the graph above to determine
(i) the scale used on the x-axis
(ii) the value ofy for which x : -1.5
(iii) the values ofx for whichy: g
Page 6
( l mark)
( 2 marks)
( 2 marks)
( l mark)
( 2 marks )
( 2 marks )
(ii)
(b) The diagram below shows the graph of y : xz + 2x- 3 for the domain - 4 < x < 2.
(iv) the range of values ofy, giving your answer in the form a < y < b, where a and
( 2 marks )
Total 12 marks
i.. l/. .l
'i.-i-j t
til:l
y:t -3
Ii i:'' )
.t...i...;.
iit"i'ir'
i
{t,'I t
I {r,rt
$ +l
:ii,i:f
i.iri'
4
N..;..i..
ti 'x
...i..fj
.i-.i- _1
..i...i...i}
l: t
{:':'i'
i.N
7
a W
N ,#
012340201F 2010
b are real numbers.

6. An
(a)
Y
Page 7
answer sheet is provided for this question.
The diagram below, not drawn to scale, shows two straight lines, PQ and R,S, intersecting
a pair of parallel Iines, TU and VW.
Determine, giving a reason for EACH of your answers, the value of
(i) x
(ii) v.
( 2 marks)
( 2 marks)
(b) The diagram below show striangle LMN, and its image, triangle L' Mll, after undergoing
a rotation.
Describe the rotation FULLY by stating
a) the centre
b) the angle
c) the direction. ( 3 marks)
(i)
(ii)
(iii)
State TWO geometric relationships betweentriangleLMNand its image, triangle
L,MI{ . ( 2 marks)
Triangle LMN istranslated by the vector f t
)
l-2)
Determine the coordinates of the image of the point Z under this transformation.
( 2 marks)
Total ll marks
tV
i..t..
'fi
L
.i..i.
i::::! l
i itr4 tl l-1 i.t
'ai..i..i..i
i..i..i..i ;
i:.i:l
L 4.
iA
i::il
W..l
-21:.
i:l::l
0t234020tF 2010

l*
7.
Page 8
A class of 24 students threw the cricket ball at sports. The distance thrown by each student was
measured to the nearest metre. The results are shown below.
22
48
55
36
50
34
29
63
35
45
46
54
52
23
s6
32
47
43
43
49
30
40
59
60
(u) Copy and complete the frequency table for the data shown above.
Distance (m) Frequency
20 -29
a
J
30-39 5
State the lower boundary for the class interval2} -29. (
using a scale of 1 cm on the x-axis to represent 5 metres, and a scale of 1
y-axis to represent I student, draw a histogram to illustrate the data.
(
Determine
(b)
(c)
3 marks)
I mark )
cm on the
5 marks)
(d)
(i) the number of students who threw the ball a distance recorded as 50 metres or
more ( lmark)
(ii) the probability that a student, chosen at random, threw the ball a distance recorded
as 50 metres or mofe. ( lmark)
Total ll marks
012340208 2010

(a)
(b)
r>
I
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Page 9
An answer sheet is provided for this question.
The diagram below shows the first three figures in a sequence of figures. Each figure is made
up of squares of side I cm.
on your answer sheet, draw the FOURTH figure (Fig. a) in the sequence.
( 2 marks)
Study the patterns in the table shown below, and on the answer sheet provided, complete
the rows numbered (i), (ii), (iii) and (iv).
(i)
(ii)
(iii)
(iv)
Figure
Area of
Figure
(cm')
Perimeter
of Figure
(cm)
I I 1x6-2: 4
2 4 2x6-2: 10
J 9 3x6-2: 16
4
5
15
n
( 2 marks)
( 2 marks)
( 2 marks)
( 2 marks)
Total l0 marks
Fig.l Fig.2 Fig.3
i::
01234020tF 2010

SECTION II
Answer TWO questions in this section.
ALGEBRAAND RELATIONS, F'UNCTIONS AND GRAPHS
9. (a) The diagram below shows the speed-time graph of the motion of an athlete during a
race.
Speed
in m/s
l4
t2
10
8
6
4
)
012345678910111213
Time in seconds
(D Using the graph, determine
a) the MAXIMUM speed
b) the number of seconds for which the speed was constant
c) the TOTAL distance covered by the athlete during the race.
( 4 marks)
(ii) During which time-period of the race was
a) the speed of the athlete increasing
b) the speed of the athlete decreasing
c) the acceleration of the athlete zero? ( 3 marks)
/
/
/
/
/
/
012340208 2010

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Page l1
(b) A farmer supplies his neighbours with x pumpkins andy melons daily, using the follow-
ing conditions:
Firstcondition : y>3
Secondcondition : y<x
Third condition : the total number of pumpkins and melons must not exceed 12.
(i) Write an inequality to represent the THIRD condition. ( lmark )
(ii) Using a scale of 1 cm to represent one pumpkin on the x-axis and I cm
to represent one melon on the y-axis, draw the graphs of the THREE lines
(iii)
(iv)
associated with the THREE inequalities. ( 4 marks)
Identif,', by shading, the region which satisfies the THREE inequalities.
( l mark)
Determine, from your graph, the minimum values of x andy which satisfz the
conditions. ( 2 marks)
Total 15 marks
0t234020/F 2010

l/
(a)10.
Page 12
MEASUREMENT, GEOMETRY AND TRIGONOMETRY
In the diagram below, not drawn to scale, PQ is a tangent to the circle PZSR, so that
LRPQ:46"
LRQP:32'
and TRQ is a straight line.
(b) The diagram below, not drawn to scale, shows a vertical flagpole, FT, with its foot,
I', on the horizontal plane EFG. ET and GT are wires which support the flagpole
in its position. The angle of elevation of 7 from G is 55o, EF : 8 m, FG: 6 m and
ZEFG: 120".
Calculate, giving a reason for EACH step of your answer,
(i) zPrR
(ii) zrPR
(iiD z.rsR.
Calculate, giving your answer correct to 3 significant figures
(i) the height, FT, of the flagpole
(iD the length of EG
(iii) the angle of elevation of Zfrom E.
( 2 marks)
( 3 marks)
( 2 marks)
( 2 marks)
( 3 marks)
( 3 marks)
Total 15 marks
..6^ 6m
012340201F 2010

-
(a)11.
VECTORS AND MATRICES
A and B are two 2 x 2 matrices such that
(t 2 (s -2)A:l I and B:l I
(2 s) -2 t)
(i) Find AB.
(ii) Determine B 1,
the inverse of B.
(iii) Given that
(s -2) r,,l = r'.).
[-z t ) [y.] [r,] '
f")
write | | as the product of TWO matrices.
Y)
(iv) Hence, calculate the values ofx andy.
The diagram below, not drawn to scale, shows triangle JKL.
Page 13
( 2 marks)
(lmark)
2 marks)
2 marks)
( 4 marks)
(b)
M and ff are points on JK and JL respectively, such that
JM:It* and rN:*tt.
(i) Copy the diagram in your answer booklet and show the points M and N.
( 2 marks)
(ii) Given thatJi: uandti:r,
write, in terms of u and v, an expression for
-)
a) JK
_>
b) MN
-)
c) KL.
(iiD Using your findings in (b) (ii), deduce TWO geometrical relationships between
( 2 marks)
Total 15 marks
KL and MN.
END OF'TEST
012340201F 20t0

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