Csec maths paper2_2010-2016

TEST CODE OI234O2OJANUARY 2O1OFORM TP 2010015

CARIBBEAN EXAMINATIONS COUNCILSECONDARY 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 setMathemati cal tables (provided)Graph paper (provided)

DO NOT TURN TIIIS PAGE UNTIL YOU ARE TOLD TO DO SO.

I

III

I

I

II

r

Copyright O 2009 Caribbean Examinations [email protected] 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 anannual commission of 2o/oon the TOTAL value of cars stld for the year. If the ,u-l"r-u1sold 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. Calculatethe number of cups of pancake mix he must use. ( 2 marks)

Neisha used 5 cups of milk to make pancakes using the same instructions. Howmany pancakes did she make? ( 3 marks)

(i)

(ii)

Total ll marks

0 1 234020/JANUARY/F 20 1 0GO ON TO THE NEXT PAGE

2. (a) Given that a: 6, b : - 4 and c : 8, calculate the value of

ctz+bc-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 inequalityin (c) (i) above. ( l mark)

Total 12 marks

3.

o 1 23 4020 I JANUARY/F 20 1 0

GO ON TO THE NEXT PAGE

(b) Using a pencil, a ruler, and a pair of compasses only:

(i) Construct, accurately, the triangle IBC shown below, where,

AC: 6cmZ 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 4020 I IAN UARY/F 20 1 0GO ON TO THE NEXT PAGE

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 toLM, 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 IThe 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 ofthe 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 ABCwith 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 theimageA'B'C'. ( 2marks)

Draw a new triangle A"B"C'with vertices A,, (-7,4),8,,(-4,4) ande'e6,7). ( lmark)

Name and describe the single ffansformation that maps triangle ABC ontotriangleA"B"C". ( 2marks)

Total12 marks

0 1 234020/JANUARY tF 2010GO ON TO THE NEXT PAGE

6.

Page 8

A class of 26 students each recorded the distance travelled to schooi. The distance. to the nearestkm, is recorded below:

6

t230

21

26

39

l1

l611

J

l722

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 612t -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 torepresent 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 of f(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.

ti..i...i..i..r..1...i...r....1

..t...+...i....i.iiit

u....i...i il""i-!_ i

1

l+-.+..

) i-i'i-i-iiii

4ii'i-ir-."_:_t_ !

I i- r-j.-it

0-f-i..i. ll.i.l.

-+-r..i 1

':i..'i...i...1

:i:i*i

o 123 4020 / JANUARY/F 20 1 0GO ON TO THE NEXT PAGE

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 thesticks used to make EACH

2 Hexagons

number of hexagons inpattern.

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

Numberof

hexagonsin the

pattern

I 2 -t 4 5 20 n

Numberof sticksused for

thepattern

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 AI\D GRAPHS

The relationship between kinetic energy, E,mass, m, and velociry v, for a moving particleis

(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 0GO ON TO THE NEXT PAGE

10. (a)

Page 12

The manager of apizza shop wishes'to makex smallpizzas and_r,large pizzas. His ovenholds 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. Themanager 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 onthey-axis to represent 5 large pizzas, draw the graphs ofthe lines associatedwith 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 thesale 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 thepflzas. ( lmark)

(iD Use the coordinates ofthe vertices given at (b) (iii) to determine the MAXIMUMprofit. ( 3 marks)

Total 15 marks

(b)

0123 4020 I 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 thebearing of Q from R is 116" and the bearing of P from R is 242". The vertical line at Rshows 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 elevationof ,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 4020 I JANUARY/F 20 1 0GO ON TO THE NEXT PAGE

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 smallercircle, 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 vectorslbt

-)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 pointFI is such that EF : 3EH. The point G is such that Mtr : 5 MG. M is the midpoint ofoE.

-+ ->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 0GO ON TO THE NEXT PAGE

14. (a) L andNare two matrices where

L:lz 2l and.^/: lr 3ll.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.ss. ."1( 3 marks)

Determine the coordinates of the image of (8,5) under the combined transformation,

(d)

(e)R followed by 7.

ot23 4020 I JANUARYiF 20 I 0

b?

FORM TP 2010087TEST CODE OI234O2O

MAY/JLINE 2O1O

ILCARIBBEAN EXAMINATIONS COUNCSECONDARY 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 calculatorGeometry setGraph paper (provided)

DO NOT TURN THrS IGE UNTTLYOU ARA TOLD TO DO SO.--E

--------

Copyright O 2008 Caribbean Examinations [email protected] 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 perpendicularlength.

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-csinA sinB sin C

Adjacent

(- b -----------__?-

012340201F 2010

a2 : b2 + c2 - 2bccosAl


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 marksGO ON TO THE NEXT PAGE

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:7x -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 Barbadosr visited neither Antigua nor Barbados

(D Copy and complete the Venn diagram below to represent the given informationabove.

( 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,wherek 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 withEG:6 cmZFEG: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 2010GO ON TO THE NEXT PAGE

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:ly:t -3

Ii i:'' )

.t...i...;.

iit"i'ir'

\i{t,'I t

I {r,rt

$ +l:ii,i:f

i.iri'

4N..;..i..

ti 'x...i..fj

.i-.i- _1

..i...i...i} l: t{:':'i'

i.N7

a WN ,#

012340201F 2010

b are real numbers.

6. An

(a)

\YPage 7

answer sheet is provided for this question.

The diagram below, not drawn to scale, shows two straight lines, PQ and R,S, intersectinga 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 undergoinga 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, triangleL,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


tVi..t..

'fiL

.i..i.

i::::! li itr4 tl l-1 i.t'a

i..i..i..ii..i..i..i \;

i:.i:lL 4.

iAi::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 wasmeasured 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 aJ

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 ormore ( lmark)

(ii) the probability that a student, chosen at random, threw the ball a distance recordedas 50 metres or mofe. ( lmark)

Total ll marks

012340208 2010GO ON TO THE NEXT PAGE

(a)

(b)

r\>I

I

I

ItI

I

I

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 madeup 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, completethe rows numbered (i), (ii), (iii) and (iv).

(i)

(ii)

(iii)

(iv)

FigureArea ofFigure(cm')

Perimeterof 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 2010GO ON TO THE NEXT PAGE

Page 10

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.

Speedin m/s

l4

t2

10

8

6

4

)

012345678910111213Time 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 2010GO ON TO THE NEXT PAGE

rl'-I

I

I

I

I

J-It,.I

I

I

I

I

I

I

I

I

I

I

I

Page l1

(b) A farmer supplies his neighbours with x pumpkins andy melons daily, using the follow-ing conditions:

Firstcondition : y>3Secondcondition : y<xThird 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 cmto 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 theconditions. ( 2 marks)

Total 15 marks

0t234020/F 2010GO ON TO THE NEXT PAGE

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 thatLRPQ: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 flagpolein 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 2010GO ON TO THE NEXT PAGE

\-

(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

cxctutor.blogspot.com































Education

Csec maths paper2_2010-2016