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CORNWALL HILL COLLEGE Mathematics Department EXAMINATIONS- 28 JULY 2014 Mathematics Paper 2 Grade: 12 Time: 3 Hours Marks: 150 Examiner: Mrs T. Knoetze Moderator(s): Mrs. M. van Niekerk, Mrs. S. Hickling and Mr. P. van Schalkwyk Instructions: 1. This question paper consists of 24 pages . Pl ease ensure that y our paper is complete. 2. Answer ALL the questions on the question paper and hand this in at the end of the examination. 3. You may use an approved non-programmable and non-graphical calculator, unless otherwise stated. 4. Round off your answers to two decimal digits where necessa ry. 5. All the necessa ry working details must be clearly shown. 6. It is in your own interest to write legibly an d to present your work neatly. Q1 (8) Q2 (26) Q3 (23) Q4 (18) QS (10) QG (17) Q7 (24) Q8 (6) Q9 (6) Q10 (12) TOTAL

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Page 1: CORNWALL HILL COLLEGE CAPS 2014 Prelim... · CORNWALL HILL COLLEGE Mathematics Department EXAMINATIONS-28 JULY 2014 Mathematics Paper 2 Grade: 12 Time: 3 Hours Marks: 150 Examiner:

CORNWALL HILL COLLEGE Mathematics Department

EXAMINATIONS- 28 JULY 2014

Mathematics Paper 2

Grade: 12 Time: 3 Hours

Marks: 150

Examiner: Mrs T. Knoetze

Moderator(s): Mrs. M. van Niekerk, Mrs. S. Hickling and Mr. P. van Schalkwyk

Instructions:

1. This question paper consists of 24 pages. Please ensure that your paper is complete.

2. Answer ALL the questions on the question paper and hand this in at the end of the

examination.

3. You may use an approved non-programmable and non-graphical calculator, unless

otherwise stated.

4. Round off your answers to two decimal digits where necessary.

5. All the necessa ry working details must be clearly shown.

6. It is in your own interest to write legibly and to present your work neatly.

Q1 (8)

Q2 (26)

Q3

(23)

Q4 (18)

QS

(10) QG (17)

Q7 (24)

Q8 (6)

Q9 (6)

Q10 (12)

TOTAL

Page 2: CORNWALL HILL COLLEGE CAPS 2014 Prelim... · CORNWALL HILL COLLEGE Mathematics Department EXAMINATIONS-28 JULY 2014 Mathematics Paper 2 Grade: 12 Time: 3 Hours Marks: 150 Examiner:

Grade12 Mathematics Paper 2 Paqe2of24

SECTION A [75}

QUESTION 1 [8}

In preparation for the Soccer World cup the Brazilian coaching team looked at the amount of goals scored by Brazil in the last nine tournaments.

(a) Fill in the missing amounts in the cumulative frequency table below.

Tournament year Goals scored Cumulative frequency

1978 10 10

1982 15 25

1986 10 35

1990 4 39

1994 11 so 1998 I'+ b'+ 2002 18 82

2006 10 92

2010 9 101 ~

............,

(2)

(b) Determine the average number of goals scored in the last nine tournaments by Brazil. (2)

(c)

/CJI ~ r¥J

Determine the standard deviation correct to two decimal places. ~ o- :: 3 7 'f '-....,; ~

(2)

(d) In how many tournaments do the goals scored, lie within one standard deviation of the

mean? (2)

{V,z?... -3,71 If, 22. + 3, 79] 1

15. OJ 7 '-....1 l"rJ '

[_ 7, '+-3 I

7 +ourname.nfs. '-...! R

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Page 3: CORNWALL HILL COLLEGE CAPS 2014 Prelim... · CORNWALL HILL COLLEGE Mathematics Department EXAMINATIONS-28 JULY 2014 Mathematics Paper 2 Grade: 12 Time: 3 Hours Marks: 150 Examiner:

Grade12 Mathematics Paper 2 Paqe3o(24

QUESTION 2 [26]

(a)

(b)

If cos 65° = m , determine the following expressions in terms of m .

(1) cos 115° (1)

= coa (,8oq- b5 o)

= - COQ 650 ~ = - rY)

(2) sin 25° (1) ::: ~,,..., f=to •- b5°)

Cl ::: roD bS :: YYJ ~ ~

(3) sin 130° ........... di (4)

= s /;') ~ (6so) . CC/.J b 5 ° ~ 19 : ~ Stn b5~

'::: ;2. m J1-m2. "'A '-....Jt9

Given: psinfJ- q = 0, and 90° :5 f3 :5 270° , with p > 0 and q > 0.

Use a sketch to evaluate, in terms of p and q:

(1)

'-........! n-,

5 Ll = _:t:_.:: ~ 1n o r

=

cos f3 (4)

= ~='~e;~:-:1~'~-~--~c~~-----------------------------­p

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Page 4: CORNWALL HILL COLLEGE CAPS 2014 Prelim... · CORNWALL HILL COLLEGE Mathematics Department EXAMINATIONS-28 JULY 2014 Mathematics Paper 2 Grade: 12 Time: 3 Hours Marks: 150 Examiner:

Grade12 Mathematics Paper 2 Paqe4of24

(2} cos zp '-..J A = 1 ~ s tn "t. t3

(2}

- I - :L{j-)z_

- I - D1. 7 '--! Cfi

(c) 2 sin(180°+A) sin(90°-A)

Prove that: 4 . 4 = tan(360° - 2A) cos A- sm A

(6}

~Jq ~A z (-s,~ A ) (('cv:JA)

- :z.s IY1 A (' 00 A

= - +Qn zA

RHS fan zA. '-' A

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Page 5: CORNWALL HILL COLLEGE CAPS 2014 Prelim... · CORNWALL HILL COLLEGE Mathematics Department EXAMINATIONS-28 JULY 2014 Mathematics Paper 2 Grade: 12 Time: 3 Hours Marks: 150 Examiner:

Grade12 Mathematics Paper 2

(d) Given f(x) = 2 cos(x + 45°) and g(x) = tanx

Determine:

(1)

(2)

The amplitude of f(x)

~ '-.1 r:}

The period of g(x)

180 o'-..J A

PageS of24

(1)

(1)

(3) Sketch the graphs of f(x) and g(x) for the interval x E [ -90°; 225°] on the (4) grid below. '-...l s t,~ Pt

cos

I ___ ---- -----'-1---ql'V\p--1,+~ £ --- ---- -~

~--­

,-- -

_! -- -

(4)

+a" -......., shr:rpe

1- - ---- -- - -

, '-J crs0mpf~t-e.a ~

- ---~1- ----- _ __ J

~2 .. -- -- ------~- - -

- -- - - - --- - - -- - 1 t --- +--- ------- - - - - - _ __. ________ ---- - - - -- ~

' 1

L __ L ___ __ __ _ _ ------ ~ --- --- ____ __ i

'l.l

Indicate, using thickened lines, the intervals on the horizontal (x)-axis where

f(x) ~ g(x) for the interval x E (-90°; 225°). (2)

'-....J 1",._/-eyy~ls

-.....; dc:JI-S

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Page 6: CORNWALL HILL COLLEGE CAPS 2014 Prelim... · CORNWALL HILL COLLEGE Mathematics Department EXAMINATIONS-28 JULY 2014 Mathematics Paper 2 Grade: 12 Time: 3 Hours Marks: 150 Examiner:

Grade 12 Mathematics Paper 2 Paqe6of24

QUESTION 3 [23)

(a) Given b. ABC with vertices A( -5; 3), B( -2; -2) and C(2; 1).

A( -5; 3)

C(2;1)

B(-2; -2)

Determine:

(1) The length of AC, in simplest surd form. (2)

Ac ~ I (2- f s ) ) z .,. ( ' - 3 ) 2.

:= J 53 'v fl J

(2) The midpoint of AC. (2)

e:-s ;~ 3+1 j I

~

:::: ( -; ;l ) J ,.

~ -........!

/.1

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Page 7: CORNWALL HILL COLLEGE CAPS 2014 Prelim... · CORNWALL HILL COLLEGE Mathematics Department EXAMINATIONS-28 JULY 2014 Mathematics Paper 2 Grade: 12 Time: 3 Hours Marks: 150 Examiner:

Grade12 Mathematics Paper 2 Page 7o(24

(3) The equation ofthe straight line passing through C, parallel to AB.

-2-~; ( ) mFIB = ~'J: (- J cz,. I

(3)

5

'j- y, = ,q rn (x - :x,) ~ "Y) ' """-1

j

(4)

.

(5)

- I = -s 3 (:x_ - z)

- .§. X. I :=. 3 T- 4-3 '-.......J f} J - .2. X- ~

J - 0 + 3

The size of sAc. +cu"'l G -

. - 3

G - "' - 5Cf o3 -+ tsro· I

=

- BAc • • ::: /bY. os - /20 9b

• ::: '+3. 0? '-...1 /Y)

The co-ordinate of D if ABCD is a parallelogram.

'-..1 fl -.....J A

I '

(5)

f - .'1 :t - (-s)

e Cl tl = - J s 9 s -t /rto I

= lblf 05 0

(2)

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Page 8: CORNWALL HILL COLLEGE CAPS 2014 Prelim... · CORNWALL HILL COLLEGE Mathematics Department EXAMINATIONS-28 JULY 2014 Mathematics Paper 2 Grade: 12 Time: 3 Hours Marks: 150 Examiner:

Grade12 Mathematics Paper 2 Page 8 o(24

(b) Sketched is the circle with the equation x 2 + 12x + y 2- 4y = - 15 passing through point

( -2; 5) .

Determine the centre and the length of the radius ofthe circle. (5)

x"l_ + 12x. t (b)-z. + Cf't._ 4-J r fz)'l. = -Js + {b)'t.-r(-zJ ( '-..J , J~ ( "A 'l.. ~!} x t b r l/ - -z ) = c25

(1)

cJ ,

r=

(2) Determine the equation ofthe t angent to t he circle passing t hrough point ( - 2; 5) .(4) 5 - Z q. 'v

m,qcJ, u-o = -2- &6J mfcmg~n+ :: - 3 , 3 ~,q

5

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Page 9: CORNWALL HILL COLLEGE CAPS 2014 Prelim... · CORNWALL HILL COLLEGE Mathematics Department EXAMINATIONS-28 JULY 2014 Mathematics Paper 2 Grade: 12 Time: 3 Hours Marks: 150 Examiner:

Gradel2 Mathematics Paper 2 Paqe9of24

QUESTION 4 {18]

(a) Prove the theorem that the angle between a tangent to a circle and a chord drawn from the point of contact is equal to an angle in the alternate segment. (S)

F

D

A c Given: Tan(J-t n r 1913 G ~11 Required to prove: ~2: ~ Proof :

~ --\ 0 -......JA f oYI _j_ !3 l + IB :z.. = 'fo rCi ciiU<J

• • E, + £z. : 9o ~A L ,_ r~mJ Ctr cle

E, = 8 l ~.,q L5 IY\ S Q'm e. s~(} h1 en?-

8 .: £ ~ 11

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Page 10: CORNWALL HILL COLLEGE CAPS 2014 Prelim... · CORNWALL HILL COLLEGE Mathematics Department EXAMINATIONS-28 JULY 2014 Mathematics Paper 2 Grade: 12 Time: 3 Hours Marks: 150 Examiner:

Grade12 Mathematics Paper 2 Paqe10of24

(b) In the diagram below 0 is the centre of the circle and sfp = 90°. If R = 43° calculate the sizes of each of the following angles. No reasons required.

R

A

(1) 01

"""" (1)

~ ;2 1<.. 0 !:.

.:::: Bb · '-JA

A

(2) s (1) A ....-'\ 0 A s ::: r<. 4-3 ~ =

e a /8'0 - 8'6

(1)

2..

.. "' A

A

(4) p3 (1) ..,.,

C!J 0 /\

f3. :: /80 'l_o s = l./-7. ~ A

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Grade12 Mathematics Paper 2 Paqe11 of24

(c) Refer to the diagram below.

s RT is a tangent to the circle at T. Lines MN and NT are produced to RandS respectively, so that

RS = RT. Sand M are joined. Let T4 = x. Supply proper reasons.

(1) Give 3 other angles that are equal to x. (6)

Ty. = T, .=. X. """'-J

/\ A '-J y,, .:: m3 :. -:;c_

I ,.... ""' /'.

.:t ~ Ti -=- 5, + S:z.. :. ~ tsos 6 · f<S = RT I

(2) Prove that RSTM is a cyclic quadrilateral (3)

prov~c/ ahove..

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Page 12: CORNWALL HILL COLLEGE CAPS 2014 Prelim... · CORNWALL HILL COLLEGE Mathematics Department EXAMINATIONS-28 JULY 2014 Mathematics Paper 2 Grade: 12 Time: 3 Hours Marks: 150 Examiner:

Grade 12 Mathematics Paper 2 Page 12o(24

SECTION B [75]

QUESTION 5 [10]

The all-t ime ran kings in World Cup tournaments of fifteen count ries are depicted below. It indicates t he matches played {MP) by that count ry and the amount of goals scored {GS).

u

..c ro ::J u ro c. ·;:: c E

C!J '+- >-'.j:j a:: "0 0 <( c ro

::J c C!J u "0 ro C!J ::J c - ~ ro u c ~ c "0 C!J '50 N Q) u "'tib c >- ·x ro 'Vi ..... C!J

t:lO t:lO ro ·- C!J ro C!J Ill ::J ro ::J

~ C!J .... ~ N c .... ro ~

0 ::J a ~ J_ .... co a::l u u UJ u... ..... 0.. 0::: ::::>

MP 70 36 97 29 33 59 54 80 49 31 37 9 56 46 47

GS 123 46 210 34 47 77 96 126 52 44 64 11 88 74 76

The scatter plot representing the relationship between t hese two sets of data is show below.

220 y

210

200

190

180 v / 170 / 160

/ v 150

./ 140 L~-'

130 / 120 .L_'r"'"

110 .L_ 100 . /'r"'" 90 L_ 80 .y . 70 / . 60 / . 50 y • 40

/-30 / 20 /" 10

" / ........ 10 20 30 40 50 60 70 80 90 100

IY7QA·cheo 12.lav.e d . • (J

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Page 13: CORNWALL HILL COLLEGE CAPS 2014 Prelim... · CORNWALL HILL COLLEGE Mathematics Department EXAMINATIONS-28 JULY 2014 Mathematics Paper 2 Grade: 12 Time: 3 Hours Marks: 150 Examiner:

Grade 12 Mathematics Paper 2 Paqe13of24

(a) Determine the equation of the regression line, give your answer correct to four decimal places. (2)

(b) Discuss with reasons the correlation of this data. (2}

(c) Germany has played in 99 world cup matches, predict the number of goals they should have scored. (1}

= /8 ~ b8

/83 (/oCL/s '-.1 "'

(d) Is your prediction in (c) considered interpolation or extrapolation? Explain. (2} , '-.1"1

Tnferpo/a)-to~

(e) Sketch the line of best fit on the given scatterplot showing at least 2 significant points. (3)

..........., 19 ';;{ ;,,~

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Page 14: CORNWALL HILL COLLEGE CAPS 2014 Prelim... · CORNWALL HILL COLLEGE Mathematics Department EXAMINATIONS-28 JULY 2014 Mathematics Paper 2 Grade: 12 Time: 3 Hours Marks: 150 Examiner:

Grade 12 Mathematics Paper 2 Page 14of24

QUESTION 6 [17]

P(4; 5), Q(2; -1) and R(10; 3) are given points in the figure alongside. QP is produced to T and TR j_ QR. The circle with centre P passes through K, the midpoint of PQ.

y

R(10; 3)

Q(2; -1)

(a) Determine: (1) the co-ordinates of K. (2)

;:: ( Y:.~Z. _, rs ) z_ I '-

' ........,,q -......J~ jC_ (3 2)

(2) the equation of the circle. (3)

(x- q )~ + (Cf- b)~ 'Z 'J19 - r

{:x_- 4)'L + (:!- 5 )~ =: r7.

Subs (=r ,· z)

(3 - Lf-)L + (2- s) ~ rz '-J, -/0 - r~ '-...1~

{JL - 4- ) L T 0 -5 ) z.. - I 0

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Page 15: CORNWALL HILL COLLEGE CAPS 2014 Prelim... · CORNWALL HILL COLLEGE Mathematics Department EXAMINATIONS-28 JULY 2014 Mathematics Paper 2 Grade: 12 Time: 3 Hours Marks: 150 Examiner:

Grade12

(3}

c!i- y,

J -s

Mathematics Paper 2

the equation of the line QP . -1 - 5

= 3 '-.J 19

- IY1 (z. -X 1 )

:. 3 (:L - 4 ) ~

= 3X.. -7 -......J,<j

11?

Page15o(24

(3}

(b) Show by calculation that T is the point (6; 11) if the equation of TR is y = -2x + 23.

(c)

</ = - ZX -!- Z 3 <!:/ ;: 3 X - 7 (4} or ~

'-....;

3X -7 '=- -2 J(. + 23 [;X- .::. 30

.):__ :. b ...._{:JJ

(/ =- 3 (b) - 7 ::. 1/ '-J IYJ

l ( b ; I/) '-.1 Ct:}

Determine (in surd form) the length of the tangent TF .

FT-z...::: PT-z.- fF' . 11 ...........,; rry

= ·(liQ) T_ ( iio ) z. 4=0 - IO

Fr = 130

(5}

PT =- /(lf-h)'l+ &-n)' = JiiQ ~~

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Page 16: CORNWALL HILL COLLEGE CAPS 2014 Prelim... · CORNWALL HILL COLLEGE Mathematics Department EXAMINATIONS-28 JULY 2014 Mathematics Paper 2 Grade: 12 Time: 3 Hours Marks: 150 Examiner:

Gradel2 Mathematics Paper 2 Paqel6o(24

QUESTION 7 [24]

(a)

(b)

2+cos{3-cos2{3 Simplify:

3sin{3-sin2B '-' 19 (4)

= ;l + CoO f3 - (;z CcY:;t./3 - I )

(, t- cao(3 ¥".3 - :z coo 8) '-....J4 = ~~--~~----~~========~~-----------------------------5,;,6 (3- ::z ca-::;B) ~ 19

{, + cm8) ---~~~~~,~~---------------------------------

sin(3

(1) Determine the genera l solution of:

cos 30° cos 2x - sin 30° sin 2x = cos 3x (5)

D 30 + ZJ<_ t. 3X. + /c · 3b0° ' k C. 2

t9

30 ° + zx ~ 3 )(_ + k. . 3 b 0 ° • -X.. ::: -30

X. '-./ :::. 30° I'll

30 + 2X.. -= - '3 X.. t- J.: '3bO •

fiX... = -3o· t 1:: • 5bo·

:x-~ : - ~ • T /: • 7:Z 0

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Page 17: CORNWALL HILL COLLEGE CAPS 2014 Prelim... · CORNWALL HILL COLLEGE Mathematics Department EXAMINATIONS-28 JULY 2014 Mathematics Paper 2 Grade: 12 Time: 3 Hours Marks: 150 Examiner:

Grade12 Mathematics Paper 2

(c)

(2) Hence determine x if x E [-90°; 90°]

)t. = • 0

-b . 30

Prove that:

L.HS =

=

sin4x

sinx 8cos3 x - 4cosx

5JY1 z (z x_) s ,, X.

'-1- CO".? X ( 2 CoO ~X. - 1 ) ;>

Paqe17of24

{2)

{5)

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Page 18: CORNWALL HILL COLLEGE CAPS 2014 Prelim... · CORNWALL HILL COLLEGE Mathematics Department EXAMINATIONS-28 JULY 2014 Mathematics Paper 2 Grade: 12 Time: 3 Hours Marks: 150 Examiner:

Grade12 Mathematics Paper 2

(d) Christ the Redeemer is a statue of Jesus Christ in Rio de Janeiro, Brazil; and was considered the largest Art Deco statue in the world from 1931 until 2010.

It is located at the peak of the Corcovado mountain overlooking the city. A symbol of Brazilian Christianity, the statue has become an icon for Rio de Janeiro and Brazil.

As part of the build up to the soccer world cup, Messi and Ronalda decided to have a competition to see who could kick a soccer ball into the hands of the statue. Both players got to choose where they would kick the ball from. The diagram below is an illustration of their positions.

Page 18of24

The base of the statue, Messi (A) and Ronalda (C) are all in the same horizontal plane. The angle of elevation from Messi (A) to the left hand (D) of the statue is a. The angle of elevation from Ronalda (C) to the left hand (D) of the statue is (90° -a). The distance the ball will travel from Messi (A) to the left hand is Zx metres and from Ronalda (C) to

the left hand is x metres. ABC= 120°.

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Page 19: CORNWALL HILL COLLEGE CAPS 2014 Prelim... · CORNWALL HILL COLLEGE Mathematics Department EXAMINATIONS-28 JULY 2014 Mathematics Paper 2 Grade: 12 Time: 3 Hours Marks: 150 Examiner:

Grade12 Mathematics Paper 2 Paqe19o(24

{1) Show that the distance between Messi (A) and B is given by

{2)

AB = 2x cos a and that the distance between Ronaldo (C) and B is given by

BC = x sin a.

Tn 61i8D :Tn 6 BeD

A8 Be

{2)

"' .;1 X c co o( """" 19 t3 G = JC. s I,.; o<. "'.J 19

---------------=~--------~----~-----

Show that the distance between Messi and Ronaldo is given by

AC = x-../1 + 3 cos2 a+ sin 2a. '-.....}roy ::,41~ ~ Sqhs ~ {6)

'2.

f-JC::

+

+ ;J Stnc< coc:;o<.)

I - c rY.J rz. o<.

A6 ___ -__ ~Jc~!~~'~+~3~c~ro-~~~--~t~S~'n_·~~~~~--------------

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Page 20: CORNWALL HILL COLLEGE CAPS 2014 Prelim... · CORNWALL HILL COLLEGE Mathematics Department EXAMINATIONS-28 JULY 2014 Mathematics Paper 2 Grade: 12 Time: 3 Hours Marks: 150 Examiner:

Grade12 Mathematics Paper 2 Paqe20of24

QUESTION 8 [6]

Below is the pyramid of The Pyramid of King Khafra, at Giza. It is made out of a square base and 4

equilateral triangles. E

(a)

(b)

Show that the height of the pyramid is 162,6 m.

Ac"Z.. ;;230 ~

230~ ::: r ::: /05 8'00

Ac = 325 27 '-.....1 19 I

AF = FC = I b "Z. 1:,3

EF :23 0 "l.. - /b"Z 63

- :1. b '+51 4-8

E/- = j/,2, faY. ~ A .

El- = /b "2 ~ ""'-....J A

Determine the volume of the pyramid if:

'-......J IYJ

~

V = ~(Area of base) x Height. 3 11]

'-...j

v ~ ~.3 (2 3 0 X 2 3 0 ) )' I b z I b

(4)

(2)

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Page 21: CORNWALL HILL COLLEGE CAPS 2014 Prelim... · CORNWALL HILL COLLEGE Mathematics Department EXAMINATIONS-28 JULY 2014 Mathematics Paper 2 Grade: 12 Time: 3 Hours Marks: 150 Examiner:

Grade 12 Mathematics Paper 2 Paqe21 o(24

QUESTION 9 [6)

(a) Complete the following sentence:

If a line cuts two sides of a triangle proportionally, then ...... (1}

-thd j,,;-e // fo fn~

(b) In the figure K is a point on AB, such that AK: KB = 3 : 2. Lis a point on AD such that

AL : LD = 3 : 1. KX = XB.

B

c

Prove that: BD 1 -= -BC 2

A (5}

AK 3

K./3 :2..

htd K.X = XB (/1ven

fJK .3 '-......./ kX J

Jocd AL 3 #' v~n ~

LD I

,. 17 }(. AL "-.....J 3 • I

K..X LD I

K.L LL XD '-......; ''"~ dl~.f,dQLJ '~ild.e,o I"" I" OJ), • I ..-,

BD BX -..........; J /,F..L II fo on e. s;ol~ ~tJ . '

DC Xh I

BD I '-...J -Be ;t

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Page 22: CORNWALL HILL COLLEGE CAPS 2014 Prelim... · CORNWALL HILL COLLEGE Mathematics Department EXAMINATIONS-28 JULY 2014 Mathematics Paper 2 Grade: 12 Time: 3 Hours Marks: 150 Examiner:

Grade12 Mathematics Paper 2 Paqe22o(24

QUESTION 10 [12]

Refer to the diagram below.

Two circles intersect at A and B. Chords AS and BS of the larger ci rcle meet the smaller circle at D and C respectively. CD produced meets the larger circle at T. AT and TS are joined.

Prove that ~ + T2 = D4 (3)

d /80 0

+ ::; 0

0 + ..-'\ B = !8"00

A..

T. + T = D

hr.A.f /\

'"""' ~ D. ~ D'f. r

-"'\ '/)!.!-r, + Tz =

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LAC/d. •

~cu:J. .

Page 23: CORNWALL HILL COLLEGE CAPS 2014 Prelim... · CORNWALL HILL COLLEGE Mathematics Department EXAMINATIONS-28 JULY 2014 Mathematics Paper 2 Grade: 12 Time: 3 Hours Marks: 150 Examiner:

Grade 12 Mathematics Paper 2 Paqe 23 af24

Qb} Prove !J.STD Ill !J.SAT {3}

Tn !::. 5rD one/ 6 5fJT

') " ;"\

S' , ::. s , '-1 ("om mon i

"' z.J """ """ '[)'+ :. Ti + T? ~ Pro v f d " A I

3) . 7'l. = A, /1"1 f- L. a-6 A .. . .

STD 1!1 SAT "-.J AAA • • 4 6

(c) Prove tJ. SDC Ill tJ. SBA (3}

In 6 50C- CIY\ d !::.. 5'8/-)

1) "" /\ s:2. ::It 5 :z... ~ Commo--

z.) A "' Lc5 c/1.. ch c 2 u t:f c/ 0.'3 :::: B ............ l e~f

"" A

3) C:z.. ... f1'2.. tnf L ~ t:J

. . l::. SDC Ill 6 58 A ~ AA!i

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Page 24: CORNWALL HILL COLLEGE CAPS 2014 Prelim... · CORNWALL HILL COLLEGE Mathematics Department EXAMINATIONS-28 JULY 2014 Mathematics Paper 2 Grade: 12 Time: 3 Hours Marks: 150 Examiner:

Grade 12 Mathematics Paper 2

( cJ) TS2 = BS. CS

~ SID II/ £3 SAT

ST SD SA ST

. '. rs oz. = so · sA "'-v

A SDC 1/1 6 SBA SD sc 56

- SO· SA = 5C · SB'-......1

' . . Ts'- -= sc · S(3

= cs . 85 "'-...1

Paqe24of24

{3)