REVISION C1 - C11 ADD MATHS F4

8/12/2019 REVISION C1 - C11 ADD MATHS F4

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Additional Mathematics (Form 4) REINFORCEMENT EXERCISES

Chapter 1 FNCTIONS

1) Given h-1:x 1

2x +

3

2. Find the value of h(4). [3 m]

!) Given f :x 2x + k and f-1 :x mx +3

2. Find the value of m and k. [2 m]

") Given f:x 2 x and f :x 3x2 12x + !. Find 2(1). [4 m]

4) Given f(x) " 3x k and (x) "2

x

#. $f f(2) " 2% find the value of k. [3 m]

#) & fun'tion f i defined a f:x 3x2+ mx n he*e m and n a*e 'ontant. $f f(1) " and f(-2) " ,%dete*mine the value of m and n. [3 m]

$ractice ma%es per&ect' eep on tr*in+ Ne,er +i,e -p


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.) Given f(x) "#

ax b+ % f(1) " # and f1

2

"#

4. Find the value of a and . [3 m]

/) Given that :x 2x 3 and h:x 2

#

x

% find

a) -1(x)) h-1(x) [4 m]

0) Given f(x) "

3x +% he*e x . Find

a) the value of ) the ex/*eion fo* the fun'tion of f2(x) [3 m]

) Given f :x 10

!

x

x

+ % x !. Find

a) the fun'tion f2

) a /oitive value of / o that f(/) " / [4 m]



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12) ket'h the *a/h of f(x) " 3 x 2 fo* the domain -4 x #. [3 m]

f(x)

x

11) Given the fun'tion f(x) " x + 2 and f(x) " x2+ 4x 1. Find

a) the fun'tion (x)) the value of k if (3k) " -4k

') ho that -1f-1" (f)-1. [ m]

1!) 5he fun'tion f and a*e defined a folloed:

f :x 10

2

x

x

+ % x 2 and :x # 2x

a) 6x/*e f -1and f-1in the ame notation.) ket'h the *a/h 7 " (x) fo* the domain -1 8 x 8 #. [ m]

1") a) 5he fun'tion f and a*e defined a folloed:

f :x ax # and :x 3

x b+ % x -b

Given f(x) "3

4 x % x

3

2

Find: i) the value of a and

ii) the value of x hen f(x) "1

2 [# m]

) 5he fun'tion / and 9 a*e /(x) " 1 2x and 9(x) " x 2. Find the 'om/oite fun'tion /9. [2 m]

14) Given the fun'tion f : x 3 4

2

x and f : x 1!x2 4!x + 40. Find

a) f2 [2 m]) [3 m]') f [3 m]d) f-1(10) [2 m]



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1#) 5he fun'tion i defined 7

: x 3 2x p

x

++ fo* all value of x ex'e/t x " h and / i a 'ontant.

a) tate the value of h.

) Given 2 i ma//ed onto itelf unde* the fun'tion % findi) the value of /ii) the othe* value of x u'h that it ma//ed onto itelfii) -1(4) [ m]

Chapter ! 3ARATIC E3ATIONS 5 Chapter " 3ARATIC FNCTIONS

1) Fo*m the 9uad*ati' e9uation hoe *oot a*e -# and -1

2. 6x/*e 7ou* ane* in the fo*m ax2+ x + '

" 0% he*e a% and ' a*e 'ontant. [2 m]

!) olve the 9uad*ati' e9uation 2x(x + 3) " (1 x)(x + 2). Give 7ou* ane* 'o**e't to 4 inifi'antfiu*e.

[3 m]

") olve the 9uad*ati' e9uation3 #

4 2x

x

= . [3 m]



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4) Given 3 and 4 a*e the *oot of the 9uad*ati' e9uation 2x2 hx + k " 0. 6x/*e k in te*m of h. [3 m]

#) Given (h + 2) and (k 1) a*e the *oot of the e9uation x2+ #x + 4 " 0. Find the /oile value of hand k. [4 m]

.) Given the 9uad*ati' e9uation (3 + m)x 2 (! + 4m)x + (3 + 4m) " 0. Find the value of m if one of the*oot i the *e'i/*o'al of the othe* *oot. [3 m]

/) ;ete*mine the t7/e of *oot of the 9uad*ati' e9uation #x2+ " x . [2 m]

0) Find the e9uation of the axi of 7mmet*7 of the 9uad*ati' fun'tion f(x) " 2x 2 #x + . [3 m]



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) 5he e9uation /x2+ 29x + 4/ " 0 ha to e9ual *oot. Given / and 9 a*e /oitive% findp

q. [3 m]

12) Given the 9uad*ati' e9uation 2x2+ 3x + h " 0 ha e9ual *oot. Find the value of h. [3 m]

11) Find the *ane of / u'h that !x 3 4x2" /x 2 ha to ditin't *oot. [3 m]

1!)


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14) Given f(x) + 3 " !x 3 4x 2. 6x/*e f(x) in the fo*m of / + 9(x + *)2he*e / and 9 a*e 'ontant.tate the value of *% / and 9. [4 m]

1#) Given f(x) " 2x2 !x + . 6x/*e f(x) in the fo*m of a(x /)2+ 9 he*e / and 9 and * a*e 'ontant.[2 m]

1.) Given the *oot of the e9uation 2x 2 3x + 4 " 0 a*e and =. Fo*m a ne e9uation ith *oot

and

. [4 m]

1/) Given and = a*e the *oot of the e9uation 3x 2 #x 1 " 0. Fo*m the 9uad*ati' e9uation ith *oot( + 1) and (= + 1). [4 m]



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10) $f the *oot of the e9uation !x2 10x + 3 " 0 a*e and = % finda) the value of + = and =) the 9uad*ati' e9uation ith *oot 3 and 3= [4 m]

1) 5he dia*am ho the *a/h of the fun'tion 7 " -(x m)2+ n he*e m and n a*e 'ontant. Find

a) the value of m and n) the e9uation of the axi of 7mmet*7

[3 m]

!2) 5he dia*am ho the *a/h of the fun'tion 7 " -(x + /)2 2 he*e / i a 'ontant. Find

a. the value of /. the e9uation of the axi of 7mmet*7'. the 'oo*dinate of the maximum /oint

[3 m]

!1) 5he dia*am ho the *a/h of the fun'tion 7 " (x 1)2 + h he*e h i a 'ontant. Find

a. the value of h. the e9uation of the axi of 7mmet*7

'. the 'oo*dinate of the minimum /oint[3 m]



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!!) & 9uad*ati' fun'tion f(x) "1

2[(x h)2+ k] ith h and k a*e 'ontant% ha the minimum /oint

&(!*% 2*2). 6x/*e h and k in te*m of *. [2 m]

!") Find the *ane of value of 9 if the *a/h of the 9uad*ati' fun'tion h(x) " x 2+ 9x + 1 doe not meetthe x-axi. [4 m]

!4) Find the *ane of k he*e the t*aiht line 7 " 2x + k doe not inte*e't the 'u*ve x2+ x7 " -12. [4 m]

!#) ket'h the *a/h of f(x) " 2x2+ x + 3 and tate it axi of 7mmet*7. [3 m]

!.) Find the *ane of x that atifie the 9uad*ati' ine9ualit7 3x 4 > -x2. [3 m]



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!/) Find the *ane of x that atifie the 9uad*ati' ine9ualit7 x >2

x . [3 m]

!0) Find the *ane of x that atifie the 9uad*ati' ine9ualit7 (2x 1)(x + 4) > 1!. [3 m]

!) Find the *ane of x that atifie the 9uad*ati' ine9ualit7 (2x 3)(x + 2) > 2x 3 [3 m]

"2) Find the *ane of x if 27 + 3x " # and 47 > 3+ x2. [3 m]

"1) $f 7 " 2x + 1 and 72 x2+ 3x + #% find the *ane of value of x. [3 m]



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"!) Given and = a*e the *oot of the e9uation x 2+ x + a " 0 and (2 + 1) and (2= + 1)a*e the *oot of the

e9uation x2+ x 2# " 0. Find the /oile value of a and . [ m]

"") 5he fun'tion f(x) " 3x2+ hx + k ha a minimum value of -11 hen x " 2.

a) Find the value of h and k. [3 m]

) ket'h the *a/h f(x) fo* 0 x 4 and dete*mine the *ane. [4 m]

"4) a) Given f(x) " 3x2+ x + k. ho that the minimum value of f(x) ha//en hen x " -1 fo* all value

of k. ?en'e% find the value of k if the minimum value i . [3 m]

) Given 7 " /x2+ 4x + / 3% find the *ane of value of / o that 7 i ala7 neative. [3 m]

"#) 5he fun'tion f(x) " x2 kx + 10k + 4 ha the minimum value *2+ 4k he*e * and k a*e 'ontant.

a) @in the 'om/letin 9ua*e method% ho that * " k 2 . [4 m]

) ?en'e% o* othe*ie% find the value of k and * if the *a/h of the fun'tion i 7mmet*i'al at

x " * + . [4 m]

".) Given a 9uad*ati' e9uation f(x) " x2+ !x + /.

a) find the *ane of value of / o that f(x) i /oitive fo* all value of x [3 m]) fo* the 'ae / " 1!%

i) find the minimum value of f(x) and the 'o**e/ondin value of x

ii) ket'h the *a/h of f(x) [# m]

"/) a) Given the e9uation(3 + m)x2 (, + 3m)x + (1 + 2m) " 0

Find the value of m if

i) one of the *oot i the neative of the othe* *ootii) one of the *oot i the inve*e of the othe* *oot [ m]

) $f1

2and -

#

4a*e the *oot of a 9uad*ati' e9uation% find the 9uad*ati' e9uation. [2 m]



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Chapter 4 SIM6TANEOS E3ATIONS

1) olve the imultaneou e9uation x + 37 " - and 72 2x + 7 " !. [# m]

!) olve the imultaneou e9uation2

1yx

y x

= and 4x #7 " 13 [ m]

") olve the imultaneou e9uation x + 27 " 3 and x2+ 2x7 + 72" #. Give 7ou* ane* 'o**e't to 2

de'imal /la'e. [# m]

4) olve the imultaneou e9uation 3x + 47 " # and 3x2+ 472 #x + 7 " 3. [ m]

#) olve the imultaneou e9uation 2(7 x) " x + 7 1 " 272 11x2 [# m]

.) olve the imultaneou e9uation x(1 + 27) " ! and 27(4 + x) " 2. [ m]

/) Given that (h% 3) i one of the olution fo* the imultaneou e9uation 3x + 7 " -3 and2x2 + kx7 + 372 " 11. Find

a) the value of h and k [3 m]

) the othe* olution fo* the imultaneou e9uation [4 m]

Chapter # INICES 5 6O7ARIT8MS

1) 6x/*e (! x 2n 2) A (2n 2n + 1) in it im/let fo*m. [3 m]

!) olve the e9uation #(3-7) " 4#. [2 m]

") olve the e9uation 33x"

2x

. [3 m]



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4) olve the e9uation 3x,x 1 " !13x 1. [2 m]

#) olve 2x - 1" #% ive 7ou* ane* 'o**e't to 3 de'imal /la'e. [3 m]

.) im/lif7 39 + 2 39 + 3 2(39 - 2) 2(39) in the fo*m k(39)% he*e k i a 'ontant. [2 m]

/) olve the e9uation 2(32x) " #(33x 1). Give 7ou* ane* 'o**e't to 4 de'imal /la'e. [4 m]

0) Find the value of x and 7 if 4x17" 2# and 3-x,-27"1

2,. [4 m]



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) Find the value of 2lo #

! ithout uin the loa*ithm tale. [2 m]

12) Find the value of n if lo32n "1

#. [2 m ]

11) Given lo23 " / and lo2# " 9% find lo!4# in te*m of / and 9. [3 m]

1!) Given lo32 " 0.30, and lo3# " 1.4#0. Find the value of1

2lo3300. [4 m]

1") Bithout uin the loa*ithm tale% find the value of (lo#)(lo22#)(lo4)(lo#2). [2 m]

14) Given that lo!7 1 " lo2x% ex/*e 7 in te*m of x. [3 m]



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1#) $f 2 lo109 " # lo10*% ex/*e * in te*m of 9. [3 m]

1.) Find the value of a iven # loa3 + loa2 loa144 " 3. [3 m]

1/) $f loa " 10x

x% find the value of a iven that x " ! and "

1

!1. [3 m]

10) olve lo3(x 1) + lo34 lo3(3 2x) " 2. [3 m]

1) olve lo (x 1) lo (# + x) + lo x " 0. [3 m]

!2) Given that lo10x72 " 1 and lo10x27 " -1. Find the value of x and 7. [4 m]



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!1) Given that lo34 " / and lo3# " 9. Find the value of x if lo3x " 2/ 9 + 2. [4 m]

!!) olve the folloin e9uation.

a) (lo2)(loC) " 2

) lo2[lox(2x2 1)] " 1 [4 m]

!") Given lo2C " a and lo2D " . 6x/*e in te*m of a andEo*

a) lo!C

) lo2P

Q

[4 m]

!4) olve the e9uation 1!x2x34x" !-1. Give 7ou* ane* 'o**e't to 4 de'imal /la'e. [# m]



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!#) olve.

a) lo2x + lo!2x " 3

)2 1

3, 3

12xx

x

= [ m]

Chapter . 7EOMETR9 COORINATES

1) Given &(2% )% (1% -1) and (,% ). H i the mid/oint of . Find the e9uation of the t*aiht line &Hhi'h Ioin the /oint & to the mid/oint of . [3 m]

!) Given /oint (!% 10) divide the line ement Ioinin &(/% 4) and (#% 9) inte*nall7 in the *atio& : " 2:3. Find the value of / and 9. [2 m]

") &; i a /a*allelo*am he*e /oint &(3% 3)% (1% -1)% (-2% -2) and ;(0%2). Find the a*ea of &;.[2 m]



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4) 5he e9uation of to t*aiht line a*e 27 + x " # and 3x 47 " 1!. Find the inte*e'tion /oint of thet*aiht line. [4 m]

#) Given


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) Given the /oint &(3% -1) and (#% 3). H i the mid/oint of & and i a /oint on the x-axi u'h that

H i /e*/endi'ula* to &. Find

a) the 'oo*dinate of H

) the e9uation of the t*aiht line H

') the 'oo*dinate of [ m]

12) 5he 'oo*dinate of /oint and 5 a*e (-2% 0) and (1% 0) *e/e'tivel7. 5he /oint C(x% 7) move u'h that

the *atio C : C5 " 2 : 1.

a) ho that the e9uation of the lo'u C i x2+ 72 4x " 0. [3 m]

) ho that the /oint H(2% 2) lie on the lo'u C. [2 m]

') Find the e9uation of the t*aiht line 5H. [2 m]

d) 5he t*aiht line 5H 'ut the lo'u C at the /oint K. Find the 'oo*dinate of K. [3 m]

11) $n the dia*am% CDJ i a *homu he*e C(-3% 12)% D(,% 11) and (-11% 3). 5he diaonal of the

*homu inte*e't at the /oint 5. Find

a) the 'oo*dinate of 5 [2 m]

) the e9uation of CJ [3 m]

') the lenth of CJ [3 m]

d) the a*ea of the *homu CDJ [2 m]

1!) 5he dia*am ho the *a/h of the t*aiht line & and 6;. 5he /oint & and lie on the 7-axi and

x-axi *e/e'tivel7. i the mid/oint of &.

a) Find

i) the 'oo*dinate of /oint ii) the a*ea of the 9uad*ilate*al


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1") 5he dia*am ho a 9uad*ilate*al &; he*e ; i /a*allel to the 7-axi and the t*aiht line & i

/e*/endi'ula* to . Given that the e9uation of the line & i x 7 " 1.

a) Find

i) the e9uation of the t*aiht line

ii) 'oo*dinate of /oint [# m]

) Given that the t*aiht line ; i /a*allel to

x-axi% find the a*ea of the 9uad*ilate*al &;.

[3 m]

') $f the t*aiht line ;& i extended to the /oint 6

u'h that #;& " 3&6% find the 'oo*dinate of

/oint 6. [2 m]

Chapter / STATISTICS

1) Find the tanda*d deviation fo* the folloin et of nume* : 3% #% !% , and 10. [4 m]

!) Given the intee* !% 1% #% 2% 10% , and x. Find

a) the *ane of x if the median i x

) the value of x if the mean i [2 m]

") 5he mean and va*ian'e fo* the et of nume* #% x 7% ,% 11 and x + 7 a*e , and ! *e/e'tivel7.

a) Find the value of x and 7.

) tate the median of the nume*. [4 m]



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4) & et of ! nume* ha a mean of 12 and a tanda*d deviation of 3. &nothe* et of 12 nume* ha a

mean of # and a tanda*d deviation of 4. al'ulate the mean and tanda*d deviation of the 20 nume*.

[4 m]

#) 5he et of data x% 4% #% !% % 12% 1!% 7 and L ha a mean of 10. Find the mean of x% 7 and L. [3 m]

.) 5he mean of the et of nume* % !% x% 12% 13 a*e 10. Find

a) the value of x

) the va*ian'e and tanda*d deviation [4 m]

/) 5he ma*k 'o*e 7 11 tudent in a mathemati' 9uiL a*e a folloed :

4,% % 3#% ,% #% 4,% !0% % #,% 4% 2

Find

a) the *ane) the inte*9ua*tile *ane fo* the ma*k. [3 m]



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0) 5he mean of a et of ten nume* i 2Mk. 5he um of the 9ua*e of the nume* i 300 and the tanda*d

deviation i 2h. 6x/*e k in te*m of h. [3 m]

) 5he tale ho the ma*k otained 7 a *ou/ of tudent in a tet. Bithout d*ain an oive% find itinte*9ua*tile *ane. [4 m]

Mar%s ! 1# 1 23 24 31 32 3, 40 4 4! ## # 3

N-m:er o& st-dents 4 ! 10 , !

12) 5he tale ho the 'umulative f*e9uen'7 dit*iution of the 'o*e ea*ned 7 30 /u/il in an a*t

'om/etition. Find the mean and median of the 'o*e. [4 m]

Score C-m-lati,e Fre;-enc*

0 31 102 133 1!4 22# 30



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11) 5he tale ho a et of nume* a**aned in de'endin o*de*% he*e n i a /oitive intee*% and thei**e/e'tive f*e9uen'ie.

N-m:er 13 11 n + 2 n 1

Fre;-enc* 1 1 3 1 2 2

a) 6x/*e the median in te*m of n.) Find the /oile value of n. [4 m]

1!) Given the mean and tanda*d deviation fo* the nume* x1% x2% x3% N % x10a*e 12 and # *e/e'tivel7.

a) Find i) Oxii) Ox2 [3 m]

) Given a ne et of nume* 3x1+ 2% 3x2+ 2% 3x3+ 2% N % 3x10+ 2 . Find fo* thee ne et of

nume*

i) mean

ii) va*ian'e [4 m]

1") Fo* a et of n nume*% it i iven that Ofx " 20 and Ofx2" 120 000.

a) $f the tanda*d deviation i !0% find

i) the value of n

ii) the mean [ m]

) $f ea'h nume* in the et i halved% find the ne va*ian'e. [2 m]

14) 5he tale ho the dit*iution of the ma*k fo* a hemit*7 tet 'o*ed 7 120 tudent.

Mar%s 20 2, 30 3, 40 4, #0 #, 0 , 0 ,

N-m:er o& st-dents 2 14 3# #0 1 2

al'ulate

a) the mean [3 m]

) the median and [4 m]

') the tanda*d deviation [3 m]

of the dit*iution



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1#) 5he f*e9uen'7 dit*iution of the 'o*e of 0 tudent ho it fo* a tet i hon in the tale elo.

Score Fre;-enc*

10 2, 30 4, 10

#0 , 300 !, 7

a) Find the value of + 7. [2 m]

) Given that the mode i 1.#. @in the loe* and u//e* ounda*ie% d*a a hito*am to dete*mine

the value of and 7. [# m]

') Find the mean . [3 m]

Chapter 0 CIRC6AR MEASRES

1) 5he dia*am ho to e'to*%


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") 5he dia*am ho a *iht-anled t*ianle CDJ. 5he a*' D i d*an ith C a it 'ent*e and CD a it

*adiu. Given that CD " , 'm and DCJ " # P. al'ulate the a*ea of the haded *eion. [4 m]

4) $n the dia*am% &


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/) 5he dia*am ho a 'i*'le ith 'ent*e < and *adiu 'm. &


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12) 5he dia*am ho a 'i*'le ith 'ent*e


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4) Find the value of f U(-3) fo* f(x) " (3x 1)3(x2 ,). [3 m]

#) Given that f(x) " (3x2 1)% evaluate f UU(-1). [4 m]

.) Given that f(x) " 22

(3 4)x % evaluate f UU (2)

[4 m]

/) Given f(x) "4

xand (x) " (3x 2)2. $f 7 " f(x)(x)% find

dy

dxin it im/let fo*m. [3 m]



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0) Given 7 "2

2(2 1)

x

x . ho that

dy

dx" 3

2

(2 1)

x

x

. [3 m]

) Given 7 " x2 # 3x . ho thatdy

dx"

220 1#

2 # 3

x x

x

. [4 m]

12) Given 7 " x(2x2 #). ho that2

2

d y

dx+

dy

dxx 37 " 22x. [3 m]

11) 6x/*e 72

2

d y

dx+ 3x

dy

dx+ 4# in it im/let fo*m iven that 7 " x(# 3x). ?en'e find the value of x that

atifie the e9uation 7

2

2

d y

dx + 3xdy

dx + 4# " 0. [4 m]



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1!) Given the e9uation of a 'u*ve 7 " -4 + x 2x2. Find the e9uation of the no*mal to the 'u*ve at (1% 0) .[4 m]

1") 5he *adient fo* the 'u*ve 7 " /x2+ 9x at the /oint (2% -2) i -. Find the value of / and 9. [2 m]

14) $f the e9uation of the no*mal to the 'u*ve 7 " 3x +1

xat (1% 4) i 7 " /x + 9% find the value of / and 9.

[4 m]

1#) 5he t*aiht line x + 7 " 0 and the 'u*ve 7 " x2 2x + 4 inte*e't at to /oint. Find

a) the 'oo*dinate of the /oint of inte*e'tion

) the *adient at thee /oint [4 m]

1.) Given that x72" #% etimate the a//*oximate 'hane in x hen 7 in'*eae f*om 3 to 3.1 [3 m]



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1/) Find the a//*oximate in'*eae in the u*fa'e a*e of a /he*e if it *adiu in'*eae f*om 2 'm to 2.3 'm.[3 m]

10) Given 7 " 3x21

2x. $f x in'*eae ith the *ate of 2 unit-1% find the *ate of 'hane of 7 hen x " 2.

[4 m]

1) 5he volume of a 'ue in'*eae at the *ate of 0.012 'm 3-1hen it ide i 2 'm. Find the *ate of thein'*eae of it ide at the time. [4 m]



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!2) Given 7 " ++4

x

. Find the value ofdy

dxhen x " 2. ?en'e% find the a//*oximate value of

( )

4

2.00.

[4 m]

!1) Given 7 " x3 3x2 ,x + . al'ulate the 'oo*dinate of it tationa*7 /oint and dete*mine hethe* it ia maximum o* minimum /oint. [ m]

!!) 5he tanent of the 'u*ve 7 " ax3+ x at the /oint (1% 1) ha a *adient of -#.

a) the value of a and [3 m]

) the 'oo*dinate of the /oint on the 'u*ve u'h that the tanent at thoe /oint a*e /a*allel to thex-axi [3 m]

Chapter 12 SO6TIONS OF TRIAN76ES

1) 5he dia*am ho a t*ianle CDJ. Given that CRQ " ,0P and 'o QJH " 0.2. Find

a) the lenth of QR [2 m]

) the lenth of QH [3 m]

') the /e*imete* of DRQH [# m]

!) 5he dia*am ho to t*ianle CJ and DCJ. $t i iven that CJ " .# 'm% C " , 'm% JCD " #0P

and CDJ " 4!P. $f the a*ea of the t*ianle CDJ i ti'e the a*ea of t*ianle CJ% find

a) the lenth of CD [3 m]

) the a*ea of t*ianle CJ [3 m]

') the lenth of J [4 m]



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") a) $n the dia*am% DJ " 'm% CJ " ! 'm and C " 10 'm. Given CJ " #0P and CJD " 120P.

DJ i a t*aiht line. al'ulate

i) the lenth of CD [3 m]

ii) JCD [3 m]

) RHK i a t*ianle ith RH " 10 'm. Given 'o HRK "3

# and in RHK "

1

#% 'al'ulate

i) RKHii) the a*ea of TRHK [4 m]

4) a) TCDJ i a t*ianle ith DJ " 13.3 'm% CJ " 12.# 'm and J " 4P 22U. Find

i) the lenth of CD

ii) C and D [# m]

) 5he dia*am ho a '7'li' 9uad*ilate*al CDJ he*e C% D% J and lie on the 'i*'umfe*en'e of the

'i*'le. Given DC " 120P% DJ " ! 'm and J " 10 'm.

al'ulate

i) the lenth of D% 'o**e't to 2 de'imal /la'e

ii) DJ [# m]

#) 5he dia*am ho T& ith " 20 'm% & " 30P and & " 0P. ; i a /oint on & u'h

that the a*ea of T; " 40 'm2.

al'ulate

a) the lenth of ; [2 m]

) the lenth of & [2 m]

') the lenth of ; [2 m]



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d) ; [2 m]

e) the ve*ti'al ditan'e f*om to &; [2 m]

.) 5he dia*am ho to t*ianle% & and &;. Given that & " 10 'm% " !.3 'm% ; " 1, 'm%

&; " 1#P% & " ##P and & i an a'ute anle.

a) Find &. [2 m]

) Find &; [2 m]

') al'ulate the a*ea% in 'm2% of the t*ianle &;. [2 m]

d) & t*ianle &UUU ha the ame meau*ement a thoe iven fo* t*ianle &% that i & " 10 'm%

" !.3 'm and U&UU " ##P% ut hi'h i diffe*ent in ha/e to t*ianle &.

i) ket'h the t*ianle &UUU.

ii) tate the iLe of &UUU.

iii) al'ulate the lenth &UU. [4 m]

/) 5he dia*am *e/*eent a 'uoid.

al'ulate

a) G; [4 m]

) ;G [3 m]

') the total u*fa'e a*ea of the lo'k ;G [3 m]



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Chapter 11 INEX NM Ii 114 103 ,# 10#?ei+hta+e> @i 4 3 x 2x 1



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") 5he 'om/oite index nume* fo* the data in the tale elo i 13!. Find the value of x. [4 m]

Inde= n-m:er> Ii 12# 13#140

1#0

?ei+hta+e> @i x + 21

3x #x + 1 x

4) 5he tale ho the /*i'e index of fou* item in 7ea* 2000 and 2001 aed on 1,, ith the *elated

eihtae.

Item$rice Inde=

?ei+hta+e!222 !221

C 12#.3 131.3 3.#D 11#.! 11.# 21.!J 104.2 10#.2 1!.3 110.2 112. 23.4

a) Given the ave*ae ex/enditu*e fo* item C i JH3#0 in 2000% find the 'o**e/ondin ex/enditu*e in

2001. [3 m]

) 5he ave*ae ex/enditu*e fo* item J i JH3!0 in 2001% find the 'o**e/ondin ave*ae ex/enditu*e

in 2000. [3 m]

') Find the 'om/oite index fo* 2001 aed on 1,,. [4 m]

#) 5he tale ho the /*i'e indi'e of the ha*e of fou* 'om/anie fo* the 7ea* 1,,# aed on the 7ea*

1,,0. 5he 'om/oite index fo* the 7ea* 1,,# aed on the 7ea* 1,,0 i 132.

Compan* $rice Inde= ?ei+hta+e

C 110 4



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D k 2

J 1#0 3

1!0 1

a) al'ulate the value of k.

) $f the /*i'e of the ha*e of 'om/an7 J in the 7ea* 1,,0 a JH3.0% 'al'ulate it ha*e /*i'e in the

7ea* 1,,#.

') F*om the 7ea* 1,,# to the 7ea* 2000% the /*i'e index of the ha*e of the 'om/an7 C in'*eaed 7 #

V% the /*i'e index of the ha*e of 'om/an7 D a un'haned and the /*i'e index of the ha*e of the

'om/an7 J and de'*eaed 7 10 V and 30 V *e/e'tivel7. al'ulate the 'om/oite index fo* the

7ea* 2000 aed on the 7ea* 1,,0.

d) F*om the 7ea* 2000 to the 7ea* 200#% the ha*e /*i'e of the 'om/anie C% D% J and in'*eaed 7 !

V% 20 V% 3# V and ,0 V *e/e'tivel7. al'ulate the 'om/oite index fo* the 7ea* 200# aed on the

7ea* 2000.

.) 5he a* 'ha*t elo ho the nume* of unit of item &% % % ; and 6 /u*'haed in the 7ea* 2003.

5he tale ho the /*i'e indi'e of thee item.

Item$rice in !22"

(RM)

$rice in !22.

(RM)

$rice Inde= in !22.

:ased on !22"

& 0.40 x 1#0

1.#0 1.# 110

4.00 4.!0 7; 3.00 4.#0 1#0

6 L 2.40 120

a) Find the value of x% 7 and L.



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) al'ulate the 'om/oite index fo* total ex/enditu*e on the item in 7ea* 200 aed on the 7ea*

2003.

') 5he total ex/enditu*e on the item in 7ea* 200 i JH#00. al'ulate the 'o**e/ondin total

ex/enditu*e in 7ea* 2003.

d) 5he /*i'e of ea'h item in'*eae 7 20 V f*om the 7ea* 200 to the 7ea* 200!. Find the 'om/oite

index fo* total ex/enditu*e on the item in 7ea* 200! aed on the 7ea* 2003.

/) 5he tale elo ho the /*i'e indi'e and the eihtae of th*ee item fo* the 7ea* 2004 aed on the

7ea* 2002.

Item $rice Inde= ?ei+hta+e

C 10! 2n 1

D 120 n

J m n + 1

5he /*i'e of item J in the 7ea* 2002 and 2004 a*e JH30 and JH31.#0 *e/e'tivel7. 5he 'om/oite

index fo* the 7ea* 2004 aed on the 7ea* 2002 i 110. Find the value of m and n.

REVISION C1 - C11 ADD MATHS F4

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Transcript of REVISION C1 - C11 ADD MATHS F4