ANALYSIS OF SPM QUESTIONS FORM 4.doc

7/21/2019 ANALYSIS OF SPM QUESTIONS FORM 4.doc

http://slidepdf.com/reader/full/analysis-of-spm-questions-form-4doc 1/8

ANALYSIS OF PAST YEAR QUESTIONS FORM 4

CHAPTER 1: FUNCTIONS2006 P1 QU 1

In diagram 1, set B shows the images of

certain elements of set A.

(a) tate the t!"e of relation #etween set

A and set B.

(#) Using the f$nction notation, write a

relation #etween set A and set B.

2. P% 2006 P1 QU 2 &iagram 2 shows

the f$nction h ' → m x

x

−, 0,

where m is a constant.

ind the *al$e of m.

+. P% 200 P1 QU1

In the diagram #elow, the f$nction h

ma"s to ! and the f$nction g ma"s ! to

-.

&etermine

(a) h1()

(#) gh(2)

/(a) 2 (#)

. P% 200 P1 QU2

3he f$nction w is defined as w() 4

, 22

x x

≠

−.

ind(a) w1()

(#) w1()

/(a) 2 x

x

−(#)

+

. P% 200 P1 QU+

3he following information refers to the

f$nction h and g.

h ' → 2 5 +

g ' → 5 1

ind gh1()

/2

CHAPTER 2: QUADRATIC

EQUATIONS1. P% 2006 P1 Q$+

A 7$adratic e7$ation 2 " 8 4 0 has two

e7$al roots.

ind the "ossi#le *al$es of ".

/,

2. P% 200 P1 Q$ 3he straight line ! 4 5 1 does not intersect

the c$r*e ! 4 22 ". ind the range

of *al$es of ".

/" 9 1

+. P% 200 P1 Q$

ol*e the 7$adratic e7$ation (2 5 ) 4 2 5

1. :i*e !o$r answer correct to three

decimal "laces.

/+.+1, 0.18

CHAPTER 3: QUADRATIC FUNCTIONS

1. P% 2006 P1 Q$

&iagram + shows the gra"h of a 7$adratic

f$nction ! 4 f(). 3he straight line ! 4 − is

a tangent to the c$r*e ! 4 f().

Compiled by Mr. SimKY Page 1



(a) ;rite the e7$ation of the ais of

s!mmetr! of the c$r*e.

(#) <"ress f() in the form ( #)2

c, where # and c are constants.

2. P% 2006 P1 Q$

ind the range of the *al$es of for

(2 5 1)( ) 9 .

/ = −, 9 1

+. P% 200 P1 Q$ 6

&iagram 2 shows the gra"h of a 7$adratic

f$nction f() 4 +( ")2 2, where " is a

constant.

3he c$r*e ! 4 f() has a minim$m "oint

(1, 7), where 7 is a constant.tate

(a) the *al$e of ",

(#) the *al$e of 7,

(c) the e7$ation of the ais of s!mmetr!.

CHAPTER 4: SIMULTANEOUS

EQUATIONS

1. P% 2006 P2 Q$1

ol*e the sim$ltaneo$s e7$ations 2 ! 4

1 and 22 !2 ! 4 . :i*e !o$r answer

correct to three decimal "laces.

/−0.68+, 1.+

2. P% 200 P2 Q$ 1

ol*e the sim$ltaneo$s e7$ations ! 4

1 and !2 5 10 4 2.

/ 4 +, ! 4 −> 41

2− , ! 4 +

CHAPTER 5: INDICES AND LOGARITHM

1. P% 2006 P1 Q$ 6

ol*e the e7$ation 2 5 + 42

1

x+ .

/ 4 1

2. P% 2006 P1 Q$?

:i*en that log2! 4 2 +log2 5 log2!,

e"ress ! in terms of .

/! 4 2

+. P% 2006 P1 Q$

ol*e the e7$ation 2 log+ ( 5 1) 4 log+ .

/ 48

. P% 200 P1 Q$ ?

ol*e the e7$ation 2 5 2 + 4 1

/+

. P% 200 P1 Q$

ol*e the e7$ation log+ 5 log+((2 5 1) 4

1

/ +2

6. P% 200 P1 Q$ 8

:i*en logm 2 4 " and logm + 4 r, e"ress

logm

2?

m ÷

in terms of " and r.

/+r 5 2" 1

CHAPTER 6: COORDINATES

GEOMETRY

1. P% 2006 P1 Q$ 12&iagram shows the straight line AB

which is "er"endic$lar to the straight line

@B at the "oint B.




3he e7$ation of the straight line @B is ! 4

2 5 1.

ind the coordinates of B.

/(2, +)

2. P% 2006 P2 Q$ 8&iagram + shows the triangle AB where

is the origin. Point @ lies on the straight

line AB.

(a) @alc$late the area, in $nit2, of triangle

AB.

(#) :i*en that A@ ' @B 4 + ' 2 find the

coordinates of @.(c) A "oint P mo*es s$ch that its distancefrom "oint A is alwa!s twice its

distance from "oint B.

(i) ind the e7$ation of the loc$s of

P.(ii) ence, determine whether or not

this loc$s intersects the !ais.

/(a) 8 $nit2 (#) @ 12 2

,

÷

(c) (i) 2 !2 5

1 ! 4 0 (ii) no

+. P% 200 P1 Q$ 13he following information refers to the

e7$ations of two straight lines, CD and E3,which are "er"endic$lar to each other.

CD' ! 4 " F

E3' ! 4 (F 5 2) "

;here " and F are constants.<"ress " in terms of F.

/" 41

2k −

−

. P% 200 P2 QU8

In the diagram #elow, ∠AB@ 4 80o and the

e7$ation of straight line B@ is 2! 6 40.

(a) ind

(i) the e7$ation of the straight line

AB,

(ii) the coordinates of B.

(#) 3he straight line AB is etended to a

"oint & s$ch that AB ' B& 4 2 ' +.

ind the coordinates of &.

(c) A "oint P mo*es s$ch that its distance

from "oint A is alwa!s $nits. ind

the e7$ation of the loc$s of P.

/(a) ! 4 2 1? (#) (1, 11) (c) 2 !2

5 1! ?2 4 0

CHAPTER 7: STATISTICS

1. P% 2006 P1 Q$ 2A set of "ositi*e integers consists of 2,

and m. 3he *ariance of the set of integers is

1.

ind the *al$e of m.

/11

2. P% 2006 P2 Q$ 6

3a#le 2 shows the fre7$enc! distri#$tion of

the scores of a gro$" of "$"ils in a game.

core G$m#er of "$"ils

10 5 18 1

20 5 28 2+0 5 +8

0 5 8 12

0 5 8 D

60 − 68 1

(a) It is gi*en that the median score of thedistri#$tion is 2, calc$late the *al$e

of F.




(#) Using a scale of 2 cm to 10 scores on

the hori-ontal ais and 2 cm to 2

"$"ils on the *ertical ais, draw a

histogram to re"resent the fre7$enc!

distri#$tion of the scores.ind the mode score.

(c) ;hat is the mode score if the score ofeach "$"il is increased #! H

/(a) F 4 (#) mode score 4 + (c)

+. P% 200 P1 Q$ 2+

3he mean of fo$r n$m#ers is . 3he s$m

of the s7$ares of the n$m#ers is 100 and the

standard de*iation is +F.

<"ress m in terms of F.

/m 4 2 5 8F 2

. P% 200 P2 QU 3he diagram is a histogram which

re"resents the distri#$tion of the marFs

o#tained #! 0 "$"ils in a test.

(a) ;itho$t $sing an ogi*e, calc$late the

median marF.

(#) @alc$late the standard de*iation of the

distri#$tion.

/(a) 2.0? (#) 11.?

CHAPTER 8: CIRCULAR MEASURE

1. P% 200 P1 QU 1

3he digram #elow shows a circle with

centre .

3he length of the minor arc AB is 16 cm

and the angle of the maor sector AB is

280o.

Using π 4 +.12, find

(a) the *al$e of θ, in radians,

(:i*e !o$r answer correct to fo$r

significant fig$res.)

(#) the length, in cm, of the radi$s of the

circle.

/(a) 1.222 rad (#) 1+.08 cm

2. P% 200 P2 QU 10

3he fig$re #elow shows a sector PQ of a

circle, centre . 3he "oint A lies on P, the

"oint B lies on Q and AB is "er"endic$lar

to Q. 3he length of A 4 cm and

∠PQ 4

6

π

radian.

It is gi*en that A ' P 4 ' ?.

(Use π 4 +.12)

@alc$late(a) the length, in cm, of AP,

(#) the "erimeter, in cm, of the shaded

region,

(c) the area, in cm2, of the shaded region.

/(a) 6 cm (#) 2.0 cm (c) +?.6

cm2

+. P% 2006 P1 QU 163he diagram shows sector AB with centre

and sector AJK with centre A.








!ear 2001 if the cost in the !ear 200

was E%28.

(c) 3he cost of maFing these #isc$its is

e"ected to increase #! 0M from the

!ear 200 to the !ear 200?.

ind the e"ected com"osite inde forthe !ear 200? #ased on the !ear 2001.

/(a) 4 12 ! 4 2.0 - 4 0.0 (#) (i)

128. (ii) E%2+06.08 (c) 18.16




2. P% 2006 P2 QU 1

A "artic$lar Find of caFe is made #! $sing

fo$r ingredients, P, Q, E and . 3he ta#le

shows the "rices of the ingredients.

Ingredient Price "er Filogram (E%)

Kear 200 Kear 200

P .00 w

Q 2.0 .00

E !

.00 .0

(a) 3he inde n$m#er of ingredient P in the

!ear 200 #ased on the !ear 200 is

120.

@alc$late the *al$e of w.

(a) 3he inde n$m#er of ingredient E in

the !ear 200 #ased on the !ear 200 is

12. 3he "rice "er Filogram of

ingredient E in the !ear 200 is

E%2.00 more than its corres"onding

"rice in the !ear 200.

@alc$late the *al$e of and !.

(c) 3he com"osite inde for the cost of

maFing the caFe in the !ear 200 #ased

on the !ear 200 is 12?..

@alc$late

(i) the "rice of a caFe in the !ear 200if its corres"onding "rice in the !ear

200 is E%+0.60.

(ii) the *al$e of m if the 7$antities of

ingredients P, Q, E and $sed are in

the ratio of ? ' + ' m ' 2.

/(a) 6.00 (#) 4 , ! 4 10 (c) (i) E%2.00 (ii)


Documents

ANALYSIS OF SPM QUESTIONS FORM 4.doc