module kertas 1(halus)

7/27/2019 Module Kertas 1(Halus)..

1/15

Kamu hanya perlu 20 markah untuk LULUS! (

).

PAPER 1Topik Bilangan Soalan Markah Topik Bilangan Soalan Markah

Function 3 9 Progression 3 9

Quadratic Equation 1 3 Linear Law 1 1

QuadraticFunctions

2 6 Integration 1 3

Indices & Log 3 9 Vectors 2 6

CoordinateGeometry

1 3 TrigonometricFunctions

1 3

Statistics 1 3 Permutations &Combinations

1 3

Circular Measures 2 6 Probability 1 3

Differentiation 1 1 ProbabilityDistribution

1 3

Pelajar hanya perlu dapatkan 30 markah daripada 80 markah. Pilihlah topic-topik yang dirasakan senang bagi pelajar. Kalau cukup latihtubi

pelajar akan perasan konsep yang ditanya adalah lebih kurang sama. Selepas membuat latihtubi topical, pelajar boleh di beri set lengkap supaya mereka dapat

dilatih mengenal soalan yang mereka boleh jawab.

Markah keseluruhan =(

)= (

) = 37%....lebih dari cukup untuk lulus!


2/15

Module Kertas 1 : Fungsi Bahagian I

1.

Based on the above information, the relation between Pand Q isdefined by the set of ordered pairs {(1,2), (1,4), (2,6), (2,8)}Berdasarkan maklumat di atas, hubungan P dan Q di definasikan olehSet pasangan tertib {(1,2), (1,4), (2,6), (2,8)}State/Nyata

a) the image of 1imej bagi 1

b) the object of 2objek bagi 2

[ a)2 or 4 b) 1 ][2marks]

2. Diagram shows the relation between set Pand set Q.Diagram menunjukkan hubungan set P dan Q

State/Nyataa) the range of the relation,

julat hubunganb) the type of the relation.

Jenis hubungan

[a) {x,y} b) Many to one ] [2marks]

3. Diagram shows function h mapsxto yand the function gmaps ytoz.Rajah menunjukkan fungsi h memetakan x ke y dan fungsi gMemetakan y ke z.

Determinea) h

-1(5)

b) gh (2)

[a) 2 b) 8] [2marks]

4. Diagram shows the linear function h.Rajah menunjukkan fungsi h

a) state the value of m.nyatakan nilai m

b) Using the function notation, express h in terms ofx.Nyatakan h dalam sebutan x.

[a)m = 3 b) 1: xxh ] [2 marks]

P = {1, 2, 3}Q = { 2, 4, 6, 8, 10} d

e

f

w x y z

SetP Set Q

2

5

8

h yx z

0

1

m

5

1

2

4

6

x h x


3/15

5.Given that g:x 5x + 1and h:x x2 - 2x + 3, find

a) g-1 (3)b) hg (x)

[2/5 ,25x2+ 2]

6.Given the functions h:x 4x + m dan h-1:x 2kx +8

5, where m

and k are constants, find the value of m and of k.

[k = 1/8 ,m = -5/2]

7.The function w is defined as 2,2

5)(

x

xxw

(a) w -1(x)

(b) w -1(4)

0,52

xx

x,

8.The following information refers to the functions h and g .

Find gh -1(x)

2x+5

h:x 2x 3

g:x

4x

1


4/15

Module Kertas 1 : Persamaan kuadratik

1. Solve the quadratic equation 12)52( xxx .

Give your answer correct to three decimal places.

Selesaikan persamaan kuadratik 12)52( xxx .

Berikan jawapan anda betul kepada tiga tempat perpuluhan. [3m]

Answer : 0.149 or 3.351

2. A quadratic equation xpxx 292 has two equal root. Find the

possible values ofp.

Suatu persamaan kuadratik xpxx 292 mempunyai dua

punca sama. Cari nilai-nilaip yang mungkin. [3m]

Answer :p = -4 or 8

3.The quadratic equation x (x +1) = px4 has two distinct roots.

Find the range of values of p.

p < -3, p > 5

4.It is given that -1 is one of the roots of the quadratic equation

x2 4x p = 0.

Find the value of p.

p = 5

5 The straight line y = 5x1 does not intersect the curve y = 2x2 +

x + p.

Find the range of values of p.

p < 1

6.Solve the following quadratic equation: 3x2 + 5x 2 = 0

2

3

1 orx


5/15

Module Kertas 1 : Fungsi kuadratik

1. Diagram 2 shows the graph y= 4 (xm) , where m is aconstant.Rajah 2 menunjukkan graf y = 4 (x m)2, dengan keadaan madalah pemalar.

Find/ Carikan(a)the value of m,

nilai bagi m,(b) the equation of the axis symmetry,

persamaan paksi simetri,(c)the coordinates of the maximum point

koordinat titik maksimum. [3m]

[ m = 3, x= 3, ( 3, - 4 )]

2.Diagram 2 shows the graph of a quadratic functions

f(x) = 3 (x + p)2 + 2, where p is a constant.

The curve y = f(x) has the minimum point (1, q ) , where q is a

constant. State(a) the value of p,

(b) the value of q,(c) the equation of the axis of symmetry. [3m]

[-1, 2, x = 1]

3.The quadratic function f(x) = p(x+ q)2 +r, where p, q and rare constants, has a minimum value of 4.

The equation of the axis of symmetry is x = 3.State

a) the range of values of p,

b) the value of q,

c) the value of r.

[p > 0 ,q = - 3 ,r= - 4]

4.Find the range of values of x for which x(x4) 12.

62 x

6,13

O x

13O

y =f(x)y

x

(1, q )


6/15

Module Kertas 1 :indices and logarithms

1.Solve the equation 32 4x = 4 8x + 6. [3m]

[x=3]

2.Given that log5 2 = m and log5 7 = p, express log5 4.9 in terms of

m and p

2

8

y

p 4 marks

3.Given log 2Tlog4V = 3, express T in term of V.

VT 8

4. Solve the equation 4 2x -1 = 7x.

677.1x


7/15

5. Solve the equation2x

3x2

4

18

[x=1]

6.Given that p2logm and r3logm , express log m

4

m27 in

terms of p andr.

123 pr 4 marks

7. Solve the equation 122 34 .

3x

8. Given a3log 2 and b5log 2 , express 45log8 in terms of

a and b.

3

2 ba


8/15

Progressions

1.The first three terms of an arithmetic progression are :Tiga sebutan pertama janjang aritmetik ialah:

k3, k + 3, 2k + 2.

Find / Cari

(a) k,

(b) the sum of the first 9 terms of the progression

Jumlah 9 sebutan pertama

[k = 7 ,S9 = 252]

2. The first three terms of a sequence are 2, x , 8.Find the positive value of x so that the sequence is

Tiga sebutan pertama suatu janjang ialah 2, x, 8. Cari nilai positif x

supaya janjang ialah

a) an arithmetic progression,

janjang aritmetik

b) a geometric progressionjanjang geometrik

[x = 5,x = 4]

3.The first three terms of an arithmetic progression are 5, 9, 13.

Tiga sebutan pertama suatu janjang aritmetik ialah 5, 9, 13

Find/ Caria) the common difference of the progression,

beza sepunya janjang

b) the sum of the first 20 terms after the 3rd term.Jumlah 20 sebutan pertama selepas sebutan ke 3

[d = 4 ,1100]

4. Three consecutive terms of an arithmetic progression are :

Tiga sebutan berturut-turut suatu janjang aritmetik ialah:

5x, 8, 2x.Find the common difference of the progression.

Cari beza sepunya janjang.

[x = 11, d = 14]


9/15

5.In a geometric progression, the first term is 64 and the fourth term is 27.

Bagi janjang geometric, sebutan pertama ialah 64 dan sebutan

keempat ialah 27Calculate / Kira

a) the common ratio,

nisbah sepunya

b) the sum to infinity of the geometric progression.

Jumlah ketakterhinggaan janjang geometric

[r = ,Sn = 256]

6.Given a geometric progresssion :

Di beri suatu janjang geometric : ....,4

,2, py

y

Express p in terms of y .Nyatakan p dalam sebutan y.

2

8

yp

7.The first three terms of a geometric progression are 27, 18, 12.Find the sum to infinity of the geometric progression.

Tiga sebutan pertama suatu janjang geometric ialah 27, 18, 12.

Jumlah ketakterhinggaan janjang geometric

[3

2,27 ra , 81S ]

8.The sum of the first n terms of the geometric progression 8, 24,72 is8744.8Jumlah n sebutan pertama janjang geometric 8,24,72 ialah 8744.

Find/ Cari

a) the common ratio of the progression,nisbah sepunya janjang

b) the value of n.nilai n

[3 , 7]


10/15

Linear Law1.x and y are related by the equation y = px2 + qx, where p and q are

constants. A straight line is obtained by plotting

x

yagainst x, as shown in Diagram 1.

Calculate the values of p and q.

[p=-2, q=13]

2.Diagram 3 shows a straight line graph ofx

y against x..

Given that y = 6xx2, calculate the value of k and of h.

[h=3, k=4]

3. The variablesx and y are related by the equation .2 hkkxhy A

straight line graph is obtained by plotting y againstx 2 as shown in

diagram.

y

(0,6)

x

0Given the gradient of the straight line is 3, find the value of h and of k.

[k=6, h=2]

4. The variables x and y are related by the equationy2 = 2x (10x). A straight line graph is obtained by plotting

x

y 2 against

x, as shown in Diagram 2.

Find the value of p and of q

[p=10,q=14]

x

y

(6, 1)

(2, 9)

Ox

(h, 3)

(2, k)

Ox

x

y

x

y2

( 3, q)

(p, 0)xO


11/15

Module Kertas 1 : Geometri Koordinat

1. The points A(2h , h) , B(p, t) and C(2p, 3t) are on a straightline. B dividesAC internally in the ratio2 : 3.

Express p in terms of t.

tp 2 3 marks

2. The straight line 16

h

yxhas a y-intercept of 2 and is

parallel to the straight line y + kx = 0.

Determine the value of h and of k.

3

1,2 kh 3 marks

3.Diagram 4 shows a straight line PQ with the equation 132

yx.

The point P lies on thex-axis and the point Q lies on the y-axis.

Find the equation of the straight line perpendicular to PQ and

passing through the point Q. [3m]

33

2 xy

4. A straight line passes through A (-2,-5) and B (6,7).a) Given C ( h, 10) lies on the straight line AB.

Find the value of h.

b) Point D divides the line segment AB in the ratio 1: 3.

a) 8 (b) (0, -2)]

P x

y

Q

O


12/15

Module kertas 1 : statistic

1.The mean of four numbers is m . The sum of the squares of the

numbers is 100 and the standard deviation is 3k. Express m in terms of k.

Min bagi empat numbor ialah m . Jumlah kuasa dua nombor-nombor ialah 100dan sishan piawai ialah 3k. Nyatakan m dalam sebutan k.

2925 km 3 marks

2.A set of 12 numbersx 1, x2, x12, has variance of 40 and it is

given that 10802x . FindSuatu set 12 numborx 1, x2, x12, mempunyai varian 40 dan diberi

10802x . Cari

(a) the mean / min : x

(b) x

(a)7.071 (b)84.85 3 marks

4.A set of data consists of 2,3,3,4,5,7 and 9. Determine the interquartile

range of data.

Suatu set data terdiri dari 2,3,3,4,5,7 dan 9. Tentukan julat antara kuartildata.

4 3 marks

5.A set of seven numbers has a mean of 9.

Suatu set tujuh numbor mempunyai min 9.

(a) Find / Cari : x

(b) When a number k is added to this set, the new mean is 8.5.

Find the value of k.Bila satu numbor k di tambah pada set ini, min baru ialah 8.5.

Cari nilai k

(a)63 (b)5 3 marks


13/15

Module kertas 1: Vektor1.Diagram 1 shows two vectors, OP and QO.

Rajah 1menunjukkan dua vector, OP dan QO.

Diagram 2

Express/Nyatakan

a) OP in the form

y

x/ OP dalam bentuk

y

x

b) OQ in the form xi + yj / OQ dalam bentukxi + yj

53 ,-8i +4j

2.

Use the above information to find the values of h and k when :

Guna maklumat di atas untuk mencari nilai-nilai h dan k bila :

r = 3 p2 q.

[h= -2, k= -13]

3.Diagram 3 shows a parallelogram ABCD with BED as a straight line.

Rajah 3 menunjukkan segiempat selari ABCD dengan BED ialah garis

lurus

Diagram 3

Given thatAB = 6p,AD = 4q and DE = 2 EB, express,in terms of p and q :

DiberiAB = 6p,AD = 4q dan DE = 2 EB, nyatakandalam sebutanpdan q :a) BD ,

b) EC.

[-6p + 4 q , 2p +

3

8q]

4. Given that O(0, 0), A(-3, 4) and B(2, 16) , find in terms of the unit

vectors,~i and

~

j .

Diberi O(0, 0), A(-3, 4) dan B(2, 16), cari dalam sebutan vector unit~i dan

~

j .

a) AB ,

b) the unit vector in the direction ofAB

.

512 3

1 512

y

x

P(5, 3) Q(8, 4)

O

p = 2a + 3bq = 4a - b

= +

A B

CD

E


14/15

5.Given that A(-2, 6), B(4, 2) and C(m, p), find the value of m and of psuch that :

Diberi bahawaA(-2, 6), B(4, 2) dan C(m, p),cari nilai m dan p jika:

AB + 2BC = 10~i - 12

~

j

[m= 6, p= -2]

6.Diagram 5 shows a parallelogram , OPQR, drawn on a Cartesian plane.Rajah 5 menunjukkan suatu segiempat selari, OPQR,dilukis pada satah

Kartesan.

Diagram 5

It is given that OP = 6~i + 4

~

j and PQ = 4~i + 5

~

j . Find PR

Diberi bahawa OP = 6~i + 4

~

j dan PQ = 4~i + 5

~

j . Cari PR

10~i +

~

j

7.Diagram 7 shows vector OA drawn on a Cartesian plane.

Rajah 7 menunjukkan OA dilukis pada satah Kartesan

Diagram 7

(a) Express OA in the form

y

x/ nyatakan OA dalam bentuk

y

x

(b) Find the unit vector in the direction of OA.

Cari vector unit dalam arah OA

12

5 ,131

12

5

8.Diagram 8 shows a rectangle OABC and the point D lies on the

straight line OB.

Rajah 8 menunjukkan suatu segiempat OABC dan titik D terletak atas

garis lurus OB

It is given that OD = 3 DB. Express OD , in terms of x and y .

Diberi OD=3DB. Nyatakan OD , dalam sebutan x dan y .

yx415

427

A

x

y

12O 108642

6

4

2

x

R

Q

P

O

y

BC

A

D

O

9x

5 y


15/15

Cadangan :Setelah membuat set-set topical, guna set lengkap P1 atauP2. Latih pelajar kenal soalan-soalan yang perlu di jawab.

module kertas 1(halus)

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