2ulangkaji T4 QE&QF

8/13/2019 2ulangkaji T4 QE&QF

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TUISYEN KITA | cgnashPENCETUS BIJAK MATEMATIK

Ulangkaji Mat Tam T4 Quadratic Equation & Quadratic Function

demo suka matematik, kawe suka matematik, kita suka matematik

(3,0)

(0,9) = ()

PAPER1QUADRATIC EQUATIONS &

QUADRATIC FUNCTIONS

1. Solve the quadratic equation = ( )

Give your answer correct to three decimal places.

Selesaikan persamaan kuadratik = ( ) Berikan jawapan anda betul kepada tiga tempat

perpuluhan

(Answers/Jawapan : = 33,03)

2. Solve the quadratic equation( ) = 3 0

Selesaikan persamaan kuadratik

( ) = 3 0 (Answers/Jawapan : = , )

3. A quadratic equation 3 = hastwo equal roots. Find the possible values ofp.

Suatu persamaan kuadratik 3 = mempunyai dua punca sama. Cari nilai-nilai p yang

mungkin.

(Answers/Jawapan : = , )

4. A quadratic equation = 9has twoequal roots. Find the possible values ofp.

Suatu persamaan kuadratik

= 9

mempunyai dua punca sama.Cari nilai-nilai p yangmungkin.

(Answers/Jawapan : = , )

5. (a) Solve the following quadratic equation:Selesaikan persamaan kuadratik berikut :

3 = 0(b) The quadratic equation = 0,

where hand k are constants, has two equal roots.

Express hin the terms of k.

Persamaan kuadratik

= 0, dengankeadaan h dan k ialah pemalar, mempunyai duapunca sama. Ungkapkan h dalam sebutan k.

(Answers/Jawapan : (a) = , () =

()

)

6. (a) Solve the following quadratic equation:Selesaikan persamaan kuadratik berikut:

3 0 = 0

(b) The quadratic equation = 0 ,wherem , nand rare constants, has two equal roots.Express nin the terms of mand r.

Persamaan kudratik = 0 ,dengankeadaan m , n dan r ialah pemalar, mempunyai dua

punca sama.Ungkapkan n dalam sebutan m dan r.

(Answers/Jawapan : (a) = , () = )

7. It is given that is one of the roots of thequadratic equation 3 = 0 Find the value ofp.

Diberi bahawa ialah satu daripada puncapersamaan kuadratik 3 = 0 Cari nilai p.

(Answers/Jawapan : p=10)

8. Given is one of the roots of the quadraticequation 3 = 0 Find the value of m.

Diberi bahawa ialah satu daripada puncapersamaan kuadratik

3 = 0 Cari nilai m.(Answers/Jawapan : m=2)

9. The quadratic equation = , wherepis a constant, has two different roots. Find the range

of values ofp.

Persamaan kuadratik = , dengankeadaan p ialah pemalar, mempunyai dua punca yang

berbeza. Cari julat nilai p.

(Answers/Jawapan : )

10. The quadratic equation ( 3) = has two distinct roots. Find the range of value of k.

Persamaan kuadratik ( 3) = mempunyai dua punca yang berbeza. Cari julat nilai

k.

(Answers/Jawapan : )

11. Diagram 1 shows the graph of a quadraticfunction() = ( ) ,wherep and qareconstant.Rajah 1 menunjukkan graf fungsi kuadratik

() = ( ) ,dengan keadaan p dan qialah pemalar.


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=()

=

State

Nyatakan

(a)The value ofp,Nilai p,

(b)The equation of the axis of symmetry.Persamaan paksi simetri.(Answers/Jawapan : (a) = 3 () = 3)

12. Diagram 2 shows the graph of quadraticfunction() = 3 ( ) , wherepis a constant.

Rajah 2 menunjukkan graf kuadratik

() = 3 ( ) , dengan keadaan p ialahpemalar.

The curve = ( )has the minimum point, where qis a constant. State

Lengkung = ( )mempunyai titik minimum (,),dengan keadaan q ialah pemalar.

Nyatakan

(a)The value ofp,Nilai p,

(b)The value of q,Nilai q,

(c) the equation of the axis of symmetry.

Persamaan paksi simetri.

(Jawapan : = () = () = )

13. Diagram 3 shows the graph of a quadraticfunction = ( ). The straight line = 3is atangent to the curve = ( ).

Rajah 3 menunjukkan suatu graf fungsi kuadratik

= ( ). Garis lurus = 3ialah tangent kepadalengkung = ( ).

(a)Write the equation of the axis of symmetry of thecurve.

Tulis persamaan paksi simetri lengkung itu.

(b)Express()in the form ( ) , wherepand q are constant.

Ungkapkan()dalam bentuk ( ) , dengankeadaan p dan q ialah pemalar.(Answers/Jawapan : (a) = 3

()() = ( 3 ) )

14. Diagram 4 shows the graph of the function() = ( ) , where his a constant. FindRajah 4 menunjukkan graf kuadratik

() = ( ) , dengan keadaan h ialahpemalar. Cari

(a)The value of h,Nilai h,

(b)The maximum value of(),Nilai maksimum bagi(),(c)The axis of symmetry.Persamaan paksi simetri.

(Answers/Jawapan :

(a) = () = () = )

15. Diagram 5 shows the graph of the function = ( ) , where kis a constant.

Rajah 5 menunjukkan graf bagi fungsi

= ( ) , dengan keadaan k ialahpemalar.

(,)

=()

Diagram 2

Rajah 2


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Find

Carikan

(a)The value of k,Nilai k,

(b)The equation of the axis of symmetry,Persamaan paksi simetr

(c) the coordinate of the maximum point.Koordinat titik maksimum.

(Answers/Jawapan : (a) = () = () (,)

16. Diagram 6 shows that the graph of the function = ( ) ,wherepand qare constants. Find

Rajah 6 menunjukkan graf bagi fungsi

= ( ) ,dengan keadaan p dan q ialahpemalar. Carikan

(a)The value ofpand q,Nilai p dan q,

(b)The equation of the axis of symmetry,Persamaan paksi simetri,

(c) the minimum value ofy.

Nilai minimum bagi y.

(Answers/Jawapan :

() = 3 = () =3 () =

17. The quadratic function() = can be expressed in the form of

() = ( ) ,where hand kare constants.Find the value of hand of k.

Fungsi kuadratik() = bolehdiungkapkan dalam bentuk

() = ( ) ,carikan nilai h dan nilai k.(Answers/Jawapan : = = )

18. The quadratic function() = ( ) ,where a, b and care constants, has a minimum valueof The equation of the axis of symmetry is = 3

Fungsi kuadratik() = ( ) ,dengankeadaan a, b dan c ialah pemalar, mempunyai nilai

minimum . Persamaan paksi simetrinya ialah = 3 State

Nyatakan

(a) The range of values of a,Julat nilai a,

(b)The value of b,Nilai b,

(c)The value of c.Nilai c.

(Answers/Jawapan : () 0() = 3 () = )

19. If the maximum value of() = is 3, find the value ofp.

Jika nilai maksimum bagi fungsi() = ,ialah 3, cari nilai p.(Answers/Jawapan :

= )

20. Given that the quadratic function() = = ( ) ,where mand nare constants. Find the value of mand of n.

Diberi fungsi kuadratik

() = = ( ) ,dengankeadaan m dan n ialah pemalar. Carikan nilai m dan

nilai n.

(Answers/Jawapan : = , = )

21. The quadratic function() = ,where kis a constant has maximum value 8. Find the

values of k.

Fungsi kuadratik() = ,dengankeadaan k ialah pemalar, mempunyai nilai maksimum

8. Cari nilai-nilai yang mungkin bagi k.

(Answers/Jawapan : = )

22. Find the range of values ofxfor which ( ) .

Cari julat nilai x bagi ( ) .(Answesr/Jawapan : )

3 (,3)


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PAPER 2

1. The quadratic equation = 0has rootsand , where

Persamaan kuadratik = 0mempunyaipunca-punca dan , dengan keadaan (a)

FindCari

(i)The value of and ,Nilai dan ,(ii) The range ofxif 0 Julat nilaixjika 0 (b)Using the values of and from 2(a)(i), form thequadratic equation which roots and 3

Menggunakan nilai dan dari 2(a)(i), bentukkanpersamaan kuadratik yang mempunyai punca-punca

dan 3 (()() = 3 = () 3 () 9 0 = 0)

2. (a) Form the quadratic equation which has theroots 3 and Give the answer in the general form.

Bentukkan persamaan kuadratik yang mempunyai

punca-punca 3 dan Berikan jawapan dalam bentuk am.

(b) Given

and

are the roots of the quadratic

equation = 0 StateDiberi ialah punca-punca persamaankuadratik = 0 Nyatakan(i) The value of

Nilai (ii) The value of

Nilai(c ) Express() = in the form of

() = ( ) ,where , and areconstants.

Nyatakan() = dalam bentuk() = ( ) ,dengan keadaan a, p dan qialah pemalar.

(() 3 = 0 ()() = () = ()() = ( )

)3. Diagram 1 shows the curve of a quadratic function

() = The curve has a maximum

point at (,)and intersects that() atpointA.Rajah 1 menunjukkan lengkung bagi fungsi kuadratik

() = Lengkung itu mempunyai titik

maksimum pada (,)dan memotong paksi()pada titik A.

(a) State the coordinates ofA.Nyatakan koordinat A.

By using the method of completing the square, find

the value of hand ofp

Dengan menggunakan kaedah penyempurnaan kuasa

dua, cari nilai h dan nilai p.

(c) Determine the range of values ofx, if() Tentukan julat nilai x, jika() )(()(0,) () = = () 0 )4. Given that() = hasminimum value of 6,

Diberi fungsi kuadratik() = ,mempunyai nilai minimum 6,

(a) Find the possible values of kby completing thesquare,

Cari nilai-nilai k yang mungkin dengan kaedah

penyempurnaan kuasa dua,

(b) State the equation of the axis of symmetry,Nyatakan persamaan paksi simetri,

(() = 3 () = = 3)5. The quadratic function() = 3 has a minimum value of

Persamaan kuadratik() = 3 mempunyai nilai minimum (a) By using completing the square , determine thevalues of m.

Menggunakan kaedah penyempurnaan kuasa dua,

cari nilai-nilai m.

(b) State the minimum points.Nyatakan koordinat-koordinat minimum.

(() = , () ,, (3,))

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2ulangkaji T4 QE&QF