Add Maths F4 Mid-Term Examination (BL)

50/2SULIT

3472/1

NAMA: _______________________________________________ TINGKATAN: ______________

MID-TERM EXAMINATION (Chapter 1 to Chapter 5)

PEPERIKSAAN PERTENGAHAN PENGGAL (Bab 1 hingga Bab 5)

[80 marks / 80 markah]

This question paper consists of 25 questions. Answer all the questions. Give only one answer for each question. Write your answers clearly in the spaces provided. Show your working. It may help you to get marks. You may use a non-programmable scientific calculator.Kertas soalan ini mengandungi 25 soalan. Jawab semua soalan. Berikan satu jawapan sahaja bagi setiap soalan. Tulis jawapan anda dalam ruang yang disediakan. Tunjukkan langkah-langkah penting dalam kerja mengira anda. Ini boleh membantu anda mendapat markah. Anda dibenarkan menggunakan kalkulator saintifik yang tidak boleh diprogramkan.

1Diagram 1 shows the relation between set M and set N.

Rajah 1 menunjukkan hubungan antara set M dan set N.

Diagram 1 Rajah 1

State

Nyatakan

(a)the codomain of the relation.

kodomain bagi hubungan itu.

(b)the type of the relation.

jenis hubungan itu.


Answer/Jawapan:

2Given f(x) = 2x 5, find the value of q if f(q) = q.

Diberi f(x) = 2x 5, cari nilai q jika f(q) = q.


Answer/Jawapan:

3Diagram 2 shows an arrow diagram representing the function f : x where m and n are constants.

Rajah 2 menunjukkan suatu gambar rajah anak panah yang mewakili fungsi f : x di mana m dan n ialah pemalar.

Diagram 2 Rajah 2

Find the value of

Cari nilai

(a)m

(b)n


Answer/Jawapan:

4Given the functions f : x x 1 and g : x , find

Diberi fungsi f : x x 1 dan g : x , cari

(a)the composite function gf,

fungsi gabungan gf,

(b)the value of x if gf(x) = 9.

nilai x jika gf(x) = 9.


Answer/Jawapan:

5Given the functions f : x 2 x and g : x 4x2 + 1, find the value of x if gf = fg.

Diberi fungsi : x 2 x dan g : x 4x2 + 1, cari nilai x jika gf = fg.


Answer/Jawapan:

6Given the function f : x 5x + 3, find the value of x if f = f 1.

Diberi fungsi f : x 5x + 3, cari nilai x jika f = f 1.


Answer/Jawapan:

7It is given that x = is one of the roots of the quadratic equation 2x2 3x + 1 = 0. Find the value of another root.

Diberi bahawa x = ialah satu daripada punca persamaan kuadratik 2x2 3x + 1 = 0. Cari punca yang satu lagi.


Answer/Jawapan:

8Form a quadratic equation which has the roots of x = 3p and x = p in the form of ax2 + bx + c = 0, where a, b, and c are constants. Then, find the values of p if f(x) = ax2 + bx + c = 27 at the y-axis.

Bentukkan satu persamaan kuadratik yang mempunyai punca x = 3p dan x = p dalam bentuk ax2 + bx + c = 0, dengan keadaan a, b, dan c adalah pemalar. Kemudian, cari nilai p jika f(x) = ax2 + bx + c = 27 pada paksi-y.


Answer/Jawapan:

9It is given that the straight line y = c 4x does not intersect the curve xy = 16. Find the range of c.

Diberi bahawa garis lurus y = c 4x tidak bersilang dengan lengkung xy = 16. Cari nilai c.


Answer/Jawapan:

10Calculate the value of k for which the line y = 5(x + 2) is a tangent to the curve y = x2 3x + k.

Hitungkan nilai k bagi garis y = 5(x + 2) ialah tangen kepada lengkung y = x2 3x + k.


Answer/Jawapan:

11The curve y2 = p(x2 1) meets the straight line y = 3 only at one point. Find the negative value of p.

Lengkung y2 = p(x2 1) bertemu dengan garis lurus pada satu titik sahaja. Cari nilai negatif bagi p.


Answer/Jawapan:

12The quadratic equation 4x + c = 16 (2 x)2 has two equal roots. Find the value of c.

Persamaan kuadratik 4x + c = 16 (2 x)2 mempunyai dua punca yang sama. Cari nilai c.


Answer/Jawapan:

13The curve y = 2x2 + 2tx + 3t 4 touches the x-axis at the values of t = a and t = b, where a < b. Find the values of a and b.

Lengkung y = 2x2 + 2tx + 3t 4 menyentuh paksi- x pada nilai t = a dan nilai t = b, dengan keadaan a < b. Cari nilai a dan b.


Answer/Jawapan:

14Find the range of values of k for which the line y = kx + 2 does not intersect the curve x2 + y2 = 2.

Cari julat nilai x dengan keadaan garis y = kx + 2 tidak bersilang dengan lengkung x2 + y2 = 2.


Answer/Jawapan:

15Find the range of values of k for which the line y + 4(kx + 1) = 0 meets the curve y = 2x2 + 7k.

Cari julat nilai k bagi garis y + 4(kx + 1) = 0 bertemu dengan lengkung y = 2x2 + 7k.


Answer/Jawapan:

16Solve the following simultaneous equations:

Selesaikan persamaan serentak yang berikut:

x = y + 1

(x y) y = 1


Answer/Jawapan:

17Solve the simultaneous equations y = 4x 1 and (x + 1)(y + 2) = 0.

Selesaikan persamaan serentak y = 4x 1 dan (x + 1)(y + 2) = 0.


Answer/Jawapan:


Selesaikan persamaan serentak berikut:

y= 2x

y2= 4x 1


Answer/Jawapan:

19Solve the simultaneous equations x y = 1 and x2 + y2 = 25.

Selesaikan persamaan serentak x y = 1 dan x2 + y2 = 25.


Answer/Jawapan:



x + 1= 2y

x2 + xy 26= 0


Answer/Jawapan:



2 log10 x= log10 (x + y)

x y= 0


Answer/Jawapan:

22Solve the equation 8x . 21 x = 321 + 2x.

Selesaikan persamaan 8x . 21 x = 321 + 2x.


Answer/Jawapan:

23Given that log3 x + 1 = 2 log9 (x + y), prove that 8x2 2xy y2 = 0.

Diberi bahawa log3 x + 1 = 2 log9 (x + y), buktikan bahawa 8x2 2xy y2 = 0.


Answer/Jawapan:

24Solve the equation log2 (5x + 2) + log2 (x 1) = 2 + log2 (1 4x).

Selesaikan persamaan log2 (5x + 2) + log2 (x 1) = 2 + log2 (1 4x).


Answer/Jawapan:

25Given that y = kxm 3 where k and m are constants. Find the values of k and m if y = 24 when x = 3 and y = 240 when x = 9.

Diberi bahawa y = kxm 3 dengan keadaan k dan m ialah pemalar. Cari nilai bagi k dan m jika y = 24 apabila x = 3 dan y = 240 apabila x = 9.


Answer/Jawapan:

1Given the function f : x 2x + 5 and g : x , x 1, find g 1 f 1.

Diberi fungsi f : x 2x + 5 dan g : x , x 1, cari g 1 f 1.


2It is given that f(x) = 0 is a quadratic equation which has the roots 4 and p.

Diberi bahawa f(x) = 0 ialah satu persamaan kuadratik yang mempunyai punca 4 dan p.

(a)Write f(x) in the form of ax2 + bx + c.

Tuliskan f(x) dalam bentuk ax2 + bx + c.

(b)The curve ky = f(x) passes through the y-axis at the point (0, 24). Given that p = 2, calculate the value of k.

Lengkung ky = f(x) melalui paksi-y pada titik (0, 24). Diberi bahawa p = 2, hitungkan nilai k.


3The quadratic equation px2 + 5qx + 25p = 0 has two equal roots.

Persamaan kuadratik px2 + 5qx + 25p = 0 mempunyai dua punca yang sama.

(a)Find the ratio p : q where p and q have positive values.

Cari nisbah p : q dengan keadaan p dan q mempunyai nilai positif.

(b)Solve the equation with p : q found in (a).

Selesaikan persamaan itu dengan p : q yang dicari di (a).


4It is given that point T(1, 5) is a point on the curve f(x) = (px 2)2 + 4, where p > 1.

Diberi bahawa titik T(1, 5) ialah satu titik pada lengkung f(x) = (px 2)2 + 4, dengan keadaan p > 1.

(a)Find the value of p.

Cari nilai p.

(b)Use the value of p obtained in (a), find the range of values of k if the equation f(x) = k has two different roots.

Dengan menggunakan nilai p yang diperoleh di (a), cari julat nilai k jika persamaan f(x) = k mempunyai dua punca yang berbeza.


5Given that is the solution of the simultaneous equations x2 + y2 = 5 and x y = 3, find the values of p and q.

Diberi bahawa ialah penyelesaian bagi persamaan serentak x2 + y2 = 5 dan x y = 3, cari nilai p dan q.




1 + log2 (x2 + 2y2)= log2 18

2 + log2 y= log2 (9 + x)


7(a)Given the function f : x 5 ax and f 1 (1) = a, find the values of a.

Diberikan fungsi f : x 5 ax dan f 1 (1) = a, cari nilai a.

(b)Given the functions f : x , x 2 and g : x 5 + 2x. Find

Diberikan fungsi f: x , x 2 dan g: x 5 + 2x. Cari

(i)f 1(x)

(ii)the value of x such that gf(x) = 5.

nilai x dengan keadaan gf(x) = 5.


8(a)Find the value of k for which the line 3y + kx = 6 is a tangent to the curve x2 + xy = 3.

Cari nilai k bagi garis 3y + kx = 6 yang merupakan tangen kepada lengkung x2 + xy = 3.

(b)Show that the line y + 2x = p will intersect the curve x2 + xy 5y = 12 at two different points if p2 + 52 > 0.

Tunjukkan garis y + 2x = p bersilang dengan lengkung x2 + xy 5y = 12 pada dua titik berlainan jika p2 + 52 > 0.


9(a)Find the range of values of m for which the line y = mx + 4 does not meet the curve xy 5x2 = 4.

Cari julat nilai m bagi garis y = mx + 4 yang tidak bertemu dengan lengkung xy 5x2 = 4.

(b)It is given that one of the roots of equation (3x 9)(x 6) + p = 0 is half of the another root. Find the value of p.

Diberi bahawa salah satu punca persamaan (3x 9)(x 6) + p = 0 adalah setengah daripada punca yang satu lagi. Cari nilai p.


10Diagram 1 shows the curve y = px2 + qx + r which passes through the origin dan point A(3, 12). Given that pq = 15, calculate the values of p, q, and r. Then, find the values of x when y = 0.

Rajah 1 menunjukkan lengkung y = px2 + qx + r yang melalui titik asalan dan titik A(3, 12). Diberi bahawa pq = 15, hitungkan nilai-nilai p, q, dan r. Kemudian, cari nilai x apabila y = 0.

Diagram 1 Rajah 1


11(a)Given that log5 2 = 0.43 and log5 3 = 0.68, find the value of log5 1.5 without using a calculator.

Diberi bahawa log5 2 = 0.43 dan log5 3 = 0.68, cari nilai log5 1.5 tanpa menggunakan kalkulator.

(b)Simplify + 2(5n).

Permudahkan + 2(5n).

(c)Given that log2 xy2 = 4 log2 x, express y in terms of x. If y + 16x = 16, find the values of x and of y.

Diberi bahawa log2 xy2 = 4 log2 x, ungkapkan y dalam sebutan x. Jika y + 16x = 16, cari nilai x dan y.


12The function h is defined as h : x a , x 0. Given that h(1) = 9 and h(2) = 3.

Fungsi h ditakrif sebagai h: x a , x 0. Diberi bahawa h(1) = 9 dan h(2) = 3

(a)Find the values of a and b.

Cari nilai a dan nilai b.

(b)Evaluate h1(1).

Nilaikan h1(1).

(c)Find the composite functions h1h and h2.

Cari fungsi gubahan h1h dan h2.


13(a)Find the range of values of c for which the equation 4cx2 + 7x + c = 0 has real roots.

Cari julat nilai c bagi persamaan 4cx2 + 7x + c = 0 mempunyai punca nyata.

(b)Determine the value of p for which the straight line y = p(4x 1) is a tangent to the curve y = 16x2 + 3.

Tentukan nilai p bagi garis lurus y = p(4x 1) adalah tangen kepada lengkung y = 16x2 + 3.


14(a)Solve the following simultaneous equations:


2x + 3y= 1

3x2 + 4xy y2 6= 0

(b)Find the coordinates of the intersection points of the curve = 10 and the line x + y = 1.

Cari koordinat titik persilangan bagi lengkung = 10 dan garis x + y = 1.


15(a)Find the value of .

Cari nilai bagi .

(b)Given that x = log5 p is the solution of the equation 52x + 1 + 10 = 51 (5x), find the value of p.

Diberi bahawa x = log5 p ialah penyelesaian bagi persamaan 52x + 1 + 10 = 51(5x), cari nilai p.


PAPER 2

KERTAS 2

3472/2

Time: Two hours and thirty minutes

Masa: Dua jam tiga puluh minit

This question paper consists of three sections: Section A, Section B and Section C. Answer all the questions in Section A, four questions from Section B and two questions from Section C. Give only one answer/solution for each question. All the working steps must be written clearly.

Kertas soalan ini mengandungi tiga bahagian: Bahagian A, Bahagian B dan Bahagian C. Jawab semua soalan dalam Bahagian A, empat soalan daripada Bahagian B dan dua soalan daripada Bahagian C. Jawapan anda hendaklah ditulis pada ruang yang disediakan dalam kertas soalan ini. Langkah-langkah kerja mesti ditulis dengan jelas. Berikan hanya satu jawapan/penelesaian bagi setiap soalan. Semua langkah kerja mesti ditulis dengan jelas. Anda dibenarkan menggunakan kalkulator saintifik yang tidak boleh diprogramkan.

Section A Bahagian A


Section B Bahagian B


Section C Bahagian C


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Add Maths F4 Mid-Term Examination (BL)

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