The document contains a 14 question mathematics assessment for Form 4 students. It covers topics including functions, graphs of quadratic functions, solving quadratic equations and simultaneous equations. Students are instructed to answer all questions within the time limit of 1 hour and 30 minutes. The questions range from 3 to 5 marks each and cover skills such as finding function values, determining function types, solving quadratic equations, sketching graphs and solving simultaneous equations.

1. PENILAIAN KURIKULUM SATU 2018
MATEMATIK TAMBAHAN
TINGKATAN EMPAT
MASA : 1 JAM 30 MINIT
Nama : _____________________________ Tingkatan : ________
JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU
Arahan:
Kertas ini mengandungi 20 soalan subjektif. Jawab semua soalan.
SOALAN MARKAH PENUH MARKAH DIPEROLEHI
Soalan 01 3
Soalan 02 3
Soalan 03 3
Soalan 04 3
Soalan 05 3
Soalan 06 3
Soalan 07 3
Soalan 08 3
Soalan 09 3
Soalan 10 3
Soalan 11 5
Soalan 12 5
Soalan 13 5
Soalan 14 5
Jumlah 50
SEKOLAH MENENGAH KEBANGSAAN AGAMA AL MASHOOR (LELAKI)
10460 JALAN AIR ITAM, PULAU PINANG
______________________________________________________

2. 1
SULIT 3472
3472/1 © 2018 Mohd Norferzly Mohamed SULIT
Answer all questions.
Jawab semua soalan.
1. Diagram 1 shows an arrow diagram for the relation between set P and set Q
Rajah 1 menunjukkan gambar rajah anak panah bagi hubungan antara set P dan set Q.
State
Nyatakan
(a) the object of 4,
objek bagi 4,
(b) the type of the relation.
jenis hubungan itu.
[3 marks/ 3 markah]
Answer / Jawapan :
(a)
(b)
P Q
2 ● 6
1 4
0 ● 2
1
1
2
0
Diagram 1
Rajah 1
PP Q
--
-

3. 2
SULIT 3472
3472/1 © 2018 Mohd Norferzly Mohamed SULIT
2. Given the function 𝑔: 𝑥 =
𝑥
𝑥+2
, 𝑥 ≠ 2.
Diberi fungsi 𝑔: 𝑥 =
𝑥
𝑥+2
, 𝑥 ≠ 2.
Find
Cari
(a) 𝑔(5) ,
(b) 𝑔−1
(2) .
[3 marks/ 3 markah]
Answer / Jawapan :
(a)
(b)
3. Given the function 𝑓: 𝑥 = |𝑥 + 2|, find the values of 𝑥 such that 𝑓(𝑥) = 3.
Diberi fungsi 𝑓: 𝑥 = |𝑥 + 2|, cari nilai-nilai 𝑥 jika 𝑓(𝑥) = 3.
[3 marks/ 3 markah]

4. 3
SULIT 3472
3472/1 © 2018 Mohd Norferzly Mohamed SULIT
4. Given 𝑔: 𝑥 = 3𝑥 + 4 and the composite function, 𝑓𝑔: 𝑥 = 12𝑥 + 16.
Diberi 𝑔: 𝑥 = 3𝑥 + 4 dan fungsi gubahan, 𝑓𝑔: 𝑥 = 12𝑥 + 16.
Find
Cari
(a) 𝑓(𝑥)
(b) value of 𝑥 when 𝑓𝑔(𝑥) =
1
3
𝑔(𝑥)
nilai 𝑥 apabila 𝑓𝑔(𝑥) =
1
3
𝑔(𝑥)
[3 marks/ 3 markah]
5. It is given that 2 is one of the roots of the quadratic equation 𝑥2
+ 3𝑥 + 𝑞 = 0.
Find the value of 𝑞.
Diberi bahawa 2 ialah satu daripada punca persamaan kuadratik 𝑥2
+ 3𝑥 + 𝑞 = 0
Cari nilai q.
[3 marks/ 3 markah]
Answer / Jawapan :

5. 4
SULIT 3472
3472/1 © 2018 Mohd Norferzly Mohamed SULIT
6. Solve the quadratic equation 3𝑥 + 1 = 2𝑥(𝑥 + 3). Give your answer correct to four significant
figures.
Selesaikan persamaan kuadratik 3𝑥 + 1 = 2𝑥(𝑥 + 3). Beri jawapan anda betul kepada empat
angka bererti.
[3 marks/ 3 markah]
Answer / Jawapan :
7. The roots of the quadratic equation 𝑥2
+ 5𝑥 + 6 = 0 are 𝛼 and 𝛽. Find the quadratic equation
which has roots 2𝛼 𝑎𝑛𝑑 2𝛽 .
Punca-punca persamaan kuadratik 𝑥2
+ 5𝑥 + 6 = 0 adalah 𝛼 𝑑𝑎𝑛 𝛽. Cari persamaan kuadratik
yang mempunyai punca-punca 2𝛼 𝑑𝑎𝑛 2𝛽 .
[3 marks/ 3 markah]
Answer / Jawapan :

6. 5
SULIT 3472
3472/1 © 2018 Mohd Norferzly Mohamed SULIT
8. Diagram 8 shows the graph of the function 𝑓(𝑥) = 2(𝑥 + ℎ)2
+ 5
Rajah 8 menunjukkan graf bagi fungsi 𝑓(𝑥) = 2(𝑥 + ℎ)2
+ 5
The curve has the minimum point (3, k) .
Lengkung tersebut mempunyai titik minimum (3, k) .
State
Nyatakan
(a) the value of h ,
nilai bagi h ,
(b) the value of k ,
nilai bagi k ,
(c) the equation of the axis of symmetry.
persamaan bagi paksi simetri.
[3 marks/ 3 markah]
Answer / Jawapan :
(a)
(b)
(c)
f (x)
f (x) 2(x h)2
5
O
x
●
(3,k)
Diagram 8
Rajah 8
𝑓(𝑥) = 2(𝑥 + ℎ)2
+ 5

7. 6
SULIT 3472
3472/1 © 2018 Mohd Norferzly Mohamed SULIT
9. Given that quadratic equation (𝑝 + 5)𝑥2
− 8𝑥 + 1 = 0 has no roots. Find the range of values of p.
Diberi persamaan kuadratik (𝑝 + 5)𝑥2
− 8𝑥 + 1 = 0 tidak mempunyai punca. Cari julat nilai p.
[3 marks/ 3 markah]
Answer / Jawapan :
10. The minimum value of the quadratic function 𝑓(𝑥) = 𝑥2
+ 10𝑥 + 𝑝 is 10, where 𝑝 is a constant.
Nilai minimum untuk fungsi kuadratik 𝑓(𝑥) = 𝑥2
+ 10𝑥 + 𝑝 adalah 10, dengan keadaan p adalah
pemalar.
Find
Cari
[3 marks/ 3 markah]
(a) the value of 𝑥 at which the function 𝑓 is minimum,
nilai 𝑥 di mana fungsi 𝑓 adalah minimum,
(b) the value of p .
nilai p.

8. 7
SULIT 3472
3472/1 © 2018 Mohd Norferzly Mohamed SULIT
11. Solve the following simultaneous equations.
Selesaikan persamaan serentak yang berikut.
2𝑥 − 𝑦 = 6
𝑥2
− 𝑦2
+ 𝑥 = 4𝑦
Give your answers correct to two decimal places.
Beri jawapan anda betul kepada dua tempat perpuluhan.
[5 marks/ 5 markah]

9. 8
SULIT 3472
3472/1 © 2018 Mohd Norferzly Mohamed SULIT
12. Given ℎ(𝑥) = 5𝑥 + 4 and 𝑔(𝑥) = 2 + 3𝑥. Find
Diberi ℎ(𝑥) = 5𝑥 + 4 dan 𝑔(𝑥) = 2 + 3𝑥. Cari
(a) 𝑔ℎ−1
(𝑥) (b) the value of 𝑥 if ℎ𝑔(𝑥) = 15.
nilai 𝑥 jika ℎ𝑔(𝑥) = 15.
[5 marks/ 5 markah]

10. 9
SULIT 3472
3472/1 © 2018 Mohd Norferzly Mohamed SULIT
13. The diagram shows a right-angled triangle. Based on the information given in the diagram,
form a quadratic equation. Hence, find the value of 𝑥 by solving the quadratic equation.
Rajah menunjukkan satu segi tiga bersudut tegak. Berdasarkan maklumat yang diberikan
dalam rajah itu, bentukkan satu persamaan kuadratik. Seterusnya, cari nilai 𝑥 dengan
menyelesaikan persamaan kuadratik itu.
[5 marks/ 5 markah]
( 𝑥 + 1) 𝑐𝑚
(2𝑥 + 1) 𝑐𝑚
2𝑥 𝑐𝑚

11. 10
SULIT 3472
3472/1 © 2018 Mohd Norferzly Mohamed SULIT
14.
(a) Find the range of the values of 𝑥 if (𝑥 + 3)(3𝑥 − 4) > (𝑥 + 3)(1 − 𝑥).
Cari julat nilai 𝑥 jika (𝑥 + 3)(3𝑥 − 4) > (𝑥 + 3)(1 − 𝑥).
(b) Given that 𝑔: 𝑥 → 𝑥2
+ 6𝑥 − 2, calculate the range of values of 𝑚 if 𝑔(2𝑚) > 5𝑚.
Diberi 𝑔: 𝑥 → 𝑥2
+ 6𝑥 − 2, hitung julat nilai 𝑚 jika 𝑔(2𝑚) > 5𝑚.
[5 marks/ 5 markah]
SOALAN TAMAT
Disediakan Disemak
……………………………………………… ………………………………………………
(MOHD NORFERZLY BIN MOHAMED) (FAEZAH BINTI AHMAD RIDZUAN)