Page 59 - Hybrid PBD 2022 Form 4 Additional Mathematics

Matematik Tambahan Tingkatan 4 Bab 3 Sistem Persamaan
SPM

PRAKTIS PdPR Jawapan
Bab 3 PRAKTIS PdPR Bab 3

Kertas 1 Kertas 2

1. Satu garis lurus yang melalui titik (1, 5) bersilang 1. Selesaikan sistem persamaan linear berikut.
dengan lengkung x − 3x − y = 18 pada titik P(6, 0) Solve the following system of linear equations.
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dan titik Q. Cari koordinat titik Q. −3x + 4y + z = 24 .................
A straight line which passes through point (1, 5) intersects with 5x − 2y − 3z = −34 ...............b
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the curve x − 3x − y = 18 at point P(6, 0) and point Q. Find the 4x − 4y − 5z = −50 ...............c
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coordinates of point Q.
[4 markah / 4 marks] [5 markah / 5 marks]
Jawapan / Answer : Jawapan / Answer :
Kecerunan garis lurus / Gradient of the straight line b × 2: 10x − 4y − 6z = −68 ...............d
5 – 0  + d = 7x − 5z = −44 .....................e
= = –1
1 – 6  + c: x − 4z = −26 ..........................f
Menggunakan y = mx + c dan (6, 0) f × 7: 7x − 28z = −182 .....................g
Using y = mx + c and (6, 0) e − g: 23z = 138
0 = −6 + c z = 6
c = 6
Gantikan z = 6 ke dalam f
Persamaan garis lurus / Equation of the straight line Substitute z = 6 into f
y = −x + 6 x − 4(6) = −26
x = −2
x − 3x − y = 18
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x − 3x − (−x + 6) = 18 Gantikan x = –2 dan z = 6 ke dalam 
2
x − 3x + x − 6 − 18 = 0 Substitute x = –2 and z = 6 into 
2
x − 2x − 24 = 0 −3(−2) + 4y + 6 = 24
2
(x − 6)(x + 4) = 0 4y + 12 = 24
x = 6, x = −4 y = 3
Apabila x = –4 / When x = –4 ∴ x = −2, y = 3, z = 6
y = −(−4) + 6 2. Selesaikan persamaan serentak berikut. Berikan
= 10 jawapan anda betul kepada tiga tempat

Maka, titik Q(–4, 10). perpuluhan.
Thus, point Q(–4, 10). Solve the following simultaneous equations. Give your answer
correct to three decimal places.
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2. Diberi bahawa lengkung y = (m + 3) − 16x + 8, h + 2k = 5 ...................
dengan keadaan m ialah pemalar, bersilang k − 3h = 7 .................b
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dengan garis lurus y = −10x + 4 pada dua titik. [5 markah / 5 marks]
Cari julat nilai m. Jawapan / Answer :
Given that the curve y = (m + 3) − 16x + 8, where m is a
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constant, intersects with the straight line y = −10x + 4 at two Dari (1) / From : h = 5 – 2k .................c
points. Find the range of values of m. Gantikan c ke dalam b / Substitute c into b
[3 markah / 3 marks] k – 3(5 – 2k) = 7
2
Jawapan / Answer : k + 6k – 22 = 0
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(m + 3) − 16x + 8 = −10x + 4 −6 ±  – 4(1)(–22)
2
6
2
(m + 3) − 16x + 10x + 8 − 4 = 0 k = 2(1)

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(m + 3) − 6x + 4 = 0 = 2.568 , –8.568
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b − 4ac  0 h = 5 − 2(2.568) , h = 5 − 2(−8.568)
2
2
(−6) − 4(m + 3)(4)  0 = –0.136 = 22.136
36 − 16m − 48  0
−16m  12 ∴ h = −0.136, k = 2.568 dan / and
3
m  − h = 22.136, k = −8.568
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