Page 23 - Top Class F5 - Mathematics (Chapter 2)

Mathematics Form 5 Chapter 2 Matrices

(c) An art centre offered two types of classes, drawing and multicultural craft. The sum of the monthly
fees of the two classes was RM90. The enrolments of pupils for drawing class and multicultural craft
class were 16 and 20 respectively. The total monthly fees collected from pupils was RM1 640. It is given
that the monthly fees for drawing class and multicultural craft class were RMx and RMy respectively.
Sebuah pusat seni menawarkan dua jenis kelas, lukisan dan kraf pelbagai budaya. Jumlah bayaran bulanan untuk kedua-dua
kelas itu ialah RM90. Enrolmen murid untuk kelas lukisan dan kelas kraf pelbagai budaya masing-masing ialah 16 dan 20
orang. Jumlah bayaran bulanan yang dikutip daripada murid ialah RM1 640. Diberi bahawa bayaran bulanan untuk kelas
lukisan dan kelas kraf pelbagai budaya masing-masing ialah RMx dan RMy.
(i) Find the value of x and of y using the matrix method.
Cari nilai x dan nilai y dengan menggunakan kaedah matriks.
(ii) If the enrolment of pupils for drawing class was 20, can the answer in (i) be found by using matrix
method? Explain your answer. HOTS Analysing
Jika enrolmen murid untuk kelas lukisan ialah 20 orang, bolehkah jawapan di (i) dicari dengan menggunakan kaedah
matriks? Jelaskan jawapan anda.

(i) x + y = 90 (ii) Cannot. It is because the determinant
16x + 20y = 1 640 1 1
of matrix  20 20  is equals to zero.
 1 1 x = 90  Tidak boleh. Hal ini demikian kerana penentu
  
16 20 y
1640
1
1
matriks  20 20  bersamaan dengan sifar.
  = 1(20) – 1(16) –16 1 1640 

90

20 –1
x
1
y
1 1800 – 1640
=  
4 –1440 + 1640
1 160
=  
4 200
40
 
= 50
Hence / Maka, x = 40, y = 50
SPM Practice 2

Paper 1

1. Umi wants to buy 4 packets of instant noodles and 5 bottles  4 –3   8 9   7 –1 
SPM of cooking oil. Lenda wants to buy 3 packets of instant 2. 5 6 2 + –13 7 – 2 9 5 =
2017 SPM
noodles and 2 bottles of cooking oil. It is given that the 2018 19 5
price of the instant noodles is RM3.50 per packet while the A  2 14 
price of the cooking oil is RM10.50 per bottle. Which of
the following is the correct method to calculate the total B  14 –4 
payment to be made by Umi, RMm, and Lenda, RMn? –1 7
Umi hendak membeli 4 paket mi segera dan 5 botol minyak  14 –8 
masak. Lenda hendak membeli 3 paket mi segera dan 2 botol C –1 27
minyak masak. Diberi bahawa mi segera berharga RM3.50 19 5
sepaket manakala minyak masak berharga RM10.50 sebotol. D  –1 14 
Antara berikut, kaedah yang manakah betul untuk mengira
4 1
jumlah bayaran yang perlu dibuat oleh Umi, RMm, dan Lenda, 3. P is a 2 × 2 matrix and P = 1   . Find the
–1
RMn? SPM value of m and of n. 2(4) – (–1)(5) m n
4 5 3.50
4 3 3.50
4 1
m
1
m

A      C      2018 P ialah satu matriks 2 × 2 dan P = 2(4) – (–1)(5) m n  .
=
=

–1
5 2 10.50
3 2 10.50
n
n
Cari nilai m dan nilai n.
4 5 10.50
4 3 10.50
          A m = 2, n = 5 C m = 2, n = –5
m
m
B 3 2 3.50 = n D 5 2 3.50 = n B m = –5, n = 2 D m = 5, n = 2
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