Page 6 - Focus KSSM SPM 2021 TG4.5 - Maths DLP

Mathematics SPM Chapter 6 Linear Inequalities in Two Variables

6.1 Linear Inequalities in Two (c) Let x = the number of rattan basket ordered
and y = the number of rattan chair ordered.
Variables The number of days needed to produce a rattan
basket is 3 days while to produce a rattan chair
A Representing situations in the form is 5 days. Total number of days to complete the
of linear inequalities order of rattan basket and rattan chairs is less

Linear inequality in two variables is an unequal than 45 days.
relation between two variables where the highest Therefore, 3x + 5y  45.
power of the variables is one. For example, x + y  1,
2x – y  5. Try Question 1 in Try This! 6.1

1 B Verifying the conjecture about the

Represent the following situations in the form of points in the region and the solution Form 4
of certain linear inequalities
linear inequalities.
Form 4
(a) Encik Zaki has two children who are studying 1. The straight line drawn on a Cartesian plane
in Indonesia and Australia respectively. The call divides the plane into two regions (half-plane).
rate to Indonesia is RM0.28 per minute while The straight line is called boundary line.
the call rate to Australia is RM0.66 per minute.
Encik Zaki wants to make a phone call to both of y y
his children and he has prepaid of RM30 in his Region
above
handphone. Region y = mx + c Region y = mx + c
above
(b) In a written quiz, the correct answer for a x below x
multiple choice question will be given 2 marks O Region O
while the correct answer for a structural question below
will be given 5 marks. Participants who earn a
total score of more than 50 are eligible to the y y
second round.
(c) Pak Abu needs 3 days to produce a rattan basket Region above Region Region
and 5 days to produce a rattan chair. He receives y = h on the on the
an order to produce x rattan baskets and y rattan O x left O right x
chairs that need to be completed in less than 45 Region below x = k
days.
Solution
(a) Let e = the duration of call, in minute made to 2. Observe the following diagram. The straight
line y = x – 1 is a straight line that divides the
Indonesia and f = the duration of call, in minute Cartesian plane into two regions..
made to Australia. The call rate to Indonesia is (a) All points that lie on the straight line, for
RM0.28 per minute while to Australia is RM0.66 example, E(–3, –4), satisfy the equation
per minute. Total prepaid is RM30. y = x – 1.
Therefore, 0.28e + 0.66f  30. (b) All points that lie in the region above the
(b) Let x = the number of correct answer of multiple straight line, for example, A(–4, 0), satisfy
choice questions and y = the number of correct the equation y  x – 1.
answer of structural questions. The marks for the (c) All points that lie in the region below the
correct answer for a multiple choice question is 2 straight line, for example, C(5, –2), satisfy
while for a structural question is 5. Participants the equation y  x – 1.
with the total marks of more than 50 is eligible
to the second round.
Therefore, 2x + 5y  50.

86

06 Focus SPM Maths F4.indd 86 17/02/2021 5:24 PM