Page 15 - Focus KSSM SPM 2021 TG4.5 - Maths DLP

Mathematics SPM Chapter 6 Linear Inequalities in Two Variables

12 SPM Highlights

An art centre offers two classes, handicraft and On the graph below, shade the region that satisfies
1
drawing. The number of pupils in the handicraft all the three inequalities y  –x + 7, y  x – 2 and
2
class is x and the number of pupils in the drawing x  2. y
class is y. The maximum number of pupils for both
classes is 30 pupils. The number of pupils in handicraft 6
class is at most twice the number of pupils in drawing 4 y = –x 7
class.
2
(a) Write two linear inequalities other than x  0 and x
y  0 that represent the situation above. O 2 4 1 6
—x – 2
–2 y = Form 4
2
(b) Draw and shade the region that satisfies above
system of linear inequalities. Solution
Form 4
y
(c) From the graph, x = 2
(i) if the number of pupils in handicraft class 6
is 15, find the number of pupils in drawing 4 y = –x 7
class. 2
(ii) can this art centre receive 25 pupils in
handicraft class? Give your justification. 0 2 4 6 x
1
—x – 2
–2 y =
2
Solution
(a) x + y  30 ⇒ y  −x + 30
1
x  2y ⇒ y  x
2 Try This! 6.2
(b) y(drawing) 1. Represent each of the following situations in the
form of system of linear inequalities.
30 x + y 30 (a) Sekolah Setia holds a charity concert in a hall.
20 Two types of concert ticket, VIP and Special,
2y x will be sold among parents. The number of VIP
10 ticket sold is x and the number of Special ticket
sold is y. The hall can provide not more than
x
O 10 20 30 (handicraft) 1 000 seats. The number of Special tickets
must exceed twice the number of VIP tickets.
(b) Lily uses flour and sugar to bake cakes. Given
(c) (i) If the number of pupils in handicraft class the mass of sugar, s kg, being used is less than
is 15, the maximum number of pupils in half the mass of flour, t kg. The price of sugar
is RM2 per kilogram while the price of flour is
drawing class = 15. RM2.50 per kilogram. The total cost of making
a cake is less than RM50.
(ii) No. This is because the value x = 25 is
outside the shaded region. (c) Hassan likes to eat burgers and chicken
nuggets. However, Hassan has been advised
by doctor that his fat and salt intake for
Try Questions 6 – 11 in Try This! 6.2 each meal should not exceed 18 g and 1.6 g
respectively. The following table shows the
fat and salt contain in a burger and chicken
nugget.

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06 Focus SPM Maths F4.indd 95 17/02/2021 5:24 PM