PT3 Mathematics 2017, Question 8 - Mathematics

Question 8 (a):
Diagram 8 shows packets A, B and C that are filled with flour according to the stated mass.

Based on Diagram 8,
(i) State the heaviest mass of flour.
(ii) Puan Chan needs 2.6 kg of flour to bake cakes.
State the two combination of containers that should be chosen in order for her to bake the cakes.

Solution:
(i)

\begin{array}{l} Container A = 1 kg 80 g \\ Container B = 1.52 kg = 1 kg 520 g \\ Container C = 1 \frac{1}{2} kg = 1 kg 500 g \\ The heaviest mass of flour \\ = B : 1.52 kg \end{array}

$\begin{array}{l} Container A = 1 kg 80 g \\ Container B = 1.52 kg = 1 kg 520 g \\ Container C = 1 \frac{1}{2} kg = 1 kg 500 g \\ The heaviest mass of flour \\ = B : 1.52 kg \end{array}$

(ii)

\begin{array}{l} A = 1 kg 80 g = 1.080 kg \\ B = 1.52 kg \\ C = 1 \frac{1}{2} kg = 1.50 kg \\ Two combination of containers that \\ should be chosen to bake cake \\ = 1.080 kg + 1.52 kg \\ = 2.6 kg \\ = Container A + container B \end{array}

$\begin{array}{l} A = 1 kg 80 g = 1.080 kg \\ B = 1.52 kg \\ C = 1 \frac{1}{2} kg = 1.50 kg \\ Two combination of containers that \\ should be chosen to bake cake \\ = 1.080 kg + 1.52 kg \\ = 2.6 kg \\ = Container A + container B \end{array}$

Question 8 (b):

Simplify \frac{p q - 3 q}{5 q} \div \frac{p^{2} - 9}{15}

$Simplify \frac{p q - 3 q}{5 q} \div \frac{p^{2} - 9}{15}$

Solution:

\begin{array}{l} \frac{p q - 3 q}{5 q} \div \frac{p^{2} - 9}{15} \\ = \frac{p q - 3 q}{5 q} \times \frac{15}{p^{2} - 9} \\ = \frac{q (p - 3)}{5 q} \times \frac{15^{3}}{(p - 3) (p + 3)} \\ = \frac{3}{p + 3} \end{array}

$\begin{array}{l} \frac{p q - 3 q}{5 q} \div \frac{p^{2} - 9}{15} \\ = \frac{p q - 3 q}{5 q} \times \frac{15}{p^{2} - 9} \\ = \frac{q (p - 3)}{5 q} \times \frac{15^{3}}{(p - 3) (p + 3)} \\ = \frac{3}{p + 3} \end{array}$

Question 8 (c):
Zaitun has 24 bags of rice with the mass of 15 kg each. She gives

1 5

\frac{1}{5}

$\frac{1}{5}$ of the total rice to Hazlina. The remainder is divided equally into 16 containers.
Calculate the mass of rice, in kg, in each container.

Solution:

\begin{array}{l} Total mass of rice \\ = 24 \times 15 kg \\ = 360 kg \\ Mass of rice given to Hazlina \\ = \frac{1}{5} \times 360 \\ = 72 kg \\ Remainder = 360 - 72 = 288 kg \\ Mass of rice in each container \\ = \frac{288}{16} \\ = 18 kg \end{array}

$\begin{array}{l} Total mass of rice \\ = 24 \times 15 kg \\ = 360 kg \\ Mass of rice given to Hazlina \\ = \frac{1}{5} \times 360 \\ = 72 kg \\ Remainder = 360 - 72 = 288 kg \\ Mass of rice in each container \\ = \frac{288}{16} \\ = 18 kg \end{array}$

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