Question 16:
SMK Indah organises a Canteen Day that involves sales booths, game booths and mini shows.
(a) There are 24 students going to Canteen Day. It is given that 6 of them buy both foods and drinks, 7/12 of them buy foods and 3 of them buy books only.
In the answer space, complete the Venn diagram based on the information.
You must label all the three sets.
[3 marks]
Answer:
(a)
(b) On the Canteen Day, Sarah buys (2x + 4) of RM1 coupons and y of RM5 coupons.
(i) If the total amount paid by Sarah is RMz, write an expression for z in terms of x and y.
(ii) It is given that the number of RM5 coupons purchased by Sarah is half the number of the RM1 coupons. Sarah spends a total of RM42 for both coupons.
Calculate the number of RM5 coupons purchased by Sarah.
[4 marks]
(c) Diagram 10 shows the dot plot of the scores of a group of students in a target board game.
(i) Calculate the mean score of these students.
(ii) The mean score increases by 4 when the scores of three new students are added.
The scores of the first and second new students are the same.
The score of the third new student is the median of the data in Diagram 10.
Calculate the score of the first new student.
[4 marks]
(d) A Drama Club organises two types of mini shows. The folk tale shows, x takes 20 minutes while the documentary shows, y takes 15 minutes.
Table 7 shows the conditions of the show.
(i) On the graph in the answer space, draw and shade the region that satisfies the system of linear inequalities.
(ii) Drama Club would like to raise RM1 000. Every show is watched by exactly 30 students. The price of the ticket for folk tale show and documentary show is RM3 and RM2 for each viewer respectively.
Based on the graph, will the Drama Club achieve its target if both shows must be watched? Justify your answer.
[4 marks]
Answer:
(a)
(b)(i) $$ z=2 x+4+5 y $$
(b)(ii) $$ \begin{aligned} & y=\frac{1}{2}(2 x+4) \\ & y=x+2 \\ & x=y-2 \\ & 2 x+4+5 y=42 \\ & 2(y-2)+4+5 y=42 \\ & 2 y-4+4+5 y=42 \\ & 7 y=42 \\ & y=42 \div 7 \\ & y=6 \end{aligned} $$
Sarah bought six RM5 coupons.
(c)(i) $$ \begin{aligned} &\text { Mean score }\\ &\begin{aligned} & =\frac{25+25+30+30+35+40+50+50+55+60+70+70}{12} \\ & =\frac{540}{12} \\ & =45 \end{aligned} \end{aligned} $$
(c)(ii) $$ \begin{aligned} \frac{540+2 x+45}{15} & =45+4 \\ \frac{585+2 x}{15} & =49 \\ 585+2 x & =49 \times 15 \\ 585+2 x & =735 \\ 2 x & =735-585 \\ 2 x & =150 \\ x & =150 \div 2 \\ x & =75 \end{aligned} $$
(d)(i)
The straight line 20x + 15y = 240 is drawn correctly. (gained 1 mark)
The region is shaded correctly. (gained 1 mark)
(d)(ii)
$$ \begin{aligned} &\text { Total amount collected }\\ &\begin{aligned} & =(\mathrm{RM} 3 \times 30 \times x)+(\mathrm{RM} 2 \times 30 \times y) \\ & =\mathrm{RM} 90 x+\mathrm{RM} 60 y \end{aligned} \end{aligned} $$
$$ \begin{aligned} &\text { Test with coordinates }(8,5)\\ &\begin{aligned} & =\text { RM90(8) }+ \text { RM60(5) } \\ & =\text { RM1 } 020 \text { Target achieved) } \end{aligned} \end{aligned} $$
*Accept coordinates (11, 1), (10, 2), (9, 4), (8, 5) or (6, 8).
OR
$$ \begin{aligned} &\text { Test with coordinates }(3,12)\\ &\begin{aligned} & =\text { RM90(3) + RM60(12) } \\ & =\text { RM990 } \end{aligned} \end{aligned} $$
(Target not achieved)
SMK Indah organises a Canteen Day that involves sales booths, game booths and mini shows.
(a) There are 24 students going to Canteen Day. It is given that 6 of them buy both foods and drinks, 7/12 of them buy foods and 3 of them buy books only.
In the answer space, complete the Venn diagram based on the information.
You must label all the three sets.
[3 marks]
Answer:
(a)
(b) On the Canteen Day, Sarah buys (2x + 4) of RM1 coupons and y of RM5 coupons.
(i) If the total amount paid by Sarah is RMz, write an expression for z in terms of x and y.
(ii) It is given that the number of RM5 coupons purchased by Sarah is half the number of the RM1 coupons. Sarah spends a total of RM42 for both coupons.
Calculate the number of RM5 coupons purchased by Sarah.
[4 marks]
(c) Diagram 10 shows the dot plot of the scores of a group of students in a target board game.
(i) Calculate the mean score of these students.(ii) The mean score increases by 4 when the scores of three new students are added.
The scores of the first and second new students are the same.
The score of the third new student is the median of the data in Diagram 10.
Calculate the score of the first new student.
[4 marks]
(d) A Drama Club organises two types of mini shows. The folk tale shows, x takes 20 minutes while the documentary shows, y takes 15 minutes.
Table 7 shows the conditions of the show.
(i) On the graph in the answer space, draw and shade the region that satisfies the system of linear inequalities.(ii) Drama Club would like to raise RM1 000. Every show is watched by exactly 30 students. The price of the ticket for folk tale show and documentary show is RM3 and RM2 for each viewer respectively.
Based on the graph, will the Drama Club achieve its target if both shows must be watched? Justify your answer.
[4 marks]
Answer:
(a)
(b)(i) $$ z=2 x+4+5 y $$
(b)(ii) $$ \begin{aligned} & y=\frac{1}{2}(2 x+4) \\ & y=x+2 \\ & x=y-2 \\ & 2 x+4+5 y=42 \\ & 2(y-2)+4+5 y=42 \\ & 2 y-4+4+5 y=42 \\ & 7 y=42 \\ & y=42 \div 7 \\ & y=6 \end{aligned} $$
Sarah bought six RM5 coupons.
(c)(i) $$ \begin{aligned} &\text { Mean score }\\ &\begin{aligned} & =\frac{25+25+30+30+35+40+50+50+55+60+70+70}{12} \\ & =\frac{540}{12} \\ & =45 \end{aligned} \end{aligned} $$
(c)(ii) $$ \begin{aligned} \frac{540+2 x+45}{15} & =45+4 \\ \frac{585+2 x}{15} & =49 \\ 585+2 x & =49 \times 15 \\ 585+2 x & =735 \\ 2 x & =735-585 \\ 2 x & =150 \\ x & =150 \div 2 \\ x & =75 \end{aligned} $$
(d)(i)
The straight line 20x + 15y = 240 is drawn correctly. (gained 1 mark)
The region is shaded correctly. (gained 1 mark)
(d)(ii)
$$ \begin{aligned} &\text { Total amount collected }\\ &\begin{aligned} & =(\mathrm{RM} 3 \times 30 \times x)+(\mathrm{RM} 2 \times 30 \times y) \\ & =\mathrm{RM} 90 x+\mathrm{RM} 60 y \end{aligned} \end{aligned} $$
$$ \begin{aligned} &\text { Test with coordinates }(8,5)\\ &\begin{aligned} & =\text { RM90(8) }+ \text { RM60(5) } \\ & =\text { RM1 } 020 \text { Target achieved) } \end{aligned} \end{aligned} $$
*Accept coordinates (11, 1), (10, 2), (9, 4), (8, 5) or (6, 8).
OR
$$ \begin{aligned} &\text { Test with coordinates }(3,12)\\ &\begin{aligned} & =\text { RM90(3) + RM60(12) } \\ & =\text { RM990 } \end{aligned} \end{aligned} $$
(Target not achieved)