Case study (4 Marks)

Questions

Question 14 Marks

Read the following text carefully and answer the questions that follow:
Statue of a Pineapple: The Big Pineapple is a heritage $-$ listed tourist attraction at Nambour Connection Road, Woombye, Sunshine Coast Region, Queensland, Australia. It was designed by Peddle Thorp and Harvey, Paul Luff, and Gary Smallcombe and Associates. It is also known as Sunshine Plantation. It was added to the Queensland Heritage Register on $6$ March $2009$.
Kavita last year visited Nambour and wanted to find the height of a statue of a pineapple. She measured the pineapple's shadow and her own shadow. Her height is $156 \ cm$ and casts a shadow of $39 \ cm$. The length of shadow of pineapple is $4 \ m$.

$i$. What is the height of the pineapple?
$ii$. What is the height Kavita in metres?
$iii.$ Write the type of triangles used to solve this problem.
OR
Which similarity criterion of triangle is used?

Answer

$\triangle ABC \sim \triangle PQR$
$\frac{1.56}{0.39}=\frac{P Q}{4}$
$\frac{1.56 \times 4}{0.39}=P Q$
$P Q=16 m$
$\therefore$ height of Pine apple $=16 m$.
$ii.$ Height of Kavita $=1.56 m$
$iii$. Right triangle
OR
$AA$ criteria

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Question 24 Marks

Read the following text carefully and answer the questions that follow:
India meteorological department observes seasonal and annual rainfall every year in different sub$-$divisions of our country

I
t helps them to compare and analyse the results. The table given below shows sub$-$division wise seasonal $($monsoon$)$ rainfall $($mm$)$ in $2018:$

Rainfall (mm)	Number of Sub-divisions
$200-400$	$2$
$400-600$	$4$
$600-800$	$7$
$800-1000$	$4$
$1000-1200$	$2$
$1200-1400$	$3$
$1400-1600$	$1$
$1600-1800$	$1$

$i.$ Write the modal class.
$ii.$ Find the median of the given data.
$iii.$ If sub$-$division having at least $1000$ mm rainfall during monsoon season$,$ is considered good rainfall sub$-$ division, then how many subdivisions had good rainfall?
$OR$
Find the mean rainfall in this season.

Answer

$i.$ Modal Class is $600-800$
$ii. \frac{N}{2}=12$, median class is $600-800$

Rainfall	$X_i$	$f_i$	$e_f$
$200-400$	$300$	$2$	$2$
$400-600$	$500$	$4$	$6$
$600-800$	$700$	$7$	$13$
$800-1000$	$900$	$4$	$17$
$1000-1200$	$1100$	$2$	$19$
$1200-1400$	$1300$	$3$	$22$
$1400-1600$	$1500$	$1$	$23$
$1600-1800$	$1700$	$1$	$24$
		$24$

$\text { Median }=600+\frac{200}{7}(12-6)$
$=\frac{5400}{7} \text { or } 771.4$
$iii.$ Sub$-$divisions having good rainfall $=2+3+1+1=7$.
$OR$

Rainfall	$X_i$	$f_i$	$x_if_i$
$200-400$	$300$	$2$	$600$
$400-600$	$500$	$4$	$2000$
$600-800$	$700$	$7$	$4900$
$800-1000$	$900$	$4$	$3600$
$1000-1200$	$1100$	$2$	$2200$
$1200-1400$	$1300$	$3$	$3900$
$1400-1600$	$1500$	$1$	$1500$
$1600-1800$	$1700$	$1$	$1700$
		$24$	$20,400$

Mean $=\frac{20400}{24}=850$

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Question 34 Marks

Read the following text carefully and answer the questions that follow:
Basketball and soccer are played with a spherical ball. Even though an athlete dribbles the ball in both sports, a basketball player uses his hands and a soccer player uses his feet. Usually, soccer is played outdoors on a large field and basketball is played indoor on a court made out of wood. The projectile (path traced) of soccer ball and basketball are in the form of parabola representing quadratic polynomial.

i. Which type the shape of the path traced shown in given figure?
ii. Why the graph of parabola opens upwards?
iii. In the below graph, how many zeroes are there?

OR
What is the condition for the graph of parabola to open downwards?

Answer

i. Parabola
ii. $a>0$
iii. $\because$ The graph cut the $x$-axis thrice
$\therefore$ No of zeroes $=3$
OR
$a < 0$

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Maths Case study (4 Marks)

Case study (4 Marks)

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