case /data -based (4 Marks)

Question 14 Marks

Riya wrote an algebraic expression.
$56t^3 + 12t^2 + 6t + 16s^2 + 2s + 106$
$1.$ Which of the following terms has 6 as the coeficient$?$
$A. s$
$B. s^2$
$C. t$
$D. t^3$
$2.$ Write the factors of $56t^3.$
$3.$ What is the type of the algebraic expression written by Riya$?$
$A.$ Monomial
$B.$ Binomial
$C.$ Trinomial
$D.$ Polynomial
$4.$ Riya said, “There are two like terms in the algebraic expression.” Is Riya correct? Give reason.
$5.$ Riya added an algebraic expression to $56t^3 + 12t^2 + 6t + 16s^2 + 2s + 106.$ The resultant expression is $14t^2+ 7t + 9s.$ Which of the following algebraic expressions did she add?
$A. 56t^3+ 2t^2+ t - 16s^2+ 7s + 106$
$B. -56t^3+ 2t^2+ t - 16s^2+ 7s – 106$
$C. -56t^3 - 2t^2 - t - 16s^2 - 7s – 106$
$D. 56t^3+ 26t^2+ 11t + 16s^2+ 11s + 106$

Answer

$6. C. t^3$
$7. 56 × t × t × t$
$8. D.$ Polynomial
$9.$ No, with valid reasoning.
● No, Riya is not correct, because there are no like terms in the given algebraic expression.
● No, Riya is not correct, because there are only unlike terms in the given algebraic expression.
$10.$ Option $B. -56t^3 + 2t^2 + t - 16s^2 + 7s – 106$

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Question 24 Marks

The amusement park is divided into three regular-shaped sections for rides, ticket room and
car parking respectively.

$1.$ What is the perimeter of the amusement park$?$
$A. 6P$
$B. 8P$
$C. 9P$
$D. 11P$
$2.$ What area of the amusement park is occupied by the parking space$?$

Answer

$4. B. 11P$
$5. P^2$

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Question 34 Marks

The costs of entry tickets to an amusement park are different for adults and children. An adult
ticket costs $Rs.800$ and a child ticket costs $Rs.500.$
$1.$ On Sunday, $x$ adult tickets and $y$ child tickets were sold. Which of the following expressions show the money collected through the ticket sale?
$A. 1300x$
$B. 800x+ 500x$
$C. 800x+ 500 y$
$D. (800 + 500) ( x + y)$
$2.$ A car parking ticket at the amusement park costs $Rs.150$ on Saturdays and Sundays and $Rs.100$ on weekdays. In a month with $5$ Saturdays and $4$ Sundays, the total parking ticket sale was worth $Rs.250,000.$ Write an equation to represent the situation algebraically.
$3.$ On Monday, the number of adults who visited the amusement park was the square of the number of children who visited. How much money was collected by selling entry tickets on Monday$?$
$A. x^2$
$B. 800x^2+ 500x$
$C. 800x + 500x^2$
$D.1300 (x+ x^2)$

Answer

$1. C. 800x + 500y$
$2.$ Uses two variables and the sum of $250,000.$
●Let $p$ be the number of cars on weekends and $q$ be the number of cars on weekdays.
$150 p + 100 q = 250,000$
● Let it be a $30-$day month and $x$ be the number of cars which used the parking lot on weekends and $y$ be the number of the cars at the park for the rest of the month.
$1350x + 2100 y = 250,000$
$3. B. 800x^2 + 500x$

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Maths case /data -based (4 Marks)

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