Hetauda_8_2081

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  1. Two sets \(A\) and \(B\) are presented below in the listing method: \(A = \{1, 3, 5, 7, 9\}\), \(B = \{2, 3, 5\}\).
    1. Present the sets \(A\) and \(B\) in a Venn diagram.[1]
    2. Illustrate all the proper subsets that can be made from set \(B\).[2]
  2. Ram’s monthly income is \(\text{Rs.}\,40{,}000\). The ratio of his saving to expenditure in a month is \(2:3\).
    1. In which month does he get an income of \(\text{Rs.}\,4{,}00{,}000\)? Find it.[1]
    2. How much amount does he save in a month? Find it.[2]
    3. By how much should Ram’s yearly expenditure be reduced to maintain a yearly expenditure of \(\text{Rs.}\,2{,}70{,}000\) only?[2]
    4. How much simple interest will Ram get if he deposits his monthly saving amount in a bank at \(10\%\) interest rate for \(2\) years?[1]
  3. Ganesh bought a laptop for \(\text{Rs.}\,75{,}000\) and fixed its marked price \(20\%\) above the cost price. The laptop is sold to Ramesh after allowing a \(20\%\) discount.
    1. Write the formula to find the discount percentage.[1]
    2. Find the marked price of the laptop.[1]
    3. What is Ganesh’s profit or loss percent in this transaction? Calculate it.[2]
  4. The age of Sabin’s father is \(52\) years.
    1. Define rational number.[1]
    2. Convert the age of Sabin’s father into the quinary number system.[2]
    3. How many maximum rational numbers can be made between \(1\) and \(2\)? Give a logical response.[1]
  5. The lengths of the diagonals of a rhombus are \(8\,\text{cm}\) and \(12\,\text{cm}\). The diameter of a circle is \(7\,\text{cm}\).
    1. Write the formula to find the area of a circle.[1]
    2. Find the area of the rhombus.[1]
    3. How much more or less is the area of the rhombus than the area of the circle? Calculate it.[2]
    4. Are all the triangles formed by intersecting the two diagonals of a rhombus equal in area? Calculate if ‘yes’; give a reason if ‘no’.[1]
    1. Write the factors of \(a^2 - b^2\).[1]
    2. Simplify: \(\dfrac{x^2 - 9}{x + 3} \div \dfrac{x - 3}{x^2 - 5x + 6}\).[2]
  7. The product of two consecutive natural numbers is \(12\).
    1. Find the two numbers. What number should be added to one of these numbers so that the product becomes the square number \(16\)?[2]
    2. Define quadratic equation.[1]
  8. Two simultaneous equations are given: \(2x + y = 5\) and \(x - y = 1\).
    1. Make a table showing the values of \(y\) for \(x = 0, 1, 2\) in both equations.[2]
    2. Find the values of \(x\) and \(y\) by solving the equations graphically.[2]
  9. In the adjoining figure, an isosceles triangle is shown with some measurements given.
    1. What is the sum of the interior angles of the triangle?[1]
    2. Find the values of \(x\) and \(y\).[2]
    3. Experimentally verify that the base angles of an isosceles triangle are equal by constructing two isosceles triangles of different measurements.[3]
  10. In the figure, the coordinates of vertices \(A(1,4)\) and \(B(1,2)\) of square \(ABCD\) with side \(2\,\text{cm}\) are given.
    1. Find the length of diagonal \(BD\) of square \(ABCD\).[2]
    2. Construct a square \(ABCD\) having side length \(4\,\text{cm}\) using a compass.[3]
    3. Define regular tessellation.[1]
  11. On a map, the scale is \(1\,\text{cm} = 2\,\text{km}\). The bearing of point \(Q\), which is \(8\,\text{cm}\) from point \(P\), is \(110^\circ\).
    1. Find the actual distance from point \(P\) to point \(Q\).[1]
    2. Compare the bearing of \(P\) from \(Q\) and the bearing of \(Q\) from \(P\).[2]
  12. The ages (in years) of \(7\) students of class VIII are: \(11, 12, 11, 12, 13, 14, 12\).
    1. What is the mode of the above data?[1]
    2. Find the average age of the students.[1]
    3. How much more or less is the median than the average? Compare.[1]

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