KENDRIYA VIDYALAYA STEEL PLANT - CLASS VIII MATHS SAMPLE PAPER (SET 2)
Time: 1.5 Hours | Total Marks: 40
Section – A (8 Questions x 1 Mark = 8 Marks)
1. In the ancient Egyptian number system, what was the base used for landmark numbers?
Click to view answer
Step 1: The sources state that in the Egyptian system, each landmark is 10 times the previous one.
Step 2: A system where landmark numbers are powers of 10 is a base-10 system.
Answer: c) 10
Step 2: A system where landmark numbers are powers of 10 is a base-10 system.
Answer: c) 10
2. Which mathematician first fully explained the Indian system of 10 symbols and used them for scientific computations?
Click to view answer
Step 1: Consult the historical section of the sources.
Step 2: Aryabhata (c. 499 CE) is credited with this explanation.
Answer: c) Aryabhata
Step 2: Aryabhata (c. 499 CE) is credited with this explanation.
Answer: c) Aryabhata
3. A quadrilateral with at least one pair of parallel opposite sides is called a:
Click to view answer
Step 1: Refer to the definition of a trapezium.
Step 2: It requires "at least one pair of parallel opposite sides".
Answer: b) Trapezium
Step 2: It requires "at least one pair of parallel opposite sides".
Answer: b) Trapezium
4. What is the expanded form of $(a - b)^2$?
Click to view answer
Step 1: Use Identity 1B from the source.
Step 2: $(a - b) \times (a - b) = a^2 - ab - ba + b^2 = a^2 - 2ab + b^2$.
Answer: c) a² - 2ab + b²
Step 2: $(a - b) \times (a - b) = a^2 - ab - ba + b^2 = a^2 - 2ab + b^2$.
Answer: c) a² - 2ab + b²
5. The ancient Indigenous Gumulgal people of Australia used which number as the base of their counting system?
Click to view answer
Step 1: The sources describe the Gumulgal system based on words like "ukasar" (2).
Step 2: It is identified as an efficient way of "counting in 2s".
Answer: a) 2
Step 2: It is identified as an efficient way of "counting in 2s".
Answer: a) 2
6. A number is divisible by 11 if the difference between the sum of digits at odd places and even places is:
Click to view answer
Step 1: Look at the "number short" vs "number in excess" logic.
Step 2: If the difference is a multiple of 11, the number is divisible.
Answer: c) A multiple of 11 (including 0).
Step 2: If the difference is a multiple of 11, the number is divisible.
Answer: c) A multiple of 11 (including 0).
7. Which of the following is true for a Rhombus?
Click to view answer
Step 1: Refer to the definition of a rhombus.
Step 2: It is a quadrilateral where "all sides have the same length".
Answer: b) All sides are of equal length.
Step 2: It is a quadrilateral where "all sides have the same length".
Answer: b) All sides are of equal length.
8. Simplify $(a + b)(a - b)$.
Click to view answer
Step 1: Apply the distributive property: $a^2 - ab + ba - b^2$.
Step 2: Cancel like terms $-ab$ and $+ba$: $a^2 - b^2$.
Answer: b) a² - b²
Step 2: Cancel like terms $-ab$ and $+ba$: $a^2 - b^2$.
Answer: b) a² - b²
Section – B (4 Questions x 2 Marks = 8 Marks)
9. If Puneeth’s father drives at 50 km/h and takes 2 hours, why can't the Rule of Three find the time taken at 75 km/h?
Click to view answer
Step 1: In previous problems, if one quantity increased, the other increased (proportional).
Step 2: Here, as speed increases, time of travel decreases.
Answer: Because the relationship is not directly proportional.
Step 2: Here, as speed increases, time of travel decreases.
Answer: Because the relationship is not directly proportional.
10. What is the "Rule of Three" (Trairasika) as defined by Aryabhata?
Click to view answer
Step 1: It is a method to find an unknown fourth quantity from three knowns.
Step 2: Formula: Multiply the Phala (fruit) by IchchhΔ (requisition) and divide by PramΔαΉa (measure).
Step 2: Formula: Multiply the Phala (fruit) by IchchhΔ (requisition) and divide by PramΔαΉa (measure).
11. In an isosceles trapezium, prove that angles opposite to equal sides are equal.
Click to view answer
Step 1: Draw perpendiculars from the top vertices to the base.
Step 2: This forms two triangles that can be shown as congruent ($\triangle UXY \cong \triangle VWZ$).
Step 3: Corresponding angles U and V are thus equal.
Step 2: This forms two triangles that can be shown as congruent ($\triangle UXY \cong \triangle VWZ$).
Step 3: Corresponding angles U and V are thus equal.
12. Check if 320,185 is divisible by 11.
Click to view answer
Step 1: Add digits at odd positions (from right): 5 + 1 + 2 = 8.
Step 2: Add digits at even positions (from right): 8 + 0 + 3 = 11.
Step 3: Difference: 8 - 11 = -3. Since -3 is not a multiple of 11, it is not divisible.
Answer: No
Step 2: Add digits at even positions (from right): 8 + 0 + 3 = 11.
Step 3: Difference: 8 - 11 = -3. Since -3 is not a multiple of 11, it is not divisible.
Answer: No
Section – C (4 Questions x 3 Marks = 12 Marks)
13. Solve the cryptarithm: BYE × 6 = RAY, given B = 1.
Click to view answer
Step 1: Since B=1, we have 1YE × 6 = RAY.
Step 2: To keep the product a 3-digit number, Y must be small (less than 7).
Step 3: Test Y=4: 14E × 6 = RA4. If E=2, 142 × 6 = 852 (Y is not 4). If E=9, 149 × 6 = 894. Here Y=9 matches! R=8, A=9.
Answer: B=1, Y=4, E=7 (147x6=882 invalid) ... Correct digits depend on unique letter assignment.
Step 2: To keep the product a 3-digit number, Y must be small (less than 7).
Step 3: Test Y=4: 14E × 6 = RA4. If E=2, 142 × 6 = 852 (Y is not 4). If E=9, 149 × 6 = 894. Here Y=9 matches! R=8, A=9.
Answer: B=1, Y=4, E=7 (147x6=882 invalid) ... Correct digits depend on unique letter assignment.
14. Use the identity $a^2 = (a+b)(a-b) + b^2$ to calculate $31^2$.
Click to view answer
Step 1: Let $a = 31$ and $b = 1$.
Step 2: Substitute: $(31 + 1)(31 - 1) + 1^2$.
Step 3: Calculate: $32 \times 30 + 1$.
Step 4: $960 + 1 = 961$.
Answer: 961
Step 2: Substitute: $(31 + 1)(31 - 1) + 1^2$.
Step 3: Calculate: $32 \times 30 + 1$.
Step 4: $960 + 1 = 961$.
Answer: 961
15. How do the diagonals of a Rectangle and a Square differ?
Click to view answer
Step 1: Diagonals of a rectangle are equal and bisect each other.
Step 2: Diagonals of a square also are equal and bisect each other.
Step 3: Differently, square diagonals bisect at 90° and bisect the internal angles.
Step 2: Diagonals of a square also are equal and bisect each other.
Step 3: Differently, square diagonals bisect at 90° and bisect the internal angles.
16. A mixture of 40 kg has sand and cement in ratio 3 : 1. Calculate the weight of each.
Click to view answer
Step 1: Total parts = 3 + 1 = 4.
Step 2: Weight of sand = $(3/4) \times 40 = 30$ kg.
Step 3: Weight of cement = $(1/4) \times 40 = 10$ kg.
Answer: Sand = 30kg, Cement = 10kg
Step 2: Weight of sand = $(3/4) \times 40 = 30$ kg.
Step 3: Weight of cement = $(1/4) \times 40 = 10$ kg.
Answer: Sand = 30kg, Cement = 10kg
Section – D (3 Questions x 4 Marks = 12 Marks)
17. Find the area of the shaded square sitting inside a larger square if the large square side is (m+n) and 4 rectangles of area 'mn' are removed.
Click to view answer
Step 1: Total area = $(m + n)^2$.
Step 2: Area of 4 rectangles = $4mn$.
Step 3: Shaded area = $(m + n)^2 - 4mn$.
Step 4: Expand and simplify: $m^2 + 2mn + n^2 - 4mn = m^2 - 2mn + n^2$.
Step 5: This is equal to $(n - m)^2$.
Answer: (n - m)²
Step 2: Area of 4 rectangles = $4mn$.
Step 3: Shaded area = $(m + n)^2 - 4mn$.
Step 4: Expand and simplify: $m^2 + 2mn + n^2 - 4mn = m^2 - 2mn + n^2$.
Step 5: This is equal to $(n - m)^2$.
Answer: (n - m)²
18. Explain the "placeholder" development in Mesopotamian and Mayan number systems.
Click to view answer
Step 1: Later Mesopotamians used a placeholder symbol to denote blank spaces where a power of 60 was missing.
Step 2: This was essential for an unambiguous place value system.
Step 3: The Mayan civilization independently developed a placeholder for '0'.
Step 4: The Mayan '0' symbol looked like a seashell.
Step 2: This was essential for an unambiguous place value system.
Step 3: The Mayan civilization independently developed a placeholder for '0'.
Step 4: The Mayan '0' symbol looked like a seashell.
19. Describe the method to multiply any 4-digit number (dcba) by 11 in one line.
Click to view answer
Step 1: Use the distributive property: $dcba \times (10 + 1)$.
Step 2: This equals $dcba0 + dcba$.
Step 3: The one-line rule: Write units digit 'a', then 'a+b', then 'b+c', then 'c+d', and finally 'd'.
Step 4: Remember to carry over if any sum exceeds 9.
Step 2: This equals $dcba0 + dcba$.
Step 3: The one-line rule: Write units digit 'a', then 'a+b', then 'b+c', then 'c+d', and finally 'd'.
Step 4: Remember to carry over if any sum exceeds 9.
No comments:
Post a Comment
Thank you