KENDRIYA VIDYALAYA STEEL PLANT - CLASS VII MATHS SAMPLE PAPER
Total Marks: 40 | Total Questions: 19 | Time: 90 Minutes
SECTION A: Multiple Choice Questions (1 Mark Each)
1. If Shabnam is 3 years older than Aftab (whose age is 'a'), which algebraic expression represents Shabnam's age?
1M
Click to view answer
Correct Option: (c)
Step 1: Identify that "older than" means we add the difference to the base age.
Step 2: Aftab's age is 'a', and the difference is 3. So, expression = a + 3.
Step 1: Identify that "older than" means we add the difference to the base age.
Step 2: Aftab's age is 'a', and the difference is 3. So, expression = a + 3.
2. When two lines intersect, adjacent angles that form a straight angle are called:
1M
Click to view answer
Correct Option: (b)
Step 1: Adjacent angles formed by two intersecting lines that add up to 180° are defined as linear pairs.
Step 1: Adjacent angles formed by two intersecting lines that add up to 180° are defined as linear pairs.
3. The parity (odd or even nature) of the sum of an even number and an odd number is always:
1M
Click to view answer
Correct Option: (d)
Step 1: An even number can be arranged in pairs; an odd number has one leftover.
Step 2: Adding them leaves one leftover, making the sum odd.
Step 1: An even number can be arranged in pairs; an odd number has one leftover.
Step 2: Adding them leaves one leftover, making the sum odd.
4. What is the algebraic expression for the perimeter of a square with side length 'q'?
1M
Click to view answer
Correct Option: (b)
Step 1: Perimeter is the sum of all sides. A square has 4 equal sides.
Step 2: Expression = 4 times the side length = 4 * q.
Step 1: Perimeter is the sum of all sides. A square has 4 equal sides.
Step 2: Expression = 4 times the side length = 4 * q.
5. In geometry, vertically opposite angles are always:
1M
Click to view answer
Correct Option: (b)
Step 1: Opposite angles formed by intersecting lines are called vertically opposite angles.
Step 2: Through reasoning, it is proved that these angles are always equal.
Step 1: Opposite angles formed by intersecting lines are called vertically opposite angles.
Step 2: Through reasoning, it is proved that these angles are always equal.
6. What is the smallest possible sum of three different numbers chosen from 1 to 9?
1M
Click to view answer
Correct Option: (c)
Step 1: Identify the three smallest numbers from the set {1, 2, 3, 4, 5, 6, 7, 8, 9}.
Step 2: Add them: 1 + 2 + 3 = 6.
Step 1: Identify the three smallest numbers from the set {1, 2, 3, 4, 5, 6, 7, 8, 9}.
Step 2: Add them: 1 + 2 + 3 = 6.
7. Letters like 'a' and 's' used to represent numbers in algebraic expressions are called:
1M
Click to view answer
Correct Option: (c)
Step 1: As per the textbook definition, letters used to represent numbers are called letter-numbers.
Step 1: As per the textbook definition, letters used to represent numbers are called letter-numbers.
8. Perpendicular lines intersect at an angle of:
1M
Click to view answer
Correct Option: (d)
Step 1: Lines intersecting at right angles are called perpendicular lines.
Step 2: A right angle measures exactly 90°.
Step 1: Lines intersecting at right angles are called perpendicular lines.
Step 2: A right angle measures exactly 90°.
SECTION B: Short Answer Questions (2 Marks Each)
9. Ketaki buys 'c' coconuts at ₹35 each and 'j' kg of jaggery at ₹60 per kg. Write the expression for total cost.
2M
Click to view answer
Step 1: Cost of coconuts = Number of coconuts × price = c × 35.
Step 2: Cost of jaggery = Kgs of jaggery × price = j × 60.
Step 3: Total amount = (c × 35) + (j × 60).
Step 2: Cost of jaggery = Kgs of jaggery × price = j × 60.
Step 3: Total amount = (c × 35) + (j × 60).
10. Two lines intersect forming angles 'a' and 'b' as a linear pair. If angle 'a' measures 120°, find the measure of 'b'.
2M
Click to view answer
Step 1: Linear pairs combine to form a straight angle, which measures 180°.
Step 2: Therefore, a + b = 180°.
Step 3: 120° + b = 180° -> b = 180° - 120° = 60°.
Step 2: Therefore, a + b = 180°.
Step 3: 120° + b = 180° -> b = 180° - 120° = 60°.
11. Why does adding any two even numbers always result in an even number? Explain using the concept of pairs.
2M
Click to view answer
Step 1: Even numbers can be arranged in pairs without leftovers.
Step 2: When you combine two sets of numbers that are already in pairs, the new collection will also be perfectly paired with no leftovers.
Step 2: When you combine two sets of numbers that are already in pairs, the new collection will also be perfectly paired with no leftovers.
12. Simplify the algebraic expression: p + p + p + q.
2M
Click to view answer
Step 1: Identify like terms. 'p' appears three times.
Step 2: Group the like terms: (1+1+1)p + q.
Step 3: Final simplified form = 3p + q.
Step 2: Group the like terms: (1+1+1)p + q.
Step 3: Final simplified form = 3p + q.
SECTION C: Descriptive Questions (3 Marks Each)
13. Parthiv makes matchstick patterns of Ls. Each L needs 2 matchsticks. If 'n' is the number of Ls, write the expression for the total matchsticks and find the requirement for 45 Ls.
3M
Click to view answer
Step 1: Establish the pattern. Each L requires 2 sticks.
Step 2: Algebraic expression = 2 * n.
Step 3: For 45 Ls, replace n with 45: 2 * 45 = 90 sticks.
Step 2: Algebraic expression = 2 * n.
Step 3: For 45 Ls, replace n with 45: 2 * 45 = 90 sticks.
14. Prove that when two lines intersect, vertically opposite angles are equal.
3M
Click to view answer
Step 1: Let lines l and m intersect, forming angles a, b, c, d (a and c are opposite; a and b are linear pair).
Step 2: Since straight angles are 180°, a + b = 180° and b + c = 180°.
Step 3: Therefore, a + b = b + c. Subtracting 'b' from both sides, we get a = c.
Step 2: Since straight angles are 180°, a + b = 180° and b + c = 180°.
Step 3: Therefore, a + b = b + c. Subtracting 'b' from both sides, we get a = c.
15. Without calculating the exact product, determine the parity (odd/even) of 27 × 13. Justify.
3M
Click to view answer
Step 1: Note that both numbers 27 and 13 are odd.
Step 2: An odd number can be seen as (even + 1). Multiplying two such numbers results in an odd value.
Step 3: Rule: odd × odd = odd. Thus, the parity is odd.
Step 2: An odd number can be seen as (even + 1). Multiplying two such numbers results in an odd value.
Step 3: Rule: odd × odd = odd. Thus, the parity is odd.
16. Simplify the expression: (40x + 75y) – (6x + 10y).
3M
Click to view answer
Step 1: Open the brackets by distributing the negative sign: 40x + 75y - 6x - 10y.
Step 2: Group like terms together: (40x - 6x) + (75y - 10y).
Step 3: Simplify the coefficients: 34x + 65y.
Step 2: Group like terms together: (40x - 6x) + (75y - 10y).
Step 3: Simplify the coefficients: 34x + 65y.
SECTION D: Long Answer Questions (4 Marks Each)
17. Explain how the perimeter of a rectangle is simplified from (l + b + l + b) to (2l + 2b). Use an example with l=3, b=4 to show they are equal.
4M
Click to view answer
Step 1: Identify that a rectangle has two lengths and two breadths. Sum = l + b + l + b.
Step 2: Use the rule that numbers can be added in any order to group like terms: (l + l) + (b + b).
Step 3: Simplify: l+l = 2l and b+b = 2b. Result = 2l + 2b.
Step 4: Verification: For l=3, b=4: (3+4+3+4) = 14. And 2(3) + 2(4) = 6 + 8 = 14. Both are equal.
Step 2: Use the rule that numbers can be added in any order to group like terms: (l + l) + (b + b).
Step 3: Simplify: l+l = 2l and b+b = 2b. Result = 2l + 2b.
Step 4: Verification: For l=3, b=4: (3+4+3+4) = 14. And 2(3) + 2(4) = 6 + 8 = 14. Both are equal.
18. Parallel lines l and m are intersected by a transversal 't'. If angle 6 is 135°, determine the measures of angle 2 and angle 5. Explain the geometric relationship used for each.
4M
Click to view answer
Step 1: Angle 6 = 135°. Angle 2 is its corresponding angle. Since lines are parallel, angle 2 = 135°.
Step 2: Angle 5 and angle 6 form a linear pair on line 'm'.
Step 3: Linear pairs add up to 180°. So, angle 5 = 180° - 135°.
Step 4: Result: angle 5 = 45°.
Step 2: Angle 5 and angle 6 form a linear pair on line 'm'.
Step 3: Linear pairs add up to 180°. So, angle 5 = 180° - 135°.
Step 4: Result: angle 5 = 45°.
19. Discuss the rules of a 3 × 3 magic square using numbers 1-9. Why must the row/column sum always be 15?
4M
Click to view answer
Step 1: In a magic square, every row, column, and diagonal adds up to the same number (magic sum).
Step 2: The sum of all numbers 1-9 is 45.
Step 3: Since there are 3 rows and they must be equal, the total sum (45) divided by 3 rows equals 15.
Step 4: Conclusion: The magic sum for a 1-9 magic square is always 15.
Step 2: The sum of all numbers 1-9 is 45.
Step 3: Since there are 3 rows and they must be equal, the total sum (45) divided by 3 rows equals 15.
Step 4: Conclusion: The magic sum for a 1-9 magic square is always 15.
No comments:
Post a Comment
Thank you