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. Write an algebraic expression for: "4 less than a number n".
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Correct Option: (b)
Step 1: "Less than" indicates subtraction from the base number 'n'.
Step 2: 4 less than n means n - 4.
Step 1: "Less than" indicates subtraction from the base number 'n'.
Step 2: 4 less than n means n - 4.
2. When a transversal intersects parallel lines, alternate angles are:
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Correct Option: (c)
Step 1: By using corresponding angles and vertically opposite angles reasoning, it is justified that alternate angles are equal.
Step 1: By using corresponding angles and vertically opposite angles reasoning, it is justified that alternate angles are equal.
3. What is the parity of the sum of two odd numbers?
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Correct Option: (b)
Step 1: Each odd number has one leftover piece from a pair.
Step 2: Combining two odd numbers joins their two leftover pieces into a new pair, making the sum even.
Step 1: Each odd number has one leftover piece from a pair.
Step 2: Combining two odd numbers joins their two leftover pieces into a new pair, making the sum even.
4. In standard practice, the expression '4 × n' is shortened to:
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Correct Option: (c)
Step 1: Omission of the multiplication symbol is a standard algebraic practice. We write the number followed by the letter.
Step 1: Omission of the multiplication symbol is a standard algebraic practice. We write the number followed by the letter.
5. Lines that lie on the same plane and never meet even if extended infinitely are called:
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Correct Option: (d)
Step 1: This is the geometric definition of parallel lines provided in the text.
Step 1: This is the geometric definition of parallel lines provided in the text.
6. What is the 100th even counting number?
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Correct Option: (b)
Step 1: The nth even number is calculated as 2 times n.
Step 2: 2 * 100 = 200.
Step 1: The nth even number is calculated as 2 times n.
Step 2: 2 * 100 = 200.
7. Terms that involve the same letter-numbers (like 5c and 10c) are called:
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Correct Option: (c)
Step 1: Sets of terms involving the same letter-numbers are defined as like terms.
Step 1: Sets of terms involving the same letter-numbers are defined as like terms.
8. When a transversal intersects a pair of lines, how many total angles are formed?
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Correct Option: (c)
Step 1: A line crossing two other lines forms two sets of four angles each, totalling 8.
Step 1: A line crossing two other lines forms two sets of four angles each, totalling 8.
SECTION B: Short Answer Questions (2 Marks Each)
9. Simplify the expression: 5c + 3c + 10c.
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Step 1: Since these are like terms, we can use the distributive property.
Step 2: Add the coefficients: (5 + 3 + 10) × c = 18c.
Step 2: Add the coefficients: (5 + 3 + 10) × c = 18c.
10. Briefly describe how to draw a line parallel to a given line using a ruler and set square.
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Step 1: Draw line 'l' with a ruler.
Step 2: Slide the set square along the ruler to draw lines perpendicular to 'l'. These new lines will be parallel to each other.
Step 2: Slide the set square along the ruler to draw lines perpendicular to 'l'. These new lines will be parallel to each other.
11. Evaluate the parity of the expression 3n + 4 for n = 3.
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Step 1: Substitute n = 3 into the expression: 3(3) + 4.
Step 2: 9 + 4 = 13. 13 is an odd number. Parity is odd.
Step 2: 9 + 4 = 13. 13 is an odd number. Parity is odd.
12. In a 2x3 calendar grid, if the bottom middle cell is 'w', what is the expression for the cell directly to its left?
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Step 1: In a calendar, dates in a row are consecutive.
Step 2: The cell to the left of 'w' is one less. Expression = w - 1.
Step 2: The cell to the left of 'w' is one less. Expression = w - 1.
SECTION C: Descriptive Questions (3 Marks Each)
13. Explain the relationship between corresponding angles and parallel lines.
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Step 1: If lines are parallel, corresponding angles formed by a transversal are always equal.
Step 2: Conversely, if one pair of corresponding angles is equal, the lines must be parallel.
Step 3: If lines are NOT parallel, corresponding angles can never be equal.
Step 2: Conversely, if one pair of corresponding angles is equal, the lines must be parallel.
Step 3: If lines are NOT parallel, corresponding angles can never be equal.
14. Describe the systematic method to find the nth odd number.
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Step 1: First find the even number at that position (2n).
Step 2: Observe that the odd sequence is always one less than the even sequence at any position.
Step 3: Subtract 1 from the even number. Formula = 2n - 1.
Step 2: Observe that the odd sequence is always one less than the even sequence at any position.
Step 3: Subtract 1 from the even number. Formula = 2n - 1.
15. Simplify the expression: 4(x + y) – y.
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Step 1: Distribute the 4 into the bracket: 4x + 4y - y.
Step 2: Group like terms: 4x + (4y - y).
Step 3: Simplify: 4x + 3y.
Step 2: Group like terms: 4x + (4y - y).
Step 3: Simplify: 4x + 3y.
16. Why must the number 5 be at the centre of a 3x3 magic square using numbers 1-9?
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Step 1: Through reasoning, if 9 or 1 were at the centre, we could not find pairs to reach the magic sum of 15 using only numbers 1-9.
Step 2: Central position is involved in 4 sums (row, column, 2 diagonals). Only 5 has enough pairs (e.g., 1-9, 2-8, 3-7, 4-6) to satisfy this.
Step 3: Thus, the central number must be 5.
Step 2: Central position is involved in 4 sums (row, column, 2 diagonals). Only 5 has enough pairs (e.g., 1-9, 2-8, 3-7, 4-6) to satisfy this.
Step 3: Thus, the central number must be 5.
SECTION D: Long Answer Questions (4 Marks Each)
17. A snail climbs 'u' cm by day and slips 'd' cm by night. If it repeats this for 10 days and nights, write the expression for its distance from the start. What happens if d > u?
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Step 1: Net distance per 24 hours = Climb (u) - Slip (d) = (u - d).
Step 2: Total distance after 10 full cycles = 10 * (u - d).
Step 3: If d > u, the snail slips more than it climbs.
Step 4: Conclusion: The snail would actually be moving backwards or downwards from its starting position.
Step 2: Total distance after 10 full cycles = 10 * (u - d).
Step 3: If d > u, the snail slips more than it climbs.
Step 4: Conclusion: The snail would actually be moving backwards or downwards from its starting position.
18. Line 'l' and 'm' are intersected by transversal 't'. Angle 'a' is 120° and angle 'f' (its corresponding angle) is 70°. Are the lines parallel? Justify.
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Step 1: Observe that angle 'a' and its linear neighbor 'b' add to 180°. So b = 180 - 120 = 60°.
Step 2: In the diagram provided in sources, 'b' corresponds to 'f'.
Step 3: For parallel lines, corresponding angles must be equal (60° should have been 70°).
Step 4: Since 60° ≠ 70°, the lines are not parallel.
Step 2: In the diagram provided in sources, 'b' corresponds to 'f'.
Step 3: For parallel lines, corresponding angles must be equal (60° should have been 70°).
Step 4: Since 60° ≠ 70°, the lines are not parallel.
19. Solve the following cryptarithm where letters stand for digits: T + T + T = UT. Show all steps.
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Step 1: We have a one-digit number 'T' added three times (3 * T).
Step 2: The sum is a two-digit number 'UT', and the units digit is the same as 'T'.
Step 3: Test values for T: 3*1=3, 3*2=6, 3*3=9, 3*4=12, 3*5=15.
Step 4: At T=5, 5+5+5 = 15. The units digit (5) matches T. So T=5 and U=1.
Step 2: The sum is a two-digit number 'UT', and the units digit is the same as 'T'.
Step 3: Test values for T: 3*1=3, 3*2=6, 3*3=9, 3*4=12, 3*5=15.
Step 4: At T=5, 5+5+5 = 15. The units digit (5) matches T. So T=5 and U=1.
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