1. Which formula gives the perimeter of a square with side s?
- As + 4
- B2s
- C4s
- Ds × s
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Answer: C) 4s
A square has 4 equal sides, so perimeter = s + s + s + s = 4s. (s × s is the area.)
Class 7 Formulas and Rules from Patterns — practice questions with answers
Algebra · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
2. A rectangle has length x cm and breadth 3 cm. Which rule gives its perimeter in cm?
- Ax + 3
- B3x
- C6x
- D2x + 6
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Answer: D) 2x + 6
Perimeter = 2(length + breadth) = 2(x + 3) = 2x + 6. (3x is the area.)
3. Ravi has 100 marbles and gives 6 marbles to each of his n friends. Which expression gives the marbles he has left?
- A100 − 6n
- B94n
- C100 − 6 − n
- D6n − 100
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Answer: A) 100 − 6n
He gives away 6 × n = 6n marbles, so 100 − 6n are left. (94n wrongly multiplies.)
4. Lata says the rule for 2, 6, 10, 14, … is 4n. Is she right?
- ANo; the rule is 4n + 2
- BNo; the rule is 2n + 4
- CYes; it goes up by 4
- DNo; the rule is 4n − 2
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Answer: D) No; the rule is 4n − 2
4n gives 4, 8, 12, … — each 2 too big. So subtract 2: 4n − 2 gives 2, 6, 10, 14 ✓.
5. A path has n white tiles in a single row, completely surrounded by one ring of black tiles. Black tiles cost ₹15 each. Which expression gives the cost of the black tiles in rupees?
- A15(2n + 2)
- B15 × 8n
- C15(2n + 6)
- D15n + 6
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Answer: C) 15(2n + 6)
The tiles fill 3 rows of (n + 2) tiles, and n of them are white, so black = 3(n + 2) − n = 2n + 6. Cost = 15(2n + 6). (2n + 2 forgets the 4 corner tiles.)
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