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PRINCIPLE OF EVALUATION / VALUATION KEY
Class: VIII | Subject: Mathematics
Slip Test – I
Max Marks: 20
SECTION I (1 × 8 = 8 Marks)
Q1. Express 0.4 in p/q form
[ Marks: 8 ]
| Let x = 0.4555... — (Eq 1) | 1.5 M |
| Multiply Eq (1) by 10 (non-repeating digit): 10x = 4.555... — (Eq 2) | 2.0 M |
| Multiply Eq (2) by 10 (periodicity = 1): 100x = 45.555... — (Eq 3) | 2.0 M |
| Subtract Eq (2) from Eq (3): 100x − 10x = 45.555... − 4.555... ⇨ 90x = 41 | 1.5 M |
| Final Answer:
x =
41
90
|
1.0 M |
Q1 (OR). Solve: (x−4)/7 − (x+4)/5 = (x+3)/7
[ Marks: 8 ]
| LCM of 7 and 5 is 35 ⇨ [5(x − 4) − 7(x + 4)] / 35 = (x + 3) / 7 | 2.0 M |
| Simplifying numerator: (5x − 20 − 7x − 28) / 35 = (−2x − 48) / 35 | 2.0 M |
| Cross multiplying or simplifying: (−2x − 48) = 5(x + 3) ⇨ −2x − 48 = 5x + 15 | 2.0 M |
| Transposing variables: −7x = 63 ⇨ x = −9 | 2.0 M |
SECTION II (2 × 4 = 8 Marks)
Q2. Find x so that l ∥ m
[ Marks: 4 ]
| Stating property: Since l ∥ m, Alternate Exterior Angles are equal | 1.0 M |
| Setting up equation: 3x − 10 = x + 10 | 1.0 M |
| Transposing terms: 3x − x = 10 + 10 ⇨ 2x = 20 | 1.0 M |
| Final Answer: x = 10° | 1.0 M |
Q3. Divide sum of (2/7 & 14/5) by product of (15/2 & 13/6)
[ Marks: 4 ]
| Sum = (2/7) + (14/5) = (10 + 98) / 35 = 108 / 35 | 1.5 M |
| Product = (15/2) × (13/6) = (5 × 13) / (2 × 2) = 65 / 4 | 1.0 M |
| Division = (108/35) ÷ (65/4) = (108/35) × (4/65) = 432 / 2275 | 1.5 M |
SECTION III (2 × 2 = 4 Marks)
Q4. Additive and Multiplicative Inverses of 5/8
[ Marks: 2 ]
| Additive Inverse of 5/8 = −5/8 | 1.0 M |
| Multiplicative Inverse of 5/8 = 8/5 | 1.0 M |
Q5. Solve: 4(t − 4) = 7(2t − 3)
[ Marks: 2 ]
| Expand brackets: 4t − 16 = 14t − 21 | 1.0 M |
| Transposing terms: 21 − 16 = 14t − 4t ⇨ 10t = 5 ⇨ t = 1/2 | 1.0 M |
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