O-LevelAdditional MathematicsDifferentiation and integration4037/22 · May/June 2010 · Q98 Marks
Given that y = (x+2) / (4x+12)½, show that dy/dx = k(x+4) / (4x+12)³/², where k is a constant to be found.
- (i)Given that y = (x+2) / (4x+12)½, show that dy/dx = k(x+4) / (4x+12)³/², where k is a constant to be found.[5]
- (ii)Hence evaluate ∫₁³ (x+4) / (4x+12)³/² dx.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2010). The mark or mark type is shown in brackets.
- M1 for d/dx (4x+12)½ = ½ (4x+12)⁻½ × 4 or d/dx (4x+12)⁻½ = -½ (4x+12)⁻³/² × 4
- M1 for Uses quotient rule or product rule
- A1 for (4x+12)½ - 2(x+2)(4x+12)⁻½ / (4x+12) or (4x+12)⁻½ - 2(x+2)(4x+12)⁻³/²
- M1 for Express with common denominator of (4x+12)ⁿ
- A1 for 2(x+4) / (4x+12)³/² or k = 2
- M1 for (x+2) / √4x+12 x 1/k
- M1 for uses both limits correctly on C(x+2) / √4x+12
- A1 for 9/16 oe
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