O-LevelAdditional MathematicsDifferentiation and integration4037/21 · May/June 2022 · Q76 Marks
Variables x and y are such that y = (1 + sin 3x)⁴ / √x. Use differentiation to find the approximate change in y when x increases from 1.9 to 1.9+h, where h is small.
- (a)Variables x and y are such that y = (1 + sin 3x)⁴ / √x. Use differentiation to find the approximate change in y when x increases from 1.9 to 1.9+h, where h is small.[6]
Mark scheme
Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.
- [B1] d/dx(sin 3x) = 3 cos 3x soi
- [M1] du/dx = 4(1 + sin 3x)³ (3 cos3x) soi FT their 3cos3x (where u = (1 + sin 3x)⁴)
- [M1] dy/dx = [√x (4(1+sin3x)³ (3 cos3x)) - (1 + sin 3x)⁴ (1/2 x^(-1/2))] / (√x)² FT their du/dx or their dv/dx but not both
- [A1] Correct derivative
- [M1] Evaluates their derivative at x = 1.9 and multiplies by h
- [A1] 0.651h
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