O-LevelAdditional MathematicsDifferentiation and integration4037/22 · May/June 2020 · Q67 Marks
Find the equation of the tangent to the curve 2y = tan2x+7 at the point where x = π/8. Give your answer in the form ax-y = π/b+c, where a, b and c are integers.
- (a)Find the equation of the tangent to the curve 2y = tan2x+7 at the point where x = π/8. Give your answer in the form ax-y = π/b+c, where a, b and c are integers.[5]
- (b)This tangent intersects the x-axis at P and the y-axis at Q. Find the length of PQ.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.
- [1] (a) dy/dx = sec² 2x
- [1] (a) their dy/dx |x=π/8 = their 2
- [1] (a) x=π/8, y=4
- [1] (a) y - their4 = (their2)(x - π/8) oe
- [1] (a) 2x-y = π/4 oe
- [1] (b) sqrt((π/4 - 2)² + (4 - 0)²) oe
- [1] (b) 3.59 or 3.59[03...] rot to four or more figs
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