9709 · topic questions
Differentiation
12 past-paper questions on Differentiation
The equation of a curve is y = e^(sinx) / cos²x for 0 ≤ x ≤ 2π. Find dy/dx and hence find the x-coordinates of the stationary…
Practise the full question →A curve is defined by the parametric equations x = 4 cos²t, y = √3 sin 2t, for values of t such that 0 < t < π/2. Find the…
Practise the full question →The equation of a curve is ye^(2x) + y²e^x = 6. Find the gradient of the curve at the point where y = 1.
Practise the full question →The diagram shows the graph of y = 5 sin 2x cos²x for 0 ≤ x ≤ ½π and its maximum point M. Find the exact x-coordinate of M.
Practise the full question →Find the exact coordinates of the stationary point of the curve y = e^(2x) sin2x for 0 ≤ x ≤ ½π.
Practise the full question →A particle P moves in a straight line and passes through the point A at time t = 0. The velocity vms¯¹ of P at time t seconds is…
Practise the full question →(a) Show that dy/dx can be expressed in the form c(3t+4) and state the value of the constant c. [5]
Practise the full question →The diagram shows the curve y = sin2x(1+sin2x), for 0 ≤ x ≤ ¾π, and its minimum point M. The shaded region bounded by the curve…
Practise the full question →(b) It is given that the gradient of the curve at the point (a, ln100) is m. Find the values of a and m. [4]
Practise the full question →The diagram shows the curve y = xe^(-ax), where a is a positive constant, and its maximum point M. Find the exact coordinates of…
Practise the full question →The equation of a curve is ln(x+y) = 3x²y. Find the gradient of the curve at the point (1,0).
Practise the full question →Hence find the equation of the normal to the curve at the point where t = π/8. Give your answer in the form y = mx+c.
Practise the full question →
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Differentiation (9709) past-paper questions — marked instantly
These are real Cambridge Mathematics past-paper questions on Differentiation. Open one, attempt it, then upload your working — MarkScheme grades it against the official 9709 mark scheme so you see exactly where the marks are won and lost on this topic.
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