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Practise

Question bank

Original exam-style questions, mapped to your syllabus. Answers are checked for mathematical equivalence and every attempt updates your mastery.

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14 questions

SA-9709-P2-DF-Q031 markL1 FoundationCalculatorImplicit
Differentiating y3y^3 with respect to xx gives
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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-D33-0011 markL1 FoundationCalculatorImplicit
Differentiating xyxy with respect to xx gives
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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-D33-G012 marksL1 FoundationCalculatorImplicit
Find the gradient of the circle x2+y2=25x^2+y^2=25 at the point (3,4)(3,4).

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P2-DF-0104 marksL2 StandardCalculatorImplicit
The curve x2+y2+2x−4y=20x^2+y^2+2x-4y=20 passes through (2,6)(2,6). Find the gradient of the curve at this point.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-D33-0022 marksL2 StandardCalculatorImplicit
Find the gradient of the curve x2+2y2=9x^2+2y^2=9 at the point (1,2)(1,2).

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-D33-0032 marksL2 StandardCalculatorImplicit
The curve xey=2xe^y=2 passes through (2,0)(2,0). Find the gradient of the curve at this point.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-DF-0084 marksL2 StandardCalculatorImplicit
The curve x2+y2−4x+6y=12x^2+y^2-4x+6y=12 passes through (5,1)(5,1). Find the gradient of the curve at this point.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P2-DF-0114 marksL3 ExamCalculatorImplicit
Find the gradient of the curve x3+xy+y3=11x^3+xy+y^3=11 at the point (1,2)(1,2).

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P2-DF-0125 marksL3 ExamCalculatorTangents
The curve x2y+y2=6x^2y+y^2=6 passes through (1,2)(1,2). (i) Find dydx\dfrac{dy}{dx} at this point. (ii) Find the equation of the tangent at this point, giving yy in terms of xx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-D33-0044 marksL3 ExamCalculatorTangents
Find the equation of the tangent to x2+xy+y2=7x^2+xy+y^2=7 at the point (1,2)(1,2), in the form y=mx+cy=mx+c.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-DF-0105 marksL3 ExamCalculatorTangents
Find the equation of the tangent to the curve x2+3xy+y2=11x^2+3xy+y^2=11 at the point (1,2)(1,2), in the form y=mx+cy=mx+c.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P2-DF-0136 marksL4 ChallengingCalculatorSpecial points
The curve x2+xy+y2=12x^2+xy+y^2=12 has two points where the tangent is parallel to the xx-axis. (i) Show that at these points y=−2xy=-2x, and find their xx-coordinates. (ii) Find the yy-coordinate of the point with positive xx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-D33-0053 marksL4 ChallengingCalculatorImplicit
By taking logarithms and differentiating implicitly, differentiate y=2xy=2^x.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-DF-0176 marksL5 ExtensionCalculatorSpecial points
Find the coordinates of the points on the curve x2−xy+y2=3x^2-xy+y^2=3 at which the tangent is parallel to the xx-axis.

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Salam Academy Original Practice · Proposed mark scheme