Practise questions · Salam Academy

SA-9709-P1-DF3-0013 marksL1 FoundationCalculatorTangents and normals

Find the equation of the tangent to

y=x^3

at the point where

x=1

, in the form

y=mx+c

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-DF3-0051 markL1 FoundationCalculatorTangents and normals

The tangent to

y=x^2-1

at

(1,0)

is

y=2x-2

. Where does it cross the

y

-axis?

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-DF3-G013 marksL1 FoundationCalculatorTangents and normals

Find the equation of the tangent to

y=x^2+1

at the point

(1,2)

, in the form

y=mx+c

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-DF3-Q011 markL1 FoundationCalculatorTangents and normals

The tangent to a curve at a point has gradient

2

. The normal at that point has gradient

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-DF-0063 marksL2 StandardCalculatorTangents and normals

Find the equation of the tangent to the curve

y=x^3-3x+4

at the point

(2,6)

. Give your answer in the form

y=mx+c

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-DF-0074 marksL2 StandardCalculatorTangents and normals

Find the equation of the normal to the curve

y=2x^2-3x+1

at the point where

x=2

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-DF3-0023 marksL2 StandardCalculatorTangents and normals

Find the equation of the normal to

y=x^2

at the point

(2,4)

, in the form

y=mx+c

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-DF3-0033 marksL2 StandardCalculatorTangents and normals

Find the equation of the tangent to

y=\dfrac4x

at the point

(2,2)

, in the form

y=mx+c

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-DF3-0043 marksL2 StandardCalculatorTangents and normals

Find the equation of the tangent to

y=\sqrt x

at the point where

x=4

, in the form

y=mx+c

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-DF3-0062 marksL2 StandardCalculatorGiven gradient

Find the

x

-coordinate of the point on

y=x^2-4x+5

where the tangent is parallel to the line

y=2x+1

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-DF-0164 marksL3 ExamCalculatorGiven gradient

Find the

x

-coordinates of the points on the curve

y=x^3-3x^2+2

where the tangent is parallel to the line

y=9x

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-DF3-0072 marksL3 ExamCalculatorGiven gradient

The normal to

y=x^2

at the point

P

has gradient

-\dfrac16

. Find the

x

-coordinate of

P

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-DF3-0084 marksL3 ExamCalculatorProblems

The tangent to

y=x^3-3x

at the point where

x=2

meets the curve again at

Q

. Find the

x

-coordinate of

Q

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-DF3-0095 marksL5 ExtensionCalculatorProblems

The tangent and the normal to

y=x^2

at

P(1,1)

meet the

x

-axis at

A

and

B

. Find the area of triangle

PAB

.

Salam Academy Original Practice · Proposed mark scheme

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