Practise

Question bank

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

TopicSkillDifficulty

12 questions

SA-IAL-P1-DF3-0012 marksL1 FoundationNon-calculatorNormals

Find the gradient of the normal to

y=x^2

at the point where

x=2

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-DF3-0023 marksL1 FoundationNon-calculatorTangents

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-IAL-P1-DF3-0071 markL1 FoundationCalculatorNormals

The normal to a curve at a point is

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-DF-Q021 markL1 FoundationCalculatorNormals

The tangent at a point has gradient

\tfrac23

. The normal has gradient

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-DF-0074 marksL2 StandardCalculatorTangents

Find the equation of the tangent to

y=x^2-4x+1

at the point where

x=3

, in the form

y=mx+c

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-DF-0084 marksL2 StandardCalculatorNormals

Find the equation of the normal to

y=\dfrac8x

at the point where

x=2

, in the form

y=mx+c

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-DF3-0033 marksL2 StandardNon-calculatorNormals

Find the equation of the normal to

y=x^2

(1,1)

, in the form

y=mx+c

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-DF3-0043 marksL2 StandardNon-calculatorTangents

The tangent to

y=x^2+2x

at the point

P

has gradient

6

. Find the coordinates of

P

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-DF3-0054 marksL2 StandardNon-calculatorTangents

Find the equation of the tangent to

y=4\sqrt x

at the point where

x=4

, in the form

y=mx+c

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-DF3-0063 marksL2 StandardNon-calculatorTangents

The tangent to

y=x^2

x=3

meets the

x

-axis at

Q

. Find the

x

-coordinate of

Q

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-DF-0095 marksL3 ExamCalculatorNormals

The point

P(1,3)

lies on

y=x^3+2

. The normal at

P

meets the

x

-axis at

Q

. Find the

x

-coordinate of

Q

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-DF-0124 marksL3 ExamCalculatorTangents

The tangents to

y=x^3-12x

at the points

A

and

B

are parallel to the line

y=15x

. Find the

x

-coordinates of

A

and

B

Salam Academy Original Practice · Proposed mark scheme