Practise questions · Salam Academy

SA-9709-P1-CG4-Q011 markL1 FoundationCalculatorTangents

The tangent to a circle at a point

P

is

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-CG4-Q021 markL1 FoundationCalculatorIntersections

After substituting a line into a circle, the quadratic has

b^2-4ac<0

. The line

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-CG-Q031 markL1 FoundationCalculatorIntersections

A line meets a curve, giving a quadratic equation. The line is a tangent when the discriminant is

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-CG4-0014 marksL2 StandardCalculatorIntersections

Find the

x

-coordinates of the points where the line

y=x+1

meets the circle

x^2+y^2=13

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-CG4-0022 marksL2 StandardCalculatorIntersections

Substituting the line

y=2x+10

into the circle

x^2+y^2=20

gives

x^2+8x+16=0

. The line

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-CG4-0032 marksL2 StandardCalculatorTangents

P(4,2)

lies on the circle

(x-1)^2+(y+2)^2=25

. Find the gradient of the normal and the gradient of the tangent at

P

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-CG4-0042 marksL2 StandardCalculatorChords

The line

y=3

cuts the circle

x^2+y^2=25

at

A

and

B

. Find the length

AB

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-CG4-0052 marksL2 StandardCalculatorChords

A circle has radius

13

. A chord has length

24

. Find the distance from the centre to the chord.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-CG4-0083 marksL2 StandardCalculatorIntersections

Find the

x

-coordinates of the points where the line

y=2x-1

meets the curve

y=x^2-2x+2

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-CG4-G013 marksL2 StandardCalculatorTangents

P(4,3)

lies on the circle

x^2+y^2=25

. The tangent at

P

is

y=mx+c

. Find

m

and

c

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-CG-0084 marksL3 ExamCalculatorTangents

The point

P(5,\,5)

lies on the circle

(x-2)^2+(y-1)^2=25

. Find the equation of the tangent to the circle at

P

, in the form

y=mx+c

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-CG-0095 marksL3 ExamCalculatorTangents

Find the coordinates of the points where the line

y=2x

meets the circle

(x-1)^2+(y-2)^2=5

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-CG-0104 marksL3 ExamCalculatorIntersections

Find the set of values of

k

for which the line

y=x+k

does not meet the curve

y=x^2-3x+2

. Give your answer in the form

k<a

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-CG-0165 marksL3 ExamCalculatorTangents

The line

x+y=9

meets the circle

(x-1)^2+(y-1)^2=25

at two points. Find their coordinates.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-CG4-0073 marksL3 ExamCalculatorIntersections

The line

y=x+c

is a tangent to the curve

y=x^2-3x+5

. Find

c

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-CG4-0093 marksL3 ExamCalculatorChords

C

is the centre of the circle

(x-1)^2+(y-1)^2=11

. A tangent is drawn from

Q(7,1)

to touch the circle at

T

. Find the length

QT

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-CG-0114 marksL4 ChallengingCalculatorIntersections

The line

y=kx+4

is a tangent to the circle

x^2+y^2=8

. Find the possible values of

k

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-CG4-0064 marksL4 ChallengingCalculatorTangents

The line

y=kx

is a tangent to the circle

(x-5)^2+y^2=9

. Find the possible values of

k

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-CG4-0104 marksL5 ExtensionCalculatorTangents

Find the values of

c

for which the line

y=2x+c

is a tangent to the circle

x^2+y^2=5

.

Salam Academy Original Practice · Proposed mark scheme

Question bank