Practise questions · Salam Academy

SA-9709-P1-QD5-0013 marksL1 FoundationCalculatorSimultaneous

Solve the simultaneous equations

x+y=5

and

xy=6

. Give the possible values of

x

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD5-G013 marksL1 FoundationCalculatorIntersections

The line

y=x+1

meets the curve

y=x^2-1

at two points. Find (a) their

x

-coordinates (b) the

y

-coordinate of the point with positive

x

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD5-Q011 markL1 FoundationCalculatorSimultaneous

To solve

y=x+2

and

x^2+y^2=20

together, the best first step is to

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD5-Q021 markL1 FoundationCalculatorTangency

After substituting a line into a curve you get a quadratic with discriminant

0

. The line is

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD5-0024 marksL2 StandardCalculatorIntersections

Find the

x

-coordinates of the points where the line

y=2x-1

meets the circle

x^2+y^2=10

, and the

y

-coordinate of the point with negative

x

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD5-0034 marksL2 StandardCalculatorIntersections

The line

y=3-x

meets the curve

y=x^2-4x+3

at

A

and

B

. Find the length

AB

, in the form

k\sqrt2

. State

k

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD5-0061 markL2 StandardCalculatorTangency

How many times does the line

y=2x-5

meet the curve

y=x^2-2x

?

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD5-0083 marksL2 StandardCalculatorSimultaneous

The curve

xy=12

meets the line

x+y=7

at two points. Find their

x

-coordinates.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD5-0103 marksL2 StandardCalculatorSimultaneous

A rectangle has perimeter

26

cm and area

40

cm

^2

. Find its length and width.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD-0215 marksL3 ExamCalculatorSimultaneous

Solve the simultaneous equations

y=x+1

and

x^2+y^2=25

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD5-0044 marksL3 ExamCalculatorSimultaneous

Solve the simultaneous equations

2x+y=7

and

x^2+xy=6

. Give the values of

x

, then the value of

y

when

x

is larger.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD5-0054 marksL3 ExamCalculatorTangency

The line

y=kx+1

is a tangent to the curve

y=x^2+2x+2

. (a) Find the possible values of

k

. (b) For the positive value of

k

, find the

x

-coordinate of the point of contact.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD5-0074 marksL3 ExamCalculatorIntersections

The line

y=x+4

meets the curve

y=x^2-2

at

A

and

B

. Find the coordinates of the midpoint of

AB

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD5-0114 marksL3 ExamCalculatorSimultaneous

Two positive numbers differ by

3

, and the sum of their squares is

89

. Find the larger number.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD5-0124 marksL3 ExamCalculatorIntersections

The line

y=2x-2

meets the curve

y=x^2-3x+4

at

P

and

Q

. Find the exact length of

PQ

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD-0225 marksL4 ChallengingCalculatorSimultaneous

Solve the simultaneous equations

x+2y=7

and

x^2-xy+y^2=7

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD5-0094 marksL4 ChallengingCalculatorTangency

Find the values of

k

for which the line

y=x+k

is a tangent to the circle

x^2+y^2=8

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD5-0135 marksL5 ExtensionCalculatorTangency

The line

y=mx

meets the curve

y=x^2+9

at two distinct points. Find the set of possible values of

m

, as

m<a

or

m>b

.

Salam Academy Original Practice · Proposed mark scheme

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