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This is answers for H2 Mathematics (9740). H2 Mathematics (9758), click here.

Numerical Answers (click the questions for workings/explanation)

Question 1: ;

Question 2: or

Question 3: 2

Question 4: ; translate the graph 4 units in negative y-direction and translate the graph 2 units in positive x-direction.

Question 5: ; ; or

Question 6:

Question 7:

Question 8: or ; ;

Question 9: ; ; ; ;

Question 10: ; ;

Question 11: ; ;

Let

or

Since is non-zero, .

Let be the preposition “” for all

Let

LHS

RHS

Since LHS = RHS, is true.

Assume is true for some ,

Want to show is true

LHS

RHS

Hence, by Mathematical Induction, since is true, is true is true, is true for all

(ii)

As

(i)

for all

(ii)

Asymptotes are and

(iii)

First, translate the graph 4 units in negative y-direction.

Then, translate the graph 2 units in positive x-direction.

(i)

Let

—(1)

—(2)

—(3)

(ii)

Since is a strictly increasing function with no stationary point. Thus, it can only have one real root.

(iii)

or

(i)

Set of points lying on the line which passes through **a** and is parallel to **b**.

(ii)

Set of points on the plane which has normal vector, **n**.

is the displacement of the plane from Origin.

(iii)

Since , line is not parallel to plane, the solution represents the point of intersection between the line and plane.

(a)

or

(b)

(i)

Comparing real and imaginary parts,

—(1)

—(2)

(1) + (2):

(ii)

Since all coefficients of are real, is a root is also a root.

(a)

(i)

(ii)

—(1)

—(2)

(2) – (1):

(b)

LHS

Using method of difference,

(c)

Let

Thus, it converges.

From MF26,

For them to intersect,

for some and

—(1)

—(2)

—(3)

Solving,

(ii)

Let for some

Since discriminant

There are no solutions for

(iii)

Let

Let

gives minimum .

m.

(i)

(ii)

, where is an arbitrary constant.

When

When ,

(iii)

, where is an arbitrary constant.

Let

When .

(iv)

As ,

Graph of 11(iv)

### Relevant materials

MF26

### KS Comments

To be honest, this paper is really the same as the H2 Mathematics (9758). They just rephrased everything. You can see for yourself here.

hello there are no answers 🙁

hi for Q10(ii) would it be sufficient to explain that for both P and Q do not lie on line L hence they are both not points of intersection, PRQ will never be 90degrees?

vectors need not intersect to be perpendicular actually.

Hello, got a quick question! For q6(ii) i remembered my teacher specifically saying r.n = d the ‘d’ is simply a constant with no meaning… so shouldnt displacement of plane from origin be d/(n^)?

Thanks!

yes. but n is given to be a unit vector.. it gives a lot of meaning then

Hi, according to the 9740 papers, may I know what are ur thoughts on the expected range of grade to score A grade? Is 70 marks overall for Ppr 1 & 2 guarantee an A?