### Random Questions from 2016 Prelims #8

ACJC P2 Q3

The function g is defined by

(ii) Explain why the composite function exist.

(iii) Sketch the graph of .

### Random Questions from 2016 Prelims #3

AJC P1 Q7

The function f is defined by .

(i) State the greatest value of for which exists.

(ii) Define in similar form.

### 2010 A-level H2 Mathematics (9740) Paper 1 Question 5 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

(i)

When

When

Coordinates are

(ii)

Some students wasted time to find the expression , which shows they have poor knowledge. Students should label the axial intercepts coordinates, .

MF26

### H2 Math Tue 7pm

MF26

10.
(i)

11.
(i)
Since P is on l, for some t
perpendicular to l

### H2 Math Tue 5pm

MF26

Differentiate with respect to t.

Substitute into given differential equation,

Since

Using the product to sum formula as shown here, we have

Note: and
— (1)
— (2)
— (3)
Using GC,

— (1)
— (2)
— (3)
Using GC,

Qn11
(i)

(ii) Since l is the common line of intersection on and , we need l to be on too. For that to happen,
1. l must be parallel to , that is, direction of l is perpendicular to normal to

2. Given that l is parallel to (since ), we need l to be on , so we need to be on

(iii)
For 3 planes to have nothing in common, then l must be parallel to (Note: if l is not parallel, l will cut at a point, which means that 3 planes will cut at a point)
from (ii)
But

12.
(i)

is on when

MF26

### H2 Math Sun 2pm

MF26

Since the

is a constant, the series convergences.
The sum to infinity

Let denote the term of the AP.

Since they are consecutive terms of a GP,

, thus its not convergent

Sum of first 3 terms

—(1)
Sum of last 3 terms ; Here we consider an AP that has first term and common difference .

—(2)
Sum of n terms =
—(3)
Solve for n.

(i) Volume,
Volume of kth later,

(ii)
Since exists.
Theoretical Max Volume, .
Total Volume,
We want

### H2 Math Sun 1130am

MF26

Vectors Q7 [Homework]
(i)

Using ratio theorem,
Since is perpendicular to

(ii)
To be a parallelogram,

(iii)
Let
Since
— (1)
— (2)
Solving,

Vectors Q8 [Homework]
(i)

(ii)
Let R be the top of the vertical pillar,

Since R is collinear with A and C, R is the intersection of line AC and QR.

, and the height is 9m.

(iii)

Vectors Q9 [Homework]
(i)

Normal of

(ii)
Let be the acute angle

(iii)
— (1)
— (2)

Using GC,

(iv)
Let be the normal of
Length of projection

(v)
Required distance

(vi)
Let normal of

If intersect at l,n lies on

### H2 Math Sun 930am

MF26

Vectors Q7 [Homework]
(i)

Using ratio theorem,
Since is perpendicular to

(ii)
To be a parallelogram,

(iii)
Let
Since
— (1)
— (2)
Solving,

Vectors Q8 [Homework]
(i)

(ii)
Let R be the top of the vertical pillar,

Since R is collinear with A and C, R is the intersection of line AC and QR.

, and the height is 9m.

(iii)

Vectors Q9 [Homework]
(i)

Normal of

(ii)
Let be the acute angle

(iii)
— (1)
— (2)

Using GC,

(iv)
Let be the normal of
Length of projection

(v)
Required distance

(vi)
Let normal of

If intersect at l,n lies on