ACJC P2 Q3

The function g is defined by

(ii) Explain why the composite function exist.

(iii) Sketch the graph of .

Cultivating Champions, Moulding Success

ACJC P2 Q3

The function g is defined by

(ii) Explain why the composite function exist.

(iii) Sketch the graph of .

AJC P1 Q7

The function f is defined by .

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

(ii) Define in similar form.

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, .

This page contains all questions and answers asked by students from this class. The most recent questions will be at the top.

This page contains all questions and answers asked by students from this class. The most recent questions will be at the top.

10.

(i)

11.

(i)

Since P is on l, for some t

perpendicular to l

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

…

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 $latex r = \frac{5}{9} <1, S_{\infty} $ exists. Theoretical Max Volume, $latex S_{\infty} = \frac{8800 \pi}{1 - \frac{5}{9}} = 19800 \pi$. Total Volume, $latex S_n = \frac{8800 \pi (1 - (\frac{5}{9})^n)}{1 - \frac{5}{9}}$ We want $latex S_n \le 0.95 S_{\infty}$

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

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