Ten-Year-Series (TYS) Solutions | Past Year Exam Questions

2000 A Level H2 Math

These Ten-Year-Series (TYS) worked solutions with video explanations for 2000 A Level H2 Mathematics are suggested by Mr Gan. For any comments or suggestions please contact us at support@timganmath.edu.sg.

Select Year
Paper 1
Paper 2
2000 A Level H2 Math Paper 1 Question 8

A ten-digit number is formed by writing down the digits $0,1,2,3,4,5,6,7,8,9$ in some order. No number is allowed to start with $0$. Find how many such numbers are odd. 

Suggested Handwritten and Video Solutions
2000 TYS 2000

Share with your friends!

WhatsApp
Telegram
Facebook
2000 A Level H2 Math Paper 1 Question 11

It is given that $x$ and $y$ satisfy the equation ${{\tan }^{-1}}x+{{\tan }^{-1}}y+{{\tan }^{-1}}\left( xy \right)=\frac{7}{12}\pi $.

(i)

Find the value of $y$ when $x=1$.

[2]

(i) Find the value of $y$ when $x=1$.

[2]

(ii)

Express $\frac{\text{d}}{\text{d}x}\left( {{\tan }^{-1}}\left( xy \right) \right)$ in terms of $x$, $y$ and $\frac{\text{d}y}{\text{d}x}$.

[2]

(ii) Express $\frac{\text{d}}{\text{d}x}\left( {{\tan }^{-1}}\left( xy \right) \right)$ in terms of $x$, $y$ and $\frac{\text{d}y}{\text{d}x}$.

[2]

(iii)

Show that, when $x=1$, $\frac{\text{d}y}{\text{d}x}=-\frac{1}{3}-\frac{1}{2\sqrt{3}}$.

[3]

(iii) Show that, when $x=1$, $\frac{\text{d}y}{\text{d}x}=-\frac{1}{3}-\frac{1}{2\sqrt{3}}$.

[3]

Suggested Video Solutions
Suggested Handwritten Solutions

2000 TYS 2000

2000 TYS 2000

2000 TYS 2000

2000 TYS 2000

2000 TYS 2000

2000 TYS 2000

Share with your friends!

WhatsApp
Telegram
Facebook
2000 A Level H2 Math Paper 2 Question 15 [Modified]

Relative to the origin $O$, the points $A$, $B$, $C$ have position vectors $5\mathbf{i}+4\mathbf{j}+10\mathbf{k}$, $-4\mathbf{i}+4\mathbf{j}-2\mathbf{k}$ and $-5\mathbf{i}+9\mathbf{j}+5\mathbf{k}$ respectively.

(i)

Find the cartesian equation of the line $AB$.

[2]

(i) Find the cartesian equation of the line $AB$.

[2]

(ii)

Find the length of projection of the vector $\overrightarrow{AC}$ on line $AB$.

[2]

(ii) Find the length of projection of the vector $\overrightarrow{AC}$ on line $AB$.

[2]

(iii)

Find the position vector of the foot of the perpendicular,$N$, from $C$ to line $AB$.

[3]

(iii) Find the position vector of the foot of the perpendicular,$N$, from $C$ to line $AB$.

[3]

(iv)

The point $D$ lies on the line $CN$ produced and is such that $N$ is the mid-point of $CD$.
Find the position vector of $D$.

[2]

(iv) The point $D$ lies on the line $CN$ produced and is such that $N$ is the mid-point of $CD$.
Find the position vector of $D$.

[2]

Suggested Video Solutions
Suggested Handwritten Solutions

2000 TYS 2000

2000 TYS 2000

2000 TYS 2000

2000 TYS 2000

2000 TYS 2000

2000 TYS 2000

2000 TYS 2000

2000 TYS 2000

Share with your friends!

WhatsApp
Telegram
Facebook

H2 Math Free Mini Course

2000 TYS 2000

Sign up for the free mini course and experience learning with us for 30 Days!

Register for FREE H2 Math Mini-course
2000 TYS 2000
Play Video

Join us to gain access to our Question Bank, Student Learning Portal, Recorded Lectures and many more.