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

2010 A Level H2 Math

These Ten-Year-Series (TYS) worked solutions with video explanations for 2010 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
2010 A Level H2 Math Paper 1 Question 7

A bottle containing liquid is taken from a refrigerator and placed in a room where the temperature is a constant $20{}^\circ \text{C}$. As the liquid warms up, the rate of increase of it temperature $\theta {}^\circ \text{C}$ after time $t$ minutes is proportional to the temperature different $\left( 20-\theta \right){}^\circ \text{C}$. Initially the temperature of the liquid is $10{}^\circ \text{C}$ and the rate of increase of the temperature is $1{}^\circ \text{C}$ per minute. By setting up and solving a differential equation, show that $\theta =20-10{{e}^{-\frac{1}{10}t}}$ 

Find the time it takes the liquid to reach a temperature of $15{}^\circ \text{C}$, and state what happens to $\theta $ for large values of $t$. Sketch a graph of $\theta $ against $t$.

Suggested Handwritten and Video Solutions


2010 TYS 2010 2010 TYS 2010


2010 TYS 2010


2010 TYS 2010


2010 TYS 2010 2010 TYS 2010


2010 TYS 2010


2010 TYS 2010

Share with your friends!

WhatsApp
Telegram
Facebook
2010 A Level H2 Math Paper 1 Question 9
2010 TYS 2010

A company requires a box made of cardboard of negligible thickness to hold $300$ cm$^{3}$ of powder when full. The length of the box is $3x$ cm, the width is $x$ cm and the height is $y$ cm. The lid has depth $ky$ cm, where $0<k\le 1$ (see diagram).

(i)

Use differentiation to find, in terms of $k$, the value of $x$ which gives a minimum total external surface area of the box and the lid.

[6]

(i) Use differentiation to find, in terms of $k$, the value of $x$ which gives a minimum total external surface area of the box and the lid.

[6]

(ii)

Find also the ratio of the height to the width, $\frac{y}{x}$, in this case, simplifying your answer.

[2]

(ii) Find also the ratio of the height to the width, $\frac{y}{x}$, in this case, simplifying your answer.

[2]

(iii)

Find the values between which $\frac{y}{x}$ must lie.

[2]

(iii) Find the values between which $\frac{y}{x}$ must lie.

[2]

(iv)

Find the value of $k$ for which the box has square ends.

[2]

(iv) Find the value of $k$ for which the box has square ends.

[2]

Suggested Video Solutions
Suggested Handwritten Solutions

2010 TYS 2010 2010 TYS 2010

2010 TYS 2010

2010 TYS 2010

2010 TYS 2010

2010 TYS 2010 2010 TYS 2010

2010 TYS 2010

2010 TYS 2010

2010 TYS 2010

Share with your friends!

WhatsApp
Telegram
Facebook
2010 A Level H2 Math Paper 2 Question 7

For events $\text{A}$ and $\text{B}$, it is given that $\text{P}(A)=0.7$, $\text{P}(B)=0.6$ and $\text{P}(A\left| B’ \right.)=0.8$. Find

(i)

$\text{P}(A\cap B’)$,

(i) $\text{P}(A\cap B’)$,

(ii)

$\text{P}(A\cup B)$,

(ii) $\text{P}(A\cup B)$,

(iii)

$\text{P}(B’\left| A \right.)$,

(iii) $\text{P}(B’\left| A \right.)$,

Find a third event $C$, it is given that $\text{P}(C)=0.5$ and that $A$ and $C$ are independent.

(iv)

Find $\text{P}\left( A’\cap C \right)$

(iv) Find $\text{P}\left( A’\cap C \right)$

(v)

Hence state an inequality satisfied by $\text{P}(A’\cap B\cap C)$.

(v) Hence state an inequality satisfied by $\text{P}(A’\cap B\cap C)$.

Suggested Handwritten and Video Solutions
2010 TYS 2010
2010 TYS 2010
2010 TYS 2010
2010 TYS 2010
2010 TYS 2010
2010 TYS 2010
2010 TYS 2010
2010 TYS 2010
2010 TYS 2010
2010 TYS 2010

Share with your friends!

WhatsApp
Telegram
Facebook
2010 A Level H2 Math Paper 2 Question 9

In this question you should state clearly the values of the parameters of any normal distribution you use.

Over a three-month period Ken makes $X$ minutes of peak-rate telephone calls and $Y$ minutes of cheap-rate calls. $X$ and $Y$ are independent random variables with the distributions $\text{N}\left( 180,{{30}^{2}} \right)$ and $\text{N}\left( 400,{{60}^{2}} \right)$ respectively.

(i)

Find the probability that, over a three-month period, the number of minutes of cheap-rate calls made by Ken is more than twice the number of minutes of peak-rate calls.

(i) Find the probability that, over a three-month period, the number of minutes of cheap-rate calls made by Ken is more than twice the number of minutes of peak-rate calls.

Peak-rate calls cost $\$0.12$ per minute and cheap-rate calls cost $\$0.05$ per minute.

(ii)

Find the probability that, over a three-month period, the total cost of Ken’s calls is greater than $\$45$.

(ii) Find the probability that, over a three-month period, the total cost of Ken’s calls is greater than $\$45$.

(iii)

Find the probability that the total cost of Ken’s peak-rate calls over two independent three-month periods is greater than $\$45$.

(iii) Find the probability that the total cost of Ken’s peak-rate calls over two independent three-month periods is greater than $\$45$.

Suggested Handwritten and Video Solutions


2010 TYS 2010


2010 TYS 2010


2010 TYS 2010


2010 TYS 2010


2010 TYS 2010


2010 TYS 2010

Share with your friends!

WhatsApp
Telegram
Facebook

H2 Math Free Mini Course

2010 TYS 2010

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

Register for FREE H2 Math Mini-course
2010 TYS 2010
Play Video

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