### 2013 A levels H1 General Paper (8807) Paper 1 Suggested Solutions

For the benefit of our students and their revision, here’s the questions for the 2013 paper. Stay tune for our short outlines on these questions. The aim of our outlines is to create discussions online on possible arguments or perspectives on the questions. Feel free to comment on these questions when we have them up. We look forward to your engagement.

1. ‘The world would be a better place if more political leaders were women.’ What is your view?

2. ‘Unlike the Arts, such as writing or music, Mathematics lacks the capacity for creativity.’ How far do you agree with this statement?

• 3. Is there any point in trying to predict future trends?

4. To what extent is it possible to make the punishment fit the crime?

5. Discuss the claim that in the modern world people should care more about international than national issues.

6. How important is it to save plant and animal species which are in danger of extinction?

7. ‘Scientific research into health and diet is unreliable as it so often contradicts itself.’ Is this a fair comment?

8. How far is increased prosperity for all a realistic goal in your society?

9. Consider the view that spoken language is more important than the written form.

10. Why should we be concerned with current affairs when most of them will soon be forgotten?

11. Education should only be concerned with what is useful in life. Discuss.

12. How far, in your society, should unpopular views be open to discussion?

### 2014 A levels H1 General Paper (8807) Paper 1 Suggested Solutions

For the benefit of our students and their revision, here’s the questions for the 2014 paper. Stay tune for our short outlines on these questions. The aim of our outlines is to create discussions online on possible arguments or perspectives on the questions. Feel free to comment on these questions when we have them up. We look forward to your engagement.
1. ‘Traditional marriage is an outdated concept.’ To what extent is this true of your society?
2. How far should firms be allowed to limit their workers’ rights when profits are at stake?
3. ‘Gambling on sport undermines its spirit and should be banned.’ How realistic is this position?
4. Discuss the view that, with an increasing global need for energy, every possible source should be exploited to the full.
5. ‘For the majority of people, the Arts are irrelevant to their daily lives.’ How true is this of your society?
6. How far is it important for people to be aware of current events in countries other than their own?
7. In times of economic hardship, should a country still be expected to provide financial or material aid to others?
8. Do films offer anything more than an escape from reality?
9. To what extent can the regulation of scientific or technological developments be justified?
10. ‘Getting what one wants in life is what matters.’ Discuss.
11. Examine the extent to which expenditure on arms and the armed forces is justifiable in the modern world.
12. Consider the view that some careers are better suited to one gender than the other.

### 2013 A-level H1 Mathematics (8864) Question 12 Suggested Solutions

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

(i)

(ii)
$\mathrm{P}(A) = \frac{1}{6} \frac{1}{6} + \frac{1}{6} \frac{1}{6} + \frac{1}{6} \frac{1}{6} +\frac{1}{6} \frac{1}{6} + \frac{1}{6} + \frac{1}{6} =\frac{4}{9}$

(iii)
$\mathrm{P}(A \cap B) = \frac{1}{9}$

(iv)
$\mathrm{P}(A \cup B) = \frac{4}{9} + \frac{2}{6} - \frac{1}{9} = \frac{2}{3}$

(v)
$\mathrm{P} (B| A \prime) = \frac{\mathrm{P}(B \cap A \prime)}{\mathrm{P}(A \prime)} = \frac{\frac{1}{6} \frac{4}{6} + \frac{1}{6} \frac{4}{6}}{5/9} = \frac{2}{5}$

The tree diagram was not easy definitely.

### 2013 A-level H1 Mathematics (8864) Question 10 Suggested Solutions

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

(i)

$H_0: \mu = 12$

$H_1: \mu \ne 12$

Under $H_0, \bar{X} ~\sim~ \mathrm{N} (12, \frac{0.8^{2}}{20})$

For $H_0$ to be not rejected at 5% level of significance, then

$latex -1.95996 < \frac{m-12}{0.8/ \sqrt{20}} < 1.95996$ $latex \therefore, \{m \in \mathbb{R} |11.6 < m < 12.4\}$ (ii) $latex H_0: \mu = 12$ $latex H_1: \mu < 12$ Under $latex H_0, \bar{X} ~\sim~ \mathrm{N} (12, \frac{0.8^{2}}{40})$ From the graphing calculator, p-value $latex = 0.02405 < 0.05$, we reject $latex H_0$. Thus, there is sufficient evidence at 5% level of significant to conclude that the mean salt content has been reduced.

Read carefully that it is two-tailed and perform the test. Bare in mind to leave answers in set notation.

### 2013 A-level H1 Mathematics (8864) Question 9 Suggested Solutions

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

(i)

(ii)
From graphing calculator, $r = 0.903$

r-value is close to 1 which suggest a strong positive correlation between the variables x and y.

(iii)
From graphing calculator, required regression line: $y = 4.46x + 87.43$

(iv)
When $x = 13.2, y = 146$.

Since r is close to 1, and we used the regression line of y on x to estimate y given an x within the range of data, the estimate will be reliable.

Very standard. Some students made mistake while keying values into the GC unfortunately.

### 2013 A-level H1 Mathematics (8864) Question 8 Suggested Solutions

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

(i)
Let X denote the number of batteries with lifetime of at least 100 hours, out of 10.

$X ~\sim~ \mathrm{B}(10, 0.8)$
$\mathrm{P} (X=10) = 0.107$

(ii)
$\mathrm{P} (X \ge 10) = 0.678$

(iii)
Let Y denote number of packs that satisfy the customer, out of 80.

$Y ~\sim~ \mathrm{B}(80, 0.6777995)$

Since $n = 80$ is large, $np = 54.224 > 5, nq = 25.776 >5$
$\Rightarrow Y ~\sim~ \mathrm{N}(54.224, 17.471)$ approximately

$\mathrm{P} (Y \ge 60)$
$= \mathrm{P} (Y \ge 59.5)$ by continuity correction

$\approx 0.103$

Remember to do CONTINUITY CORRECTION!!!

### 2013 A-level H1 Mathematics (8864) Question 6 Suggested Solutions

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

(i)
Stratified random sampling.
Split the population of people into three mutually exclusive strata, $X,$Y, and $Z. Number of$X to be surveyed $= \frac{5000}{30000} \times 150 = 25$
Number of $Y to be surveyed $= \frac{10000}{30000} \times 150 = 50$ Number of$Z to be surveyed $= \frac{15000}{30000} \times 150 = 75$

Select the required number of people within each strata using simple random sampling.

(ii)
The sample she gets will be more representative of the population since she split them into mutually exclusive strata.

Students can also present answers in a neat table for (i). Do take note that you must mention the use of simple random sampling.

### 2013 A-level H1 Mathematics (8864) Question 5 Suggested Solutions

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

(i)
$\mathrm{ln} e^{2-2x} = \mathrm{ln}2 + \mathrm{ln}e^{-x}$
$2 - 2x = \mathrm{ln} 2 - x$
$x = 2 - ln2$

(ii)
$\frac{dy}{dx} = -2 e^{2-2x} + 2 e ^{-x} = 0$
$e^{2-2x} = e^{-x}$
$x = 2$
$y = -e^{-2}$
$\therefore, \mathrm{required~coordinates~is~} (2, -e^{-2})$

(iii)

(iv)
Area $= \int_0^1 e^{2-2x} - 2e^{-x} dx = 1.93 units^{2}$ using graphing calculator.

Students must show all the requirements of the graph, and please use a GC to check it. Lastly, since (iv) did not require exact answers, we can easily use a GC

### 2013 A-level H1 Mathematics (8864) Question 4 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.
(i)
$\frac{dy}{dx} = 3x^{2} - 2ax + 3$

When $x = 1, ~\frac{dy}{dx} = 6 - 2a$

$m_{normal} = -\frac{1}{6-2a}$

(ii)
Equation of normal: $y - (10-a) = - \frac{1}{6-2a} (x-1)$

Subs $(-5, 3)$,

$\Rightarrow a - 7 = \frac{6}{6-2a}$

$a^{2} - 10a + 24 = 0$

$(a-4)(a-6) = 0$

$a = 4 \mathrm{~or~} 6$.

(iii)
If $a =4$, Normal: $y - 6 = 0.5 (x-1)$

$\therefore, x = 11$

Required coordinates $= (11,11)$