##### Math Learning Reflection: How to Assess Your Progress and Plan Ahead

As we approach the end of another year, it’s the perfect time to pause and reflect on the educational journey, particularly in subjects like mathematics

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

# 2019 A Level H2 Math

These Ten-Year-Series (TYS) worked solutions with video explanations for 2019 A Level H2 Mathematics are suggested by Mr Gan. For any comments or suggestions please contact us at support@timganmath.edu.sg.

**2019 A Level H2 Math Paper 1 Question 3**

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**2019 A Level H2 Math Paper 1 Question 4**

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**2019 A Level H2 Math Paper 1 Question 8**

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**2019 A Level H2 Math Paper 1 Question 9 **

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**2019 A Level H2 Math Paper 1 Question 10**

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**2019 A Level H2 Math Paper 1 Question 11**

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**2019 A Level H2 Math Paper 1 Question 12**

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**2019 A Level H2 Math Paper 2 Question 1**

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**2019 A Level H2 Math Paper 2 Question 2**

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**2019 A Level H2 Math Paper 2 Question 3**

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**2019 A Level H2 Math Paper 2 Question 4**

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**2019 A Level H2 Math Paper 2 Question 5**

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**2019 A Level H2 Math Paper 2 Question 7**

A company produces drinking mugs. It is known that, on average, $8\%$ of the mugs are faulty. Each day the quality manager collects $50$ of the mugs at random and checks them; the number of faulty mugs found is the random variable $F$.

The company also makes saucers. The number of faulty saucers also follows a binomial distribution. The probability that a saucer is faulty is $p$. Faults on saucers are independent of faults on mugs.

The mugs and saucers are sold in sets of $2$ randomly chosen mugs and $2$ randomly chosen saucers. The probability that a set contains at most $1$ faulty item is $0.97$.

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Math Learning Reflection: How to Assess Your Progress and Plan Ahead

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**2019 A Level H2 Math Paper 2 Question 8**

**Suggested Handwritten and Video Solutions**

Paper 1

Paper 2

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- Q8
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- Q10
- Q11
- Q12

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- Q1
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- Q7
- Q8

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A solid cylinder has radius $r$ cm, height $h$ cm and total surface area $900$ cm$^{2}$. Find the exact value of the maximum possible volume of the cylinder. Find also the ratio $r:h$ that gives this maximum volume.

[7]

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(i)

State, in the context of the question, two assumptions needed to model $F$ by a binomial distribution.

[2]

(i) State, in the context of the question, two assumptions needed to model $F$ by a binomial distribution.

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You are now given that $F$ can be modelled by a binomial distribution.

(ii)

Find the probability that, on a randomly chosen day, at least $7$ faulty mugs are found.

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(ii) Find the probability that, on a randomly chosen day, at least $7$ faulty mugs are found.

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(iii)

The number of faulty mugs produced each day is independent of other days. Find the probability that, in a randomly chosen working week of $5$ days, at least $7$ faulty mugs are found on no more than $2$ days.

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(iii) The number of faulty mugs produced each day is independent of other days. Find the probability that, in a randomly chosen working week of $5$ days, at least $7$ faulty mugs are found on no more than $2$ days.

[2]

(iv)

Write down an expression in terms of $p$ for the probability that, in a random sample of $10$ saucers, exactly $2$ are faulty.

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(iv) Write down an expression in terms of $p$ for the probability that, in a random sample of $10$ saucers, exactly $2$ are faulty.

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(v)

Write down an equation satisfied by $p$. Hence find the value of $p$.

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(v) Write down an expression in terms of $p$ for the probability that, in a random sample of $10$ saucers, exactly $2$ are faulty.

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Assumptions:

- The probability of each mug being faulty is constant, i.e. $0.08$.
- The event of choosing a faulty mug is independent of other mugs being faulty.

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Assumptions:

- The probability of each mug being faulty is constant, i.e. $0.08$.
- The event of choosing a faulty mug is independent of other mugs being faulty.

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Timothy Gan
7th December 2023

As we approach the end of another year, it’s the perfect time to pause and reflect on the educational journey, particularly in subjects like mathematics

Timothy Gan
30th November 2023

In our modern digital era, the internet has become a pivotal aspect of our daily lives, influencing how we communicate, work, and learn. This digital

Timothy Gan
24th November 2023

Experiencing a disappointing exam is an almost universal part of the educational journey. For students, exams often carry a significant weight – they are not

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