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.

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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

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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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 $F$.

(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.

[2]

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.

[2]

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

[2]

(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]

(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]

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.

(iv)

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

[1]

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

[1]

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 $0.97$.

(v)

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

[4]

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

[1]

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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.

2019 TYS 2019

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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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2019 A Level H2 Math Paper 2 Question 8
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