H2 Mathematics (9740) 2016 Prelim Papers

H2 Mathematics (9740) 2016 Prelim Papers

JC Mathematics

So many students have been asking for more practice. I’ll put up all the Prelim Papers for 2016 here. Do note that the syllabus is 9740 so students should practice discretion and skip questions that are out of syllabus. ūüôā

Here are the Prelim Paper 2016. Have fun!

Here is the MF26.


2016 ACJC H2 Math Prelim P1 QP
2016 ACJC H2 Math Prelim P2 QP


2016 CJC H2 Math Prelim P1 QP
2016 CJC H2 Math Prelim P2 QP


2016 HCI JC2 Prelim H2 Mathematics Paper 1
2016 HCI JC2 Prelim H2 Mathematics Paper 2


2016 IJC H2 Math Prelim P1 QP
2016 IJC H2 Math Prelim P2 QP


2016 JJC H2 Math Prelim P1 QP
2016 JJC H2 Math Prelim P2 QP


2016 MI H2 Math Prelim P1 QP
2016 MI H2 Math Prelim P2 QP


2016 MJC H2 Math Prelim P1 QP
2016 MJC H2 Math Prelim P2 QP


2016 NJC H2 Math Prelim P1 QP
2016 NJC H2 Math Prelim P2 QP


2016 NYJC H2 Math Prelim P1 QP
2016 NYJC H2 Math Prelim P2 QP


2016 PJC H2 Math Prelim P1 QP
2016 PJC H2 Math Prelim P2 QP


2016 SAJC H2 Math Prelim P1 QP
2016 SAJC H2 Math Prelim P2 QP


2016 SRJC H2 Math Prelim P1 QP
2016 SRJC H2 Math Prelim P2 QP


2016 TJC H2 Math Prelim P1 QP
2016 TJC H2 Math Prelim P2 QP


2016 TPJC H2 Math Prelim P1 QP
2016 TPJC H2 Math Prelim P2 QP


2016 VJC H2 Math Prelim P1 QP
2016 VJC H2 Math Prelim P2 QP


2016 YJC H2 Math Prelim P1 QP
2016 YJC H2 Math Prelim P2 QP


Thinking Math@TheCulture #3

Thinking [email protected] #3

JC Mathematics, Mathematics

[email protected] is a series of questions that we, as tutors feel that are useful in helping students think and improve their understanding.

Thinking [email protected] is curated by KS. More of him can be found¬†here.

This is a question from 1976 A’levels Paper 2. I thought it is pretty interesting to discuss the question with a little extension.

(a) In how many ways can 5 copies of a book be distributed among 10 people, if no-one gets more than one copy?

(b) In how many ways can 5 different books be distributed among 10 people if each person can get any number of books?

So now, let us modify it a bit.

(c) In how many ways can 5 copies of a book be distributed among 10 people if each person can get any number of books?

Notice that the difference between (b) and (c) is that the book distributed is not identical. So for (c), we are pretty much distributing r identical balls to n distinct boxes. Whereas for (b) , we are pretty much distributing r distinct balls to n distinct boxes.

Probability Question #4

Probability Question #4

JC Mathematics

A gambler bets on one of the integers from 1 to 6. Three fair dice are then rolled. If the gambler’s number appears k times (k = 1, 2, 3), he wins $ k. If his number fails to appear, he loses $1. Calculate the gambler’s expected winnings

2016 A-level H2 Mathematics (9740) Paper 2 Suggested Solutions

2016 A-level H2 Mathematics (9740) Paper 2 Suggested Solutions

JC Mathematics

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

Numerical Answers (click the questions for workings/explanation)

Question 1: 0.0251 \text{~m/min}
Question 2: \frac{x^2}{2} \text{sin}nx + \frac{2x}{n^2} \text{cos}nx - \frac{2}{n^3} \text{sin}nx + C;~ a = 2 \text{~or~} 6;~ \pi (\frac{2}{5} - \text{ln} \frac{3}{\sqrt{5}})
Question 3: a + \frac{3}{4} - \text{sin}a - \text{cos}a + \frac{1}{4} \text{cos}2a;~ \frac{1}{4}(\pi + 1)^2
Question 4: z = 2.63 + 1.93i, ~ 3.37 + 0.0715i ;~8^{\frac{1}{6}}e^{i(-\frac{\pi}{12})}, ~8^{\frac{1}{6}}e^{i(-\frac{3 \pi}{4})}, ~8^{\frac{1}{6}}e^{i(\frac{7\pi}{12})};~ n=7
Question 5: \frac{11}{42};~ \frac{4}{11};~ \frac{4}{1029}
Question 6: 60;~ 10;~ \{ \bar{x} \in \mathbb{R}, 0 \textless \bar{x} \le 34.8 \};~ \{ \alpha \in \mathbb{R}, 0 \textless \alpha \le 8.68 \}
Question 7: 24;~ 576;~ \frac{1}{12};~ \frac{5}{12}
Question 8: r = -0.980;~ c = -17.5;~ d = 91.8;~ y = 85.9
Question 9: a = 7.41;~ p = 0.599 \text{~or~} 0.166;~ 0.792
Question 10: 0.442;~ 0.151 ;~ 0.800;~ \lambda = 1.85

 

Relevant materials

MF15

KS Comments

2015 A-level H2 Mathematics (9740) Paper 2 Question 11 Suggested Solutions

JC Mathematics

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

(i)
Number of ways = \frac{8!}{2!2!} = 10080 ways

(ii)
Number of ways = 10080 -1 = 10079 ways

(iii)
Number of ways = 6! = 720 ways

(iv)
Case 1: 2 A’s together and B’s separated
5! \times ^6 C_2 = 1800
Case 2: 2 B’s together and A’s separated
5! \times ^6 C_2 = 1800
Case 3: 2 A’s together and 2 B’s together
720

Number of ways =10080 – 1800 – 1800 – 720 = 5760 ways

2015 A-level H2 Mathematics (9740) Paper 2 Question 8 Suggested Solutions

JC Mathematics

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

Let X denote the mass of pineapple tarts and \mu denote the population mean mass of pineapple tarts.

H_0: \mu = 0.9

H_1: \mu ~ \textless ~ 0.9

Unbiased estimate of population mean = 0.8825

s^2 = 0.0747854073^2 \approx 0.00559 (3 SF)

Under H_0, \bar{X} \sim \mathrm{N} (\mu, \frac{s^2}{n})

Test Statistic, T = \frac{\bar{X}- \mu}{\frac{s}{\sqrt{n}}} \sim t(7) at 10% level of significance.

Using GC, p-value = 0.264619 > 0.1

\Rightarrow, do not reject H_0

There is insufficient evidence at 10% significance level to reject the stall owner’s claim.