In today’s digital age, the internet has seamlessly woven itself into the fabric of our daily lives, becoming an indispensable tool for communication, information, and, notably, entertainment. The allure of online entertainment lies in its accessibility and immediacy. With the internet at our fingertips, we can satisfy our cravings for entertainment anytime, anywhere, with just the tap of a screen or the click of a mouse. This convenience has transformed how we unwind, relax, and escape from the pressures of daily life. However, this easy access to entertainment comes with its own set of chall ..read more

2024 SMO Open Category Let $n$ denote the number of ways of arranging all the letters of the word MATHEMATICS in one row such that (1) both M’s precede both T’s and (2) neither the two M’s not the two T’s are next to each other. Determine the value of $\frac{n}{6!}$. Suggested Video and Handwritten Solutions H2 Math Tuition Students Only Login here to view Email Address Password Remember Me Log In Join Us Our H2 Math Tuition includes Question Bank with Video solutions to 1400+ questions Online Portal H2 Math Summary Notes Structured Curriculum and Notes H2 Math Tu ..read more

JPJC Sampling Tutorial Q4 $X$ and $Y$ are random variables with $Y$ being defined as $Y=aX+b$, where $a$ and $b$ are positive constants, and $\text{E}\left( X \right)=0$ and $\text{Var}\left( X \right)=\frac{4}{5}$. It is given that $\text{E}\left( Y \right)=50$ and $\text{Var}\left( Y \right)=80$. Find $a$ and $b$. A random sample consists of $160$ independent observations of $Y$. Find the probability that the sample mean lies between $49.0$ and $50.5$. [6] Suggested Video and Handwritten Solutions H2 Math Tuition Students Only Login here to view Email Address Passwor ..read more

2008 IJC P1 Q2 In triangle $OAB$, $\angle OAB=90{}^\circ $ and the point $C$ on $AB$ is such that $AC=\frac{2}{3}CB$. With respect to the origin $O$, the position vectors of $A$ and $B$ are given as $\mathbf{a}$ and $\mathbf{b}$ respectively. (i) Show that $\mathbf{a}\cdot \mathbf{b}={{\left| \mathbf{a} \right|}^{2}}$. [1] (ii) Find $\mathbf{c}$, the position vector of $C$ in terms of $\mathbf{a}$ and $\mathbf{b}$. [1] (iii) Given that the lengths of $OA$ and $OB$ are $3$ and $5$ units respectively, find the length of projection of $\mathbf{c}$ onto $\mathbf{b ..read more

ASRJC Sampling Tutorial Q5 A random sample of $100$ packets of a breakfast cereal was examined and the mass, $m$ grams, of the contents recorded. The results revealed that $\sum{m=3010}$ and $\sum{{{m}^{2}}=91\,280}$. Obtain an unbiased estimate of the population variance. [2] By taking the unbiased estimate obtained above to be the population variance, find the size of the random sample required so that there is a probability of at least $0.98$ that the sample mean will be within $0.5$g of the true mean. [5] Suggested Video Solutions H2 Math Tuition Students Only Login he ..read more

In the pursuit of academic success, setting and achieving goals play a pivotal role, particularly in disciplines like mathematics. Effective goal setting not only provides students with a roadmap for their studies but also instills a sense of direction, purpose, and accountability. This guide will focus on how students can set SMART goals for their math studies and provide tools and strategies to help them achieve these goals. Understanding SMART Goals SMART goals are a proven framework for setting clear, attainable objectives. SMART stands for Specific, Measurable, Achievable, Relevant, and T ..read more

These Ten-Year-Series (TYS) worked solutions with video explanations for 1998 A Level H2 Mathematics Paper 2 Question 7 are suggested by Mr Gan. For any comments or suggestions please contact us at support@timganmath.edu.sg. 1998 A Level H2 Math Paper 2 Question 7 A computer can give independent observations of a random variable $X$ with probability distribution given by $\text{P}\left( X=0 \right)=\frac{3}{4}$ and $\text{P}\left( X=2 \right)=\frac{1}{4}$. It is programmed to output a value for the random variable $Y$ defined by $Y={{X}_{1}}+{{X}_{2}}$, where ${{X}_{1}}$ and ${{X}_{2 ..read more

2022 ASRJC BT2 P2 Q6 On average, it is known that $1$ in $12$ peaches produced in a farm are classified as very sweet. A farmer randomly selected $40$ peaches from the farm. (i) State, in this context, two necessary assumptions to model the random variable representing the number of very sweet peaches by a binomial distribution. [2] The farmer randomly selects $5000$ peaches and packs them into boxes of $40$ peaches each for shipment.  (ii) Obtain an approximate distribution for the mean number of very sweet peaches in a box for this shipment. Hence find the proba ..read more

As June holidays approach, students find themselves at a crucial juncture in their academic journey. With the semester winding down and exams looming on the horizon, the pressure to excel intensifies. For many students, this extended break presents a valuable opportunity to recalibrate, review, and reinforce their understanding of key subjects. Among the myriad of options available for holiday study, crash courses stand out as a compelling choice, particularly for subjects with complex concepts like mathematics. Then the question arises: is joining a crash course during school holidays necessa ..read more

2010 HCI P1 Q11 [Modified] The diagram above shows part of the structure of a modern art museum designed by Marcus, with a horizontal base $OAB$ and vertical wall $OADC$. Perpendicular unit vectors, $\mathbf{i}$, $\mathbf{j}$ and $\mathbf{k}$ are such that $\mathbf{i}$ and $\mathbf{k}$ are parallel to $OA$ and $OC$ respectively. The walls of the museum $BCD$ and $ABD$ can be described respectively by the equations $\mathbf{r}\cdot \left( \begin{matrix} -1 \\ -5 \\ 6 \\ \end{matrix} \right)=36$ and $\mathbf{r}=\left( \begin{matrix} 14 \\ 0 \\ 0 \\ \end{matrix} \right)+\lambda \le ..read more