2017 HCI P2 Q6

Timothy Gan 20th April 2024

2017 HCI P2 Q6 A biased tetrahedral ($4$-sided) die has its faces numbered ‘$-1$’, ‘$0$’, ‘$2$’ and ‘$3$’. It is thrown onto a table and the random variable $X$ denotes

2013 NJC P2 Q6 [Modified]

Timothy Gan 20th April 2024

2013 NJC P2 Q6 [Modified] Find the number of ways in which the letters of the word STATISTICS can be arranged if (i) the $3$ S’s are all not together,

2022 NYJC P2 Q9

Timothy Gan 19th April 2024

2022 NYJC P2 Q9 A bag contains three yellow marbles, one blue marble and $x$ red marbles, where $x>1$. In a game, Lily takes $~2$ marbles at random from the

2022 CJC P2 Q7 The probability distribution for the random variable $X$ is shown in the table. Another random variable $Y$ is defined by $Y=2{{X}_{1}}+{{X}_{2}}$, where ${{X}_{1}}$ and ${{X}_{2}}$ are

2012 NJC P1 Q2

Timothy Gan 16th April 2024

2012 NJC P1 Q2 Relative to the origin $O$, the position vectors of the points $A$, $B$ and $P$ are $-mathbf{i}-3mathbf{j}+2mathbf{k}$, $5mathbf{i}+2mathbf{k}$ and $left( 1+2lambda right)mathbf{i}+left( lambda -2 right)mathbf{j}+2mathbf{k}$ respectively,

2018 EJC Promo Q5

Timothy Gan 16th April 2024

2018 EJC Promo Q5 (a) Given that $mathbf{u}$ and $mathbf{v}$ are non-zero vectors such that $mathbf{u}times mathbf{v}=left( mathbf{u}-mathbf{v} right)times left( mathbf{u}+mathbf{v} right)$, what can be deduced about $mathbf{u}$ and $mathbf{v}$?

ACJC Discrete Random Variables Tutorial Q1

Timothy Gan 15th April 2024

ACJC Discrete Random Variables Tutorial Q1 A biased six-sided die is such that $text{P}left( X=1 right)=p$ and $text{P}left( X=r+1 right)=frac{1}{2}text{P}left( X=r right)$, $r=1$, $2$, $3$, $4$, $5$ where $X$ denotes

2015 NYJC P1 Q9

Timothy Gan 11th April 2024

2015 NYJC P1 Q9 (a) A geometric sequence ${{x}_{1}}$, ${{x}_{2}}$, ${{x}_{3}}$, … has first term $a$ and common ratio $r$, where $a>0$, $r>0$. The sequence of numbers ${{y}_{1}}$, ${{y}_{2}}$, ${{y}_{3}}$,

TJC Inequalities Tutorial Q10

Timothy Gan 11th April 2024

TJC Inequalities Tutorial Q10 (i) A wooden artwork is designed to take the form of a right pyramid with square base of sides $2x$m and fixed volume $frac{4}{3}$m$^{3}$. All its

HCI Sequence and Series Tutorial Q7

Timothy Gan 11th April 2024

HCI Sequence and Series Tutorial Q7 The Sierpinski sieve, which is an example of a fractal, is constructed by starting with a solid black equilateral triangle. This triangle is divided

H2 Math Student Only

Timothy Gan