The radius of a circle is $$\frac{1}{2}$$~the length of the side of the square. How many times the perimeter of a square is the diameter of a circle?


Putting these lines~$\left\textbar{} \right\textbar$ round a number or calculation makes sure the answer is positive; for example both $\left\textbar{} 8\right\textbar$~and $\left\textbar{} -8\right\textbar$~ would give the answer $8$.What is the answer to:$\left\textbar{} 4-20\right\textbar$

Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers->Understanding Numbers and Digits


What is the value of the digit $1$ in the number $6543.2109$.

t\emph{e}n

one tenth

one hundred

one hundredth

One thousandth

Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases


Which of these numbers is exactly divisible by $$2$$ and $$8$$?

Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules->Simple Questions of Division without Remainders


\textbf{If he pressed the remote a total of 9 times throughout the day, was the TV on or off at the end of the day?}

On

Off

I dont know

Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers


Elmo is packing $$107$$ cookies. He wants to put $$5$$ cookies in each plastic bag. How many cookies will not be packed into plastic bags?

Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules


Fifteen people play a one-on-one knockout tournament. How many games will be played to determine the winner? ．

$$5$$ games

$$14$$ games

$$16$$ games

$$49$$ games

$$50$$ games

Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Sports Competition


$$\boxed{1}\textasciitilde\textasciitilde\boxed{2}\textasciitilde\textasciitilde\boxed{3}\textasciitilde\textasciitilde\boxed{4}$$  Jane uses these four number cards to make two 2-digit numbers and works out the sum.  $$\square\textasciitilde\textasciitilde\square+\square\textasciitilde\textasciitilde\square$$  How many different sums can she get?

Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Complex Forming Numbers->Complex Forming Numbers (with special requirements)


Issy tosses a fair coin four times. She gets Heads, Heads, Heads, Tails. If she tosses it afifth time, is she more likely to get Heads or Tails?

equally likely

H\emph{e}ads

T\emph{a}ils

not enough information

Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Typical Probability Problems->Tossing Coins


The five symbols $$\bigcirc$$, $$\triangle$$, $$\diamond$$, $$\star$$ and $$\oplus$$ used in the equations below represent different digits.  $$\bigcirc + \bigcirc + \bigcirc = \triangle$$  $$\diamond + \diamond + \diamond = \oplus$$  $$\triangle + \oplus = \star$$  What is the value of $$\star$$?

Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles->Number Puzzles (horizontal forms)


6.Pip wants you to help him choose his outfit. A top, a pair of pants and shoes are a must however a hat is optional. How many different choices are there for Pip?

Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Enumeration


String $$A$$ is longer than String $$B$$.  String $$C$$ is the same length as String $$B$$.  String $$D$$ is longer than String $$A$$.  Which is the longest string?

$$A$$

$$B$$

$$C$$

$$D$$

Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning by Comparing


How many three-digit numbers can you create using the digits $$3$$, $$0$$, and $$7$$, and using each digit only once? ($$1998$$ Math Kangaroo Problems, Level $$3-4$$, Question \#$$6$$)

Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Complex Forming Numbers->General Complex Forming Numbers


There are $$30$$ pupils in my class. $$20$$ pupils like Maths and $$18$$ pupils like English. Twice as many pupils like both subjects as compared to those that like neither of them. How many pupils like only Maths?

Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations


Kathy started doing her homework at $$09:15$$. She used $$2\text{h }45\min $$ to complete her homework. Then she took a nap for $$20$$ minutes before she had her lunch, At what time did she have her lunch ? ．

Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation


Consider these two operations: $a\Psi b=a^{2}-b$ and $a \nu b=\sqrt{ab}$.  Which of these values are possible answers of $4 \nu (2 \Psi 3)^{2}$?

Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle


Issy tosses a fair coin four times. She gets Heads, Heads, Heads, Tails. If she tosses it a fifth time, is she more likely to get Heads or Tails?

equally likely

Heads

Tails

not enough information


The total of five different, positive odd numbers is $$85$$. What's the most that the largest number could be?

Overseas Competition->Knowledge Point->Combinatorics->Combinatorics Involving Extreme Values->Extreme Value with Fixed Sums


How many balls does Pip want to take out?

Overseas Competition->Knowledge Point->Counting Modules


Overseas In-curriculum->Knowledge Point->Operations of Numbers ->Division of Whole Numbers->Division Within the Multiplication Tables

Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication


After shopping for clothes, Andy has 2 shirts and 3 trousers. Can you work out how many combinations of outfits Andy has?


Adrian finished doing his homework at $$1$$ p.m. He started doing his homework $$2$$ hours ago. At what time did he start to do his homework?

$$11$$ a.m.

$$11$$ p.m.

$$3$$ a.m.

$$3$$ p.m.


The Pythagoras School of Music has $$100$$ students. Of these, $$60$$ are in the band and $$20$$ are in the orchestra.  Given that $$12$$ students are in both the band and the orchestra, how many are in neither the band nor the orchestra?

Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle->Inclusion-Exclusion Principle for Two Sets


Bud wants to arrange $$4$$ different soft toys side by side in a row. Find the number of ways that she can arrange them.


The total of four different, positive odd numbers is $$62$$. What's the most that the largest number could be?


What is the smallest possible sum of two positive integers whose product is $$120$$?


Carol brought $$6$$ cookies, Gina brought $$7$$ cookies, Sarah brought $$3$$ cookies, and Judy didn\textquotesingle t bring cookies. They put all the cookies together and divide them equally. How many cookies does each girl get?

Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems ->Using Formulas


Students Arn, Bob, Cyd, Dan, Eve, and Fon are arranged in that order in a circle. They start counting: Arn first, then Bob, and so forth. When the number contains a $7$ as a digit (such as $47$) or is a multiple of $7$ that person leaves the circle and the counting continues. Who is the last one present in the circle?

Arn

Bob

Cyd

Dan

Eve


There are 4 types of cakes available in a cake shop: chocolate, cheese, blueberry and  blackforest. Naomi wants to buy 2 different types of cakes. How many different  choices does she have?

Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations


The desks in a Primary $$2$$ classroom are arranged in straight rows. Each row has the same number of desks. Robert sits at the desk that is in the third row from the front and the fifth row from the back. He sits at the centre of his row and there are $$4$$ desks to his left. How many desks are in the classroom?

None of the above

Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Queuing Problems


Kelly is facing the north-east direction. How should she turn so that she faces west?

$$45^{\circ}$$ clockwise

$$135^{\circ}$$ clockwise

$$135^{\circ}$$ anti-clockwise

$$225^{\circ}$$ anti- clockwise


Four boys each prepared $$1$$ gift for a party. How many ways can these $$4$$ gifts be distributed among the $$4$$ kids so that no one receives his own gift?

None of the above


Four people each take a bucket of water to the faucet and the time required to fill the buckets of the four people are $$1$$ minutes, $$3$$ minutes, $$2$$ minutes, and $$5$$ minutes respectively. If only one tap is available, how can we arrange the order of the four people getting water so that their total waiting time is the shortest? This minimum total time by all four people is  minutes. (The time spent fetching water is also counted within waiting time)


Alvin scored $$872$$ points.  Bala scored two times as many points as Alvin had scored.  Chandran scored $$926$$ more points than Bala.  How many points did Chandran score?

Overseas In-curriculum->Knowledge Point->Operations of Numbers ->Mixed Operations->Mixed Operations of Multiplication and Addition of Whole Numbers


Uncle John has a farm. His wife and his two sons are staying with him in the farm. They raise 10 cows and 20 chickens. How many total legs are there in the farm?


Ten students record their scores of hitting balls: $20$, $16$, $16$, $21$, $18$, $11$, $20$, $32$, $16$, and $21$. If the boy with the score of $32$ realizes that he actually gets only $22$, which of the following is correct?

The mean decreases by $2$.

The mean increases by $1$.

The mode changes.

The median stay the same.

The median decreases by $1$.

Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability


Distance between A and B is $$900$$m. Eddy and Vicky start from A and B at the same time and walk in the same direction. Vicky walks $$60$$m per minute while Eddy walks $$80$$m per minute. How long does it take Eddy to catch up with Vicky?

Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle->Extreme Value in Inclusion-Exclusion for Multi-sets


A conductor wanted to make a trio consisting of a fiddler, a pianist, and a drummer. He had to choose one of two fiddlers, one of two pianists, and one of two drummers. He decided to try each of the possible trios. How many attempts did he have to make?

Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration


Chin Lee has $12$ dino models and $6$ bear soft toys. The remainder of her toys were caterpillar soft toys. She had a total of $40$ toys in total. What percentage of her toys were soft toys?


How many minutes are there in two and a half hours?


Find the missing digit in the blank. ．  $$\begin{matrix}\& \&~9~\&~\boxed{?}~\& 4 \textbackslash\textbackslash\& \times\& \& \&~6 \textbackslash\textbackslash{} \hline~\&5~\&~6~\& 0~\& 4\end{matrix}$$


None of the above.


Katie bought a plate of tonkatsu that cost $\textbackslash$12$. She added on a salad that cost $\textbackslash$2$. She paid for her meal and had to pay an additional $8\textbackslash\%$ GST on the price. How much did she have to pay for her meal?


How long is it, in hours and minutes, between $$10:28$$ and $$16:06$$?

$$5$$ hrs $$38$$ mins

$$8$$ hrs $$34$$ mins

$$5$$ hrs $$36$$ mins

$$26$$hrs $$34$$ mins


9. Each item below has two types with different prices:  Pens:  Rulers:  Peter wants to buy one pen and one ruler.  (1) How many combinations are there?~\uline{~~~~~~~~~~}~

aaa

bbb

Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Enumeration


There is a $\dfrac{3}{10}$~chance that Justin will win the lottery. There is a $\dfrac{4}{5}$~chance that Ivy will win the same lottery. Who has a higher probability of winning this lottery?

Justin

Ivy


The ratio of boys to girls in a school was $4:3$. The ratio of girls to teachers was $9:1$. If there were $144$ boys, how many people were there in the school in total?


There are 50 stories in a book.~ Pip read 24 stories, Bud read 16 stories, Mary read 12 stories.~~What is the largest possible number of children who read only one kind of these stories?


How many shortest paths are there from point A to point B?

Overseas Competition->Knowledge Point->Counting Modules->Finding the Shortest Path by Number Notation->Finding the Shortest Path by Number Notation (simple)->Finding the Shortest Routes


In Jane\textquotesingle s school, there are $30$ students born in April, and each of them was born in a different day. What is the probability of choosing one student who was exactly born in the first ten days of April?

$\frac {1}{30}$

$\frac {1}{3}$

$\frac {1}{4}$

$\frac {1}{15}$


What time is $$300$$ minutes after $$10$$ A.M.? ．

$$3:00$$ A.M.

$$15:00$$ A.M.

$$5:00$$ P.M.

$$ 3:00$$ P.M.

Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations


Hansen took a flight to Perth from Singapore and arrived at $$05:30$$. If the journey took him $$5\text{h}$$ $$40$$$$\min$$, at what time did the plane take off from Changi Airport in Singapore?


How many numbers that the digit in tens place is $5$ less than the digit in ones place?


Aaron finished watching a concert at $$2.45$$ p.m. The concert lasted $$\text{1h}$$$$\text{20min}$$.  What time did the concert start?

$$1.25$$ p.m.

$$1.45$$ p.m.

$$3.05$$ p.m.

$$3.35$$ p.m.


How many squares are there in equal part?

Overseas Competition->Knowledge Point->Counting Modules->Counting the Number of Figures


A stationery shop is selling several items at different prices:  Highlighters: $\textbackslash$3$, $\textbackslash$6$  Scissors: $\textbackslash$6$, $\textbackslash$9$, $\textbackslash$11$, $\textbackslash$14$  If you want to buy one highlighter and one pair of scissors, then there are~\uline{~~~~~~~~~~}~combinations with different total prices.


Susan prepared a plate of cookies for her friends Ashley, Sam, Max and Olivia, Susan tried the first cookie before serving them to her friends. Ashley took $2$ cookies and gave $1$ to Sam. Max then took $3$ cookies, and gave $1$ to Olviia and $1$ to Susan. If they each ate the cookies they ended up with, who ate the most cookies?

Susan

Ashley

Sam

Max

Olivia

Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Law of Addition


What is the missing digit represented by $$B$$?

Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles->Number Puzzles (vertical forms)


Johnathan has $176$ stickers. If he wants to paste $8$ stickers on each page of his sticker album, he will need $16$ more stickers. How many pages are there in the sticker album?


Ali took a bus from Singapore to Malacca at $$10:45$$. The bus ride took $$4\text{h}40$$$$\min $$. What time did he reach Malacca?

Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation


Here is a figure with 12 matchsticks.  How many squares are there in the figure?  There are~\uline{~~~~~~~~~~}~squares.

Overseas Competition->Knowledge Point->Counting Modules->Counting the Number of Figures->Classifying and Enumerating->Counting Regular Figures


David takes 30 seconds to climb from the first floor to the third floor. How many seconds will it take him to climb from the third floor to the sixth floor?

$$30\rm{ seconds}$$

$$35\rm{ seconds}$$

$$40\rm{ seconds}$$

Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication


Seven out of forty pupils said they watch the news on television. What angle would this be on a pie chart?

Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Statistical Graphs->Pie Charts


The "Think Imaginary Academy" is trying to collect opinions to improve the school lunch program, which of the following information should not be collected via samples?

students\textquotesingle{} allergy situation

students\textquotesingle{} food preference

students\textquotesingle{} health demand

students\textquotesingle{} cultural background


The correct information we can get from the statement~"the chance of raining tomorrow in Boston is $$20\textbackslash\%$$"~is~\uline{~~~~~~~~~~}~.

It will rain in $$20\textbackslash\%$$ of the regions of Boston tomorrow.

It will rain $$20\textbackslash\%$$ of the time tomorrow in Boston.

The probability of raining in Boston tomorrow is low.

It won\textquotesingle t rain in Boston tomorrow.


Casey placed the cake batter in the oven at $$10:35$$ and she took the cake out at $$11:20$$. How long did it take for the cake to bake?

$$20$$ minutes

$$25$$ minutes

$$45$$ minutes

$$85$$ minutes


There are $$4$$ children in a queue.  Ravi is in front of Janice.  Huiling is behind Siti.  Siti is $$2^{{nd}}$$ from the back in the queue.  Which of the following shows the correct order of the children in the queue counting from the front?

Huiling, Janice, Ravi, Siti

Ravi, Siti, Janice, Huiling

Ravi, Janice, Siti, Huiling

Siti, Huling, Ravi, Janice


What sign is missing from this number sentence?  Choose the answer.  $$720\textasciitilde?\textasciitilde16 = 45$$

$$\times $$

$$\div $$

Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles->Number Puzzles (sign of operations)


Three children are queueing up.  Cindy is third in the queue.  Ali is standing between Cindy and Danny.  Who is second in the queue?

Ali

Cindy

Danny


Some children are queuing up to buy books in the bookshop.  Ali is first in the queue.  Edward is standing between Ali and Geetha.  Geetha is queuing in front of Xueli.  Who is second in the queue?

Ali$$\textasciitilde$$

Edward $$\textasciitilde$$

Geetha$$\textasciitilde$$

Xueli$$\textasciitilde$$


Find the digits represented by $$A$$ and $$B$$.


Sandra has a bag of $12$ counters.  $3$ of the counters are red.  $2$ of the counters are blue.  The rest of the counters are yellow.  Sandra takes at random a counter from the bag.  What is the probability that the counter is yellow?

Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Simple Questions Involving Probability->Possibility


How many 2-digit numbers contain at least one sixs?

Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Complex Forming Numbers->Complex Forming Numbers (with special requirements)


How many positive factors does $9072$ have?

Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle


Find the missing digit in the box. What is the missing digit?  $$\begin{matrix}\& \&~9~\&~\boxed{?}~\& 4 \textbackslash\textbackslash\& \times\& \& \&~6 \textbackslash\textbackslash{} \hline~\&5~\&~6~\& 0~\& 4\end{matrix}$$


What is $$2014 + 2 \times 0 \times 1 \times 4$$ equal to?

None of the above


Elizabeth watched a movie that lasted $$1$$ $$\text{h}$$ $$50$$ $$\rm min$$.  The movie ended at $$1.40$$ p.m.  What time did the movie start?

$$11.50$$ a.m.

$$11.50$$ p.m.

$$12.10$$ a.m.

$$12.10$$ p.m.


In a family, each boy has 3 sisters and each girl has 3 brothers. How many children are there in the family?

None of the above

Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability


Each of $$100$$ participants of a mathematical competition received four problems to solve. The first question was solved by $$90$$ of the participants, the second by $$85$$, the third by $$80$$, and the fourth by $$70$$. From this information we can deduce that the number of participants who solved all four questions is at least:．

Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle->Extreme Value in Inclusion-Exclusion for Multi-sets


Eight people play a one-on-one knockout tournament. How many games will be played to determine the winner?

$$8$$ games

$$7$$ games

$$6$$ games

$$4$$ games

Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Sports Competition


A movie ended at $$3.35$$ p.m. It lasted $$\rm 1$$ $$\text{h}$$ $$\rm 50$$ $$\min $$. What time did the movie start?

$$1.45$$ p.m.

$$2.15$$ p.m.

$$2.45$$ p.m.

$$5.25$$ p.m.


Every day Tom leaves home at $$8:30$$. It takes him $$30$$ minutes to get to the company.  What time will he get to the company?


How many different five digit numbers can be made using the digits $6$~~ $3$~~ $2$~~ $6$~~ $1$?

Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Questions Involving Permutations and Combinations


The correct information we can get from the statement~"the chance of raining tomorrow in Boston is $$20\textbackslash\%$$"~is~\uline{~~~~~~~~~~}~．


We call a number palindromic if it doesn\textquotesingle t change after its digits are written in reverse order. Some examples of such numbers are $$1331$$ and $$24642$$. A certain car\textquotesingle s odometer shows $$15951$$ kilometers. After how many more kilometers will a palindromic number show up on the odometer again? (2007 Math Kangaroo Problem, Level 3-4, Question \#18)

after $$100$$ km

after $$110$$ km

after $$710$$ km

after $$900$$ km

after $$1010$$ km

Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Dictionary Ordering->Forming Multi-Digit Numbers->Symmetric Numbers


Ben lives on the floor just below Chris.  Denise lives on the floor just above Alvin.  Denise lives on a higher floor than Chris.  Who lives on the lowest floor?

$$\textasciitilde$$Alvin

$$\textasciitilde$$Ben

$$\textasciitilde$$Chris

$$\textasciitilde$$Denise

Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning by Conditions


The number of purple cupcakes is $\frac{32}{56}$ the number of pink cupcakes. There were $49$ pink cupcakes. What is the ratio of the number of pink cupcakes to purple cupcakes?


Femi takes $$2$$ hours and $$53$$ minutes to cycle from London to Reading. If he arrived at~ $$15:21$$, at what time must he have set off?

Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations


$3$ plumbers were needed to fix $4$ identical pipes in $2$ days. How many plumbers are needed to fix $6$ identical pipes in a day?


Amy tosses two dice.  Before she saw the results, she asked her three friends to guess what the sum of the two dice she threw was.  Jimmy gave the answer of 6, Daisy gave the answer of 7, and Kitty gave the answer of 8.  Who had the best chance of winning?

Jimmy

Daisy

Kitty

Jimmy and Daisy

Daisy and Kitty

Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Typical Probability Problems->Tossing Coins


Elizabeth watched a movie that lasted $$1$$ $$\text{h}$$ $$50$$ $$\rm min$$. The movie ended at $$1.40$$ p.m. What time did the movie start?

$$11.50$$ a.m.

$$11.50$$ p.m.

$$12.10$$ a.m.

$$12.10$$ p.m.


There are $$25$$ players in a chess tournament. If each game is played by $$2$$ players, and each player plays every other player exactly once, what is the total number of games played in the tournament?


There are $$9$$ players in a chess tournament. If each game is played by $$2$$ players and each player plays every other player exactly once, what is the total number of games played in the tournament?


Which of the following is the correct order of the fractions $1\frac{3}{5}$, $\frac{20}{14}$, $\frac{14}{11}$ from least to greatest?

$1\frac{3}{5}$\textless$\frac{20}{14}$\textless$\frac{14}{11}$

$\frac{14}{11}$\textless$\frac{20}{14}$\textless$1\frac{3}{5}$

$1\frac{3}{5}$\textless$\frac{14}{11}$\textless$\frac{20}{14}$

$\frac{14}{11}$\textless$1\frac{3}{5}$\textless$\frac{20}{14}$

$\frac{20}{14}$\textless$\frac{14}{11}$\textless$1\frac{3}{5}$


If a fair die is rolled $30$ times, how many times would you expect to get a \textquotesingle$2$\textquotesingle?

Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Typical Probability Problems->Rolling Dice


Express $9k-4-5k+6+2k$ in the simplest form.


James has $12$ strawberries that he wants to split into $3$ groups so that each group is not empty and has a different number of strawberries. How many different ways can he do that?

Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Splitting Whole Numbers


During a party four friends are going to give each other gifts in such a way that everybody gives one gift and receives one gift (of course, no one should receive a gift from himself or herself). In how many ways can this be accomplished?

Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Principle of Multiplication->Matching Objects (with specific requirements)


Adam can travel from City $$A$$ to City $$B$$ by a bus, a train or a plane. To get from City $$B$$ to Town $$C$$, he can hire a taxi, rent a car, a motorcycle or a bicycle. There is no direct transportation from City $$A$$ to Town $$C$$. How many ways can Adam travel from City $$A$$ to Town $$C$$?

None of the above

Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Enumeration


Noa is deciding what to wear. He has $$5$$ T-shirt and $$6$$ jeans to choose. He hasdifferent ways of dressing.

Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Principle of Multiplication


Barbie purchased $\textbackslash$52$ worth of mangoes. The mangoes were priced at $\textbackslash$25$ per$\textasciitilde kg$. Determine the mass of mangoes purchased.

$2.8\textasciitilde kg$

$2\textasciitilde kg$ $8\textasciitilde g$

$28\textasciitilde kg$

$2\textasciitilde kg$ $80\textasciitilde g$


$13\textasciitilde cm$

$23\textasciitilde cm$

$48\textasciitilde cm$


The total of five different, positive odd numbers is $$85$$. What's the most that the largest number could be?

Overseas Competition->Knowledge Point->Combinatorics->Combinatorics Involving Extreme Values->Extreme Value with Fixed Sums


If today is Sunday, tomorrow will be Monday.

Certain

Impossible

Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Simple Questions Involving Probability->Possibility


None of the above.

Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication


$72$ people play a one-on-one knockout tournament. How many games will be played to determine the winner?

$$24$$ games

$$36$$ games

$$71$$ games

$$72$$ games

$$144$$ games


The desks in a Primary $$3$$ classroom are arranged in straight rows. Each row has the same number of desks. Greggory sits at the desk that is in the fourth row from the front and back. He sits at the centre of his row and there are $$5$$ desks to his left. How many desks are in the classroom?

None of the above

Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Queuing Problems


Any of the signs $$+$$, $$-$$, $$\times$$, $$\div$$ and brackets can be filled in the gaps below to make the equality true. Which of the following choices is true?  $$8\textasciitilde\textasciitilde\textasciitilde8\textasciitilde\textasciitilde\textasciitilde8\textasciitilde\textasciitilde\textasciitilde8\textasciitilde\textasciitilde\textasciitilde=8$$

$\left( 8-8\right)\times8+8=8$


Zachary left a birthday party at $$2.05$$ p.m.  He was at the party for $$3$$ h $$15$$ min.  At what time did he arrive at the party?

$$5.20$$ a.m.

$$10.50$$ a.m.

$$5.20$$ p.m.

$$10.50$$ p.m.

Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation


How many different real numbers $x$ satisfy the equation $(\sqrt{x}-4)^{2}=16$?

Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle


The year $$2022$$ is an $$interesting$$ year because it contains only digit $$2$$ and $$0$$. How many years later will be the next interesting year?

None of the above


Water is dripping from a tap into a pail, at a rate of $$4\rm ml$$ every second.  At this rate, how much water will be in the pail after $$2$$ minutes?

$$120\rm ml$$

$$240\rm ml$$

$$480\rm ml$$

$$800\rm ml$$

Overseas In-curriculum->Knowledge Point->Operations of Numbers ->Multiplication of Whole Numbers->Multiplication of Multi-Digit Numbers and 1-Digit Numbers->Multiplication of 3-digit Numbers(with 0 in the tens or ones place) and 1-digit Numbers


Which one of the following is not a common factor of $$12$$ and $$18$$?

Overseas In-curriculum->Knowledge Point->Knowing Numbers->Characteristics of Numbers ->Factors and Multiples->The Common Factors of Two Given Numbers

Overseas Competition->Knowledge Point->Counting Modules


Which of the following statements is false about MAD?

For every given finite data set, we can find its MAD.

In order to find the MAD of a data set, we have to first find its mean.

MAD is a measure of center.

MAD is a measure of spread.

Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Basic Concepts of Statistics


None of the above


How many of the numbers between $1$ and $50$ are divisible by both $2$ and $5$?

Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations


SASMO 2014 P2 Q4  Jane wrote the word STUDENTS thrice. How many times did she write the letter S?

Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability


In a class of $50$, every student had to take an extra module. Some students took extra mathematics modules while some students took extra science modules. A total of $38$ students took the extra mathematics modules while $24$ students took extra mathematics and science modules. How many students took extra science modules?


If a fair dice is rolled $30$ times, how many times would you expect to get a ``$2$''?

Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Typical Probability Problems->Rolling Dice


Mark has some one-dollar coins and some two-dollar coins, and there are $$48$$ coins in total.  The total value of them is the same.  Given that the one-dollar coin weighs $8$ grams and the two-dollar coin weighs $9$ grams.  What is the total weight of all the coins?

Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Typical Probability Problems->Tossing Coins


Every day John leaves home at $$8:45$$. It takes him $$15$$ minutes to get to school.  What time does he get to school?


Boston left his home at $$\text{11.58 a}\text{.m}.$$ to meet his friend for lunch at the mall. He took $$\text{1h 12min}$$ to reach the mall. What time did Boston arrange to meet his friend?

$$10\text{.46 a}\text{.m}.$$

$$10\text{.46 p}\text{.m}.$$

$$1\text{.10 a}\text{.m}.$$

$$1\text{.10 p}\text{.m}.$$


Which of the following is the same as $40010\textasciitilde g$?

$4.01\textasciitilde kg$

$40\textasciitilde kg$ $10\textasciitilde g$

$40.1\textasciitilde kg$

$40\textasciitilde kg$ $100\textasciitilde g$


Mrs Lim completed a puzzle at $$5.45$$ p.m.  She took $$\rm 3h15min$$ to complete it.  At what time did she start working on the puzzle?

$$2.30$$ p.m.

$$3.00$$ p.m.

$$3.30$$ p.m.

$$9.00$$ p.m.


Length of tunnel $=$~\uline{~~~~~~~~~~}~$\textasciitilde m$


In Jane\textquotesingle s school, there are $30$ students born in April, and each of them was born in a different day. What is the probability of choosing one student who was exactly born in the first ten days of April?

$\frac {1}{30}$

$\frac {1}{3}$

$\frac {1}{4}$

$\frac {1}{15}$

$\frac {1}{10}$


$$45\div 5=3\square 3$$  Choose a suitable sign to be put in the box for the above number sentence.

$$\times $$

$$\div $$


Nellie went for a movie. The movie ended at $$23$$ $$50$$.  If the movie lasted for $$2\text{h}$$ $$5$$$$\min $$, at what time did the movie start?

$$1.55$$ a.m.

$$1.55$$ p.m.

$$9.45$$ a.m.

$$9.45$$ p.m.


What is the sum of the $$2^{\text{nd}}$$ multiple and the $$4^{\text{th}}$$ multiple of $$8$$?

Overseas In-curriculum->Knowledge Point->Knowing Numbers->Characteristics of Numbers ->Factors and Multiples->Finding Multiples of a Given Number


Which of the following numbers, when rounded to the nearest thousand, hundred, and ten, equals $$3000$$, $$3500$$, and $$3460$$ respectively?


A drawer contains ten identical yellow socks, eight identical blue socks and four identical pink socks. Amrita picks socks from the drawer without looking. What is the smallest number of socks she must pick to be sure that she has at least three pairs of matching socks?

Overseas Competition->Knowledge Point->Combinatorics->Pigeonhole Principle->Worst Case in Pigeonhole Principle Problems


Fourteen cats took part in a cat play. Some of them played moms and some of them played their kids. Every mom in this play had at least two kids. What is the greatest possible number of cat-moms in the play?

Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations->Questions Involving Combinations


Elizabeth watched a movie that lasted $$1$$ $$\text{h}$$ $$50$$ $$\rm min$$. The movie ended at $$1.40$$ p.m. What time did the movie start?

$$11.50$$ a.m.

$$11.50$$ p.m.

$$12.10$$ a.m.

$$12.10$$ p.m.


A bag contains $$20$$ red discs, $$10$$ green discs and $$30$$ blue discs. A disc is chosen at random. Which of these events is the \textbf{most} likely?

The chosen disc is red.

The chosen disc is blue

The chosen disc is not red.

The chosen disc is green or blue.

The chosen disc is not green.

Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Basic Concepts of Probability


After giving $$8$$ stickers each to $$38$$ pupils in school, Mrs Ho had $$12$$ stickers left.  How many stickers did Mrs Ho have at first?

Overseas In-curriculum->Knowledge Point->Operations of Numbers ->Mixed Operations->Mixed Operations of Multiplication and Addition of Whole Numbers

Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication


In a family, each boy has $$3$$ sisters and each girl has $$3$$ brothers. How many children are there in the family?

None of the above


The students had a race. Can you tell who runs the fastest?  \textbf{Pip came in third.}  \textbf{Bud was in front of Eddie.}  \textbf{Avril lost to Pip in the race.}

Bud

Avril

Eddie

Pip

Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning by Conditions


How many minutes are there in three and a half hours?


Suppose you estimate the flu vaccine has an external benefit of ¥10/shot. The government recognizes this positive externality and votes to give people who get vaccinated a ¥15/shot subsidy. What happens as a result

there is no longer a market failure

too many people get vaccinated but there is no DWL

too few people get vaccinated so there is DWL

too many people get vaccinated so there is DWL


How many different ways are there of paying exactly £$$1$$ using $$5$$p and/or $$10$$p pieces?


What is the second smallest positive integer greater than $1$ that leaves a remainder of $3$ when divided by $8$, $9$, and $10$?


$$\underbrace{55\ldots\ldots 5}\_{50 "5"s}805$$

$$\underbrace{55\ldots\ldots 5}\_{49 "5"s}705$$

$$\underbrace{55\ldots\ldots 5}\_{49 "5"s}805$$

$$\underbrace{55\ldots\ldots 5}\_{49 "5"s}750$$


Marcus took half an hour to complete his homework. He started doing his homework at $$11.50 \rm a.m$$. What time did Marcus complete his homework?

$$11.20 \rm a.m$$.

$$11.20 \rm p.m$$.

$$12.20 \rm a.m$$.

$$12.20 \rm p.m$$.


What is the missing sign in the box?  $8\square2=16$

$$\times$$

$$\div$$


There were $$10$$ students in a class. Each student shook hands only once with the other $$9$$ students in the class. How many handshakes were there in total?

Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Law of Addition->Number of Handshake Problem

Overseas In-curriculum->Knowledge Point->Fun Problems in Math->Reasoning


Toss a fair coin three times. What is the probability of getting one head and two tails?


Find the missing digit in the box. What is the missing digit?  $$\begin{matrix}\& \&~9~\&~\boxed{?}~\& 4 \textbackslash\textbackslash\& \times\& \& \&~6 \textbackslash\textbackslash{} \hline~\&5~\&~6~\& 0~\& 4\end{matrix}$$

Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles->Number Puzzles (vertical forms)


How many whole numbers from $$1$$ to $$201$$ consist of only even digits?

None of the above

Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Enumeration


Granny went out to the yard and called all the hens and her cat. All 20 legs ran to her. How many hens does granny have?

Overseas Competition->Knowledge Point->Counting Modules


None of the above


Mary\textquotesingle s violin class started at $$11.15\textbackslash{} \text{a .m.}$$ It lasted for $$90$$ minutes.  What time did her violin class end?

$$12.05\textbackslash{} \text{a. m.}$$

$$12.05\textbackslash{} \text{p. m.}$$

$$12.45\textbackslash{} \text{a. m.}$$

$$12.45\text{ p. m.}$$


How would determine $\angle DKI$ from $\angle KIJ$ and $\angle KJI$?

Vertically opposite angles

Exterior angles

Alternate angles

Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle


Which of the following expressions is easier to calculate if we do it in order?


How many different three-digit numbers can we make that have three different digits using the digits $$1$$, $$2$$ and $$3$$? ($$2009$$ Math Kangaroo Problem, Level $$1-2$$, Question \#$$24$$)

Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations->Basic Operations of Combinations


How many of the numbers between $1$ and $150$ are divisible by neither $3$ nor $10$?

Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations


Grandmother made $$20$$ gingerbread cakes for her grandchildren. She decorated them with raisins and nuts. First she decorated $$15$$ cakes with raisins and then $$15$$ cakes with nuts. At least how many cakes were decorated with both raisins and nuts?

Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle->Inclusion-Exclusion Principle for Two Sets


Issy tosses a fair coin four times. She gets Heads, Heads, Heads, Tails. If she tosses it a fifth time, is she more likely to get Heads or Tails?

equally likely

Heads

Tails

not enough information

Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Typical Probability Problems->Tossing Coins


A shop sells sweets where every 3 sweet wrappers can be exchanged for one more sweet. Ali has enough money to buy only 7 sweets. What is the biggest number of sweets that he can get from the shop?

Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Law of Addition


Use the digits below to make up the largest possible number without repeating digits.  $$3$$, $$9$$, $$1$$, $$5$$  This number is (~ ~~\uline{)}.

Overseas Competition->Knowledge Point->Combinatorics->Combinatorics Involving Extreme Values->Extreme Value in Enumeration Problems


Which of the following decimals is the greatest?

Overseas In-curriculum->Knowledge Point->Knowing Numbers->Comparing and Ordering->Comparing and Ordering Decimals


The total of six different, positive even numbers is $$96$$. What\textquotesingle s the most that the largest number could be? ．

Overseas Competition->Knowledge Point->Combinatorics->Combinatorics Involving Extreme Values->Extreme Value with Fixed Sums


Can you use 6 matchsticks to make a square and a triangle?

Yes

No


By using $$1$$、$$3$$、$$5$$,  different two-digit numbers can be formed.

Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Enumeration->Ordered Enumeration


A party game played with a six---sided dice is fair if the chance of winning is equal to  the chance of losing each time the dice is rolled. Which one of these games is fair?

You win if you roll a 6.

You win if you roll a 2 or a 5.

You win if you roll a number greater than 4.

You win if you roll a number less than 3.

You win if you roll an odd number.

Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability


Linda invents a code which uses letters to represent digits, in which the same letter represents the same digit, and the different letters represent different digits. She uses the word \textquotesingle$$\text{MEMBER}$$\textquotesingle{} to represent a six-digit number which is smaller than $$223114$$. The largest possible number that the word \textquotesingle$$\text{MEMBER}$$\textquotesingle{} can represent is~\uline{~~~~~~~~~~}~.


Oliver, Cici, and Lucy said three words.  Oliver said: "I am $$22$$ years old now, I am two years younger than Lucy, and I am one year older than Lucy.~"  Cici said: "I am not the youngest one, Lucy and I are three years apart, and Lucy is $$25$$ years old now."  Lucy said: "I am younger than Oliver, Oliver is $$23$$ years old now, and Cici is three years older than Oliver."  If two out of three sentences of each persion are true. Oliver is~\uline{~~~~~~~~~~}~years old.

Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning using Hypothesis


We call a number palindromic if it doesn\textquotesingle t change after its digits are written in reverse order. Some~ ~ ~ ~examples of such numbers are $$1331$$ and $$24642$$. A certain car\textquotesingle s odometer shows $$15951$$ kilometers. After how many more kilometers will a palindromic number show up on the odometer again?

after $$100\rm km$$

after $$110\rm km$$

after $$710\rm km$$

after $$900\rm km$$

after $$1010\rm km$$

Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Dictionary Ordering->Forming Multi-Digit Numbers->Symmetric Numbers


Clair has $$5$$ apples, Alice has $$8$$ apples, Betty has $$2$$ apples. They put all the apples together and divide them equally. How many apples does everyone get?

Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems ->Using Formulas


There are twelve rooms in a building. Each room has two windows and one light. Last evening, eighteen windows were lighted. In how many rooms was the light off?


There are $2009$ white balls and $2010$ black balls in the box. There are enough black balls outside the box. Take two balls out of the box at any time, and if they are of the same color, take one black ball and put it back into the box. If they are of different color, put one of the white balls back into the box. After doing this operation $4018$ times, how many balls are left in the box and what color are they?

$1$, white

$2$, white

$1$, black

$2$, black


Toss a fair coin four times. What is the probability of getting four heads?

Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Basic Concepts of Probability


In a cave, there were two horses, one bear and three turtles. Later, five horses, three bears and four turtles joined them. How many animals are in the cave now?


Students Arn, Bob, Cyd, Dan, Eve, and Fon are arranged in that order in a circle. They start counting: Arn first, then Bob, and so forth. When the number contains a 7 as a digit (such as 47) or is a multiple of 7 that person leaves the circle and the counting continues. Who is the last one present in the circle?

Arn

Bob

Cyd

Dan

Eve


The sum of five different positive odd numbers is $$85$$. The largest number among them can at most be~\uline{~~~~~~~~~~}~.


Alice has 3 white, 2 black and 2 grey pieces of paper. She cuts every non-black piece of paper in half. Then she cuts every non-white piece of paper in half. How many pieces of paper will she have?


Which of the following expressions is easier to calculate if we do it in order?


What is the probability of rolling a fair six-sided die twice and getting a total of $$8$$?


Which of the following statements about a histogram is false?

A histogram is a bar graph.

A histogram can have an interval where the frequency or count is 0.

Given a data set, the histogram we can make from this data set is unique.

The sizes of all intervals in a histogram must be the same.

Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Statistical Graphs


A clock is set correctly at $2 \text{P.M}$. It loses $3$ minutes every hour. What will the clock read when the real-time is $9 \text{A.M}$. the next day?

$8 \text{A.M}$.

$8:03 \text{A.M}$.

$9:57 \text{A.M}$.

$10 \text{A.M}$.


A bag contains $$20$$ red discs, $$10$$ green discs and $$30$$ blue discs. A disc is chosen at random. Which of these events is the \textbf{most} likely?

The chosen disc is red.

The chosen disc is blue

The chosen disc is not red.

The chosen disc is green or blue.

The chosen disc is not green.


Jane wrote the word $STUDENTS$ thrice. How many times did she write the letter $S$?


The year 2022 is an $$interesting$$ year because it contains only digits $$2$$ and $$0$$. How many years later will be the next interesting year?

None of the above

Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Enumeration


How many four-digit numbers are there such that if we add $$2020$$ to each of the numbers, the results are still four-digit numbers?

None of the above


There are 4 types of cakes available in a cake shop: chocolate, cheese, blueberry and  blackforest. Naomi wants to buy 2 different types of cakes. How many different  choices does she have?

Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations


Ali took a bus from Singapore to Malacca at $$10:45$$pm. The bus ride took $$4\text{h}40$$$$\min $$. What time did he reach Malacca?


Susan prepared a plate of cookies for her friends Ashley, Sam, Max and Olivia, Susan tried the first cookie before serving them to her friends. Ashley took 2 cookies and gave 1 to Sam. Max then took 3 cookies, and gave 1 to Olviia and 1 to Susan. If they each ate the cookies they ended up with, who ate the most cookies?

Susan

Ashley

Sam

Max

Olivia


I am rolling a die two times. What is the probability that I get a number greater than $$3$$ both times?


$36$ people play a one-on-one knockout tournament. How many games will be played to determine the winner?

$$9$$ games

$$18$$ games

$$35$$ games

$$36$$ games

$$72$$ games

Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Sports Competition


Overseas In-curriculum->Knowledge Point->Knowing Numbers->Decimals->Converting Between Fractions and Decimals->Converting Fractions to Decimals

Overseas Competition->Knowledge Point->Counting Modules


A $$3$$-digit code is needed to open a safe. How many possible codes are there if it is known that only three numbers, $$1$$, $$3$$, and $$5$$, are used in this code, and each of them is used only once?

Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Permutations->Basic Applications of Permutations


Teacher Jerry is looking at the mid-term report of his class. He wants to find the spread of his students\textquotesingle{} scores. Which diagram should he use to find out the measure he wants?

bar chart

pie chart

line diagram

box plot


How many numbers are there from $$1$$ to $$100$$ are multiples of $$7$$?

None of the above

Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication


The ratio of Marnie\textquotesingle s $\textbackslash$2$-notes to $\textbackslash$5$-notes was $5:2$. She had a total of $\textbackslash$160$. How many notes did she have?

Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle


In the number sentence below, what number is the $\oplus$?  $$\oplus \times 5 + 4 - \oplus = 32$$


$$\boxed{8}\textasciitilde\textasciitilde\boxed{9}\textasciitilde\textasciitilde\boxed{9}\textasciitilde\textasciitilde\boxed{9}\textasciitilde\textasciitilde\boxed{9}\textasciitilde\textasciitilde\boxed{9}$$  Craig uses these six number cards to make two numbers with three digits, for example $$989$$ and $$999$$.  How many different versions of this inequality can Craig make?  $$\square\textasciitilde\textasciitilde\square\textasciitilde\textasciitilde\square\textless{}\square \textasciitilde\textasciitilde\square\textasciitilde\textasciitilde\square$$

Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Complex Forming Numbers->Complex Forming Numbers (with special requirements)


A clock was set correctly at $2:00$ p.m., but it lost three minutes every hour. When the real time is $9:00$ a.m. on the next day, the clock reads ．

$8:00$ a.m.

$8:03$ a.m.

$9:57$ a.m.

$10:00$ a.m.

$9:03$ a.m.

Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations


The total of six different, positive even numbers is $$96$$. What's the most that the largest number could be?


$$45\bigcirc 9=5$$. What is the missing sign?

$$\times $$

$$\div $$


The total of five different positive odd numbers is $$85$$. What\textquotesingle s the most that the largest number could be? ．


The correct information we can get from the statement~"the chance of raining tomorrow in Boston is $\dfrac{1}{5}$"~is~\uline{~~~~~~~~~~}~.

It will rain in $\dfrac{1}{5}$ of the regions of Boston tomorrow.

It will rain~$\dfrac{1}{5}$ of the time tomorrow in Boston.

The probability of raining in Boston tomorrow is low.

It won\textquotesingle t rain in Boston tomorrow.


Consider these two operations: $a\Psi b=a^{2}-b$ and $a \nu b=\sqrt{ab}$.  Which of these values are possible answers of $4 \nu (2 \Psi 3)^{2}$?


Which of the number is the third common multiple of $$4$$ and $$8$$?

Overseas In-curriculum->Knowledge Point->Knowing Numbers->Characteristics of Numbers ->Factors and Multiples->The Common Multiples of two Given Numbers


（2021 Selective Question \#7）Amrita has a bag of 36 marbles. Some are blue, some are red and the rest are yellow. There are 16 blue marbles in the bag. If she takes out a marble without looking, the probability that it is red is $\dfrac{1}{2}$. How many yellow marbles are in the bag?

Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability


There are $6$ three-digit numbers which is formed using each of the digits $$1$$, $$2$$ and $$3$$ once only. When all of these $$6$$ three-digit numbers are put in order from smallest to largest, which one is in the fourth position?


Zachary left a birthday party at $$2.05$$ p.m.  He was at the party for $$3$$ $$\text{h}$$ $$15$$ $$\min $$.  At what time did he arrive at the party? ．

$$5.20$$ a.m.

$$10.50$$ a.m.

$$5.20$$ p.m.

$$10.50$$ p.m.

Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation


David takes $$30$$ seconds to climb from the first floor to the third floor. How many seconds will it take him to climb from the third floor to the sixth floor?

$$30$$ seconds

$$35$$ seconds

$$40$$ seconds

$$45$$ seconds

$$50$$ seconds


There are $$3$$ red balls, $$5$$ blue balls and $$2$$ yellow balls of the same size in an opaque bag. Amy takes one randomly from the bag. The probability of choosing a red ball is~\uline{~~~~~~~~~~}~.

Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability


Ali took a bus from Singapore to Malacca at $$10.45$$ p.m. The bus ride took $$4\text{h}40$$$$\min $$. What time did he reach Malacca?


What is the missing sign in the box?  $$18=3\square 6$$

$$\times $$

$$\div $$

Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles->Number Puzzles (sign of operations)


How long is it, in hours and minutes, between $$10:28$$ and $$16:06$$?


A bag contains $3$ red and $6$ green marbles. If you pick out a marble at random, what isthe chance that it will be red?

Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Simple Questions Involving Probability->Possibility


Beartrice purchased an enomous pie weighing $2.5\textasciitilde kg$. She gave $\frac{3}{13}$ of her pie to her friend Platilocks. She cut the remainder equally into $5$ slices. What fraction of the whole cake was each slice?


Three kids $$A$$、$$B$$、$$C$$ are playing the game "pass the ball". If it starts with A, he can pass the ball to~\uline{~~~~~~~~~~}~.

$$A$$ or $$B$$ or $$C$$

$$B$$ or $$C$$

$$A$$ or $$C$$

Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Tree Diagrams


Uncle John has a farm. His wife and his two sons are staying with him in the farm. They raise $$10$$ cows and $$20$$ chickens. How many total legs are there in the farm?


How many more rabbits than ducklings are there?

Overseas Competition->Knowledge Point->Counting Modules->Carroll Diagrams


Toss a fair coin five times. What is the probability of getting five heads?

Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Basic Concepts of Probability


The athlete receives $10$ grades in the exercise: $$4$$, $$6$$, $$8$$, $$7$$, $$6$$, $$6$$, $$5$$, $$6$$, $$6$$, and $$5$$.  Which of the following are of two same numbers?

The median and the mean

The mean and the mode

The median and the mode


The sum of five different positive odd numbers is $$85$$. The largest number can at most be~\uline{~~~~~~~~~~}~.

Overseas Competition->Knowledge Point->Combinatorics->Combinatorics Involving Extreme Values->Extreme Value with Fixed Sums


A shop sells sweets where every $3$ sweet wrappers can be exchanged for one more sweet. Ali has enough money to buy only $7$ sweets. What is the biggest number of sweets that he can get from the shop?

Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Law of Addition


$$\boxed{1}\textasciitilde\textasciitilde\boxed{2}\textasciitilde\textasciitilde\boxed{3}\textasciitilde\textasciitilde\boxed{4}$$  Jane uses these four number cards to make two 2-digit numbers and works out the sum.  $$\square\textasciitilde\textasciitilde\square+\square\textasciitilde\textasciitilde\square$$  How many different sums can she get?


There is $$\text{560mL}$$ of milk in Bottle $$A$$ and $$\text{440mL}$$ of milk in Bottle $$B$$. How much milk should be poured from Bottle $$A$$ to Bottle $$B$$ so that both bottles have the same amount of milk?


There are 4 types of cakes available in a cake shop: chocolate, cheese, blueberry  and blackforest. Naomi wants to buy 2 different types of cakes. How many  different choices does she have?

Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations


John goes from his home to the playground. He walks 50 meters west, then turns~right~and walks~70 meters, then turns left and walks 40 meters, then 20 meters south, and finally 30 meters west. What is the direction John is facing now?

East

West

South

North

Southeast

Overseas Competition->Knowledge Point->Counting Modules


How many different numbers greater than 10 and smaller than 25 with different digits can we make by using two of the digits 2, 0, 1, and 8?


Paul is taller than Joe.  William is shorter than Paul.  Eddie is taller than William but shorter than Joe.  Jason is shorter than William.  Who is the shortest person?

Paul

William

Joe

Eddie

Jason

Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning by Comparing


Kofi leaves for the shops at $$11:23$$am and returns $$2$$ hours $$48$$ minutes later. At what time does he return?


There are 5 red balls and 6 green balls. Pip takes out 5 balls at random. How many possible combinations are there? Try to list all the situations in order in the following table.


In the ones place

In the tens place

Both A and B are correct


How many shortest paths are there from point A to point B?

Overseas Competition->Knowledge Point->Counting Modules->Finding the Shortest Path by Number Notation->Finding the Shortest Path by Number Notation (simple)->Finding the Shortest Routes


$$150$$ students went to a $$\text{CCA}$$ fair and all of them at least tried out one activity. $$85$$ students tried out Sports activity. $$77$$ students tried out Art activity. How many students tried out both Sport activity and Art activities?


Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle


How long is it, in hours and minutes, between $$10:28$$ and $$16:06$$?

$$5$$ hrs $$38$$ mins

$$8$$ hrs $$34$$ mins

$$5$$ hrs $$36$$ mins

$$26$$hrs $$34$$ mins

$$4$$ hrs $$33$$ mins

Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations


Any of the signs $$+$$, $$-$$, $$\times$$, $$\div$$ and brackets can be filled in the gaps below to make the equality true. Which of the following choices is true?  $$2\textasciitilde\textasciitilde\textasciitilde3\textasciitilde\textasciitilde\textasciitilde6\textasciitilde\textasciitilde\textasciitilde=36$$

$\left( 2+3\right)\times6=36$


There are $$8$$ gloves of each colour, white, black, blue, red and yellow, in a drawer. Two gloves are consider to be a pair only if their colour is the same. How many gloves must Rona take out from the drawer randomly to ensure that she has $$5$$ pairs of gloves?

Overseas Competition->Knowledge Point->Combinatorics->Pigeonhole Principle->Worst Case in Pigeonhole Principle Problems


A movie ended at $$3.35$$ p.m. It lasted $$\rm 1h$$ $$\rm 50min$$. What time did the movie start?

$$1.45$$ p.m.

$$2.15$$ p.m.

$$2.45$$ p.m.

$$5.25$$ p.m.


Ben lives on the floor just below Chris.  Denise lives on the floor just above Alvin.  Denise lives on a higher floor than Chris.  who lives on the lowest floor?

$$\textasciitilde$$Alvin

$$\textasciitilde$$Ben

$$\textasciitilde$$Chris

$$\textasciitilde$$Denise


Sort the following names: Tom, Bob, Alice, Liz in alphabetical order. The correct format is .

Bob, Tom, Alice, Liz

Tom, Bob, Liz, Alice

Tom, Liz, Bob, Alice

Alice, Bob, Liz, Tom


There are $$4$$ different colours of bags available in a stationery shop: blue, red, green and yellow. Angel wants to buy $$3$$ different colour of bags. How many different choices does she have?

Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Enumeration


The baby crawls 1m east then turns left and crawls 1m, then turns right and crawls 1m again, then turns to the left and crawls 2m, then turns to the right and crawls 1m, and then finally turns right and crawls 2m to grab the toy. What is the direction the baby is facing now?

East

West

South

North

Southeast


What should 19:20 be written for the 12-hour clock time?

7:20 a.m.

19:20 p.m.

7:20 p.m.


What is the sum of all the even numbers between $30$ and $40$?

Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication


There are $$29$$ students in a certain class. $$12$$ of the students have a sister and $$18$$ of the students have a brother. In this class, only Tania, Barbara, and Anna do not have any siblings. How many students from this class have both a brother and a sister?

$$$$None

Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle->Inclusion-Exclusion Principle for Two Sets


The average of six numbers is $$29$$. The sum of the first five numbers is $$135$$. What is the sixth number?

Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability


An elementary school is arranging students\textquotesingle{} schedules. For the first class in the morning, it has to be Chinese or Maths or English. Students won\textquotesingle t start the day with the same class for two days in a row. If Friday starts with Chinese, then Thursday can start with~\uline{~~~~~~~~~~}~.

Chinese or Maths

Maths or English

English or Chinese


There are $$9$$ pink, $$7$$ grey and $$11$$ blue marbles in a box. How many marbles shoud you draw to ensure that a blue marble can be drawn without looking inside the box?


Jane wrote the word STUDENTS thrice. How many times did she write the letter S?


Divide $$60$$ robots into several groups such that the number of robots in any group should be different. How many groups can be made at most?

Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Splitting Whole Numbers


Ten friends came to John\textquotesingle s birthday party, six of them were girls. How many boys were there in the party?


A

B

C

D

Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration


A packet of biscuits costs $$x$$ pence.  I buy $$6$$ packets.  Which expression shows how much change I will get from £$$5$$?

Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Using a Letter to Represent an Unknown Number


Under a null hypothesis, a sample value yields a P-value of 0.015. Which of the following statements is (are) true?  I. This finding is statistically significant at the 0.05 level of significance.  II. This finding is statistically significant at the 0.01 level of significance.  II. The probability of getting a sample value as extreme as this one by chance alone if the null hypothesis is true is 0.015.

I and III only

I only

III only

II and III only

I, II, and III

Overseas Competition->Knowledge Point->Calculation Modules


Farmer Frank has an orchard of $15$ trees. Each tree has $4$ trunks and each trunk has $8$ branches. Each branch has $20$ apples and $5$ boughs. Each bough has $6$ apples. How many apples does Farmer Frank have?


$3.7\times9=33.3$ Write down the value of.

Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Multiplication and Division of Decimals->Multiplication of Decimals


The height of a seedling is $$7.2\text{cm}$$. It grows $$0.6\text{cm}$$ every day. What is the seedling\textquotesingle s height after $$3$$ days?

Overseas In-curriculum->Knowledge Point->Operations of Numbers ->Multiplication and Division of Decimals->Multiplication of Decimals->Multiplication of Decimals and Whole Numbers

Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Multiplication and Division of Decimals


What is the product of $$819$$ and $$7$$?

Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division


Suppose that a firm in perfect competition is producing 6 tons of wheat with an average variable cost of $\textbackslash$50$/ton, an average total cost of $\textbackslash$70$/ton, and selling the wheat for a price of $\textbackslash$60$/ton. Will it make a positive or negative profit? Should this firm shut down?

positive profit, don't shut down

positive profit, shut down

negative profit, don't shut down

negative profit, shut down

Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation


Which of the following numbers is the smallest?

Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating->Comparing and Ordering->By Converting Fractions into Decimals


$$\begin{cases}x=3+2y \textbackslash\textbackslash{} 3x+5y=64 \textbackslash\textbackslash\end{cases}$$, find the value of $y$.

Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions


$6$ can be made in $2$ different ways: $1\times6$ or $2\times3$. In how many different ways is it possible to make $24$?


Every half hour, one bacteria divides into two bacterias. After $$2$$ hours, there are  bacterias.

Overseas Competition->Knowledge Point->Calculation Modules->Power->Computing Powers->Exponentiation of Powers


Find the $$3$$ equivalent fractions of the given fraction.  $\dfrac{75}{100}$

Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Operations of Fractions


Paul draws a plan of his school using a scale of $$2\text{cm}$$ to $$5\text{m}$$.  On the plan, the school hall is $$6\text{cm}$$ long.  What is the real length of the hall?

Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions->Proportions->Scale


Ten balls are put into a bag. On each ball is a number from $1$ to $10$.  The $1^{st}$~ball has the number $1$ on it.  The $2^{nd}$~ball has the number $2$ on it, and so on\ldots{}  $3$ balls are taken out and numbers on them are added up together.  We can know that $5$ was included in the numbers were taken, and the result can be divieded by $3$ and $4$. Which of the following numbers was definitly not taken out?


$$\frac{30}{8}=3\frac{\square{ }}{4}$$  The missing number in the box is．

Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Basic Understanding of Fractions


Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns in Number Sequences


Two sets of numbers are given. The second set of numbers is obtained by doing something to the first set.  $\left\textbackslash{ 1,2,3,4,5\right\textbackslash}\textbackslash{} \Rightarrow\left\textbackslash{ 2,5,10,?,26\right\textbackslash}$  What is the missing number?

Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Finding Patterns->Looking For Patterns


A school district claims that the average teacher in the district earns $\textbackslash$$48,000 per year. The teachers\textquotesingle{} organization argues that the average salary is less. A random sample of 25 teachers yields a mean salary of $\textbackslash$$47,500 with a sample standard deviation of $\textbackslash$$2,000. Assuming that the distribution of all teachers\textquotesingle{} salaries is approximately normally distributed, what is the value of the t-test statistic and the P-value for a test of the hypothesis H\textsubscript{0}:~$\mu$~= 48,000 against H\textsubscript{a}: $\mu$ \textless{} 48,000? (Remember, df= 25 - 1 = 24.)

t=1.25, 0.10\textless P\textless0.15

t=-1.25, 0.20\textless P\textless0.30

t=1.25, 0.20\textless P\textless0.30

t=-1.25, 0.10\textless P\textless0.15

t=-1.25, P\textgreater0.25


What is the value of~$\dfrac{1}{3}\cdot\dfrac{2}{4}\cdot\dfrac{3}{5}\cdot\cdot\cdot\dfrac{18}{20}\cdot\dfrac{19}{21}\cdot\dfrac{20}{22}$?


A number consists of $5$ ten thousands, $6$ thousands, $1$ tens and $3$ ones. What number is it?

Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations


Which of the following is true of an economy\textquotesingle s production possibilities curve?

It shows the combinations of any two resources that can be used to produce an efficient level of output.

It shows the alternative combinations of goods that can be produced by fully employing scarce resources.

It must be a straight line when all resources are fully employed.

It is bowed in (convex to the origin) because of changing levels of technology.

It is bowed out (concave to the origin) when marginal opportunity costs are constant.


Express $$\frac{62}{5}$$ as a mixed number in its simplest form.


What is the missing number in the box?  $$\boxed{~ ~ ?~ ~ ~}-2852=2569$$

Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction


Suppose that on a hypothesis test for a single population mean, $H\_{a}:\textbackslash{} \mu\textbackslash{} \lt\textbackslash{} 10$. Assume that $H\_{a}$~is true. For a fixed sample size and significance level $\alpha$, the power of the test will be greatest if the actual mean is which of the following?


To calculate the area of a rectangle with a length of $$7$$ and a breadth of $$5$$, we can use $$7\times 5$$. Therefore, the formula of a rectangle can be summarised as:．

Area of rectangle $$=$$ breadth $$\times $$ breadth

Area of rectangle $$=$$ length $$\times $$ length

Area of rectangle $$=$$ length $$\times $$ breadth


Which of the following is the simplest form of~$\dfrac{3}{12}$?

Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Basic Understanding of Fractions->Using Common Factors to Simplify Fractions


When the price of bananas increases by 20\%, the quantity demanded of apples increases by 30\%. What is the value of the cross-price elasticity of demand?


Which of the following is true if consuming one unit of a good yields 100 utils and consuming the second unit of the good increases satisfaction by 20 utils?

The marginal utility of the first unit is 20.

The marginal utility of the second unit is 20.

The marginal utility of the second unit is 120.

The total utility of consuming two units is 120.

The total utility of consuming one unit is greater than the total utility of consuming two units.

Overseas Competition->Knowledge Point->Calculation Modules


Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Calculation of Multi-digit Numbers


\textbf{Use Punnett squares to answer questions 8, 9 and 10. In guinea pigs, coat texture is determined by a complete dominance gene: rough coats are dominant to smooth coats.}  Two guinea pigs heterozygous for coat texture have offspring. What is the percent of their offspring expected to have smooth coats?


The price of a good increases by 20\% and as a result, the quantity demanded decreases by 10\%. What is the price elasticity of demand for this good?


Which fraction is \textbf{NOT~}equivalent to $\frac{1}{2}$?

Overseas Competition->Knowledge Point->Calculation Modules->Fractions


Pauline has $2$ erasers, $3$ notebooks, $1$ carrot, $5$ toy cars, $7$ fans and $3$ bowls. How many pieces of stationeries does Pauline have?


Which of the following statement about $$0$$ is true?

$$0$$ is positive

$$0$$ is negative

$$0$$ is neither positive nor negative

Do not know

Overseas Competition->Knowledge Point->Calculation Modules->Negative Numbers


What is the place value of the digit $3$ in the number $19.324$?

ones

tens

tenths

hundredths

thousandths

Overseas Competition->Knowledge Point->Calculation Modules->Operations through Formulas


Consider repeated trials of a binomial random variable. Suppose the probability of the first success occurring on the second trial is 0.25. What is the probability of success the first trial?


Which ratio is NOT the same as the ratio $$12:60$$?  Choose the letter.

Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions->Ratio


Fill in the blank:~\uline{~~~~~~~~~~}~is $$7$$ tens $$7$$ ones more than $$3$$ tens $$9$$ ones.

None of the above


$$8\times 7=14+4\times 7+$$~\uline{~~~~~~~~~~}~$$\times 7$$.  What is the missing number in the box?

Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Distributive Law of Whole Numbers


Which of the following does not contain a constant?

Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions


$$5+5+5+5+5=6\times $$$$\square $$  What is the missing number in the box?（


Which one of the following has the greatest value?

$$\frac{3}{5} \times \frac{2}{3}$$

$$\frac{5}{3} \times \frac{1}{2}$$

$$\frac{3}{4} \times \frac{2}{3}$$

$$\frac{4}{3} \times \frac{1}{2}$$


To investigate whether the consumption of beetroot juice enhances exercise performance, a researcher selected a random sample of 50 student athletes from all the student athletes at a college. The athletes in the sample were randomly assigned to one of two groups. In one group, 25 athletes were given a daily dose of beetroot juice, and in the other group, the remaining athletes were given a daily dose of a placebo. At the end of six weeks of exercise training, the resear her compared the performances of the two groups. Based on the design of the  investigation, which of the following is the largest population to which the results can be generalized?

The 25 student athletes assigned to the beetroot juice group

The 50 student athletes in the sample

All student athletes at the college

All students at the college

All people who exercise


Which of the following statement(s) is or are correct?  Statement A: $$7+(0\times2)=7$$  Statement B: $$7+(0\div2)=7$$  Statement C: $$7+(2\times0)=7$$

All the three statements are correct.

Only Statement $$A$$ and $$B$$ are correct.

Only Statement $$A$$ and $$C$$ are correct.

Only Statement $$B$$ and $$C$$ are correct.

None of the above


In a square, all sides are~\uline{~~~~~~~~~~}~

Different

the same

Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns in Number Sequences->Pyramid Sequences


They are all even numbers.

All of them can be written as $n^{2}$ ($n$ is a whole number).

There is no similarity.

Overseas Competition->Knowledge Point->Calculation Modules->Power->Understanding the meaning of Power


A packet of biscuits costs $$x$$ pence. I buy $$4$$ packets. Which expression shows how much change in pence I will get from £$$8$$?

Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Using a Letter to Represent an Unknown Number


Mrs Scan reads $32$ pages of her book every day.  The book has $16$ chapters.  There are $36$ pages in each chapter.  How long will it take Mrs Scan to finish the book?

$$18$$ days

$$14$$ days

$$16$$ days

$$20$$ days

$$12$$ days


Laura bought a whole carton of milk.  Peter drank~$\dfrac{2}{3}$~of it and his sister, Mary, drank~$\dfrac{4}{9}$~of it.  How much less of the carton of milk did Mary drink than Peter?

Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Basic Understanding of Fractions


May and Megan wanted to buy some fruits. May bought $6$ apples, $8$ pears and $13$ plums. Megan bought $9$ apples, $2$ pears and $11$ plums. How many more pieces of fruits did May buy than Megan?


In a certain school, 17 percent of the students are enrolled in a psychology course, 28 percent are enrolled in a foreign language course, and 32 percent are enrolled in either a psychology course or a foreign language course or both. What is the probability that a student chosen at random from this school will be enrolled in both a foreign language course and a psychology course?

Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables


Which of the following numbers is closest to zero?

Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Basic Understanding of Decimals->Comparing Decimals


Which one of the following has the same value as $$\frac{6}{7}\div 4$$?

$$3 \frac{3}{7}$$

$$4 \frac{2}{3}$$

Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Operations of Fractions


When the following numbers are put in order of size, which comes in the middle?  $0.75, 79\textbackslash\%, \frac79, 0.7, \frac57$

Overseas Competition->Knowledge Point->Calculation Modules->Decimals


Ms. Tucker travels through two intersections with traffic lights as she drives to the market. The traffic lights operate independently. The probability that both lights will be red when she reaches them is 0.22. The probability that the first light will be red and the second light will \uline{not} be red is 0.33. What is the probability that the second light will be red when she reaches it?


Which of the followings is an arithmetic sequence?

$$2$$, $$5$$, $$9$$, $$14\cdots~ $$

$$5$$, $$9$$, $$13$$, $$18\cdots$$

$$1$$, $$2$$, $$1$$, $$2\cdots$$

$$0$$, $$0$$, $$0$$, $$0\cdots$$

Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences


Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction


A fair six-sided die, with sides numbered 1-6, is rolled five times in a row. On each roll, the result was a 3. What is the probability of rolling a 3 on the next roll?

$\left( \dfrac{1}{6}\right)^{5\textbackslash{} }\left( \dfrac{5}{6}\right)$

$\left( \dfrac{6}{1}\right)\left( \dfrac{1}{6}\right)^{5}\left( \dfrac{5}{6}\right)$

Overseas Competition->Knowledge Point->Calculation Modules


One day Randy was bored and he wrote all the whole numbers from 49 to 97  on his paper. How many times did he write the digit"8" on his paper?

None of the above


A football weighs $450\rm g$ and an empty box weighs $1.5\rm kg$.  After some identical footballs are placed inside a box, the box weighs $12.3\rm kg$.  How many footballs are there in the box?


Which of these expressions equals $2009$?


Which is the best estimate for $\frac{0.521\times59.34}{5.89}$?

Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating


Which fraction is equivalent to $$\frac{28}{35}$$?

Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Basic Understanding of Fractions->Properties of Fractions


Express $$1\frac{17}{25}$$ as a decimal.


$$16+4\times 8=$$  What should we do first?

x

Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations


Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Substituting the Values into the Expressions


$$5$$ and $$4$$

$$5$$ and $$7$$

$$5$$ and $$9$$

$$5$$ and $$10$$

Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division


To the number $$209$$ we add $$212$$. Then we multiply the result by $$29$$ and then we add $$208$$. Then the final result will be same as the result of the computation:．

$$209+212\times 29+208$$

$$(209+212\times 29)+208$$

$$(209+212)\times 29+208$$

$$(209+212)\times (29+\textasciitilde208)$$


A book has $$80$$ pages. On day 1, Danny read $$15\textbackslash\%$$ of the book. On day 2, he read $$25\textbackslash\%$$ of the book. How many pages are left to read?

Overseas Competition->Knowledge Point->Calculation Modules->Percentage Calculation


Which of the following equations is correct?

$2\times 3\times5\times2\times3=2^{2}\times3\times5$

$5\times11\times2\times5\times3\times11=2\times3\times5^{2}\times11^{2}$

Overseas Competition->Knowledge Point->Calculation Modules->Power->Computing Powers->Exponentiation of Powers


The sum of two numbers is 300. One number is 5 times of the other number. What is the difference between the two numbers?

None of the above


The harmonic mean of a set of non-zero numbers is the reciprocal of the average of the reciprocals of the numbers. What is the harmonic mean of $1$, $2$, and $4$?

Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating->Comparing and Ordering->Comparing and Ordering Fraction by Comparing Its Reciprocal


Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Addition and Subtraction of Decimals->Addition of Decimals


How many numbers are there in the list below?  $$6\frac{1}{3}, 7, 7\frac{2}{3}, 8\frac{1}{3}, \cdots, 30\frac{1}{3}, 31$$

None of the above

Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Finding Patterns


${\frac{9}{24}=\frac{15}{\Box}}$  What is the missing number in the box? $$

Overseas Competition->Knowledge Point->Calculation Modules->Fractions


Ron and Steven start driving towards each other from two places that are $2000$ metres apart at the same time. When they pass through each other, Ron has driven $500$ metres. What is the ratio of the speeds of Ron to Steven?

Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions


None of the above


Yes

No

Not sure

Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers


Study the number pattern below.  $$4$$, $$8$$, $$12$$,~\uline{~~~~~~~~~~}~, $$20$$, $$24$$, $$28$$  What is the missing number in the pattern?


$$6$$, $$-6$$

$$-6$$, $$6$$

$$6$$, $$6$$

$$-6$$, $$-6$$


The length of a sheet of paper is $10$ inches. What is this length in centimeters ?

Overseas Competition->Knowledge Point->Calculation Modules->Unit Conversion


Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns in Number Sequences


Geena had $$8y$$ paper clips. She used $$4$$ paper clips and gave the rest to her friends, Megan and Bryan. Megan received twice as many paper clips as Bryan. Find the number of paper clips Bryan received in terms of $$y$$.．

Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions


Debbie is interested in determining if music helps people study. To do this, she uses the help of 40 students in her psychology class. She randomly assigns half the people to study with music in the background for an hour, and the other half study with no music for an hour. The students then take a test on that material. In this example, what is the independent variable?

Music versus no music

Group that studies with no music

Group that studies with music

~Scores on the exam

Students in the class

Overseas Competition->Knowledge Point->Calculation Modules


Let $$a\square b=ab+a+b$$ for any real numbers $$a$$, $$b$$. The solution of the equation $$3\square 5=2\square x$$ is:．

Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Finding Unknowns Using the Given Operations


Put these numbers in order from the smallest to the biggest.  $$0.525\textasciitilde\textasciitilde\textasciitilde\textasciitilde{} 0.7\textasciitilde\textasciitilde\textasciitilde\textasciitilde0.35\textasciitilde\textasciitilde\textasciitilde\textasciitilde0.175$$

$$0.7$$, $$0.525$$, $$0.35$$, $$0.175$$

$$0.175$$, $$0.525$$, $$0.35$$, $$0.7$$

$$0.175$$, $$0.35$$, $$0.525$$, $$0.7$$

$$0.7$$, $$0.35$$, $$0.175$$, $$0.525$$

$$0.175$$, $$0.35$$, $$0.7$$, $$0.525$$

Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Basic Understanding of Decimals->Comparing Decimals


There are 70 teachers in an elementary school. The male to female ratio of this school can\textquotesingle t be~~\uline{~~~~~~~~~~}~.（⭐⭐）


There are two options with $$\triangle $$ and $$\bigcirc $$.  $$\bigcirc +8=13 $$  $$\triangle \times \bigcirc =15 $$.  What number does the $$\triangle$$ represent?

Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations


$$209+212\times 29+208$$

$$(209+212\times 29)+208$$

$$(209+212)\times 29+208$$


If we remove the percentage sign in $$31.4\textbackslash\%$$, then the result will be．

$$100$$ times the origional

$$\frac{1}{100}$$ of the original

the same


At a launch angle of 45°, the range of a launched projectile is given by


What is the product of $$628$$ and $$6$$?

Overseas Competition->Knowledge Point->Calculation Modules->Operations through Formulas

Overseas In-curriculum->Knowledge Point->Operations of Numbers ->Multiplication of Whole Numbers->Multiplication of Multi-Digit Numbers and 1-Digit Numbers->Multiplication of 3-Digit and 1-Digit (with regrouping for more than once)


$$30 \div 2 \textgreater{}x^{2}$$  Which of these numbers is the largest number $$x$$ could be?

Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities->Solving Inequalities

N/A.  revise from (GL Assessment book$$2$$《Paper $$6$$》 $$6$$ years Question \#$$15$$)


Function $$f$$ is defined for the set of all natural number as follows:  $$f(n)=\begin{cases}n+5, \text{when } n \text{ is odd}\textbackslash\textbackslash{} \dfrac{n}{2}, \text{when } n \text{ is even}\end{cases}$$,  What is the sum of the digits of the odd number $$k$$ if $$f(f(f(k)))=35$$?

Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Operations with New Definition in Flow Charts


Which of the following is equivalent to the expression $\frac{a^{-2}b^{3}}{ab^{-1}}$ ?  $\textasciitilde$


$6, 10, 18, 30, 46\dots$What number comes next in the sequence?


Martha prepares cupcakes with $3$ eggs each. A package of eggs has $18$ eggs. How many cupcakes can she prepare from two and a half packages of eggs?


Which of these numbers is closest in value to $$1$$?


Find the next term of the following sequence: 1, 1, 2,~ 3, 5, $\cdots $

Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences


Bud practises her violin for $25$ minutes every day. For how long does she practise each week?


Every half hour, one bacterium divides into two bacterias. In the very beginning, there is only 1 bacterium. After $$2$$ hours, there are  bacteria.

Overseas Competition->Knowledge Point->Calculation Modules->Power->Computing Powers->Exponentiation of Powers


A computerized sewing machine has four independent parts: mechanical, circuit board, touch screen, and power control. The probability that each wil fail within the first year is 0.01, 0.02, 0.001, and 0.03, respectively. If one of them fails then the machine does not work. What is the approximate probability that the machine is still working at the end of the first year?

greater than 99\%


There are $$4$$ number patterns as shown below.  In a number pattern, the digit in the ones place increases by $$1$$.  Tick the correct box that shows the number pattern.

$$47$$, $$57$$, $$67$$, $$77$$

$$57$$, $$56$$, $$55$$, $$54$$

$$92$$, $$93$$, $$94$$, $$95$$

$$68$$, $$70$$, $$72$$, $$74$$


If Marlon, there were $$30$$ days last month, $$12$$ of which were sunny. What is the percent of the days NOT sunny?


The numbers $2$, $3$, $4$, $5$, $7$, $13$ and $14$ are divided into $$3$$ groups of one or more numbers. The sum of the numbers in each group is the same. Which number must be in the group with the number $5$?

Only $$7$$

Only $$3$$

Only $$4$$

$$7$$ and $$3$$

$$7$$ and $$4$$


Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division


In an ice-cream shop there was some money in a drawer. After selling 6 ice cream cones, there are 70 dollars in the drawer. After selling a total of 16 ice cream cones, there are 120 dollars in the drawer. How many dollars were there in the drawer at the start? (2021 Math Kangaroo Problem, Level 3-4, Question \#13)


What number is forty times greater than $1.5$?


In a class of $$40$$ pupils, there are $$10$$ more boys than girls.  What is the ratio of the number of girls to the number of boys?

Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions->Ratio


$300$; $700$

$3000$; $7000$

$300$; $7000$


The $5$-digit number $\overline {2023A}$ is divisible by $9$.  What is the remainder when this number is divided by $5$?

Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Calculation of Multi-digit Numbers


Round off $$61805$$ to the nearest thousand.

Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating->Estimating Large Numbers


$126\div x=14$  What is the value of $x$?


What is another way of writing $a + a + a + a$ ?

$$aaaa$$


MIke has $2$ shirts, $5$ pens, $4$ pairs of trousers, $2$ coats, $5$ apples, $3$ hammers and $1$ bottle. How many pieces of clothes does Mike have?


Find the equation of the line using the following information:  slope=$-32$, $y$-intercept=$56$.

Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Linear Equations with one Variable


What is the next number in the pattern below?  $$4, 8, 8, 7, 12, 6, 16, 5, $$~\uline{~~~~~~~~~~}~

None of the above

Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns in Number Sequences


What does the digit $$9$$ in $$7.69$$ stand for?

$$9$$ tens

$$9$$ ones

$$9$$ tenths

$$9$$ hundredths

Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Basic Understanding of Decimals


Calculate in a vertical form: $$36\times14=$$~\uline{~~~~~~~~~~}~．

Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Addition of Whole Numbers->Addition in Vertical Form


What fraction is half-way between $$2$$ and $$2.5$$?

Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Operations of Fractions->Mixed Four Operations of Fractions


If BOB is $19$ and JANE is $30$, who is $10$ less than LIZ?

$$ $$AMY$$ $$

$$ $$KATE$$ $$

$$ $$JIM$$ $$

$$ $$JOE$$ $$

$$ $$SAM$$ $$

Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Using a Letter to Represent an Unknown Number


Marko has 9 pieces of candy and Tomo has 17 pieces of candy. How many pieces of candy does Tomo need to give to Marko so that each boy has the same number of pieces of candy?


Which fraction is greater than $$\frac{2}{3}$$?

Overseas Competition->Knowledge Point->Calculation Modules->Fractions

Overseas In-curriculum->Knowledge Point->Knowing Numbers->Comparing and Ordering->Comparing and Ordering Fractions


Kevin writes a sequence starts with the number $-2$ and goes up by $8$  For example, $-2, 6, 14\dots$  What is the first number that Kevin arrives at that is greater than $100$?

Overseas Competition->Knowledge Point->Calculation Modules


Which Law is used in the following calculation: $$2.76+10+3.75=10+(2.76+3.75)$$?

The Commutative Law of Addition

The Associative Law of Addition

Both

Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Addition and Subtraction of Decimals->Addition of Decimals


Two college roommates have each committed to donating to charity each week for the next year. The roommates\textquotesingle{} weekly incomes are independent of each other. Suppose the amount donated in a week by one roommate is approximately normal with mean $\textbackslash$$30 and standard deviation $\textbackslash$$10, and the amount donated  in a week by the other roommate is approximately normal with mean $\textbackslash$$60 and standard deviation $\textbackslash$$20. Which of the following is closest to the expected number of weeks in a 52-week year that their combined donation will exceed $\textbackslash$$120?

0; the combined donation never exceeds $\textbackslash$$120 in a week

1 week

3 weeks

5 weeks

8 weeks


Which of the following statements is false?

Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating


Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Operations of Fractions->Multiplication of Fractions


Yes

No

Not sure

Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers


Which one of these fractions is not equivalent to~$\dfrac{2}{5}$?

Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Basic Understanding of Fractions->Using Common Factors to Simplify Fractions


7 Nanyang Primary School, Preliminary Examination, Primary 6, Question \#15)  Geena had 8y paper clips. She used 4 paper clips and gave the rest to her friends, Megan and Bryan. Megan  received twice as many paper clips as Bryan. Find the number of paper clips Bryan received in terms of y. (  ).

\[  \frac{8y-4}{2}\]

\[  \frac{8y-4}{3}\]

\[  \frac{16y-8}{2}\]

\[  \frac{16y-8}{3}\]

Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions


Garcia is currently spending his entire lunch budget on 3 sodas and 4 hot dogs. At his current level of consumption, Garcia\textquotesingle s marginal utility for sodas is 5 utils and his marginal utility for hot dogs is 10 utils. In order to maximize his total utility, Garcia should

consume more sodas and fewer hot dogs regardless of the prices

consume more hot dogs and fewer sodas regardless of the prices

maintain his current level of consumption of sodas and hot dogs regardless of the prices

maintain his current level of consumption if the price of a soda is 1 dollar and the price of a hot dog is 2 dollars

maintain his current level of consumption if the price of a soda is 2 dolalrs and the price of a hot dog is 1 dollar


What is the solution set of the equation $\sqrt{2x+4}+4=x+2$ ?  $\textasciitilde$

$\textbackslash{0, 6\textbackslash}$

There are no solutions to the given equation


Simplify the expression． ~\hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}  $$a+2a=$$~\uline{~~~~~~~~~~}~


What is the value of this expression: $$2\times0\times0\times6+2006$$? (2006 Math Kangaroo Problem, Level 3-4, Question \#2)

Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations


Paul draws a plan of his school using a scale of $$2\text{cm}$$ to $$5\text{m}$$.  On the plan, the school hall is $$6\text{cm}$$ long.  What is the real length of the hall?

Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions->Proportions->Scale


The harmonic mean of a set of non-zero numbers is the reciprocal of the average of the reciprocals of the numbers. What is the harmonic mean of 1, 2, and 4?

Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating->Comparing and Ordering->Comparing and Ordering Fraction by Comparing Its Reciprocal


Which number is the only factor of both $56$ and $36$?


Which of the following does not contain a constant?


$$3$$ ones, $$6$$ tenths and $$7$$ thousandths is ．


They are equal.

Overseas Competition->Knowledge Point->Calculation Modules->Power->Understanding the meaning of Power


The first two terms of a sequence are $1$ and $2$. Each of the following terms in the sequence is the sum of all the terms which come before it in the sequence. Which of these is not a term in the sequence?

Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences


A 99\% confidence interval for the weights of a random sample of high school wrestlers is reported as (125, 160). Which of the following statements about this interval is true?

At least 99\% of the weights of high school wrestlers are in the interval (125, 160).

The probability is 0.99 that the true mean weight of high school wrestlers is in the interval (125, 190).

99\% of all samples of this size will yield a confidence interval of (125,160).

The procedure used to generate this confidence interval will capture the true mean weight of high school wrestlers 99\% of the time.

The probability is 0.99 that a randomly selected wrestler will weigh between 125 and 160 lb.


We've compared two sets of data in a correlational study and have found a correlation coefficient of +.83. We can legitimately conclude that there's what kind of relationship between our measures?

No relationship

Strong inverse relationship

Strong positive relationship

Weak inverse relationship

Weak positive relationship


A popular computer card game keeps track of the number of games played and the number of games won on that computer. The cards are shuffled before each game, so the outcome of the game is independent from one game to the next and is based on the skill of the player. Let X represent the number of games that have been won out of 100 games. Under which of the following situations would X be a binomial random variable?

All games were played be the same player, whose skill improved over the course of the 100 games.

A group of 5 players of different skill levels were each allowed to play 20 games in a row.

A group of players of different skill levels were each allowed to play until they had lost 3 games and this resulted in 100 games played.

Two players of equal skill level each played one game a day for 50 days and their skill level did not change from day to day.

Two players of different skill levels competed by allowing one player to continue until a game was lost, then the other player to continue until a game was lost, and so on, until 100games were played.


After we simplify $$2+2-2+2-2+2-2+2-2+2$$ the resut will be :．

Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Addition and Subtraction of Whole Numbers->Questions Involving Addition and Subtraction


$a$ is $25\textbackslash\%$ more than $2022$, and b is $20\textbackslash\%$ less than $a$. What is the value of $b$?


Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Multiplication and Division of Decimals


Which of the following is equivalent to $$\frac{6}{8}$$?

Overseas In-curriculum->Knowledge Point->Knowing Numbers->Fractions->Basic Properties of Fractions->Using Common Factors to Simplify Fractions

Overseas Competition->Knowledge Point->Calculation Modules->Fractions


Study the number pattern below. What is the missing number?  $$395$$, , $$415$$, $$425$$, $$435$$

Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns in Number Sequences


Jack spent~$\dfrac{1}{24}$~of money on a new watch and~$\dfrac{5}{6}$~of money on a new phone. What fraction of the money did Jack spend altogether?

Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Operations of Fractions


Hans has $9$ dollars and $20$ cents. One can of soft drink costs $1.20$ dollarss, and one chocolate bar is $60$ cents cheaper than one can of soft drink. After buying $3$ cans of soft drink and two chocolate bars, how much does he have left?

$4.8.$ dollars

$4.2.$ dollars

$4.4.$ dollars

$5.4.$ dollars

$6.4.$ dollars

Overseas Competition->Knowledge Point->Calculation Modules


In one of the following lists, the numbers are~\uline{not}~all increasing.

$$\frac{1}{3}$$, $$0.25$$, $$\frac{3}{10}$$, $$0.5$$

$$\frac{3}{5}$$, $$0.7$$, $$\frac{4}{5}$$, $$1.5$$

$$\frac{2}{5}$$, $$0.5$$, $$\frac{7}{10}$$, $$0.9$$

$$\frac{3}{5}$$, $$0.5$$, $$\frac{4}{5}$$, $$0.9$$

$$\frac{2}{5}$$, $$1.5$$, $$\frac{10}{5}$$, $$2.3$$  Which list is it? Just write down the letter.  (For this question, we do not need to see any working).

Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating->Comparing and Ordering->By Converting Fractions into Decimals


Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction


The outside temperature in a town is $-18$ $^{}o$$C$. What change in the temperature, would bring the outside temperature to $0$ $^{}o$$C$?

Overseas Competition->Knowledge Point->Calculation Modules->Negative Numbers


Which of the following is not an algebraic expression?


Find the equation of a line using the following information:  slope=$-32$, $y$-intercept=$56$.

Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Linear Equations with one Variable