Solve the equation below.  $$5x+15=8x-12$$

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


Which of these fractions expressions has the \textbf{largest}~value?

$$\frac{1}{3} \times \frac{1}{6}$$

$$\frac{1}{3} \div \frac{1}{6}$$

$$\frac{1}{6} \div \frac{1}{3}$$

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


Calculate:  $400 \times 20 =$~\uline{~~~~~~~~~~}~$\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde$$60 \times 30 =$~\uline{~~~~~~~~~~}~

$6000$; $1800$

$800$; $900$

$800$; $1800$

$8000$; $1800$

Overseas Competition->Knowledge Point->Calculation Modules


Which of the following statements is false?

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


Leander has a box with fewer than $80$ erasers in it. The erasers can be divided evenly between $2$, $3$, or $4$ children. However, they cannot be divided evenly between $11$ children because $5$ more erasers would be needed. How many erasers are there in the box?


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


Which of the following expression(s) is equivalent to $\frac{1}{27}$ ?  $I.$ $3^{-3}$  $II.$ $\left( \frac{1}{3} \right)^{3}$  $III.$ $\left( -\frac{1}{3} \right)^{3}$  $\textasciitilde$

$I$ only

$II$ only

$I$ and $II$

$I$, $II$, and $III$


none of these

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


Eddie has $$y$$ toys. Bob has $$150$$ more than two times the number of toys Eddie has. Bob hastoys．


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


Use the numbers $2$, $3$, $8$ to form a three-digit number, the number cannot be reused.  What is the sum of the maximum $3$-digit number~and the minimum $3$-digit number？

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


The students in a class sit in rows. There is the same number of students in each row. There are 2 rows of students in front of Robert and 1 row of students behind him. In his row, there are on 3 students on his left and 5 students on his right. How many students are there in this class? (2022 Math Kangaroo Problem, Level 3-4, Question \#15)


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


Wade\textquotesingle s birthday was yesterday. It\textquotesingle s Monday tomorrow. What day was Wade\textquotesingle s birthday?

Monday

Thursday

Friday

Saturday

Sunday


Which of the following is the best estimate of $$62\times 35$$?

$$60\times 30$$

$$60\times 40$$

$$70\times 30$$

$$70\times 40$$

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


Which of the following fractions is closet to $$\frac{3}{4}$$?

Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating->Comparing and Ordering->By Using Common Multiples to Express Fractions in the Same Denomination->Expressing Fractions with the Same Denominator


A local restaurant gives teachers a 20\% discount on all their meals. If a teacher pays $14.00 for a meal after the discount was applied, what was the price of the meal before the discount?

$ \textbackslash$16.90$

$ \textbackslash$17.50$

$ \textbackslash$20.00$

$ \textbackslash$25.20$


Which number is the only multiple of both $9$ and $12$?


How many terms and variables does the expression $$5ab-6ac+7b-8+a$$ have, respectively?

$$3, 3$$

$$3, 4$$

$$4, 3$$

$$5, 3$$

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


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->Whole Numbers->Whole Numbers Addition and Subtraction


Which of the following inequalities is always true?

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


Ted has exactly one of every type of UK coin and one of every UK bank note up to and including £$50$.  What is the median amount that Ted has?

$20\rm p$

$35\rm p$

$50\rm p$

$75\rm p$


Julie and Angela played "kangball", a ball game. Each goal in their game scores 2 points. Julie scored 5 goals and Angela scored 9 scores. How many more points than Julie did Angela score?


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


A rubber ball with mass 0.20kg is dropped vertically from a height of 1.5m above a floor. The ball bounces off of the floor, and during the bounce 0.60J of energy is dissipated. What is the maximum height of the ball after the bounce?


Which of the following inequalities is always false?

$\vert x\vert\textless-1$


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

N/A.(UK maths-$$2$$-fam-bookletqueen elizabeth boys\textquotesingle school $$6$$ years Question \#$$21$$)


Divide $$51$$ by $$7$$.The remainder is.

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

Overseas In-curriculum->Knowledge Point->Operations of Numbers ->Division of Whole Numbers->Division with Remainder->Long Division with Remainder


Find the value of~$\left( \dfrac{1\cdot3}{2\cdot2}\right)\left( \dfrac{2\cdot4}{3\cdot3}\right)\left( \dfrac{3\cdot5}{4\cdot4}\right)\cdot\cdot\cdot\left( \dfrac{97\cdot99}{98\cdot98}\right)\left( \dfrac{98\cdot100}{99\cdot99}\right)$?

Overseas Competition->Knowledge Point->Calculation Modules


There are two piles of matches. Pile A has $38$ matches and Pile B has $49$ matches. Eddie and Vera take turns to take matches from either pile. The number of matches they can take is unlimited, but they can\textquotesingle t end their turn them without taking any match. The person who takes the last match is the winner. If Eddie goes first, who do you think will win?

Eddie

Vera

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


There are $25$ questions in a math contest. The testee receives 4 points for each correct answer and loses $2$ points for each problem left unanswered and each incorrect answer. If Irene took part in this test and got a score that is more than $$60$$, she should answer at leastquestions correctly．


Which of the following pairs of sample size n and population proportion p would produce the greatest standard deviation for the sampling distribution of a sample proportion~$\overset{\wedge}{p}$?

n = 1,000 and p close to 0

n = 1,000 and p close to 1

n = 1,000 and p close to~$\dfrac{1}{2}$

n = 100 and p close to 0

n = 100 and p close to~$\dfrac{1}{2}$


Which one of the following has the same value as $$7\div\frac{3}{5}$$?

$$\frac{7}{1} \times \frac{5}{3}$$

$$\frac{7}{1} \times \frac{3}{5}$$

$$\frac{1}{7} \times \frac{3}{5}$$

$$\frac{1}{7} \times \frac{5}{3}$$

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


A meter shows that a household uses $6$p of electricity per hour from $00:00$ to $07:00$, $8$p of electricity per hour from $07:00$ to $16:00$, $10$p of electricity per hour from $16:00$ to $00:00$. What is the cost of electricity over $24$ hours?


Find the difference between the largest possible number and the smallest possible number that can be made by rearranging the digits $82561$.


The length of a sheet of paper is $12.5$ inches. What is this length in centimeters ?

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


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


$\frac{320}{x}=64$  What is the value of $x$?


The average of two numbers is $$38$$. When a third number is added, the average of the three numbers is $$40$$. Find the third number.

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

Overseas In-curriculum->Knowledge Point->Data->Data Analysis->Mean->Application the Mean


What is the next number in the sequence below?  29, 28, 25, 20, 13, $\cdots $

None of the above

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


What is the sum: $$3+7+2+8+1=$$. ($$2007$$ Math Kangaroo Problem, Level $$1-2$$, Question \#$$17$$)

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


Randy buys a box of paperclips for $45$ cents, a marker for $65$ cents, and a note pad for $90$ cents. How much does he pay in total in dollars?

Overseas Competition->Knowledge Point->Calculation Modules->Unit Conversion->Converting between Units of Money


Complete the number pattern.  $$2946$$, $$2926$$, $$2906$$, $$^{}\boxed ~{\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde}$$, $$2866$$ .


Which of the following is the reciprocal of $\frac{2}{7}$?


The volume formula of rectangular prism is $$V=Bh$$. How many variables are dependent variables?

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


A sweet costs 9p. How many sweets can Avril buy for 56p?~\uline{~~~~~~~~~~}~


Which of the following is equivalent to $\sqrt[3]{a^{2}} \cdot a^{}\frac{1}{2}$ ?  $\textasciitilde$


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


What is the next number in the sequence below?  7, 8, 6, 9, 5, 10, $\cdots $

None of the above


Which of the following has the same value as $$\frac{2}{9}\div\frac{3}{5}$$?

$$\frac{2}{9}\times \frac{3}{5}$$

$$\frac{9}{2}\times \frac{3}{5}$$

$$\frac{2}{9}\times \frac{5}{3}$$

$$\frac{9}{2}\times \frac{5}{3}$$

Overseas In-curriculum->Knowledge Point->Operations of Numbers ->Multiplication and Division of Fractions->Division of Fractions->Dividing Fractions by Fractions


$$4\times 4$$

$$4 + 5$$

$$4\times4\times4\times4 \times4$$

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


Derrick lists down all whole numbers from $$1$$ to $$40$$. Lisa selects all odd numbers and adds them up. Aisha selects all the even numbers and adds them up. What is the difference between Aisha\textquotesingle s and Lisa\textquotesingle s sums?

None of the above


Lisa writes six numbers which contain all the digits from $$1$$ to $$6$$, and each digit from $$1$$ to $$6$$ only appears once. What number comes next?  $$1$$, $$3$$, $$6$$, $$4$$, $$2$$,~\uline{~~~~~~~~~~}~.

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


Express $$0.\dot{2}1\dot{0}$$ as a fraction.

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


What is the mode of these numbers? $1, 1, 1, 2, 3, 4, 6$

Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Read and Write numbers


A car is traveling at a speed of 30 m/s. If the car decelerates uniformly at a rate of 5 m/s^{2} for a distance of 80 meters, what is its final speed?

5 m/s

10 m/s

20 m/s

30 m/s


Overseas Competition->Knowledge Point->Calculation Modules


How many $$10\text{p}$$ coins can I get for £$$1.80$$?

$$10$$ coins

$$18$$ coins

$$88$$ coins

$$108$$ coins

$$180$$ coins


What number is half way between $$3.5$$ and $$6.9$$?

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


SASMO 2018  A mother gave the same number of cheese sticks to each of her 4 children---  Wendy, Xander, Yasmin and Zane. Wendy gave half of her cheese sticks to  Yasmin, then Yasmin gave 2 to Xander. After that, Zane gave 3 to Yasmin. In  the end, Yasmin had 10 cheese sticks. What was the total number of cheese  sticks that the mother gave to her 4 children?


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


In a park there are 15 animals: cows, cats, and kangaroos. We know that precisely 10 are not cows and precisely 8 are not cats. How many kangaroos are there in the park? (2019 Math Kangaroo Problem, Level 3-4, Question \#21)


Stamps cost $0.65$p each.  How many stamps can Peter purchase with a £$5$ note?


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


The caffeine content of 8-ounce cans of a certain cola drink is approximately normally distributed with mean 33 milligrams (mg). A randomly selected 8-ounce can containing 35 mg of caffeine is 1.2 standard deviations above the mean. Approximately what percent of 8-ounce cans of the cola have a caffeine content greater than 35 mg?


The digit $9$ in which number represents a value of $0.09$?

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


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


A watermelon weighs as much as three apples, and one apple weighs as much as three strawberries. How many strawberries weigh the same as one watermelon?

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


Fountain X has $245$ ℓ of water. Fountains X and Y have $600$ ℓ of water altogether. How much water does Fountain Y have?

$$355$$ ℓ

$$465$$ ℓ

$$555$$ ℓ

$$565$$ ℓ

Overseas Competition->Knowledge Point->Calculation Modules->Unit Conversion->Converting between Units of Volume and Capacity


The mass of a crate with $$8$$ glass bottles is $$\text{4450 g}$$.  The mass of the same crate and $$5$$ glass bottles is $$\text{3100 g}$$.  Find the mass of the empty crate.

$$\text{450 g}$$

$$\text{850 g}$$

$$\text{1350 g}$$

$$\text{250 g}$$


Calculate:  $10 \times 10 =$~\uline{~~~~~~~~~~}~$\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde$$200 \times 10 =$~\uline{~~~~~~~~~~}~

$100$; $2000$

$10$; $2000$

$100$; $200$


$49, 38, 27, 16, 5,\dots$  Which number comes next in the sequence?


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


Which of the following numbers can be divided by $2$, $4$ and $6$ exactly with no remainder?

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


Tony has $44$ shoes. He has $11$ more sneakers than boots. Which equation represents this situation?

$a+(a+11)=44$, where $a$ is the number of sneakers

$a+(a-11)=44$, where $a$ is the number of sneakers

$a+11a=44$, where $a$ is the number of boots

$a+(a-11)=44$, where $a$ is the number of boots

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


Based on the information provided in the chart above, which correlational coefficient best represents the relationship between the test score and time spent?


A lizard is $20\rm cm$ in length.  The lizard can walk $1.5$ times its own length every second.  How long would it take the lizard to walk $36\rm m$?

$2\textasciitilde\rm minutes$

$20\textasciitilde\rm seconds$

$40\textasciitilde\rm seconds$

$20\textasciitilde\rm minutes$

$1\textasciitilde\rm minute$


Two satellites are in circular orbits around Earth. Satellite A has speed $v\_{A}$. Satellite B has an orbital radius nine times that of satellite A. What is the speed of satellite B?


From 1990 to 2001, German currency included coins called $pfennigs$, worth 1 pfennig each, and $groschen$, worth 10 pfennigs each. Which equation represents the number of pfennig coins, $p$, and groschen coins, $g$, that have a combined value of $85$ pfennigs?


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 for the area 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

Overseas Competition->Knowledge Point->Geometry Modules->Objects with Straight Sides->Knowing Graphs


The best way to write the product of $z$ and $-1$ is~\uline{~~~~~~~~~~}~.

z

$-z$

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


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


（$$2017$$ Nanyang Primary School, First Semestral Examination, Primary Three, Question \#$$9$$)  Study the number pattern below.  $$\boxed{4168}$$,~ $$\boxed{4318}$$,~ $$\boxed{4468}$$,~ $$\boxed{4618}$$,~ $$\boxed{?}$$,~ $$\boxed{4918}$$  What is the missing number?


At a large conference of teachers from a variety of subjects, a random sample of 50 mathematics teachers attending the conference was selected. Among the selected mathematics teachers, 28 percent had taken one or more courses in statistics. For which of the following populations is 28 percent a reasonable estimate of the percentage of those who have taken one or more courses in statistics?

All mathematics teachers

All mathematics teachers who attended the conference

All mathematics teachers who have taken one or more courses in statistics

All teachers who attended the conference

All teachers


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


$36, 64, 80, 96, 108$  Which number is the only multiple of $8$ and $12$?


Find the next number in the sequence below.  8, 10, 6, 12, 4, 14, 2,~\uline{~~~~~~~~~~}~

None of the above

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


How many times bigger is $7\textasciitilde520\textasciitilde000$ than $75.2$?

10 000

100 000

1 000 000

75 200

Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Basic Understanding of Decimals->Move the Decimal Point to Change a Number’s Value


Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division->Multiplication and Division of Whole Numbers->Multiplication out of the Multiplication Table


$12, 1, 7, -3, 9, -6$  What is the difference between the range and median of these numbers?

Overseas Competition->Knowledge Point->Calculation Modules


Yes

No

Not sure


Grace went out to the yard and called all her cats, hens and kids. All $25$ heads ran to her. There were three times as many legs as tails and more kids than cats. How many cats did Grace have?


Calculate: $$0.3\overset{\centerdot }{\mathop{2}}+0.4\overset{\centerdot }{\mathop{1}}=$$~\uline{~~~~~~~~~~}~．

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


In $$26.73$$, the digit $$3$$ has the value of ．

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


What is the sum of the first $20$ digits in the decimal part of $0.\dot{1}2\dot{3}$?


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


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


Which of the following does not contain a constant?


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


Ms. Costas owns a business with nine other employees. Ms. Costas\textquotesingle s annual salary is \textbackslash$\textbackslash{} 90,000. Her manager\textquotesingle s salary is \textbackslash$\textbackslash60,000. Of her other employees, three earn \textbackslash$\textbackslash{} 25,000 each and five earn \textbackslash$\textbackslash{} 15,000 each. The range of this distribution is

$ 75,000

$ 50,000

$ 25,000

$ 20,000

$ 15,000


Study the pattern below carefully and find the missing number.  $$ 0 7\textasciitilde1 5$$, $$ 0 7\textasciitilde3 5$$, $$ 0 8\textasciitilde{} 0 5$$, $$ 0 8\textasciitilde4 5$$, $$ 0 9\textasciitilde3 5$$,~\uline{~~~~~~~~~~}~

$$ 0 9\textasciitilde5 5$$

$$ 0 9\textasciitilde7 5$$

$$ 1 0\textasciitilde3 5$$

$$ 1 0\textasciitilde4 5$$

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


$$(21\times55)+20=1175$$ is a correct calculation.  Which one of the following calculations is INCORRECT?

$$21\times (55+20)=1175$$


Nina and Nora went to buy some stationeries. Nina bought $4$ notebooks, $5$ rulers and $3$ pens. Nora bought $6$ notebooks, $7$ rulers and $1$ pen. How many more pieces of stationeries did Nora buy than Nina?


$2$ potatoes, $3$ peas and $1$ tomato together weigh $18$ lbs. One pea and one tomato together weigh $8$ lbs. $2$ potatoes and $1$ pea together weigh $2$ lbs more than one pea and one tomato weigh together. Each potato weighs the same and each pea weigh the same. How much does one potato weigh?

$2$ lbs

$3$ lbs

$4$ lbs

$5$ lbs

$6$ lbs

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


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


Jane goes shopping.  She spends half her money in the supermarket.  She then spends one third of what she has left in a coffee bar.  Finally, Jane returns home in a taxi that costs her £$8$.  If Jane has £$12$ left, how much money did she start with?


Which of the following inequalities is always true?

$$3-x\geqslant 0$$

$$\textbar x\textbar\leqslant 0$$

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


$$\frac{1}{3}+\square =\frac{3}{4}$$  What is the missing fraction in the box? ．

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


Elma took $$2$$ candy bars to school. First, she traded each of them for $$4$$ apples, and then she traded each of the apples for $$3$$ mandarin oranges. How many mandarin oranges did she have after all the trading?

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


Peter has $15$ dollars and $80$ cents. Two pencils cost $3.80$ dollars, and one ruler is $70$ cents cheaper than one pencil. After buying one pencil and two rulers, how much does he have left?

$11.5.$ dollars

$10.5.$ dollars

$10.8.$ dollars

$12.7.$ dollars

$9.5.$ dollars


What is the value of $(2\times10^{3})\times (3\times10^{2})$?  $\textasciitilde$

$6\times 10^{6}$

$6\times 10^{5}$

$5\times 10^{6}$

$5\times 10^{5}$


A number when rounded to the nearest tenth is $$4.0$$. Which of the following is the original number?


Let $$a\square b=a(b+3)-4b$$ for any real numbers $$a$$, $$b$$. The solution of the equation $$8\square 5=6\square x$$ is:．

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


MIchael had several books. He sold half of them, and then he bought $20$ books. Finally the number of his books wasn\textquotesingle t changed. How many books did he have at first?


A number when rounded off to the nearest ten has a value of $$400$$.  What could be the number?．

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


Which of the following is the correct expression of $0.4666\dots$?


Which of the following fraction is the largest?

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


I am making a scale model of a ship, which is 120m long. If the scale is 1:400, how long will the model yacht be (in cm)?

$$3 \text{cm}$$

$$0.03 \text{m}$$

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


Which one of the following expressions has the same result as~$43.23\div7.2$?


If Coke makes the Bill Cosby ad and Pepsi makes no ad then what is Pepsi's payoff?


I buy $6$ packets of crisps from the $98$p store where everything costs $98$p.Howmuch change do I get from￡$10$？

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


Study the number pattern below. What is the missing number in the pattern?  $$1015$$, $$1025$$, $$1045$$, $$1075$$,~\uline{~~~~~~~~~~}~, $$1165$$


A lot of babies were born in the zoo last year: two baby tigers, three baby whales and four baby parrot. How many legs do all these babies have altogether?

Overseas Competition->Knowledge Point->Calculation Modules


Two friends, Andy and Bob, participate in a game of bowling every week. From past experiences, it is known that both friends \textquotesingle scores are approximately normally distributed, where Andy has a mean score of 150 with a standard deviation of 30, and Bob has a mean score of 165 with a standard deviation of 15. Assuming that their scores are independent, which of the following values is closest to the probability that Andy will have a greater score than Bob in single game?


You are going to create a 95\% confidence interval fora population proportion and want the margin of error to be no more than 0.05. Historical data indicate that the population proportionis about 0.7. What is the minimum size random sample you need to construct this interval?


Which of the following is a correct unit for acceleration?

$m/s$

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


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


A shopkeeper sold 101 pineapples in a day. The pineapples sold in the afternoon is 31 more than the pineapples sold in the morning. How many pineapples were sold in the afternoon?

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


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


I am thinking of two numbers. Their common factors are only $$1$$ and $$2$$. Their first (lowest) common multiple is $$12$$. If one of the numbers is $$6$$, what is the other number?


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 $$y$$.．


Taylor buys two hats that cost £$7.15$ each. How much change does Taylor receive from a £$20$ note?


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


The numbers in each of the three brackets follow the same rule. Find the missing number.  $$\left[10, 50, 15 \right]\textasciitilde\textasciitilde\left[37, 120, 23 \right]\textasciitilde\textasciitilde\left[16, 56, ?\right]$$

Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns in Number Sequences->Filling Sequences according to the Patterns


714 000

713 700

713 680

713 670

713 600

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


My friend Sanjay is making a scale model of the London Ear (a famous landmark in London). The London Ear is 80m tall and his model is 150cm tall. What is the scale of the model, in its simplest form?


Divide $$6$$ by $$7$$.  Round your answer to the nearest tenth.

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

Overseas In-curriculum->Knowledge Point->Operations of Numbers ->Multiplication and Division of Decimals->Division of Decimals->Approximate Numbers of Quotients in Decimal Division


Mom divides 8 cupcakes into 3 kids equally. Assume $$x$$ represents the number of cupcakes each kid gets, which of the following inequalities can represent this situation?

$$3x\geqslant 8$$

$$3x\leqslant 8$$

$$3x = 8$$

$$x\geqslant 8$$

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


Which of the following groups has equivalent ratios?

$4$ to $3$, $\frac{0.4}{3}$

$\frac{4}{3}$, $8$ to $9$

$$\frac{4}{3}$$, $8:6$

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

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


Helen said to Mary, "If you give me 4 apples, I will have exactly as many apples as you." How many more apples does Mary have than Helen?

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


What is the sum of the following numbers?  $$2017+7012+271=$$

None of the above


Suppose a block with mass 4kg is placed on a horizontal table. Ryan tried to push the block to right with force 4N but failed. He then tried to push with 6N and 8N, both didn\textquotesingle t work. Lastly, Ryan pushed with 8.1N force, and the block finally moved. What is the friction acting on the block when Ryan pushes with 4N, 6N, and 8N, separately?  $\textasciitilde$  $\textasciitilde$

4N, 6N, 8N, all to left

8N, 8N, 8N, all to left

4N, 6N, 8N, all to right

8.1N, 8.1N, 8.1N, all to right

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


Five girls ate some plums. Lauren ate two plums more than sophie. Betty ate three plums fewer than lauren. Claire ate one plum more than Betty and three plums fewer than Alice. Which two girls ate the same number of plums? (2022 Math Kangaroo Problem, Level 3-4, Question \#22)

Claire and Lauren

Claire and Sophie

Lauren and Alice

Sophie and Alice

Alice and Betty


A large-sample 98 percent confidence interval for the proportion of hotel reservations that are canceled on the intended arrival day is (0.048,0.112). What is the point estimate for the proportion of hotel reservations that are canceled on the intended arrival day from which this interval was constructed？

It cannot be determined from the information given.


A hypothesis test in which n = 250 is set up so that P (rejecting H\textsubscript{0}, when H\textsubscript{0~}is true) = 0.05. Which of the following is true?

We can increase the power if we let alpha = 0.05.

We can increase the power if we let alpha = 0.01.

We can increase the power if we let n = 200.

We can decrease the power if we let n = 200.

We can decrease the power if we let n = 300.


What is the tax incidence on the sellers in this market?

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


A state study on labor reported that one-third of full-time teachers in the state also worked part time at another job. For those teachers, the average number of hours worked per week at the part-time job was 13. After an increase in state teacher salaries, a random sample of 400 teachers who worked part time at another job was selected. The average number of hours worked per week at the part-time job for the teachers in the sample was 12.5 with standard deviation 6.5 hours. Is there convincing statistical evidence. at the level of a = 0.05, that the average number of hours worked per week at part-time jobs decreased after the salary increase?

No. The p-value of the appropriate test is greater than 0.05.

No. The p-value of the appropriate test is less than 0.05.

Yes. The p-value of the appropriate test is greater than 0.05.

Yes. The p-value of the appropriate test is less than 0.05.

Not enough information is given to determine whether there is convincing statistical evidence.


What is the least possible value of $$21x+14y$$, if $$xy=6$$ and $$y\textgreater0$$?

Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Indefinite Equations->Indeterminate Addition Equations


Amul divided a whole number less than $$200$$ by a whole number greater than $$15$$.  The result was a whole number.  What is the largest possible result of Amul\textquotesingle s division?


If $6x+3y=3$, then what is the value of $16^{}x\cdot 4^{}y$ ?  $\textasciitilde$


Observe the number pattern below. What is the missing number?  $1$, $1$, $2$, $3$, $5$, $8$,~\uline{~~~~~~~~~~}~

Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns in Number Sequences->The Fibonacci Sequences (Rabbit Sequences)


If $x^{}\frac{y}{3}=3$ for some positive $x$ and $y$, which of the following is a possible value of $x$ ?  $\textasciitilde$

Overseas Competition->Knowledge Point->Calculation Modules


Jerry wanted to buy an eraser at $35$ cents. He paid the cashier $1.00$ dollar.  How much change did he receive?

$1.35$ dollars

$0.75$ dollars

$0.65$ dollars

$0.55$ dollars

$0.35$ dollars


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


What\textquotesingle s the product of 16 and 5?

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


A university will add fruit juice vending machines to its classroom buildings if the student body president is convinced that more than 20 percent of the students will use them. A random sample of n students will be selected and asked whether or not they would use the vending machines. A large-sample test for proportions at the significance level of $\alpha$=0.05 will be performed. The null hypothesis that the proportion of all students who would use the vending machines is 20 percent will be tested against the alternative that more than 20 percent of all students would use them. For which of the following situations would the power of the test be highest?

The sample size is n= 750, and 20 percent of all students use the vending machines.

The sample size is n=750, and 25 percent of all students use the vending machines.

The sample size is n=1,000, and 25 percentof allstudents use the vending machines.

The sample size is n=500, and 50 percent of all students use the vending machines.

The sample size is n=1,000, and 50 percent of all students use the vending machines


What is the value of $$20-6\div2\times ( 2+3)$$?

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


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


What number is $$339$$ less than two thousand and eighteen?

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


How long Jingyi used to drive across US?

2 hours

1 day

5 days

10 day

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


Find the next number in the sequence below.  $$8, 10, 6, 12, 4, 14, 2,$$~\uline{~~~~~~~~~~}~

None of the above

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


The largest of the following numbers is~\uline{~~~~~~~~~~}~. ($$2011$$ Math Kangaroo Problems, Level $$7-8$$, Question \#$$1$$)

Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating->Comparing and Ordering->Comparing and Ordering the Value of Expressions


Mia prepares apple pies with $4$ apples each. A bag of apples has $16$ apples. How many apple pies can she prepare from three and a half bags of apples?


The probability of winning a certain game is 0.5. If at least 70 percent of the games in a series of n games are won, the player wins a prize. If the possible choices for n are  n=10, n=20, and n=100  which value of n should the player choose in order to maximize the probability of winning a prize?

n=10 only

n=20 only

n=100 only

n=10 or n=20 only;~the probabilities are the same.

n=10 or n=20 or n=100; the probabilities are the same.


Look at the number pattern below.  What number comes next?  $731$, $729$,~\uline{~~~~~~~~~~}~, $725$, $723$, $721$


37 coins are shared equally among 5 children. How many coins are left?

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


none of these

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


Which of the following is not a function?

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


$$(21\times55)+20=1175$$ is a correct calculation.  One of the following calculations is INCORRECT  Put a cross in the box next to the INCORRECT calculation.

$$21\times (55+20)=1175$$


Which of the following numbers is the largest?


The sum of $$7$$ numbers in an arithmetic sequence is $$448$$. What is the smallest possible value of the smallest number in this sequence?


Which of the following can be reducted into $\frac16$?


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


If $3m+2n=4$, then what is tha value of $8^{}m \cdot 4^{}n$?  $\textasciitilde$


Consider these two operations:~$a\textbackslash{} ◊\textbackslash{} b=a^{2}-b^{2},\textbackslash{} a\textbackslash{} \bigstar\textbackslash{} b=(a-b)^{2}$  What is the value of~$(5\textbackslash{} ◊\textbackslash{} 3)\textbackslash{} \bigstar\textbackslash{} 6$?

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


Two guinea pigs heterozygous for coat texture have offspring. What is the percent of their offspring expected to have smooth coats?


Jim weighed his four dogs, weighing 10.8kg, 13.5kg, 16kg and 14.2kg respectively. What is their total weight?

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


Elisa reads $2$ pages of her book on Day $1$.  Then Mr Scan reads $4$ pages of her book on Day $2$, $8$ pages on Day $3$, and then $16$ pages on Day $4$, which continues until Elisa finishes her book.  If there are $254$ pages in her book, how many days does it take her to read the whole book?

$$5$$ days

$$6$$ days

$$7$$ days

$$8$$ days

$$9$$ days


What is the next number in the sequence below?  $$47, 44, 38, 29, 17$$

None of the above

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


Which of the following is equivalent to $a^{2}$?

$a\times a$

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


The sum of two numbers is $$5077$$. If the smaller number is $$1289$$. What is the other number?

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


$7-3\times\square+1=2$  What number must go in the box to make the statement correct?

Overseas Competition->Knowledge Point->Calculation Modules


Which of the following expressions has the same result as $$293-56-44$$?

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


Six pencils and two erasers cost $$3.80$$ dollars. One pencil costs $$40$$ cents.  How much does one eraser cost?

$$20$$ cents

$$30$$ cents

$$40$$ cents

$$50$$ cents

$$60$$ cents

Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division->Division of Whole Numbers->Division out of the Multiplication Table


An empty jar weighs $375\rm g$. When it is filled with jam it weighs $1.1\rm kg$. How much does the jam weigh?

$$475$$$\rm g$

$$775$$$\rm g$

$$575$$$\rm g$

$$725$$$\rm g$

$$675$$$\rm g$


If the demand curve for apples is given by $Q\_d = 50 - 2P$ and the supply curve is given by $Q\_s = 10 + 3P$, what is the equilibrium price and quantity of apples in the market?

$P = \textbackslash$8, Q = 34$

$ P = \textbackslash$10, Q = 30$

$P = \textbackslash$12, Q = 26$

$P = \textbackslash$14, Q = 22$


A 99 percent one-sample z-interval for a proportion will be created from the point estimate obtained from each of two random samples selected from the same population: sample R and sample S. Let R represent a random sample of size 1,000, and let S represent a random sample of size 4,000. If the point estimate obtained from R is equal to the point estimate obtained from S, which of the following must be true about the respective margins of error constructed from those samples?

The margin of error for S will be 4 times the margin of error for R.

The margin of error for S will be 2 times the margin of error for R.

The margin of error for S will be equal to the margin of error for R.

The margin of error for R will be 4 times the margin of error for S.

The margin of error for R will be 2 times the margin of error for S.


For number $$80$$, what is its factor form and exponential form?

Factor form: $$2\times 2\times 2\times 2\times 5$$; Exponential form: $$2^{3}\times 5^{2}$$

Factor form: $$2\times 2\times 2\times 2\times 5$$; Exponential form: $$2^{4}\times 5$$

Factor form: $$2\times 2\times 2\times 5\times 5$$; Exponential form: $$2^{3}\times 5^{2}$$

Factor form: $$2\times 2\times 2\times 5\times 5$$; Exponential form: $$2^{4}\times 5$$

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


Fill in the blanks with ``$$+$$'' to make the equation true. (Hint: Two adjacent numbers can form a new number)  $\textasciitilde$  $$1$$~ ~ ~ ~ ~ $$2$$~ ~ ~ ~~ ~ $$3$$~ ~ ~ ~ ~~$$4$$~ ~ ~ ~ ~$$5$$~ ~ ~ ~ $$6$$ =$$48$$．

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


Which of the following expression was written correctly?

$-2\times x+3$


Overseas In-curriculum->Knowledge Point->Measurement->Time->Conversion among Hours, Minutes and Seconds

Overseas Competition->Knowledge Point->Calculation Modules->Unit Conversion->Converting between Units of Length


Continue this sequence: $2\times61$~ ~$3\times41$~ ~$4\times31$~ ~$5\times25 \cdots$

$$ 6\times22 $$

$$ 7\times18 $$

$$ 8\times16 $$

$$ 9\times13 $$

$$ 10\times12 $$

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


What is the missing number in the number pattern below?  2750,2950 ,2850 ,~\uline{~~~~~~~~~~}~,2950 ,3150 ,3050 .


Which of these fractions is the smallest?

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


Add brackets to this calculation to that the answer is $$5$$．  $$22-10 + 8 \div 4$$

$$22 - (10 + 8) \div 4$$

$$(22 - 10) + 8 \div 4$$

$$(22 - 10 + 8) \div 4$$

$$22-10 + (8 \div 4)$$

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


Each of the faces of a fair six-sided number cube is numbered with one of the numbers 1 through 6, with a different number appearing on each face. Two such number cubes will be tossed, and the sum of the numbers appearing on the faces that land up will be recorded. What is the probability that the sum will be 4, given that the sum is less than or equal to 6?


The function $f$ is defined by the equation $f(x)=3^{}x+2$. What is the value of $f(0)$?  $\textasciitilde$


Four candy bars and three lollipops cost $$4.50$$ dollars. One candy bar costs $$90$$ cents.  How much does one lollipop cost? (2000 Math Kangaroo Problem, Level 3-4, Question \#5)

$$20$$ cents

$$30$$ cents

$$40$$ cents

$$50$$ cents

$$60$$ cents


Which of the following options is the solution of $x-3=5$?

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


l am a number. If you count by tens you will say my name. I am not ten. If you add me to 30, you will get a number less than 60. Who am I?


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

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


(2) Eddie has~\uline{~~~~~~~~~~}~more books than Squary.


At an ice cream shop, a sundae is made by selecting two flavors of ice cream and topping them with fudge, whipped cream, nuts, and a cherry. The available flavors of ice cream are chocolate, vanilla, strawberry, rocky road, chocolate chip cookie dough, and mint chip. How many different sundae combinations are possible?


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


There are  rational numbers whose distance to the origin are less than 2 units.

infinite

Overseas Competition->Knowledge Point->Calculation Modules->Knowing the Number Lines


What is the value of the following sum?  $$99+97+95+96+98$$

None of the above


I think of a number,double it and add $5$. If I think of $21$, what is my answer?


In a large set data that are approximately normally distributed,  $\textasciitilde$  r is the value in the data set that has a z-score of -1.00,  $\textasciitilde$  s is the value of the first quartile, and  $\textasciitilde$  t is the value of the 20th percentile.  $\textasciitilde$  Which of the following is the correct order from least to greatest for the values of r, s, and t?

r, s, t

r, t, s

s, t, r

t, r, s

t, s, r


How many terms and variables does the expression $$2ab-4ac+b-5$$ have, respectively?

$$3, 3$$

$$3, 4$$

$$4, 4$$

$$4, 3$$

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


What is the correct answer to $6+4\times3$.

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


Pushing on a mass of 15 kg with a sideways force of 120 N is not enough to get the~mass to start sliding across the floor. Which of the following best describes the coefficient of static friction between the floor and the mass?

$\mu\textbackslash{} =\textbackslash{} 0.8$

$\mu\textbackslash{} \gt\textbackslash{} 0.8$

$\mu\textbackslash{} \lt\textbackslash{} 0.8$

$\mu\textbackslash{} =\textbackslash{} 1.25$


What is the result of $\frac13\div 1\frac23 \times \frac57\div 1\frac27\cdots \times \frac{2021}{2023} \div 1\frac{2}{2023}$?

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


Overseas Competition->Knowledge Point->Calculation Modules


While preparing for the Kangaroo Maths contest, Jack decided to solve one question from each odd numbered page in his collection of worksheets. He began on page $$15$$ and finished on page $$53$$. How many problems did Jack solve?

Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences->The Number of Terms in an Arithmetic Sequence


$$\left(\left(\left(\frac 12\div \frac 13\right)\div \frac 14\right)\div \frac 14\right)=$$~\uline{~~~~~~~~~~}~. ($$1986-87$$ MATHCOUNTS, G$$7$$, Problem $$29$$)

$$\frac 1{48}$$

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


N/A.(Targeting Mathematics Workbook 《Decimals》Primary $$4$$B Question \#$$44$$)


Jimmy buys $6$ apples for $1.99$p each.  How much do the apples cost altogether?


The most likeiy height of an eleven-year-old boy is:


Which of the following lists is not a number pattern?

$1$,$3$,$5$,$7$,$9$$\cdots $

$4$,$7$,$10$,$13$,$16$$\cdots $

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

$3$,$27$,$9$,$81$,$28$$\cdots $

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


There are $35$ children in a class. Three-fifths of the class are girls and the rest are boys. How many boys are there in the class?


The numbers $4$, $5$, $6$, $7$ and $8$ are divided into 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 $8$?

Not sure.

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


Step $1$

Step $2$

Step $3$

Step $4$

Step $5$


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


Which \textbf{one} of the following statements is false?


A boy bought a baseball and a bat, paying $1.25$ dollars for both items. If the ball cost $25$ cents more than the bat, how much did the ball cost?

$1$ dollar

$0.75$ dollars

$0.65$ dollars

$0.5$ dollars

$0.45$ dollars


Which of the following numbers is repeating decimal?

$$3.02525 \cdots $$

$$\pi$$

$$5.010010001 \cdots $$

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


A frog fell into a drain that was 20 cm deep. After one hour, it mastered enough  energy to make a jump of 6 cm but it then slid down 4 cm. If it continued in this  manner after every one hour, how many hours will it take to get out of the drain?

Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Number Machine


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


Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division->Multiplication and Division of Whole Numbers->Multiplication in Vertical Form


Peter plants a pot of flower on Monday. It will takes it $4$ days to bloom. What day of the week will it be when it bloom?

Tuesday

Wednesday

Thursday

Friday

Saturday


If $a^{-\frac{1}{3}}=x$, what is $a$ in terms of $x$ ?  $\textasciitilde$


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


Which fraction is equivalent to $\frac{3}{8}$?


Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division->Multiplication and Division of Whole Numbers->Multiplication out of the Multiplication Table


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


A company that makes fleece clothing uses fleece produced from two farms, Northern Farm and Western Farm. Let the random variable X represent the weight of fleece produced by a sheep from Northern Farm. The distribution of X has mean 14.1 pounds and standard deviation 1.3 pounds. Let the random variable Y represent the weight of fleece produced by a sheep from Western Farm. The distribution of Y has mean 6.7 pounds and standard deviation 0.5 pound. Assume X and Y are independent. Let W equal the total weight of fleece from 10 randomly selected sheep from Northern Farm and 15 randomly selected sheep from Western Farm. Which of the following is the standard deviation, in pounds, of W?

$\sqrt{10^{2}(1.3)^{2}+15^{2}(0.5)^{2}}$

$\sqrt{\dfrac{1.3^{2}}{10}+\dfrac{0.5^{2}}{15}}$


Look at the number pattern below. What is the missing number in the blank?  $$3010$$, $$3110$$, $$3310$$,~\uline{~~~~~~~~~~}~, $$4010$$, $$4510$$


A tropical storm is classified as major if it has sustained winds greater than 110 miles per hour. Based on data from the past two decades, a meteorologist estimated the following percentages about future storms.  $\textasciitilde$  ·20\% of all tropical storms will originate in the Atlantic Ocean, of which 20\% will be classified as major.  $\textasciitilde$  · 30\% of all tropical storms will originate in the eastern Pacific Ocean, of which 15\% will be classified as major.  $\textasciitilde$  ·50\% of all tropical storms will originate in the western Pacific Ocean, of which 25\% will be classified as major.  $\textasciitilde$  Based on the meteorologist\textquotesingle s estimates, approximately what is the probability that a future tropical storm will originate in the Pacific Ocean and be classified as major


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

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


Students in a large psychology class measured the time, in seconds, it took each of them to perform a certain task. The times were later converted to minutes. If a student had a standardized score of z = 1.72 before the conversion, what is the standardized score for the student after the conversion?

z = 0.26

z = 1.03

z = 1.72

z = 1.98

The standardized score for the student after the conversion cannot be determined.


Six friends share four pizzas between them. If each pizza is cut into three pieces and the friends share the pizzas equally, how many pieces does each friend get?


Calculate:  $10 \times 12 =$~\uline{~~~~~~~~~~}~$\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde$$47 \times 100$ =~\uline{~~~~~~~~~~}~

$1200$; $4700$

$120$; $4700$

$120$; $470$


Which of the following fractions is the largest?


Andy thinks of a cube number less than $1000$.  He divides it by four it and says, ``Now I have a square number.''  What is his new square number?


In $$26.73$$, the digit $$3$$ has the value of ．

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


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


$$27 \times 3 \textgreater{}x^{2}$$  Which of these numbers is the largest number $$x$$ could be?

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


Which of these fractions is the smallest?

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


A block of mass m slides along a frictionless surface with kinetic energy K\textsubscript{i}. It collides with a block of mass 3m that is initially at rest, and the two blocks stick together and slide with total kinetic energy K\textsubscript{f} . What is the ratio K\textsubscript{f} : K\textsubscript{i}？

Overseas Competition->Knowledge Point->Calculation Modules


Dissolve $$20\textasciitilde\text{g}$$ sugars in $$100\textasciitilde\text{g}$$ water, what is the mass ratio of sugar to sugar water?

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


$$\frac{2}{3}$$ of the area of a triangle is equal to $$\frac{1}{4}$$ of the area of a rectangle. What is the ratio of the area of the triangle to the area of the rectangle?


Arrange the following fractions from the greatest fo the smallest．  $$\frac{2}{3}$$,$$\frac{3}{10}$$,$$\frac{5}{9}$$

$$\frac{3}{10}$$,$$\frac{5}{9}$$,$$\frac{2}{3}$$

$$\frac{2}{3}$$,$$\frac{5}{9}$$,$$\frac{3}{10}$$

$$\frac{5}{9}$$,$$\frac{3}{10}$$,$$\frac{2}{3}$$

$$\frac{3}{10}$$,$$\frac{2}{3}$$,$$\frac{5}{9}$$


Lilac makes a $$\frac{1}{2}$$ turn. How many degrees has she turned?


Sara has 16 blue marbles. She can trade marbles in two ways: 3 blue marbles for 1 red marble, and 2 red marbles for 5 green marbles. What is the maximum number of green marbles she can get? (2019 Math Kangaroo Problem, Level 3-4, Question \#13)


$$a^{4}\times b^{2}$$

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


The digit $3$ in what number represents a value of $0.3$?


Which of the following fractions is equivalent to $$\frac{2}{3}$$?


Given that $x^{3}y^{6}z^{9}=27$, then $xy^{2}z^{3}=$ ?  $\textasciitilde$

Can\textquotesingle t determine.


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


None of the above


Which one of the following expressions has the \uline{\textbf{same}}~result as~$2.5\times0.4$? (Hint: Try to do this problem without calculating the product.)

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


Which of the following is not equivalent to~$\dfrac{2}{6}$?

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

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


29 - 16 \div 2  what should we do first？

$$\div $$


Which of the following expressions has the same result as $$637-(137-79)$$?

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


Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Distributive Property of Decimals->Applying Distributive Law in Decimal Multiplication


Think Teacher divides $$33$$ gifts into $$12$$ kids equally. Assume $$x$$ represents the number of gifts each kid gets, which of the following inequalities can represent this situation?

$$12x\geqslant 33$$

$$12x\leqslant 33$$

$$12x = 33$$

$$x\geqslant 33$$

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


Leonard is going to play a game the day after tomorrow. It is Friday yesterday. What day will it be when Leonard play the game?

Monday

Tuesday

Thursday

Saturday

Sunday


There is $480ml$ of water in Jug A and $120ml$ of water in Jug B. How much water must be poured from Jug A into Jug B so that Jug A will have twice as much water as Jug B?

Overseas Competition->Knowledge Point->Calculation Modules->Unit Conversion->Converting between Units of Volume and Capacity


Three positive integers are equally spaced on a number line. The middle number is 15, and the largest number is 4 times the smallest number. What is the smallest of these three numbers?

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


The distance between Nicole\textquotesingle s hotel and the entrance of Disneyland is 50 kilometres. If  1000 metres = 1 kilometres,  100 centimetres = 1 metre,  Find the distance between Nicole\textquotesingle s hotel and the entrance of Disneyland in centimetres.

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


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


Gabe has $12y+9$ cans of coke. He takes one out with him every day for 5 consecutive days. On the fifth day, he also brings each of his $x$ friends a can of coke. How many cans of coke does he have left?

$$12y + 9$$

$$7y + 9 -x$$

$$12y +4 -x$$

$$12y + 4 +x$$


Which number doesn\textquotesingle t round to 60?

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


In a triangle, what is the ratio of the measure of a right angle to the sum of its interior angles?


Calculate the following sum.  $$2021+1202+110$$

None of the above


Which of the following fractions is not an equivalent fraction of $$\frac{5}{6}$$?

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


Complete the calculation correctly.  $$553-$$~\uline{~~~~~~~~~~}~$$=427$$

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


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


Which of the following expressions have the same value as the fraction $$\frac{7}{11}$$?

$$11\div 7$$

$$7\div 11$$

$$4\div 7$$

$$7\div 18$$


$2$ ducks, $2$ rabbits and $1$ dog together weigh $14$ kg. $3$ ducks and $1$ rabbit together weigh $6$ kg. $1$ dog weigh $1$ kg more than $1$ rabbit and $1$ duck weigh together. How much does a duck weigh?

$$1$$ kg

$$2$$ kg

$$3$$ kg

$$4$$ kg

$$5$$ kg

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


Judy draws a plan of her bedroom using a scale of $$2\text{cm}$$ to $$7\text{m}$$.  On the plan, the playground is $$10\text{cm}$$ long.  What is the real length of the playground?

$$20 \text{m}$$

$$70 \text{m}$$

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

N/A.  Revise from (GL Assessment book$$2$$《Paper $$4$$》 $$6$$ years Question \#$$5$$)


Ordering the following numbers: $$0.06$$, $$22.2\textbackslash\%$$, $$\frac{22}{100}$$, $$\frac{1}{9}$$, which of the following is correct?

$$22.2\textbackslash\%\textgreater\frac{1}{9}\textgreater\frac{22}{100}\textgreater0.06$$

$$\frac{1}{9}\textgreater22.2\textbackslash\%\textgreater\frac{22}{100}\textgreater0.06$$

$$22.2\textbackslash\%\textgreater\frac{22}{100}\textgreater\frac{1}{9}\textgreater0.06$$

$$22.2\textbackslash\%\textgreater\frac{22}{100}\textgreater0.06\textgreater\frac{1}{9}$$

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


$$\frac 12$$

$$\frac 23$$

$$\frac 43$$

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


Which one of the following sets is arranged in decreasing order?

$$7510$$, $$7020$$, $$6990$$, $$6750$$

$$6830$$, $$8310$$, $$9040$$, $$7990$$

$$5870$$, $$6840$$, $$6820$$, $$5470$$

$$8490$$, $$8790$$, $$9480$$, $$9740$$

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


Last year, the level of support for a yerly community event was estimated to be 83\%. Officials would like to estimate the level of support this yearwith 95\% confdence and a margin of error no larger than 4\%. Which of the following is the smallest sample size that would do so?

Overseas Competition->Knowledge Point->Calculation Modules


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


Of the following, which ratio is equivalent to $$13:12$$?(Adapted from $$1996$$ Math League, Grade $$6$$, Question \#$$21$$)

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


A large grocery store chain wants to determine the proportion of its customers who redeem coupons in its stores. They intend to use a 99 percent confidence interval on a large sample with a margin of error of no more than 2 percent. What is the mini-mum sample size to produce this margin of error?


Overseas Competition->Knowledge Point->Calculation Modules->Operations through Formulas-> Difference of Two Squares Formula


A lizard is $20\rm cm$ in length.  The lizard can walk $1.5$ times its own length every second.  How long would it take the ant to walk $36\rm m$?

$2\textasciitilde\rm minutes$

$20\textasciitilde\rm seconds$

$40\textasciitilde\rm seconds$

$20\textasciitilde\rm minutes$

$1\textasciitilde\rm minute$


Cici\textquotesingle s sister is three times as tall as Cici. Cici\textquotesingle s dad is taller than Cici\textquotesingle s sister. If Cici is $1.5$ feet tall, write an inequality to represent Cici\textquotesingle s dad\textquotesingle s height $x$.

$x \textgreater{} 1.5$

$x \textgreater{} 4.5$

$x \geq 1.5$

$x \geq4.5$

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


It started to snow at $10$am and at that time my garden thermometer registered $1$$^{\circ}\text{C}$.  I checked the thermometer an hour later and found that the temperature had fallen by half of a degree.  If the temperature continues to drop by half of a degree every hour what is the temperature at $6$pm?

Overseas Competition->Knowledge Point->Calculation Modules->Negative Numbers->Operations on Negative numbers


Which of the following decimals is equivalent to $\frac{3}{11}$?

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


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


Usually, people spend $\frac{1}{4}$ of their sleeping time dreaming. If Poole slept $8$ hours last night, how much time did he spend dreaming yesterday?

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


Lili bought a coffee that cost $$\textbackslash$8.50$$ and a shirt that cost $$\textbackslash$25.62$$. How much money did she spend? $$\textbackslash$$$~\uline{~~~~~~~~~~}~.

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


Given that nitrogen has a valence of 3, how many hydrogen atoms can a nitrogen atom bond to?


Express $$\frac{18}{25}$$ as a percentage.

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


To solve the problem $9\times(10+5)-(7-2)$, John writes the steps below. In which step the first mistake was written?  Step $1$: $=9\times10+9\times5-(7-2)$  Step $2$: $=9\times10+9\times5-7+2$  Step $3$: $=90+45-9$  Step $4$: $=145-9$  Step $5$: $=136$

Step $1$

Step $2$

Step $3$

Step $4$

Step $5$


What is the sum of interior angles of a triangle?


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


Lin, Mat, and Ned went for a run of different distances L, M, and N respectively. During the run, they covered an equal distance before they stopped for a water break. At that time, Lin had completed $$\frac{1}{2}$$ of distance L, Mat had completed $$\frac{2}{3}$$ of distance M and Ned had completed $$\frac{3}{5}$$ of distance N.  What is the ratio of the distance L to distance M to distance N?

Overseas In-curriculum->Knowledge Point->Algebra->Problems Involving Proportions->Solving Problems Involving Proportion


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


What number is $$339$$ less than two thousand and eighteen?

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


$$\frac{6}{7} \times \frac{14}{9}=$$~\uline{~~~~~~~~~~}~.  What is the answer in its simplest form?

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


Which of the following expressions has the same result as $$463-(238-37)$$?

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


Which number is one hundred times smaller than $4250$?

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


The digit $8$ in what number represents a value of $0.8$?

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


Sammy and Tricia started doing a math test at the same time. Sammy completed the paper in $$1\text{h}$$ $$15\min$$. Tricia completed the paper $$20\min $$ earlier than Sammy. How much time did Tricia take to complete the paper?．

$$135\rm min$$

$$95\rm min$$

$$55\rm min$$

$$35\rm min$$

Overseas In-curriculum->Knowledge Point->Measurement->Time->Time Calculation

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


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


Events D and E are independent, with with P(D) = 0.6 and P(D and E) = 0.18. Which of the following is true?

P(E) = 0.12

P(E) = 0.4

P(D or E) = 0.28

P(D or E) = 0.72

P(D or E) = 0.9

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


Which of these pairs of numbers are equally distant from $$5$$?

$$5.01$$ and $$4.91$$

$$5.01$$ and $$4.99$$

$$5.11$$ and $$4.91$$

$$5.11$$ and $$4.99$$

$$5.19$$ and $$4.91$$

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

N/A.  revise from (GL Assessment book$$2$$《Paper $$6$$》 $$6$$ years Question \#$$17$$)


$a-b$

$a+b$

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


$$16\times 2$$

$$12\times 3$$

$$7\times 5$$

$$38\times 1$$

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


When $$\frac 89$$ is divided by $$\frac 43$$, the result is~\uline{~~~~~~~~~~}~. ($$1978-79$$ MATHCOUNTS, G$7$, Problem $$5$$)

$$\frac {32}{27}$$

$$\frac 23$$

$$\frac 2{27}$$


Rachel practices singing and dancing every week. Each day she practices either singing for $2$ hours or dancing for $3$ hours. She practiced dancing for $12$ hours last week. How many hours did she practice singing last week?

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


Some children were queueing up outside the classroom. Counting from the front to the back, Chris was $13$\textsuperscript{th}~in line. Counting from the back to the front, Becky was $10$\textsuperscript{th}~in line. Chris was in front of Becky, and there were $$12$$ people standing between Chris and Becky. How many people were there in the queue?

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


For flights from a particular airport in January, there is a 30 percent chance of a flight being delayed because of icy weather. If a flight is delayed because of icy weather, there is a 10 percent chance the flight will also be delaved because of a mechanical problem. If a flight is not delayed because of icy weather, there is a 5 percent chance that it will be delaved because of a mechanical problem. If one flight is selected at random from the airport in January, what is the probability that the flight selected will have at least one of the two types of delays\textquotesingle?


A moon of Jupiter has a nearly circular orbit of radius R and an orbit period of T. Which of the following expressions gives the mass of Jupiter?  $\textasciitilde$  $\textasciitilde$  $\textasciitilde$

$\dfrac{2\pi R^{3}}{(GT^{2})}$

$\dfrac{4\pi R^{2}}{(GT^{2})}$

$\dfrac{4\pi^{2} R^{3}}{(GT^{2})}$

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


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


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?

Overseas Competition->Knowledge Point->Calculation Modules


ones

tenths

hundredths

thousandths

N/A.($$2013$$ Ai Tong School, Semestral Assessment $$2$$, Primary $$4$$, Question \#$$5$$)


Calculate:  $100 \times 32 =$~\uline{~~~~~~~~~~}~$\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde$$1000 \times 72 =$~\uline{~~~~~~~~~~}~

$2200$; $72000$

$320$; $72000$

$3200$; $72000$


$15\textbackslash\%$ of a number is $27$. What is five ninths of the number?

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


A frog fell into a drain that was 20 cm deep. After one hour, it mastered enough  energy to make a jump of 6 cm but it then slid down 4 cm. If it continued in this  pattern every hour, how many hours in total will it take to get out of the drain?

Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Number Machine


How many different real numbers~$x$~satisfy the equation~$(x^{2}-5)^{2}=16$?


Mrs Lim had $$$99$$. She spent $$\frac{1}{3}$$ of it on a blouse and $$\frac{2}{9}$$ of it on a skirt. How much did she spend altogether?

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


$$5\textasciitilde\text{meters}:2\textasciitilde\text{km}$$


$$12\times 7=14+4\times 7+$$~\uline{~~~~~~~~~~}~$$\times 7$$  What is the missing number in the box?

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


Find the opposite of $$\textbar-0.\overline3\textbar$$:~\uline{~~~~~~~~~~}~.

Overseas Competition->Knowledge Point->Combinatorics->Mathematical Thoughts


$a$ and $$b$$ are reciprocals， $$\frac{12}{a}\div \frac{b}{7}\times 7=$$．

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


Ala has $$24$$ dollars,Barb has $$66$$ dollars, and Sophia has as many dollars more than Ala as she has less than Barb. How many dollars does Sophia have?

Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences->Applying the Theorem of Middle Term


Study the number pattern below. What is the missing number?  $$3, 4, 7, 11, 18, 29, ?, 76$$

None of the above


Which of the following is NOT equivalent to $P\textbackslash\%$?


Which fraction is equivalent to $$\frac{25}{35}$$?

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


A distribution of test scores can be described as N(77, 8). If the distribution is represented as X, which of the following answer choices would be equivalent to P(X \textless{} 65)?

P(65\textless X\textgreater89)


Which Law is used in the following calculation: $$1.25+3.33+8.75=3.33+(1.25+8.75)$$?

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


Given that $$p:q=5:2$$ and $$q:r=3:4$$, express $$r$$ as a fraction of $$p$$.

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


Each cantaloupe melon costs £1.04.  Mark buys eight and pays with a~£$$10$$ note. All the change he gets is coins.  What is the smallest number of coins that he can receive in change?

Overseas Competition->Knowledge Point->Calculation Modules->Unit Conversion->Converting between Units of Money


In Mathematics, the product of the first $$n$$ whole numbers starting from $$1$$ is written as $$n!=1\times2\times3\times \cdots \times n$$. For example, $$2!=1\times2$$ and $$7!=1\times2\times3\times4\times5\times6\times7$$. The number of hours in September can be written as $$n!$$. Find the value of $$n$$.

None of the above


In $$26.73$$, the digit $$3$$ has the value of ．

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


An airplane lands on a runway with a velocity of 150 m/s. how far~will it travel until it stops if its rate of deceleration is constant at -3m/s\textsuperscript{2}?


What is this number rounded to the nearest tenth．  $$\boxed{9.95}$$

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

N/A.  Revise from (GL Assessment book$$1$$《Paper $$2$$》 $$6$$ years Question \#$$15$$)


Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division->Multiplication and Division of Whole Numbers->Multiplication out of the Multiplication Table


What is the difference between $$\frac{2}{3}$$ and $$\frac{5}{12}$$?


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


Which of the following statements is false?

$$3 + 5 \times 4 = 23$$

$$20 − 5 \times 4 = 0$$

$$12 − 5 \times 2 = 2$$

$$3 + 6 \times 4 = 36$$

$$5 \times 3 − 2 = 13$$

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


Find the next number in the sequence:  $12,7,9,12,6,17,3,$~\uline{~~~~~~~~~~}~

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


Mom divides 12 cupcakes into 5 kids equally. Assume $$x$$ represents the number of cupcakes each kid gets, which of the following inequalities can represent this situation?

$$5x\geqslant 12$$

$$5x\leqslant 12$$

$$5x = 12$$

$$5x\geqslant 12$$

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


The breadth of a rectangular bookmark is $9$ cm. It\textquotesingle s length is $3$ times its breadth. What is the area of the bookmark?

27 cm\textsuperscript{2}

81 cm\textsuperscript{2}

162 cm\textsuperscript{2}

243 cm\textsuperscript{2}

Overseas Competition->Knowledge Point->Calculation Modules->Unit Conversion->Converting between Units of Area


The sum of $$5$$ consecutive whole numbers is $$110$$. What is the largest odd number among the $$5$$ numbers?

None of the above

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


When calculating $12\div1000$, each digit of $12$ moves~\uline{~~~~~~~~~~}~place(s) to the~\uline{~~~~~~~~~~}~, and we obtain the result~\uline{~~~~~~~~~~}~.

two; left; $12$

three; right; $0.00012$

three; left; $120$

two; right; $0.12$

three; right; $0.012$

Overseas Competition->Knowledge Point->Calculation Modules


Two wodgets make a finkle. Five finkles make a splot. Three splots make a tink. How many wodgets make four tinks?

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


The little kangaroo was sick. Dr. Ohpain prescribed $$3$$ pills for him to take one at a time every twenty minutes. How many minutes after taking the first pill will the little kangaroo take the last pill?


If you put the following in order of size, which one is the largest?

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


Which of the following is nearest to $$2$$?

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

Overseas In-curriculum->Knowledge Point->Knowing Numbers->Fractions->Classifying Fractions ->Mixed Numbers


What is the value of the digit `$$5$$'~in $$48.05$$?


Yes

No

Not sure

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


Fiona measured the length of her house.  It was $$18$$ metres to the nearest tenth of a metre.  Between what limits was the actual length?

$$17.99$$ to $$18.01$$

$$17.9$$ to $$18.1$$

$$17.995$$ to $$18.009$$

$$17.95$$ to $$18.05$$

$$17.5$$ to $$18.5$$


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


The day before yesterday is Thursday. What day is tomorrow?

Monday

Wednesday

Thursday

Saturday

Sunday


A lot of babies were born in the zoo last year: two baby lions, three baby dolphins and four baby eagles. How many legs do all these babies have altogether?


A packet of chocolates costs $a$ pence and a glass of orange juice costs $b$ pence.  Mike buys $4$ packet of chocolates and $4$ glasses of orange juice.  Which expression shows how much change he will receive in pence from a £$10$ note?


What is the value of the $5$ in the number $25673$

fifty thousands

five thousands

five hundreds

fifty

five


A complex electronic device contains three components, A, B, and C. The probabilities of failure for each component in any one vear are 0.01, 0.03, and 0.04, respectively. If any one component fails, the device will fail. If the components fail independently of one another, what is the probability that the device will \uline{not} fail in one year？

Less than 0.01

Greater than 0.99

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


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


The distribution of heights of 6-year-old girls is approximately normally distributed with a mean of 46.0 inches and a standard deviation of 2.7 inches. Aliyaah is 6 years old, and her height is 0.96 standard deviation above the mean. Her friend Jayne is also 6 years old and is at the 93rd percentile of the height distribution. At what percentile is Aliyaah\textquotesingle s height, and how does her height compare to Jayne\textquotesingle s height?

Aliyaah\textquotesingle s height is at the 17th percentile of the distribution, and she is shorter than Jayne.

Aliyaah\textquotesingle s height is at the 67th percentile of the distribution, and she is shorter than Jayne.

Aliyaah\textquotesingle s height is at the 67th percentile of the distribution, and she is taller than Jayne.

Aliyaah\textquotesingle s height is at the 83rd percentile of the distribution, and she is shorter than Jayne.

Aliyaah\textquotesingle s height is at the 83rd percentile of the distribution, and she is taller than Jayne.


The area formula of the triangle is $$A=\frac{1}{2}ab$$, there is(are)  variable(s).

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


Mike draws a shape with four sides of equal length.  The shape has exactly two lines of symmetry.  What shape has Mike drawn?

Square

Rectangle

Trapezium

Pentagon

Rhombus


Which measurement is the same as $3.5\text{m}$?

Overseas Competition->Knowledge Point->Calculation Modules->Unit Conversion->Converting between Units of Length


Using the same amount of time and resources, Jack can assemble either 10 bikes or 5 computers, whereas Sam can assemble either 5 bikes or 5 computers. Based on the data, which of the following statements is correct?

Sam has an absolute advantage in assembling bikes.

Sam has an absolute advantage in assembling computers.

Sam has a comparative advantage in assembling bikes.

Jack has a comparative advantage in assembling bikes.

Jack has a comparative advantage in assembling both bikes and computers.


19+23-21，$$Which$$ country does the number "19" from?

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


Who is right?  Anna: "The largest number possible has $$6$$ digits."  Boris: "The largest number possible has $$1000$$ digits."  Caroline: "The largest number possible can be only written with the $$9$$ digits."  Daniel: "The largest number possible cannot be written."  Else: "The largest number possible has $$0$$ as the last digit."~($$2006$$ Math Kangaroo Problem, Level $$1-2$$, Question \#$$21$$)

$$$$Anna

$$$$Boris

$$$$Caroline

$$$$Daniel

$$$$Else

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


A produce supplier ships boxes of produce to individual customers. The distribution of weights of shipped boxes is approximately normal with mean 36 pounds and standard deviation 4 pounds. Which expression represents the weight, in pounds, at the 75th percentile of the distribution?

-1.96(4) + 36

-0.25(4) + 36

0.25(4) + 36

0.67(4) + 36

0.75(4) + 36


Which of the following numbers\textquotesingle{} value does not change after removing all ``$$0$$''s ．

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


$\textasciitilde$  Which of the following numbers when rounded off to the nearest ten becomes $$26500$$?

Overseas In-curriculum->Knowledge Point->Operations of Numbers ->Estimation->Estimating the Results of Computations->Rounding Whole Numbers

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


Dean swims for $72$ minutes. To keep his mind active, he works out what fraction of the total time has passed at each half minute and minute from the start. How many of the results of his calculations can be expressed in the form $\frac{1}{n}$, where $n$ is an integer greater than $1$?

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


Stamps cost $65$p each.  How many stamps can Peter purchase with a £$5$ note?

Overseas Competition->Knowledge Point->Calculation Modules


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


when we know the total number, and want to part of it,which operation should be used?

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


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


Sean and Evan are college roommates who have part-time jobs as servers in restaurants. The distribution of Sean\textquotesingle s weekly income is approximately normal with mean $\textbackslash$$225 and standard deviation $\textbackslash$$25. The distribution of Evan\textquotesingle s weekly income is approximately normal with mean $\textbackslash$$240 and standard deviation $\textbackslash$$15. Assuming their weekly incomes are independent of each other, which of the following is closest to the probability that Sean will have a greater income than Evan in a randomly selected week?


For a Fibonacci sequence, from the third term, each term in the sequence is the sum of the previous two terms in that sequence. Given that in a Fibonacci sequence, the fifth term is $17$ and the sixth term is $27$. What is the first term in this Fibonacci sequence?


How many numbers from $$2$$ to $$99$$ are equal to the square of an integer?

Overseas Competition->Knowledge Point->Calculation Modules->Power->Application of Powers


Originally, Andy and Bill had the same salary, which was $$\textbackslash$6000$$ per month. Recently, Andy gets a promotion and his salary is $$150\textbackslash\%$$ of the original salary. On the other hand, Bill made a mistake at work. Now, His salary is $$90\textbackslash\%$$ of the original salary.What is the difference between Andy\textquotesingle s and Bill\textquotesingle s monthly salary now?


Two wodgets make a finkle. Five finkles make a splot. Three splots make a tink. Howmany wodgets make four tinks?

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


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


When 0.000315 is multiplied by 7,928,564 the product is closest to which of the following?


Three football teams participate in a sport tournament. Each team plays the other two teams exactly once. In each game, the winner gets three points and the loser doesn\textquotesingle t get any points. If the game ends in a tie, each team gets 1 point. At the end of tournament, Which number of points is it impossible for any team to have? (2022 Math Kangaroo Problem, Level 3-4, Question \#18)


Carol is $x$ years old. Sam is $5$ years older than Carol. Sam's age in years is．

$x -- 5$

$x + 5$

$5 -- x$

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


Which of the following decimals is the smallest?

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


Cart A moves horizontally on a frictionless track. It collides and sticks to identical cart B, which is at rest. The speed of cart A before the collision is measured to be 3.0 m/s , with an uncertainty of\uline{+}~0.2 m/s. Students are asked to predict the speed of the carts after the collision. Given the uncertainty of the measurement for the speed ofcart A, which of the following is the best prediction?

1.1 to 1.9 m/s

1.2 to 1.8 m/s

1.3 to 1.7 m/s

1.4 to 1.6 m/s


$\textgreater$

$\textless$


The volume formula of the cube is $$V=l^{3}$$. Which of the following quantities is the independent variable?

$$V$$

$$l$$

The volume

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


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


($2$) Brenda bought $12$ boxes of sweets. Each box has $26$ sweets. How many sweets are there in total?


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．


Which of the following is the simplest form for $$\frac{56}{80}$$?

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


Which of the following equations is equivalent to $x=3$

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


What is $7.469$ rounded to the nearest tenth?


Which improper fraction is equivalent to $2\frac34$?


Tom shared $72$ pictures with his friends equally. He also got some and there was not any pictures left. Which of the following was definitely not the number of his friends?


The distribution of weights of female college cross-country runners is approximately normal with mean 122 pounds and standard deviation 8 pounds. Which of the following is closest to the percent of the runners who weigh between 114 pounds and 138 pounds?


Which of the following values of $x$ is not a solution to the equation $\sqrt{x^{2}}=x$ ?  $\textasciitilde$


Yes

No


$${{3}^{45}} ~\textless{} ~{{5}^{30}} ~\textless{} ~{{2}^{60}}$$

$${{2}^{60}} ~\textless{} ~{{3}^{45}} ~\textless{} ~{{5}^{30}}$$

$${{2}^{60}} ~\textless{} ~{{5}^{30}} ~\textless{} ~{{3}^{45}}$$

$${{5}^{30}} ~\textless{} ~{{2}^{60}} ~\textless{} ~{{3}^{45}}$$

$${{3}^{45}} ~\textless{} ~{{2}^{60}} ~\textless{} ~{{5}^{30}}$$

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


A group of students wanted to investigate the claim that the average number of text messages sent yesterday by students in their school was greater than 100. They asked each student in a random sample of 50 students how many text messages he or she sent yesterday. An appropriate t-test was conducted and resulted in a p-value of 0.0853. Assuming the conditions for the t-test were met, which of the following is an appropriate conclusion?

Because p \textless{} 0.10, at the 10\% significance level, it can be concluded that the mean number of text messages sent yesterday by students in the school is less than 100.

Because p \textless{} 0.10, at the 10\% significance level, it cannot be concluded that the mean number of text messages sent yesterday by students in the school is greater than 100.

Because p \textgreater{} 0.05, at the 5\% significance level, it can be concluded that the mean number of text messages sent yesterday by students in the school is greater than 100.

Because p \textgreater{} 0.05, at the 5\% significance level, it can be concluded that the mean number of text messages sent yesterday by students in the school is less than 100.

Because p \textgreater{} 0.05, at the 5\% significance level, it cannot be concluded that the mean number of text messages sent yesterday by students in the school is greater than 100.


Derrick lists down all whole numbers from $$1$$ to $$20$$. Lisa selects all odd numbers and adds them up. Aisha selects all the even numbers and adds them up. What is the difference between Aisha\textquotesingle s and Lisa\textquotesingle s sums?

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


Each of the numbers $$138$$ and $$243$$ has digits whose product is $$24$$ How many three-digit numbers are there whose digits have a product of $$24$$?

None of the above


Find the quotient and remainder of $$64\div5$$.

$13$ R $$1$$

$$12$$ R $0$

$10$ R $$14$$

$12$ R $$4$$


Which one of the folowing fractions is in its simplest form?

Overseas In-curriculum->Knowledge Point->Knowing Numbers->Fractions->Basic Properties of Fractions->Simplest Form of Fraction


Julia bought $1$ pen, $3$ erasers and $1$ pencil box, which cost a total of $$1$6$$. Clair bought $2$ pens and $1$ pencil box, which cost $$$3$$ less than Julia. The unit price of pencil box is $$$3$$ higher than that of eraser. How much does it cost to buy $2$ pens, $1$ eraser and $1$ pencil box?

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


$$\frac {12}{7}$$

$$\frac {3}{11}$$

$$\frac 3{28}$$

$$\frac {12}{28}$$

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


If a 2\% change in the price of a good leads to a 10\% change in the quantity demanded of a good, what is the price elasticity of demand?

Overseas Competition->Knowledge Point->Calculation Modules


Denise fired a silver rocket and a gold rocket at the same time. The rockets exploded into 20 stars in total. The gold rocket exploded into 6 more stars than the silver one. How many stars did the gold rocket explode into? (2021 Math Kangaroo Problem, Level 3-4, Question \#7)


Tom and Tiffany each picks a natural number. Tom writes the number $100$ times. After multipling them together, Tom gets a result $1.$ Tiffany write the number she picks $100$ times. After adding up them together, Tiffany gets a result $0.$ What is the difference between the two natural numbers?

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


Choose the answer to this calculation.  $$67.9-32.68$$

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


Arrange the following fraction in \uline{increasing} order.  $$\frac{1}{6} , \frac{1}{12} , \frac{1}{5} , \frac{1}{15}$$

$$\frac{1}{5} , \frac{1}{6} , \frac{1}{12} , \frac{1}{15}$$

$$\frac{1}{6} , \frac{1}{5} , \frac{1}{12} , \frac{1}{15}$$

$$\frac{1}{15} , \frac{1}{12} , \frac{1}{6} , \frac{1}{5}$$

$$\frac{1}{12} , \frac{1}{15} , \frac{1}{5} , \frac{1}{6}$$


What number should go in the box?  $$666+666+666+666+666={\huge\square} \times 333$$

Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Operation Strategy in Addition and Subtraction of Rounding Whole Numbers->Converting Continued Addition into Multiplication


Preview Question:  Which of the following does not contain a constant?

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


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


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


A simple pendulum swings about the vertical equilibrium position with a maximum angular displacement of $$5^{\circ} $$ and period T. If the same pendulum is given a maximum angular displacement of $$ 10^{\circ} $$, then which of the following best gives the period of the oscillations?  $\textasciitilde$  $\textasciitilde$

$$ \frac{T}{2} $$

$$ \frac{T}{\sqrt{2}} $$

$$T$$

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


A bag of flour weighs $1.5\rm kg$. Bud uses $300\rm g$ of flour to make a strawberry cake and a further $150\rm g$ of flour to make biscuits.  What fraction of the bag of flour has she used?


Calculate the sum of the following mixed fractions.  $\textasciitilde$  $1\frac{1}{3} + 2\frac{9}{12} + 3\frac{3}{5} + 4\frac{1}{4} + 5\frac{4}{6} + 6\frac{10}{25}$ =~\uline{~~~~~~~~~~}~  $\textasciitilde$


The largest one-digit number is~\uline{~~~~~~~~~~}~, and the least two-digit number is~\uline{~~~~~~~~~~}~.

$9; 99$

$10; 9$

$10; 1$

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


Henry has $8$ dollars. He is going to buy $5$ bowls which cost $90$ cents each and a certain number of~ glasses which cost $1.2$ dollars each. How many glasses at most can he buy?


Three athletes, Jay, Kevin, Larry and Mars, took part in a marathon race. In the beginning, Jay, Kevein, Larry and Mars were in the first, second, third and fourth place respectively. Then, the second to last player passed one player ahead of him. Next the last player passed three players ahead of him. After that, the third player passed two players ahea of him. In what order did they finish?

Jay, Kevin, Larry and Mars

Larry,~ Mars, Jay, Kevin

Larry, Kevin, Jay, Mars

Mars, Jay, Larry, Kevin

Mars, Larry, Jay, Kevin

Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Word Problems Involving Comparing and Ordering


Hou many minutes are there in four hours?

Overseas Competition->Knowledge Point->Calculation Modules->Unit Conversion->Converting between Units of Time


What is the missing number from the following equation?  $3\times\left( 16-\boxed{\textbackslash{} \textbackslash{} \overset{ }{\overset{ }{ }}}\right)=36$．


If $P = 4$, $Q = 2$ and $R = 5$, what is the value of $R(2P + Q)$?

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