TOÁN QUỐC tế violympic

Question 10:The area of trapezoid ABCD is 180 .The altitude is 8 cm,AD is 10 cm,and BC is 17 cm.What is AB,in centimeters?. Question 11:Jane draws a circle and a triangle on each page o

TOÁN QUỐC TẾ VÒNG 1

EX1 Fill in the blank with the correct number

Question 1:There are two parallel lines in the figure What is the value of x?

Answer: x =

Question 2:

ABC and RTS are similar triangles.The value of x is

Question 3:If x<0 and 5x+8+|3x|=0 then x=

Question 4:I am a multiple of 70 between 400 and 600 My tens digit is odd Who am I?

Answer:

Question 5:Mary is 24 years old She is twice as old as Bella was when Mary was as old as Bella is now

How old is Bella now?Answer: years

Question 6:The sum of 2 positive integer numbers is greater than their product if the smaller number

is

Question 7:How many different real numbers satisfy the following equation?

Answer:

Question 8:How many triples of integers (a,b,c) are there such that ?

Question 9:There are 115 cars in a village of 26 families Each family has either 4 or 5 cars

How many families have 4 cars? Answer: families

Question 10:The area of trapezoid ABCD is 180 .The altitude is 8 cm,AD is 10 cm,and BC is 17 cm.What is AB,in centimeters?

Question 11:Jane draws a circle and a triangle on each page of her booklet, and near each drawing she

writes the number of common points of the circle and the triangle.How many different numbers can she

EX2 ARRANGE: Use the mouse cursor Choose consecutively the cells with increasing value to remove them from the table If you choose wrong more than 3 times the test will end.

EX3 TALENTED GOLDEN TOAD: Choose the most suitable answer in 4 available answer

1 The product of 2015 and any number is always…

2 In this figure, AB is perpendicule to BC

Find the measure of the angle ABD?

3 Express the given phrase into algebraic expression

“6 less than the sum of 3 the product of x and 5”

3 + 5x - 6 6 – 3 + 5x 6 + 3 – 5x 6 – 3 – 5x

4 Which to following points on the number line represents a number that has a square root greater than

itself? X X

5 Three girls put $7; $8; and $9 in a piggy bank How can they share the money in ratio 1:2:3

6 Find the value of n if

Answer: n = ……

7 Start with a unit square Connect midpoints and vertices as shown in the figure below Find the area of

the shared square

1

5

1 2 1

8

1 3

8 Which of the following gives the greatest value

9

VÒNG 2 EX1 Fill in the blank with the correct number

Question 5:A book uses 2568 digits altogether for its page numbers.How many pages does the book

have?Answer: The book has pages

Question 6:A bus was travelling from Town A to Town B If it increased its speed by 18 km/h then it

would take 3h, instead of 4h, to reach Town B.Find the distance between the two towns

Answer: The distance between the two towns was km

?

Question 1:Fill the suitable number in the following blank:

1, 3, 7, 13, 21,

Question 2:The ratio of x and y is 3:4 and the sum of them is 28

Find the product of x and y.Answer: Product of x and y is

Question 3:Given the isosceles triangle ABC, BC is base segment If then find the

measure of angle at A?Answer: The measure of angle at A is degrees

Question 4:The ratio of x to y is 3:7 If y=112 then x=

Question 5:Given the numbers sequence: 2, 8, 14, 20, 26, …Which term is number 668?

Answer: Number 668 is the term

Question 6:The sum of twelve consecutive whole numbers is 330 Find the greatest number.

Answer: The greatest number is

Question 7:The ratio of the age of Mimi to the age of her mother is 1:6 and the ratio of the age of her

grandmother to the age of her mother is 8:3 If her grandmother is 80 years old then how old is Mimi? Answer: Mimi is years old

Question 8:A number is added to 7 The sum is then multiplied by 5 The product is divided by 3 9 is

then subtracted from the quotient The answer is 11.Find the number

Answer: The number is

Question 9:The sum of 21 consecutive numbers is 567 Find the sum of the next 12 consecutive numbers.

Answer: The sum of the next 12 consecutive numbers is

Question 10:What is the sum of all digits of the page numbers of a 76-page book?

EX2 FIND EQUAL PAIRS:

EX3 OBSTACLE

1 Suppose 3a ×

b = 217 Find the value of a ×

(-3b) = ………

2 In the summer, Mark get a part – time job He work 8 hours per day, 6 days a week and his hourly

salary is $7.5 How much is his weekly salary rate?

3 Given that 3x < 28 Find the greatest possible value of x if x is a prime number

………

4 Convert the following speed 216km/h = ………… m/s

5 Suppose -2 < a < 5 and 3 < b < 9, a and b are interger numbers The smallest value of a + b

is………

6 Given a%b = (a – 3) ×

b + b – a Find the value of b if 7%b = 13

7 There are 60 trees along a stretch of road and the trees are planted at opposite ends of the road If each

tree is 3 metres away from another how long is road? ………

8.

9 150 postcard are given away to a group of children in this manner

Who will get the 102th postcard?

10.6 bakers take 15 minutes to base 30 pieces of cake How many pieces of cake can 11 baker in 1 hour?

11 3 kg of apple and 5 kg of guava cost $84 6kg of guava and 2kg of apple cost $80 How much is one

kg of apple, one kg of guava?

12 The ratio of the distance from Anna’s house to Marry’s house and from Mary’s house to Tom’s house

is 3: 5 Anna drives at a contant speed of 60km/h from her house and she takes 12 minutes to reach Mary’s house Find the greatest possible distance from Anna’s house to Tom’s house?

VÒNG 3 EX1 FIND EQUAL PAIRS:

EX2 TALENTED GOLDEN TOAD:

1 How many whole numbers lie in the interval between

5 3 and 2π

?

2 Aunt Anna is 42 years old Caitlin is 5 years younger than Brianna and Brianna is half as old as aunt

Anna How old is Caitlin?

3 Each principal of Lincoln High School server exactly one 3-year term What is the maximum number

of principals this school could have during an 8-year period?

4 What is the minimum possible product of three different numbers of the set

{-8;-6;-4;0;3;5;7}

5 At Victoria Secondary School the mathematics teachers are Miss Anna, Mr Jonh, and Mrs Jeny There

are 11 students is Miss Anna’s class, 8 students in Mr Jonh’s class, and 9 students in Mr Jeny’s class taking the Gobal test this year How many mathematics students ats Victoria Secondary School are taking the contest?

6 The lengths of the sides of a triangle in inches are three consecutive intergers The length of the shoterst

side is 30% of the perimeter What is the length of the longest side?

7 A collector to buy state quarters for 2000% of their face value At that rate how much will Bryden get

for his four state quarters?

8 Using the function below, evaluate g(16)

G(x) = 4x3 – 3x(x2 + 4) + 4(3x + 8) Answer:………

9 Three circular arcs of radius 5 units

bound the region shown Arcs AB and AD

are quarter-circles and arc BCD is a semicircle

What is the area, in square units, of the region?

10

A B C D

EX3 OBSTACLE

1 In the diagram below AB = AC = AD

ABC= and ACD=

Find ·BAD

2 Given -6

≤ ≤ − ≤ ≤

Find the smallest value of x ×

y ?

3 What line is paraller to 2x + 3y = 6 at (3;2)?Answer: ……….

4 The sum of 3 exterior angles of a triangle is 360o

The ratio of these angles is 2:3:4

Find the ratio of the 3 interior angles respectively

5 There are five red balls, six yellow balls and seven bue balls hidden in a box You are allowed to take

out some balls without looking at their colors At least how many balls must you take to guarantee that you have two bue balls among them?

6 If the line through the point (5;-3) and (-2; p) is parallel to the line y = -2x – 3, what is the value of p?

Answer:………

7 ABCD is a square and BCE is equilateral

Find ·AED

?

Answer:………

8 Find the missing number x in the following number sequence

2, 9, -18, -11, x, 29, -58, -51, …

9 As shown in the diagram, the points L and M

Lie on QP and QR respectively O is the point

Os intersection of the lines LR and PM Given

That MP = MQ, LQ = LR; PL = PO and

POR x=

Find the value of x?

VÒNG 4 EX1 TALENTED GOLDEN TOAD:

1 A shopper buys a 100 dollar coat on sale 20% off An addition 5 dollars are taken off the sale price by

using a discount coupon A sale tax of 8% is paid on the final selling price The total amount the shopper pays for the coats

2 For how many positive interger values of N make the expression

36 2

N+

an interger?

3 Which of the following is the largest?

5

12

1 3

1 4

3 8

4 Calculate:

10 10 10 10 10 10 10 10 10 10+ + + + + + + + + =

5 The number halfway between

6 and 4

is 5

24

1 5

7 24

1 10

6 Calculate: 33 + 33 + 33 = ?

7 The perimeter of a square is 3 times larger than the perimeter of the other square The area of the larger

square is how many times larger than the area of the smaller one?

6 9 3 4

8.The arithmetic mean (average) of four number is 85 If the largest of these numbers is 97, then the mean

of the remaining three numbers is

9

1

1

1

1

2

3

= +

+

10

EX2 INTELLECTUAL PEAKS

1 The average of n whole numbers is 80 One of the number is 100 After removing the number 100 the

average of the remaining numbers is 78 Find the value of n?

2 Find the 10th term of this sequence: 1; 4; 9; 16; 25; …

3 The side of the square ABCD are 15cm long.

E and F are respectively the midpoints of AB and AD

Find the area of the shaded region?

4 The list price of an article is $6000 If is sold at half price, the profit is 25% At what price must it be

sold to have the profit of 50%

5 What is the next number of the sequence?

1, 2, 4, 7, 11, …

6 In 2014, both John and Mary have the same amount of pocket money per month In 2015, John had an

increase of 10% and Mary a decrease of 10% in their pocket money In 2016, John had a decrease of 10% and Mary an increase of 10% in their pocket money Compare the amount of pocket money between John and Mary, in 2016?

Mary’s money is 2 times John’s money John’s money is 2 times Mary’s money

John’s money = Mary’s money John’s money is 3 times Mary’s money

7 If the first three Fibonacci numbers are given as 1, 1, and 2, then what is the eleventh number?

8 Find the next number of this sequence: 2, 6, 18, 54, ….

9 Jessica has taken 4 exams and her average score so far is 79 If she gets 100, a perect score, on the next

2 exams, what will her new average be?

10 Sally receiver the following scores on her Math tests: 78, 92, 83, 99 What score does she need on the

next in order to have an average of 90 on her 5 math tests?

11 A language school has 100 pupils in which 69% of the pupils study French, 79% study German, 89%

study Japanese and 99% study English Given that at least x% of the sudent study all four languages Find the value of x

EX3 ARRANGE

VÒNG 5 EX1 Fill in the blank with the correct number

Question 1:In a group of 100 persons, 72 people can speak English and 43 can speak French How many can speak English only? Answer: There are persons.

Question 2:Mary has six cubes When she arranges them from smallest to largest, the difference between the heights of any two neighbouring cubes is 3 cm The largest cube is as high as tower built from the two smallest cubes How high is a tower built from all cubes?Answer: cm.

Question 3:Find the value of x if: (x+ 70) 3 = 357911.Answer: x =

Question 4:Tom can build a wall in 6 hours, Peter can build it in 10 hours and Mark can build it in 15 hours, separately In how many hours can they do it together?Answer: They can do it together in hours.

Question 5:In triangle PQR, PQ=PR,

· 60o RPQ=

PQS is a straight line.

Find

·RQS

Answer: =

Question 6:The figure shown below is not drawn to scale EFGH and WXYZ are parallelograms Find

·WFG

Answer:

·WFG

Question 7:How many prime numbers are there from 20 to 69?

Answer: There are prime numbers.

Question 8:In the figure below, ABCD is a parallelogram and CDE is an isosceles triangle.Find

Answer:

Question 9:How many composite numbers are there from 20 to 29?Answer:

There are composite numbers.

Question 10:The height of two building is 34 m and 29 m respectively If the distance between the two building is 12 m, find the distance between their tops.

Answer: The distance between their tops is m.

EX2 OBSTACLE

1 When three diffierent numbers from the set {-3; -2; -1; 4; 5} are multiplied, the largest possible product

is………

2 Which digit of 12345, when changed into 9, gives the largest number?

3

1

1

1

1

3

4

+

+

=………

4 Compute the following equation 2016 – 1 – 2 – 3 – 4 - …- 50 = ………

5 A ladder 13m long is placed on the ground in the such a way that it touches the top of a vertical wall

12m high Find the distance of the foot of the ladder from the bottom of the wall

6 If the square of the hypotenuse of the an isosceles right triangle is 128cm2 find the area of the triangle

7 The sum of three numbers is 98 The ratio of the first to the second is 2:3; and the ratio of the second to

the third is 5:8 The second number is:

EX3 TALENTED GOLDEN TOAD:

VÒNG 6

Question 1:

What is the difference between the smallest 5-digit odd number and the largest 4-digit even number?

Answer:

Question 2:

Given the following addition

What is the sum of the missing digits?

Answer:

Question 3:

Find two consecutive prime numbers with a sum of 144.

Answer:

(write your answer from least to greatest and use ";" between two numbers)

Question 4:

A right triangle has The circumradius of is cm.

Question 5:

How many two-digit numbers have the property of being equal to 7 times the sum of their digits?

Answer:

Question 6:

ABCD is a rectangle with a length of 22cm and an area of E and F are respectively midpoints of AC and AB

Find the area of the shaded triangle?

Answer:

Question 7:

If an arc of of circle A has the same length as an arc of of circle B The ratio of the area of circle A to the area of circle B is then the smallest value of a+b is

Question 8:

A Ferris wheel has 32 passenger cabins If you are sitting in cabin 14 which is currently at the top of the wheel, what is the number of the cabin at the bottom of the wheel?

Answer:

Question 9:

A box of erasers cost 4 dollars A box of pencils cost 6 dollars more Darwin spent 240 dollars on some boxes

of erasers and pencils The ratio of the number of pencil boxes to the number of eraser boxes was 4:5 How many boxes of pencils did he buy?

Answer:

Question 10:

Ann has walked 8km at a speed of 4 km/h She then run at a speed of 8 km/h How long does she have to run

in order to have an overall average speed of 5 km/h?

Answer: minutes.

Fill in the blank with the correct number

Question 1:

Find two consecutive prime numbers with a sum of 144.

Answer:

(write your answer from least to greatest and use ";" between two numbers)

Question 2:

A right triangle has The circumradius of is cm.

Question 3:

What is the difference between the smallest 5-digit odd number and the largest 4-digit even number?

Answer:

Question 4:

Given the following addition

What is the sum of the missing digits?

Answer:

Question 5:

ABCD is a rectangle with a length of 22cm and an area of E and F are respectively midpoints of AC and AB

Find the area of the shaded triangle?

Answer:

Question 6:

How many two-digit numbers have the property of being equal to 7 times the sum of their digits?

Answer: