Bài thi số 3
19:25
Câu 1:
A man drove a car from A to B at speed 60km/h. After arriving B, he took a rest for 30 minutes then turned back to A at speed 40km/h. Known that he started from A at 7:00 am and he reached A again at 3:15pm on the same day. The distance between A and B is km.
Câu 2:
The minimum of the expression is
Câu 3:
Given that is a positive integer such that and are perfect squares.
The sum of such integers is
Câu 4:
Given two triangles and...
Đọc tiếp
Bài thi số 3
19:25
Câu 1:
A man drove a car from A to B at speed 60km/h. After arriving B, he took a rest for 30 minutes then turned back to A at speed 40km/h. Known that he started from A at 7:00 am and he reached A again at 3:15pm on the same day. The distance between A and B is km.
Câu 2:
The minimum of the expression
![](http://latexapp.violympic.vn/?$A=(x-1)(x+2)(x+3)(x+6)$)
is
Câu 3:
Given that
![](http://latexapp.violympic.vn/?$x$)
is a positive integer such that
![](http://latexapp.violympic.vn/?$x$)
and
![](http://latexapp.violympic.vn/?$x+99$)
are perfect squares.
The sum of such integers
![](http://latexapp.violympic.vn/?$x$)
is
Câu 4:
Given two triangles
![](http://latexapp.violympic.vn/?$ABC$)
and
![](http://latexapp.violympic.vn/?$DEF$)
. Known that
![](http://latexapp.violympic.vn/?$\widehat{B}=\widehat{D}$)
,
![](http://latexapp.violympic.vn/?$AB=\frac{4}{3}DE$)
and
![](http://latexapp.violympic.vn/?$DF=0.75BC$)
.
If
![](http://latexapp.violympic.vn/?$|AC-EF|=5$)
then
![](http://latexapp.violympic.vn/?$AC=$)
Câu 5:
How many real numbers
![](http://latexapp.violympic.vn/?$x$)
are there such that
![](http://latexapp.violympic.vn/?$x^4+x^3+x^2+x+1=0$)
?
Answer: There are numbers
![](http://latexapp.violympic.vn/?$x$)
.
Câu 6:
The operation
![](http://latexapp.violympic.vn/?$@$)
on two numbers produces a number equal to their sum minus 2.The value of
![](http://latexapp.violympic.vn/?$\(...\(\(1@2\)@3\)...@2017\)$)
is
Câu 7:
ABC is a triangle. AM is the bisector of angle CAB. Given that AM = 4cm, AB = 6m and AC = 12cm.Then the measurement of angle BAC is degrees.
Câu 8:
![](http://latexapp.violympic.vn/?$x^4+2x^2+m^2-4=0.$)
In the equation above, where
![](http://latexapp.violympic.vn/?$m$)
is a constant.The greatest possible value of
![](http://latexapp.violympic.vn/?$m$)
such that the equation has at least one solution is
Câu 9:
![](http://latexapp.violympic.vn/?$m$)
and
![](http://latexapp.violympic.vn/?$n$)
are positive integers such that
![](http://latexapp.violympic.vn/?$10(m^2+1)=n^2+1$)
, where
![](http://latexapp.violympic.vn/?$m^2+1$)
is a prime number.
The number of pairs
![](http://latexapp.violympic.vn/?$(m;n)$)
is
Câu 10:
Given that
![](http://latexapp.violympic.vn/?$f(x)=\frac{x^2}{2x-2x^2-1}$)
.
Calculate:
![](http://latexapp.violympic.vn/?$f\(\frac{1}{2016}\)+f\(\frac{2}{2016}\)+f\(\frac{3}{2016}\)+...+f\(\frac{2015}{2016}\)+f\(\frac{2016}{2016}\)$)
=
(Input the answer as a decimal in its simplest form)
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