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
(x+2)(x+3)(x+6)$)
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
. Known that
,
and
.
If
then
Câu 5:
How many real numbers
are there such that
?
Answer: There are numbers
.
Câu 6:
The operation
on two numbers produces a number equal to their sum minus 2.The value of
@3\)...@2017\)$)
is
Câu 7:
ABC is a triangle. AM is the bisector of angle CAB. Given that AM = 4cm, AB = 6m and AC = 12cm.Then the measurement of angle BAC is degrees.
Câu 8:
In the equation above, where
is a constant.The greatest possible value of
such that the equation has at least one solution is
Câu 9:
and
are positive integers such that
=n^2+1$)
, where
is a prime number.
The number of pairs
$)
is
Câu 10:
Given that
=\frac{x^2}{2x-2x^2-1}$)
.
Calculate:
+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)
Nộp bài
câu 7 mk bấm nhầm đáp án là 120
qua B kẻ đường thẳng song song với AM cắt AC ở N.
vì AM là phân giác góc BAC nên có :
\(\dfrac{AC}{AB}=\dfrac{CM}{BM}=\dfrac{12}{6}=2\) suy ra \(\dfrac{CM}{BC}=\dfrac{CM}{CM+BM}=\dfrac{12}{12+6}=\dfrac{2}{3}\)
vì AM song song với BN nên có :
1,\(\dfrac{CA}{AN}=\dfrac{CM}{BM}=\dfrac{12}{AN}=2\) suy ra AN=6
2,\(\dfrac{AM}{BN}=\dfrac{CM}{BC}=\dfrac{2}{3}=\dfrac{4}{BN}\)suy ra BN=6
vì AB=6 nên tam giác ABN đều
suy ra \(\widehat{NAB}\)=\(60^0\)
mà \(\widehat{NAB}+\widehat{BAC}=\)\(180^0\)
nên \(\widehat{BAC}=\)\(120^0\)
bài này bữa mình thi có 50đ à