o_19lld1olm1tin4f514hc1muj15ada.pdf

Бодлого 1. (Бодолттой)
ASB is a quarter circle. PQRS is a rectangle with sides PQ = 8 and PS = 6. What is the length
of the arc AQB ?
Solution:
Arc AQB is one quarter the perimeter of the circle (because angle S is a right angle).
To find the radius we need to see that the diagonal SQ of the rectangle= radius.
Now use Pythagoras to find the diagonal; 82 + 62 = r2
So r = 10 (You could have spotted that this is a 3-4-5 triangle and so saved this part of the
calculation) The length of the arc = ¼ 20 π = 5π

Бодлого 2. (Бодолттой)
Which of the following describes the relationship between A and B as shown in the pairs of
numbers in the table below?
Solution:
You can try out the relationships using at least two pairs from the table to see whether the
relationship holds. But it is relatively easy to spot that the first number squared + 1 gives the
second number in each case. So correct answer is B = A² + 1
Бодлого 3. (Бодолттой)
Which of the following pairs of angles must be equal?
Solution:
This question is testing that you know that the angle between a tangent to a circle and a chord
(angle c is such an angle) is equal to the angle in the opposite segment (angle d is in the
segment opposite to c in this case). Similarly, angle a is equal to angle e for the same reason.
So correct answer is B /a and e, and c and d only/

Бодлого 4. (Бодолттой)
3 3
A 38 17 5 16 4 20 0,1(6)
бол
1.
A 3 38 17 5 a b (2 oноо)
2.
3.
3 16 4 20 c b
d
0,1(6)
e
4. А=
f
g
байна.
байх тул
(2 оноо)
(1 оноо)
Бодолт:
1.
3 3 2 3 2
( ) 3 3 ( 3 ) (3 )
a b a a b ab b b a ab a b b
3
a
ab
3 38
2
3a
b17
гэж хувиргаад
системээс а ба в-г олно. (a=2; b=5) b=5 гэдгийг харчихвал
өмнөхөөс ч хялбараар олж болно.
2. Дээрх аргаар 2 дахь нэмэгдэхүүнийг олвол с=1; b=5
3. Холимог үет бутархайг энгийн бутархай болгох аргаар энгийн бутархайд
4.
шилжүүлнэ.
16 1 1
0,1(6)
90 6
1 5
A 2 5 1 5 6 6
d=1; e=6
f=5; g=6
IQ бодлого.
Асуултын тэмдгийн оронд тохирох тоог ол.

Бодлого 5. (Бодолттой)
2
tg(arcsin( )) a
5
бол
x
lim
xa
2
8x12
2
x 4
хязгаарыг бод.
Бодолт: Урвуу функцийн хамаарлын
tg(arcsin x)
x
1
x
2
ашиглавал:
2 2 2
2
tg(arcsin( ))
5
5
5
2 a 2
5 2 1
2 4
1 ( ) 1
5 5 5
хязгаарыг f(a)=0; g(a)=0 байгаа тохиолдолд уламжлал ашиглан
боддог аргыг ашиглавал:
2
x 8x 12 2x
8 2 ( 2) 8
lim lim 1
x 4 2x
2 ( 2)
x2 2
x2
болно. Функцийн
'
f ( x) f ( x)
lim lim
x a '
g( x) x a g ( x)
гэж гарна.
гэж
Толгойгоо сэргээгээрэй.

Функцийн графикуудаа цээжлээрэй.
Элсэлтийн ерөнхий шалгалтанд бэлтгэхдээ
аль болох олон бодлого бодож, олон
бодлогын бодолттой танилцаж,
хөдөлмөрлөсөн хүн амжилтанд
хүрдэг гэдгийг байнга санаж яваарай.
Good luck!

Mathematics Crossword Puzzle
/12 жилийн сурагчидад зориулав/
Across
6. A quadrilateral having both pairs of opposite
sides parallel to each other.
7. A ratio of algebraic quantities similarly
expressed.
9. the result of division
10. a symbol or number placed above and after
another symbol or number to denote the power to
which the latter is to be raised
12. The act or process of dividing; state of being
divided.
13. Something having magnitude, or size, extent,
amount, or the like.
14. relative rapidity in moving, going, etc.; rate
of motion or progress
Down
1. A quantity of which a given quantity is the
square. /2 words/
2. Pertaining to tenths or to the number 10.
3. The operation or process of finding the
difference between two numbers or quantities,
denoted by a minus sign (−).
4. A series of points, discrete or continuous, as in
forming a curve or surface, each of which
represents a value of a given function.
5. A strong likelihood or chance of something8. the
branch of mathematics that deals with the
deduction of the properties, measurement, and
relationships of points, lines, angles, and figures
in space
11. The amount of space, measured in cubic units,
that an object or substance occupies.