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Бодлого 1. (Бодолттой)<br />
ASB is a quarter circle. PQRS is a rectangle with sides PQ = 8 and PS = 6. What is the length<br />
of the arc AQB ?<br />
Solution:<br />
Arc AQB is one quarter the perimeter of the circle (because angle S is a right angle).<br />
To find the radius we need to see that the diagonal SQ of the rectangle= radius.<br />
Now use Pythagoras to find the diagonal; 82 + 62 = r2<br />
So r = 10 (You could have spotted that this is a 3-4-5 triangle and so saved this part of the<br />
calculation) The length of the arc = ¼ 20 π = 5π
Бодлого 2. (Бодолттой)<br />
Which of the following describes the relationship between A and B as shown in the pairs of<br />
numbers in the table below?<br />
Solution:<br />
You can try out the relationships using at least two pairs from the table to see whether the<br />
relationship holds. But it is relatively easy to spot that the first number squared + 1 gives the<br />
second number in each case. So correct answer is B = A² + 1<br />
Бодлого 3. (Бодолттой)<br />
Which of the following pairs of angles must be equal?<br />
Solution:<br />
This question is testing that you know that the angle between a tangent to a circle and a chord<br />
(angle c is such an angle) is equal to the angle in the opposite segment (angle d is in the<br />
segment opposite to c in this case). Similarly, angle a is equal to angle e for the same reason.<br />
So correct answer is B /a and e, and c and d only/
Бодлого 4. (Бодолттой)<br />
3 3<br />
A 38 17 5 16 4 20 0,1(6)<br />
бол<br />
1.<br />
A 3 38 17 5 a b (2 oноо)<br />
2.<br />
3.<br />
3 16 4 20 c b<br />
d<br />
0,1(6) <br />
e<br />
4. А=<br />
f<br />
g<br />
байна.<br />
байх тул<br />
(2 оноо)<br />
(1 оноо)<br />
Бодолт:<br />
1.<br />
3 3 2 3 2<br />
( ) 3 3 ( 3 ) (3 )<br />
a b a a b ab b b a ab a b b<br />
3<br />
a<br />
ab <br />
3 38<br />
<br />
2<br />
3a<br />
b17<br />
гэж хувиргаад<br />
системээс а ба в-г олно. (a=2; b=5) b=5 гэдгийг харчихвал<br />
өмнөхөөс ч хялбараар олж болно.<br />
2. Дээрх аргаар 2 дахь нэмэгдэхүүнийг олвол с=1; b=5<br />
3. Холимог үет бутархайг энгийн бутархай болгох аргаар энгийн бутархайд<br />
4.<br />
шилжүүлнэ.<br />
16 1 1<br />
0,1(6) <br />
90 6<br />
1 5<br />
A 2 5 1 5 6 6<br />
d=1; e=6<br />
f=5; g=6<br />
IQ бодлого.<br />
Асуултын тэмдгийн оронд тохирох тоог ол.
Бодлого 5. (Бодолттой)<br />
2<br />
tg(arcsin( )) a<br />
5<br />
бол<br />
x<br />
lim<br />
xa<br />
2<br />
8x12<br />
2<br />
x 4<br />
хязгаарыг бод.<br />
Бодолт: Урвуу функцийн хамаарлын<br />
tg(arcsin x)<br />
<br />
x<br />
1<br />
x<br />
2<br />
ашиглавал:<br />
2 2 2<br />
<br />
2<br />
tg(arcsin( )) <br />
5<br />
<br />
5<br />
<br />
5<br />
2 a 2<br />
5 2 1<br />
2 4<br />
1 ( ) 1<br />
5 5 5<br />
хязгаарыг f(a)=0; g(a)=0 байгаа тохиолдолд уламжлал ашиглан<br />
боддог аргыг ашиглавал:<br />
2<br />
x 8x 12 2x<br />
8 2 ( 2) 8<br />
lim lim 1<br />
x 4 2x<br />
2 ( 2)<br />
x2 2<br />
x2<br />
болно. Функцийн<br />
'<br />
f ( x) f ( x)<br />
lim lim<br />
x a '<br />
g( x) x a g ( x)<br />
гэж гарна.<br />
гэж<br />
Толгойгоо сэргээгээрэй.
Функцийн графикуудаа цээжлээрэй.<br />
Элсэлтийн ерөнхий шалгалтанд бэлтгэхдээ<br />
аль болох олон бодлого бодож, олон<br />
бодлогын бодолттой танилцаж,<br />
хөдөлмөрлөсөн хүн амжилтанд<br />
хүрдэг гэдгийг байнга санаж яваарай.<br />
Good luck!
Mathematics Crossword Puzzle<br />
/12 жилийн сурагчидад зориулав/<br />
Across<br />
6. A quadrilateral having both pairs of opposite<br />
sides parallel to each other.<br />
7. A ratio of algebraic quantities similarly<br />
expressed.<br />
9. the result of division<br />
10. a symbol or number placed above and after<br />
another symbol or number to denote the power to<br />
which the latter is to be raised<br />
12. The act or process of dividing; state of being<br />
divided.<br />
13. Something having magnitude, or size, extent,<br />
amount, or the like.<br />
14. relative rapidity in moving, going, etc.; rate<br />
of motion or progress<br />
Down<br />
1. A quantity of which a given quantity is the<br />
square. /2 words/<br />
2. Pertaining to tenths or to the number 10.<br />
3. The operation or process of finding the<br />
difference between two numbers or quantities,<br />
denoted by a minus sign (−).<br />
4. A series of points, discrete or continuous, as in<br />
forming a curve or surface, each of which<br />
represents a value of a given function.<br />
5. A strong likelihood or chance of something8. the<br />
branch of mathematics that deals with the<br />
deduction of the properties, measurement, and<br />
relationships of points, lines, angles, and figures<br />
in space<br />
11. The amount of space, measured in cubic units,<br />
that an object or substance occupies.