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1 1. , , , , 2. . . 3. . 4. . 5. .
6. x,y, . a) max(x,y) b) min(x,y)
7. 8. .
) T . b) .
9. n.k . ) ) )
10. H N 5- ? ( 0 5 ) 11. .
a. N b. 1- 31
12. 1+2+3+ . +30 . 13. [10,100] .
2
1. R 3- 2. . 3. 2 . 4. 100300 . 5. N . 6. . 7. P- 2p-1 . 10 . 8. , 2 500
. 9. . 10. 1000- . 11. N 1990 N . 12. . . 13. .
3 1. . 2. a [10] . 3. a [20] 2, 1 . 4. a [15] max, min . 5. a [10] 2 , 2 . 6. a [10] max, min . 7. a[n] . a[n] a[n+1]
. 8. a[n] . a[n] a[n-1]
. 9. , . - - . 10. .
a. Y=sin(x) b) Y=cos(x) c) Y=tg(x) b. d) Y=sin(2*x+0.5) e) Y= 2*sin(x)+4*cos(x)
11. (x1,y1) (x2,y2) 12. .
a. . 13. ,, .
a. S= p(p-a)(p-b)(p-c) p=(a+b+c)/2
2
4
1. [ -1;1], [ 3;5] . 2. X, Y, Z .
a. a) max (X, Y, Z ) ) min (X, Y, Z ) 3. a, b, c
3
11. M . 12. N! N- . (N
4
9
1. X,Y,Z . i. X,Y,Z ii. iii.
2. a,b,c,d , c,d 3. 4. N Y Y=10*N+150 , 5. Y=20*N+150 6. N .
a. . b. 9- c. N d. 10- 5- .
7. 3- 10- 5 . 8. 4- . . 9. 4- . 10. 19 3- . 11. - 3- . 12. 3- . 13. N! 3 N- .
10
1. 100! - 3 . 2. , A=X! . 3. .
a. b. 4. . 5. N . . 6. .
7. , . 8. a[n], b[n] c[n] . c[n]
. a. c[i]=a[i]+b[i] b. c[i]=a[i]xb[i] c. c[i]=|a[i]-b[i]| d. c[i]=a[i]+b[i]
9. a[n] . a. k- i=k+1,k+2,..N . b. . : k=5
i. a[1]a[6], a[2]a[7],a[3]a[8],..,a[i]a[i+5],a[n]a[5] 10. a[n] . a[n] a[n+1]
. 11. a[n] . a[n] a[n-1]
. 12. R1,R2.R3 . . 13. h .
11
1. . a. a) 2
x-3
x+4
x-5
x b) 1- 2
x-3
x+4
x-5
x
2. , a. a) b)
3. X,Y,Z . 4. a) X,Y,Z b) 5. c) 6. a,b,c,d , c,d 7. 8. N Y Y=10*N+150 ,
a. Y=20*N+150 9. N .
a. . b) 9- b. c) N d) 10- 5- .
10. 3- 10- 5 .
5
11. 4- . . 12. 7- . 13. 5 .
12
1. : 4 3- . 2- . 4!=2*3*4=24 5!=4*5*6=120
a. 2- . 2. N! N . 3. 123456789 +,-,: ,x 99
. 4. .
a. 123........8910111213........ b. 14916253649........ c. 0112358132134.......... d. 110100100010000........
5. N . a. . b. .
6. . 7. N . . 8. . 9. , . 10. N M . 11. . 12. --- 2, --- 4 13. a[n] M .
a. M a[n] . b. . c. M a[n] . d. a[n]
a[n] .
13
1. a[n] . .
2. a[n] . a. k- i=k+1,k+2,..N . b. . : k=5
i. a[1]a[6], a[2]a[7],a[3]a[8],..,a[i]a[i+5],a[n]a[5] 3. a[n] . a[n] a[n+1]
. 4. N . . 5. A . 6. 3- . 7. , , . 8. .
a. a+bx+cyz b. |a(x-b)-x+c|x-d c. ab/c+c/ab d. (x+y)/a+a/x+y e. 104 f-1/5h
b. (1+x/2!+y/3!)/ (1+2/3+xy) g. (1+x2 ) h. |a+bx| k. sin8
9. ax+bx=0 . 10. a,b,c, , , 11. k,l,m,n . (1
6
a. A=1.8*N+2.4 . 13. >=4500m P=H-10 H
7
16
1. . 2. 130 .
C=9.5*b+5500 , C=3.5*b+4500 .
3. M=V*0.75+600, M=V*0.95+575 a. . V b. .
4. N N , N 4- 5. , 100- 400- , 1700, 1800, 1900
, 2000 6. 80 2 . 7. 19 3- . 8. - 3- . 9. 3- . 10. . 11. - 05 3- . 12. 3- . 13. 3- .
17
1. 100 2,5,20,50 . 2. .
a. . 3. ,,,D 3- .
a. (a,b,c) (a+b, b+c, a+c) . 4. . 5. N . . 6. . 7. , . 8. N M . 9. N . .
a. . 10. m,n . (0
8
c. N 9. 10- 5- . 10. 2 . A(x1,y1),B(x2,y2)
a. . 11. a,b,c . (a>0) , ax+bx+c=0 . 12. (x,y) cc
.
i. Y>=X2
ii. Y
9
21
1. H N 5- ? ( 0 5 ) 2. .
a. N b. 1- 31 3. 1+2+3+ . +30 . 4. [10,100] . 5. . 6. y=ax
2+bx+c (xo,yo) .
7. N .
8. P N . 9. . 10. . 11. 10- . 12. a[n] M .
a. M a[n] . b. . c. M a[n] . d. a[n]
a[n] . 13. 19 3- .
22
1. 3- . 2. N! 3 N- . 3. N! N- . 4. N .
5. N 2 , . 6. , , n,p,k .
a. 7 b. .
7. a[n] . a. k- i=k+1,k+2,..N . b. . : k=5
i. a[1]a[6], a[2]a[7],a[3]a[8],..,a[i]a[i+5],a[n]a[5] 8. k,l,m,n . (1
10
a. a) max(x,y) b) min(x,y) 13.
24
1. 2 . 2. 100300 . 3. N . 4. . 5. P- 2p-1 . 10
a. . 6. , 2 500
. 7. 2- N . 8. 123........1990 1990- . 9. 4- N . 10. . N
a. . 11. 2 . . 12. 3- . 13. .
25
1. P N . 2. . 3. --- 2, --- 4 4. 3- . 5. N! 3 N- . 6. N! N- . 7. N .
8. N 2 , . 9. N M . 10. . 11. --- 2, --- 4 12. a[n] M .
a. M a[n] . b. . c. M a[n] . d. a[n]
a[n] . 13. 2 15 . : (3,5) (11,13) ..
26
1. [1,100] 7- . 2. n,p .
a. n b. p
n
3. . 4. x 5. . 6. [ 2;5] . 7. . 8. 2- N . 9. ,
. a. F=1.8*C+32 b. R=0.8*C
10. - . (1 =0,4 ) 11. N .
a. : 0,1,1,2,3,5,8,13,21 12. N M .
11
13. a[n] . .
27 1. . 2. . 3. , 4. 5. ) 6. N! N- . 7. N .
8. a,b,c . . 9. . 10. . 3- . 11. K . 12. , . 13. a[n] .
28
1. N . (N