РЕШЕНИЯ ЗАДАНИЯ ДЛЯ ВЫПУСКНОГО ЭКЗАМЕНА ПО АЛГЕБРЕ И НАЧАЛАМ АНАЛИЗА 11 класс 1-задание

1-nji iş. Çep tarap
Aňlatmany ýönekeýleşdiriň:
a0,75-1a0,25-1+a0,25:4a+12a23 = a0,75-1+a0,5-a0,25a0,25-1 · a234a+12 =
= a0,51+4a-1+4a)·a23(a0,5-1)(4a+1) = a23(a0,5-1)4a+1(a0,5-1)(4a+1) = a23 = 3a2 ;
Jogaby: 3a2Deňlemeler sistemasyny çözüň:
x2-y2=-5,2x2-y2=-1. -x2+y2=5,2x2-y2=-1. => x2=5-1=4; x=±2;y2=2x2+1=9; y=±2; Jogaby: ( 2; 3), ( 2; - 3), ( - 2; 3), ( - 2; - 3);
Deňsizligi çözüň:
log0,22x-6>log0,2x2+3; 0.2< 1; 2x – 6 < x2 + 3;
x2 + 3 - 2x – 6 > 0; 3 - 2x + 9 > 0; (x-1) 2 + 8 > 0; deňsizlik islendik
x üçin ýerine ýetýär. Onda, x€-∞; +∞;2x – 6 > 0; => x> 3; x€ 3; +∞;
Jogaby: x€ 3; +∞;
4. Abssissalar okunyň üstünde A(-1;-2) we B(2;5) nokatlardan deňdaşlaşan nokady tapyň.
A(-1;-2), B(2;5), M(x;0); MA=MB; M(x;0)-nokady tapmaly.
MA=(-1-x)2+(-2)2 ; MB=(2-x)2+52 ; =>
=> (1+x)2+4 = (2-x)2+25 ; => x2 + 2x + 5 = x2 - 4x + 29;
2x + 4x = 29 – 5 ; 6x = 24; x = 4; M(4; 0);
Jogaby: M(4; 0);
5. Eger sinα=-23, π<α<3π2 bolsa, cos α+tg αtg α aňlatmanyň bahasyny tapyň.
cos α= 1-(-23)2 = - 53 ; tg α= sinαcosα = 25 ;
cos α+tg αtg α = - 53+2525 = 135 · 52 = 16 ; Jogaby: 16; 6. a-nyň haýsy bahalarynda y=( 3 a+x )x funksiýanyň minimumy 63 -e deň bolar?
miny = 65 ; a-?
yˊ = x + ( 3 a+x) 2x ; yˊ = 0; ( 3 a+x) 2x = 0; a= - x; x= - a; a<0;
ymin= y(-a)=(3a-a)-a = 2a-a = - 63 ; a = - 3;
Jogaby: a = - 3;
7. Material nokat a(t) = 3 cos3t m / s2 tizlenme bilen gönüçyzykly hereket edýär. Wagtyň t=0 pursatynda nokadyň tizligi 4,5 m/s deň bolsa, nokadyň tizliginiň deňlemesini tapyň.
a(t)=3cos3t m/s2; v(0)=4.5 m/s, v(t) - ?
v(t) = a(t)dt =3cos3t dt= sin3t+C; v(0)= sin0+C= 4.5;
C=4.5; v(t) = sin3t+4.5; Jogaby: v(t) = sin3t+4.5;
1-nji iş. Sag tarap
1. Aňlatmany ýönekeýleşdiriň:
b1,5+1b0,5+1-b0,5:1-b2b1,5 = b1,5+1-b-b0,5 b0,5+1 · b1,5 (1-b0,5)2 =
= (1-b)(1-b0,5)b1,5 (1-b)(1-b0,5) = b1,5 = 3b2; Jogaby: 3b22. Deňlemeler sistemasyny çözüň:
x2+y2=5,x2-2y2=-7. -x2-y2=-5,x2-2y2=-7. => -3y2= -12; y2= 4; y= ±2; x2= - 7 + 2y2 = 1; x = ±1; Jogaby: (1;2), (1; - 2), (-1;2), (-1; - 2);
3.Deňsizligi çözüň:
log2x2+5>log2x+7; 2>1 => x2+5> x+7; x2- x-2>0;x2- x-2>0;x+7; ( x-2)(x+1)>0;x>0; x€(-∞; -1 )∪( 2; +∞);x( -7; +∞); =>
=> ( 2; +∞); Jogaby: x€( 2; +∞);
4. Ordinatalar okunyň üstünde C-4;1 we D2;-5 nokatlardan deňdaşlaşan nokady tapyň.
C-4;1, D2;-5, N(0;y), CN = ND, N(0;y)- nokady tapmaly.
CN = 42+(y-1)2 ; ND=22+(-5-y)2 ; =>
=>42+(y-1)2= 22+(-5-y)2; y2 – 2y + 17 = y2 + 10y + 29; =>
=> -2y – 10y = 29 -17 = 12; y = - 1; N( 0; 1 ) ; Jogaby: N( 0; 1 ) –nokat.
5.Eger sinα=-12, π<α<3π2 bolsa, tg αtg α+cosα aňlatmanyň bahasyny tapyň.
cosα= - 1- 14 = - 32 ; tg α = sinαcosα = 13 ;
tg αtg α+cosα = 13- 123 = - 2; Jogaby: - 2;
6. b-niň haýsy bahalarynda y=2x b- x funksiýanyň maksimumy 4-e deň bolar? Maxy=4;
yˊ =2b- x - xb- x = 2b-3xb- x ; yˊ = 0; 2b – 3x = 0; x = 23b;
y( 23b ) = 23b · 2b- 23b = 43b b3 ; 43b b3 = 4; b = 3 ;
Jogaby: b = 3;
7. Material nokat a(t)=1t+e t m/s2 tizlenme bilen gönüçyzykly hereket edýär. Eger wagtyň t = 1s pursatynda nokadyň tizligi 2e m/s deň bolsa, nokadyň tizliginiň deňlemesini tapyň.
a(t)=1t+e t m/s2; v(1)=2e m/s, v(t) - ?
v(t) = a(t)dt =1t+e tdt= lnt +et+C; v(1)=ln1+e+C=2e;
C=e; v(t) = lnt +et+e; Jogaby: v(t) = lnt +et+e;