TeXで高校数学 数学IA
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問題文
(a^ma^n=a^{m+n})
a^ma^n=a^{m+n}
((a^m)^n=a^{mn})
(a^m)^n=a^{mn}
((ab)^m=a^mb^m)
(ab)^m=a^mb^m
((a¥pm b)^2=a^2¥pm2ab+b^2)
(a\pm b)^2=a^2\pm2ab+b^2
((a+b)(a-b)=a^2-b^2)
(a+b)(a-b)=a^2-b^2
((x+a)(x+b)=x^2+(a+b)x+ab)
(x+a)(x+b)=x^2+(a+b)x+ab
((a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca)
(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca
((a¥pm b)^3=a^3¥pm3a^2b+3ab^2¥pm b^3)
(a\pm b)^3=a^3\pm3a^2b+3ab^2\pm b^3
((a¥pm b)(a^2¥mp ab+b^2)=a^3+b^3)
(a\pm b)(a^2\mp ab+b^2)=a^3+b^3
(¥sqrt{a^2}=¥lvert a¥rvert)
\sqrt{a^2}=\lvert a\rvert
((¥sqrt{a})^2=a)
(\sqrt{a})^2=a
(¥sqrt{a}¥sqrt{b}=¥sqrt{ab})
\sqrt{a}\sqrt{b}=\sqrt{ab}
(¥dfrac{¥sqrt{a}}{¥sqrt{b}})
\dfrac{\sqrt{a}}{\sqrt{b}}
(¥lvert x¥rvert¥leftrightarrow)
\lvert x\rvert
(y=a(x-p)^2+q)
y=a(x-p)^2+q
(x=¥dfrac{-b¥pm¥sqrt{b^2-4ac}}{2a})
x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}
(d=b^2-4ac)
D=b^2-4ac
(¥sin¥theta=¥dfrac{y}{r})
\sin\theta=\dfrac{y}{r}
(¥cos¥theta=¥dfrac{x}{r})
\cos\theta=\dfrac{x}{r}
(¥tan¥theta=¥dfrac{y}{x})
\tan\theta=\dfrac{y}{x}
(¥sin(90^¥circ-a)=¥sin a)
\sin(90^\circ-A)=\sin A
(¥cos(90^¥circ-a)=¥sin a)
\cos(90^\circ-A)=\sin A
(¥sin(180^¥circ-a)=¥sin a)
\sin(180^\circ-A)=\sin A
(¥tan(90^¥circ-a)=¥dfrac{1}{¥tan a})
\tan(90^\circ-A)=\dfrac{1}{\tan A}
(¥sin(180^¥circ-a)=¥sin a)
\sin(180^\circ-A)=\sin A
(¥cos(180^¥circ-a)=-¥cos a)
\cos(180^\circ-A)=-\cos A
(¥sin^2a+¥cos^2a=1)
\sin^2A+\cos^2A=1
(¥tan a=¥dfrac{¥sin a}{¥cos a})
\tan A=\dfrac{\sin A}{\cos A}
(1+¥tan^2a=¥dfrac{1}{¥cos^2a})
1+\tan^2A=\dfrac{1}{\cos^2A}
(0^¥circ¥leqq¥theta¥leqq180^¥circ)
0^\circ\leqq\theta\leqq180^\circ
(m=¥tan¥theta)
m=\tan\theta
(¥dfrac{a}{¥sin a}=2r)
\dfrac{a}{\sin A}=2R
(a^2=b^2+c^2-2bc¥cos a)
a^2=b^2+c^2-2bc\cos A
(b^2=c^2+a^2-2ca¥cos b)
b^2=c^2+a^2-2ca\cos B
(c^2=a^2+b^2-2ab¥cos c)
c^2=a^2+b^2-2ab\cos C
(s=¥dfrac{1}{2}bc¥sin a)
S=\dfrac{1}{2}bc\sin A
(s=¥dfrac{1}{2}r(a+b+c))
S=\dfrac{1}{2}r(a+b+c)
(¥{1, 2, 3¥})
\{1, 2, 3\}
(¥{a, b, c¥})
\{a, b, c\}
(a¥in a)
a\in A
(a¥subset b)
A\subset B
(a¥cap b)
A\cap B
(a¥cup b)
A\cup B
(p¥rightarrow q)
p\Rightarrow q
(¥bar{q}¥rightarrow¥bar{p})
\bar{q}\Rightarrow\bar{p}
(s^2=¥bar{x^2}=(¥bar{x})^2)
s^2=\bar{x^2}=(\bar{x})^2
(n(a¥cup b)=n(a)+n(b)-n(a¥cap b))
n(A\cup B)=n(A)+n(B)-n(A\cap B)
(n(¥overline{a})=n(u)-n(a))
n(\overline{A})=n(U)-n(A)
({}_n¥mathrm{p}_r)
{}_n\mathrm{P}_r
(0!=1)
0!=1
({}_n¥mathrm{p}_0=1)
{}_n\mathrm{P}_0=1
({}_n¥mathrm{p}_n=n!)
{}_n\mathrm{P}_n=n!
({}_n¥mathrm{c}_r)
{}_n\mathrm{C}_r
({}_n¥mathrm{c}_0={}_n¥mathrm{c}_n=1)
{}_n\mathrm{C}_0={}_n\mathrm{C}_n=1
({}_n¥mathrm{h}_r)
{}_n\mathrm{H}_r
(0¥leqq p(a)¥leqq 1)
0\leqq P(A)\leqq 1
(p(a¥cup b)=p(a)+p(b)-p(a¥cap b))
P(A\cup B)=P(A)+P(B)-P(A\cap B)
(p(¥overline{a})=1-p(a))
P(\overline{A})=1-P(A)
(p_a(b))
P_A(B)
(¥lvert b-c¥rvert<a<b+c)
\lvert b-c\rvert<a<b+c
(¥angle a)
\angle A
((-2ab^2)^2¥times a^2b)
(-2ab^2)^2\times a^2b
((-xy^3z)^3¥times(3x^2z)^2)
(-xy^3z)^3\times(3x^2z)^2
((x^2-3x+2)(x^2+x+3))
(x^2-3x+2)(x^2+x+3)
((4x-y)^2)
(4x-y)^2
((5a+3b)(5a-3b))
(5a+3b)(5a-3b)
((3a-2)(7a+5))
(3a-2)(7a+5)
((x+3y)^3)
(x+3y)^3
((x-3y)(x^2+3xy+9y^2))
(x-3y)(x^2+3xy+9y^2)
((x^2+x+3)(x^2+x-2))
(x^2+x+3)(x^2+x-2)
((x+y-z)(x-y+z))
(x+y-z)(x-y+z)
((x-y)(x+y)(x^2+y^2))
(x-y)(x+y)(x^2+y^2)
((a+b)^2(a-b)^2)
(a+b)^2(a-b)^2
((a-1)(x-2)(x+3)(x+4))
(a-1)(x-2)(x+3)(x+4)
(2ax-4ay+8az)
2ax-4ay+8az
(a(3a-b)-b(b-3a))
a(3a-b)-b(b-3a)
(4x^2+40x+25)
4x^2+40x+25
(16a^2-9b^2)
16a^2-9b^2
(x^2+x-6)
x^2+x-6
(6a^2-11ab-10b^2)
6a^2-11ab-10b^2
((x+y+2)(x+y)-8)
(x+y+2)(x+y)-8
(x^3-x(y+3z)^2)
x^3-x(y+3z)^2
(x^2+xz-y^2-yz)
x^2+xz-y^2-yz
(x^2+x-(y+2)(y+3))
x^2+x-(y+2)(y+3)
(2x^2-3xy+4x-2y^2-3y+2)
2x^2-3xy+4x-2y^2-3y+2
(x^4+3x^2-4)
x^4+3x^2-4
(x^4+9)
X^4+9
(x^2(y-z)+y^2(z-x)+z^2(x-y))
x^2(y-z)+y^2(z-x)+z^2(x-y)
(8x^3+y^3)
8x^3+y^3
(x^3-x^2+x-1)
x^3-x^2+x-1
(x(x+1)(x+2)(x+3)-24)
x(x+1)(x+2)(x+3)-24
(x^3-6x^2y+12xy^2-8y^3)
x^3-6x^2y+12xy^2-8y^3
(¥sqrt{18}+¥sqrt{72}-¥sqrt{32})
\sqrt{18}+\sqrt{72}-\sqrt{32}
((2-¥sqrt{3})(3+¥sqrt{3}))
(2-\sqrt{3})(3+\sqrt{3})
((2¥sqrt{3}+¥sqrt{5})^2)
(2\sqrt{3}+\sqrt{5})^2
((2¥sqrt{2}-¥sqrt{6})^2)
(2\sqrt{2}-\sqrt{6})^2
(¥dfrac{1}{1+¥sqrt{2}+¥sqrt{3}})
\dfrac{1}{1+\sqrt{2}+\sqrt{3}}
(¥sqrt{7+2¥sqrt{12}})
\sqrt{7+2\sqrt{12}}