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頻出問題

ランク	トピック	問題	フォーマット化された問題
50101	関数演算を解く	7.37910^-4 m^3((100(cm))/(1(m)))^3*(19.3(g))/(cm^3)	$7.379 \times 10^{- 4}$ $m^{3} \times {(\frac{100 (cm)}{1 (m)})}^{3} \times \frac{19.3 (g)}{{cm}^{3}}$
50102	漸近線を求める	y=(3x)/(x-3)*(x-4)/(x+1)	$y = \frac{3 x}{(x - 3)} \cdot \frac{(x - 4)}{(x + 1)}$
50103	関数演算を解く	If f(x)=x^2-5x+6 and g(x)=2x^2+4x-1 ; find: f(5)	If $f (x) = x^{2} - 5 x + 6$ and $g (x) = 2 x^{2} + 4 x - 1$ ; find: $f (5)$
50104	関数演算を解く	f(x)=7(x^(1/5)+7) ; find f^-1(x)	$f (x) = 7 (x^{\frac{1}{5}} + 7)$ ; find $f^{- 1} (x)$
50105	定義域を求める	F(x) = log base 2 of x^2	$F (x) = \log_{2} (x^{2})$
50106	関数演算を解く	Given that f(x)=x^2-16x+60 and g(x)=x-6 ; find (f(x))÷(g(x)) and express the result in standard form.	Given that $f (x) = x^{2} - 16 x + 60$ and $g (x) = x - 6$ ; find $f (x) \div g (x)$ and express the result in standard form.
50107	関数演算を解く	g(x)=-4x-2 ; find g(-2)	$g (x) = - 4 x - 2$ ; find $g (- 2)$
50108	関数演算を解く	f(x)=5(x^(1/3)-6) ; find f^-1(x)	$f (x) = 5 (x^{\frac{1}{3}} - 6)$ ; find $f^{- 1} (x)$
50109	関数演算を解く	x-6)/4 ; find f^-1(x)の立方根f(x)=(	$f (x) = \frac{\sqrt[3]{x - 6}}{4}$ ; find $f^{- 1} (x)$
50110	関数演算を解く	Given f(x)=6(1-x) ; what is the value of f(-8) ?	Given $f (x) = 6 (1 - x)$ ; what is the value of $f (- 8)$ ?
50111	関数演算を解く	f(x)=( x-4)/8 ; find f^-1(x)の5乗根	$f (x) = \frac{\sqrt[5]{x} - 4}{8}$ ; find $f^{- 1} (x)$
50112	最大公約数を求める	14 and 49	$14$ and $49$
50113	楕円であるかどうかを証明しなさい。	(x^2)/9+(y^2)/4=1	$\frac{x^{2}}{9} + \frac{y^{2}}{4} = 1$
50114	漸近線を求める	(x^2+x-20)/(2x^2+10x)	$\frac{x^{2} + x - 20}{2 x^{2} + 10 x}$
50115	定義域を求める	f(x)=(sin(x))/(x+1)	$f (x) = \frac{\sin (x)}{x + 1}$
50116	頂点を求める	f(x)=-1/2(x+3)^2	$f (x) = - \frac{1}{2} {(x + 3)}^{2}$
50117	定義域を求める	L(t)=(t^2-4)/(t^2-t-2)	$L (t) = \frac{t^{2} - 4}{t^{2} - t - 2}$
50118	関数演算を解く	f(x)=-4x+1 g(x)=4x+3 Find (fog)(9)	$f (x) = - 4 x + 1$ $g (x) = 4 x + 3$ Find $((f \circ g)) (9)$
50119	関数演算を解く	Given that f(x)=x^2-16x+60 and g(x)=x-10 ; find f(x)-g(x) and express the result in standard form.	Given that $f (x) = x^{2} - 16 x + 60$ and $g (x) = x - 10$ ; find $f (x) - g (x)$ and express the result in standard form.
50120	関数演算を解く	Given that f(x)=x^2+17x+70 and g(x)=x+7 ; find (f-g)(x) and express the result in standard form.	Given that $f (x) = x^{2} + 17 x + 70$ and $g (x) = x + 7$ ; find $(f - g) (x)$ and express the result in standard form.
50121	最大公約数を求める	12a^4b^2c^2 , 20a^3bc^2	$12 a^{4} b^{2} c^{2}$ , $20 a^{3} b c^{2}$
50122	傾きを求める	(9,3) and (2,1)	$(9, 3)$ and $(2, 1)$
50123	漸近線を求める	f(x)=((x-3)(x-6)(x+4))/((x-3)^2(x-6)(x-8))	$f (x) = \frac{(x - 3) (x - 6) (x + 4)}{{(x - 3)}^{2} (x - 6) (x - 8)}$
50124	漸近線を求める	y=x/(a+bx)	$y = \frac{x}{a + b x}$
50125	関数演算を解く	h(a)=-2a^3+3a g(a)=a-3 find h(g(-1))	$h (a) = - 2 a^{3} + 3 a$ $g (a) = a - 3$ find $h (g (- 1))$
50126	関数演算を解く	f(x)=5(x-5)^7 ; find f^-1(x)	$f (x) = 5 {(x - 5)}^{7}$ ; find $f^{- 1} (x)$
50127	関数演算を解く	(x^2)/(x-3)+9/(3-x) , x!=3	$\frac{x^{2}}{x - 3} + \frac{9}{3 - x}$ , $x \neq 3$
50128	漸近線を求める	y=(x+3)/(2(x+4))	$y = \frac{(x + 3)}{2 (x + 4)}$
50129	定義域を求める	g(x)=(5x+\|x\|)/x	$g (x) = \frac{5 x + \| x \|}{x}$
50130	無限等比級数の和を求める	120+20+10/3+5/9+...	$120 + 20 + \frac{10}{3} + \frac{5}{9} + \dots$
50131	関数演算を解く	g(t)=2t+5 f(t)=-t^2+5 Find (g+f)(t)	$g (t) = 2 t + 5$ $f (t) = - t^{2} + 5$ Find $(g + f) (t)$
50132	最大公約数を求める	20 and 45	$20$ and $45$
50133	数列の和を求める	-12-4-4/3-...-4/243	$- 12 - 4 - \frac{4}{3} - \dots - \frac{4}{243}$
50134	漸近線を求める	(x^2+11x+28)/(3x^2+21x)	$\frac{x^{2} + 11 x + 28}{3 x^{2} + 21 x}$
50135	関数演算を解く	f(5) if f(x)=3x-2	$f (5)$ if $f (x) = 3 x - 2$
50136	定義域を求める	h(k)=k+ 6-4k-の平方根k-7の立方根	$h (k) = k + \sqrt{6 - 4 k} - \sqrt[3]{k - 7}$
50137	関数演算を解く	g(x)=-x-1 ; find g(-4)	$g (x) = - x - 1$ ; find $g (- 4)$
50138	定義域を求める	f(x) = square root of 1-5/x	$f (x) = \sqrt{1 - \frac{5}{x}}$
50139	傾きを求める	P=35-1/4Q	$P = 35 - \frac{1}{4} Q$
50140	傾きを求める	(-5,1) and (-5,7)	$(- 5, 1)$ and $(- 5, 7)$
50141	漸近線を求める	y=(x^2-9)/(2x^2+5x-3)	$y = \frac{x^{2} - 9}{2 x^{2} + 5 x - 3}$
50142	漸近線を求める	f(x)=(2x^2+3x+7)/( x^6+2)の平方根	$f (x) = \frac{2 x^{2} + 3 x + 7}{\sqrt{x^{6} + 2}}$
50143	傾きを求める	What is the slope of the line through (-1,8) and (3,-4) ?	What is the slope of the line through $(- 1, 8)$ and $(3, - 4)$ ?
50144	差商を求める	x^2+1	$x^{2} + 1$
50145	最大公約数を求める	6xy , 15x^2 , 9xy^4	$6 x y$ , $15 x^{2}$ , $9 x y^{4}$
50146	漸近線を求める	(x^2-9)/(2x^2+1)	$\frac{x^{2} - 9}{2 x^{2} + 1}$
50147	定義域を求める	(63x^2+81x)/(81x^2-126x+49)	$\frac{63 x^{2} + 81 x}{81 x^{2} - 126 x + 49}$
50148	関数演算を解く	g(x)=-3x-4 ; find g(1)	$g (x) = - 3 x - 4$ ; find $g (1)$
50149	最大公約数を求める	6 and 8	$6$ and $8$
50150	定義域を求める	f(x)=(1+ 1-x)/(の平方根4x-2x^2)の平方根	$f (x) = \frac{1 + \sqrt{1 - x}}{\sqrt{4 x - 2 x^{2}}}$
50151	最大公約数を求める	15 and 64	$15$ and $64$
50152	関数演算を解く	((13 1/4-2 5/27-10 5/6)*230,4+46,75)/(0,1)	$\frac{(13 \frac{1}{4} - 2 \frac{5}{27} - 10 \frac{5}{6}) \cdot 230, 4 + 46, 75}{0, 1}$
50153	傾きを求める	(-4,-2) and (-3,5)	$(- 4, - 2)$ and $(- 3, 5)$
50154	傾きを求める	(-1,7) and (3,107)	$(- 1, 7)$ and $(3, 107)$
50155	頂点を求める	f(x)=-2(x+4/5)^2-8	$f (x) = - 2 {(x + \frac{4}{5})}^{2} - 8$
50156	関数演算を解く	f(x)=(( x)/7)^3 ; find f^-1(x)の7乗根	$f (x) = {(\frac{\sqrt[7]{x}}{7})}^{3}$ ; find $f^{- 1} (x)$
50157	傾きを求める	(3,4) and (8,1)	$(3, 4)$ and $(8, 1)$
50158	関数演算を解く	If (x-1)/3=k and k=3 ; what is the value of x ?	If $\frac{x - 1}{3} = k$ and $k = 3$ ; what is the value of $x$ ?
50159	漸近線を求める	y=3 x+4の対数	$y = 3 \log (x + 4)$
50160	頂点を求める	y=-1/2x(x-8)	$y = - \frac{1}{2} x (x - 8)$
50161	傾きを求める	(-10,8) and (-15,-7)	$(- 10, 8)$ and $(- 15, - 7)$
50162	最大公約数を求める	15 and 35	$15$ and $35$
50163	傾きを求める	(2,7) and (5,8)	$(2, 7)$ and $(5, 8)$
50164	定義域を求める	(2x^3+3x)/(x^3-x^2-6x)	$\frac{2 x^{3} + 3 x}{x^{3} - x^{2} - 6 x}$
50165	関数演算を解く	If h(x)=x-7 and g(x)=x^2 ; which expression is equivalent to (goh)(5) ?	If $h (x) = x - 7$ and $g (x) = x^{2}$ ; which expression is equivalent to $((g \circ h)) (5)$ ?
50166	傾きを求める	Find the slope of the line passing through the points (-3,7) and (2,-6)	Find the slope of the line passing through the points $(- 3, 7)$ and $(2, - 6)$
50167	関数演算を解く	If P(x)=x^2+x+1 ; find P(8)	If $P (x) = x^{2} + x + 1$ ; find $P (8)$
50168	定義域を求める	(5x-15y)/(x^2-9y^2)	$\frac{5 x - 15 y}{x^{2} - 9 y^{2}}$
50169	頂点を求める	y=-1/3(x+1)(x-5)	$y = - \frac{1}{3} (x + 1) (x - 5)$
50170	定義域を求める	(ax-ay)/(5x^2y^2)*(-(5xy)/(by-bx))	$\frac{a x - a y}{5 x^{2} y^{2}} \times (- \frac{5 x y}{b y - b x})$
50171	定義域を求める	((x^2+9x+8)/(x^2))÷((x^2-1)/(x^3+3x^2-4x))	$\frac{x^{2} + 9 x + 8}{x^{2}} \div \frac{x^{2} - 1}{x^{3} + 3 x^{2} - 4 x}$
50172	傾きを求める	(-3,5) and (-7,7)	$(- 3, 5)$ and $(- 7, 7)$
50173	定義域を求める	(x+3)/(4- x^2-9)の平方根	$\frac{x + 3}{4 - \sqrt{x^{2} - 9}}$
50174	漸近線を求める	(3(x-8))/((3x-10)(x-8))	$\frac{3 (x - 8)}{(3 x - 10) (x - 8)}$
50175	関数演算を解く	a town has a population of 5000 and grows at 3.5% every yr What will be the population after 15yr ; to the nearest whole number?	a town has a population of $5000$ and grows at $3.5 %$ every $year$ What will be the population after $15 years$ ; to the nearest whole number?
50176	関数演算を解く	f(x)=7(x^(1/5)-10) ; find f^-1(x)	$f (x) = 7 (x^{\frac{1}{5}} - 10)$ ; find $f^{- 1} (x)$
50177	傾きを求める	(-5,-3) and (2,4)	$(- 5, - 3)$ and $(2, 4)$
50178	傾きを求める	Find the slope of the line passing through the points (-6,-5) and (4,4)	Find the slope of the line passing through the points $(- 6, - 5)$ and $(4, 4)$
50179	頂点を求める	2y^2+x+20y+51=0	$2 y^{2} + x + 20 y + 51 = 0$
50180	関数演算を解く	If f(x)=x^3-2 ; find f(3)	If $f (x) = x^{3} - 2$ ; find $f (3)$
50181	関数の値を求める	g(x)=-1/2x+9 , g(-8)	$g (x) = - \frac{1}{2} x + 9$ , $g (- 8)$
50182	関数演算を解く	f(x)=3x-5 ; find f(x+2)	$f (x) = 3 x - 5$ ; find $f (x + 2)$
50183	漸近線を求める	3/x+4	$\frac{3}{x} + 4$
50184	定義域を求める	f(x)=(x^4)/( 16-x^2)の平方根	$f (x) = \frac{x^{4}}{\sqrt{16 - x^{2}}}$
50185	傾きを求める	(-3,5) and (-12,8)	$(- 3, 5)$ and $(- 12, 8)$
50186	漸近線を求める	f(x)=(x^5-3x-1)/(x^2+4)	$f (x) = \frac{x^{5} - 3 x - 1}{x^{2} + 4}$
50187	関数演算を解く	If P(x)=x^2+x+2 ; find P(6)	If $P (x) = x^{2} + x + 2$ ; find $P (6)$
50188	関数演算を解く	g(n)=3n-2 h(n)=3n+3 Find (2g+5h)(n)	$g (n) = 3 n - 2$ $h (n) = 3 n + 3$ Find $(2 g + 5 h) (n)$
50189	関数演算を解く	If f(x)＝x+12 and g(x)=2の平方根x ; what is the value of (f-g)(144)の平方根	If $f (x) = \sqrt{x} + 12$ and $g (x) = 2 \sqrt{x}$ ; what is the value of $(f - g) (144)$ ?
50190	関数の値を求める	-2x+y=0 , x<=0	$- 2 x + y = 0$ , $x \leq 0$
50191	傾きを求める	(-4,7) and (4,-3)	$(- 4, 7)$ and $(4, - 3)$
50192	関数演算を解く	If P(x)=x^2+x+1 ; find P(7)	If $P (x) = x^{2} + x + 1$ ; find $P (7)$
50193	傾きを求める	Find the slope of the line passing through the points (-7,8) and (5,-7)	Find the slope of the line passing through the points $(- 7, 8)$ and $(5, - 7)$
50194	関数演算を解く	g(n)=2n+3 h(n)=n-1 Find (goh)(n)	$g (n) = 2 n + 3$ $h (n) = n - 1$ Find $((g \circ h)) (n)$
50195	関数演算を解く	If f(x)=x-1 and g(x)=5x-2 ; then (f/g)(x)	If $f (x) = x - 1$ and $g (x) = 5 x - 2$ ; then $(\frac{f}{g}) (x)$
50196	傾きを求める	(3,-1) and (7,-5)	$(3, - 1)$ and $(7, - 5)$
50197	定義域を求める	f(x)＝x+2+の平方根5-xの平方根	$f (x) = \sqrt{x + 2} + \sqrt{5 - x}$
50198	漸近線を求める	(3x^2-6x)/(2x^2-24x+70)	$\frac{3 x^{2} - 6 x}{2 x^{2} - 24 x + 70}$
50199	傾きを求める	(-3,7) and (6,-1)	$(- 3, 7)$ and $(6, - 1)$
50200	関数演算を解く	f(x)=6x+2 ; find f(x-3)	$f (x) = 6 x + 2$ ; find $f (x - 3)$