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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
50001	傾きを求める	(7/10,-1/2) and (1/5,1/5)	$(\frac{7}{10}, - \frac{1}{2})$ and $(\frac{1}{5}, \frac{1}{5})$
50002	傾きを求める	(-4,1) and (2,5)	$(- 4, 1)$ and $(2, 5)$
50003	漸近線を求める	f^-1(x)=(x-3)/(1-x)	$f^{- 1} (x) = \frac{x - 3}{1 - x}$
50004	頂点を求める	f(x)=-4/5x^2+48/5x-114/5	$f (x) = - \frac{4}{5} x^{2} + \frac{48}{5} x - \frac{114}{5}$
50005	関数演算を解く	If P(x)=x^2+x+5 ; find P(6)	If $P (x) = x^{2} + x + 5$ ; find $P (6)$
50006	関数演算を解く	If g(x)=3x^2+5 and h(x)=x^2-1 ; find (g-h)(x)	If $g (x) = 3 x^{2} + 5$ and $h (x) = x^{2} - 1$ ; find $(g - h) (x)$
50007	関数演算を解く	If f(x)=3x+6 then find f^-1(x)	If $f (x) = 3 x + 6$ then find $f^{- 1} (x)$
50008	関数演算を解く	f(x)=3x^2-11 Find f(-5)	$f (x) = 3 x^{2} - 11$ Find $f (- 5)$
50009	関数演算を解く	f(x)=(x-3)^(1/2) ; find f^-1(x)	$f (x) = {(x - 3)}^{\frac{1}{2}}$ ; find $f^{- 1} (x)$
50010	漸近線を求める	f(x)=1/2* xの対数の底1/4	$f (x) = \frac{1}{2} \cdot \log_{\frac{1}{4}} (x)$
50011	定義域を求める	(x^2-4y^2)÷((5x-10y)/x)	$(x^{2} - 4 y^{2}) \div \frac{5 x - 10 y}{x}$
50012	最大公約数を求める	24 and 40	$24$ and $40$
50013	関数演算を解く	g(x)=-x+3 ; find g(1)	$g (x) = - x + 3$ ; find $g (1)$
50014	傾きを求める	y/3-2x+4=5	$\frac{y}{3} - 2 x + 4 = 5$
50015	漸近線を求める	f(x)=((x+10)(x+6)(x-8))/(-2x^3+7x^2-x-10)	$f (x) = \frac{(x + 10) (x + 6) (x - 8)}{- 2 x^{3} + 7 x^{2} - x - 10}$
50016	漸近線を求める	f(x)=(x^3+4x^2-21x)/(x^2+4x-21)	$f (x) = \frac{x^{3} + 4 x^{2} - 21 x}{x^{2} + 4 x - 21}$
50017	最大公約数を求める	15 and 18	$15$ and $18$
50018	関数演算を解く	If f(x)=4x^2-3x and g(x)=6-7x ; find: (f-g)(-2)	If $f (x) = 4 x^{2} - 3 x$ and $g (x) = 6 - 7 x$ ; find: $(f - g) (- 2)$
50019	部分分数分解を用いて分割する	(6x^2+1)/(x^2(x-1)^3)	$\frac{6 x^{2} + 1}{x^{2} {(x - 1)}^{3}}$
50020	奇関数、偶関数、どちらでもないかを判断する	f(x)=1/5x^6-3x^2	$f (x) = \frac{1}{5} x^{6} - 3 x^{2}$
50021	定義域を求める	((x-3)(x+2))/(x^2-5x-6)	$\frac{(x - 3) (x + 2)}{x^{2} - 5 x - 6}$
50022	定義域を求める	xの自然対数の自然対数	$\ln (\ln (x))$
50023	関数演算を解く	f(x)=x^2-4x-9 g(x)=-3x-5 Find: f(g(x))	$f (x) = x^{2} - 4 x - 9$ $g (x) = - 3 x - 5$ Find: $f (g (x))$
50024	最大公約数を求める	6 and 9	$6$ and $9$
50025	傾きを求める	(-1,-7) and (0,-9)	$(- 1, - 7)$ and $(0, - 9)$
50026	関数演算を解く	If f(x)=1/x and g(x)=3x+2 find f(g(x))	If $f (x) = \frac{1}{x}$ and $g (x) = 3 x + 2$ find $f (g (x))$
50027	傾きを求める	(-4,-9) and (0,-8)	$(- 4, - 9)$ and $(0, - 8)$
50028	関数演算を解く	Given that f(x)=x^2+4x-32 and g(x)=x+8 ; find (f(x))÷(g(x)) and express the result in standard form.	Given that $f (x) = x^{2} + 4 x - 32$ and $g (x) = x + 8$ ; find $f (x) \div g (x)$ and express the result in standard form.
50029	傾きを求める	(-9,-9) and (-6,0)	$(- 9, - 9)$ and $(- 6, 0)$
50030	定義域を求める	(x(x-2))/((x-2)(x+3))=x/(x+3)	$\frac{x (x - 2)}{(x - 2) (x + 3)} = \frac{x}{x + 3}$
50031	定義域を求める	f(x)=( x+4)/(x^2+5x)の平方根	$f (x) = \frac{\sqrt{x + 4}}{x^{2} + 5 x}$
50032	漸近線を求める	((2x+3)(x-4))/(3(x-4))	$\frac{(2 x + 3) (x - 4)}{3 (x - 4)}$
50033	傾きを求める	(-3,-4) and (2,-1)	$(- 3, - 4)$ and $(2, - 1)$
50034	定義域を求める	2-xの立方根の平方根	$\sqrt{\sqrt[3]{2 - x}}$
50035	定義域を求める	f(x)=\|x\|*x	$f (x) = \| x \| \cdot x$
50036	部分分数分解を用いて分割する	-(5x-4)/((x+1)(x-2))	$- \frac{5 x - 4}{(x + 1) (x - 2)}$
50037	漸近線を求める	(3x(3x-5))/((x+5)(x+9))	$\frac{3 x (3 x - 5)}{(x + 5) (x + 9)}$
50038	関数演算を解く	9f=2 1 (12f-2)	$9 f = 2$ $1$ $(12 f - 2)$
50039	傾きを求める	(-3,5) and (3,3)	$(- 3, 5)$ and $(3, 3)$
50040	傾きを求める	(10,7) and (1,2)	$(10, 7)$ and $(1, 2)$
50041	関数演算を解く	Given that f(x)=x^2-19x+90 and g(x)=x-9 ; find (f(x))÷(g(x)) and express the result in standard form.	Given that $f (x) = x^{2} - 19 x + 90$ and $g (x) = x - 9$ ; find $f (x) \div g (x)$ and express the result in standard form.
50042	傾きを求める	(9,9) and (1,16)	$(9, 9)$ and $(1, 16)$
50043	関数の値を求める	(1,206.4)/x=52	$\frac{1, 206.4}{x} = 52$
50044	関数演算を解く	(1,206.4)/x=52	$\frac{1, 206.4}{x} = 52$
50045	定義域を求める	(x-1)/(2x^2+x-3)	$\frac{x - 1}{2 x^{2} + x - 3}$
50046	関数演算を解く	g(x)=-3x+3 ; find g(-2)	$g (x) = - 3 x + 3$ ; find $g (- 2)$
50047	関数演算を解く	Given that f(x)=x^2-3x-54 and g(x)=x-9 ; find (f÷g)(x) and express the result in standard form.	Given that $f (x) = x^{2} - 3 x - 54$ and $g (x) = x - 9$ ; find $(f \div g) (x)$ and express the result in standard form.
50048	最大公約数を求める	4 and 12	$4$ and $12$
50049	定義域を求める	m(x) = square root of x-4	$m (x) = \sqrt{x - 4}$
50050	定義域を求める	(x^2)/(x+1)の平方根	$\sqrt{\frac{x^{2}}{x + 1}}$
50051	差商を求める	2x^2	$2 x^{2}$
50052	関数演算を解く	f(x)=x-6 if x<0; 3 if x=0; 6x-9 if x>0 Find f(0)	$f (x) = {\begin{cases} x - 6 & x < 0 \\ 3 & x = 0 \\ 6 x - 9 & x > 0 \end{cases}$ Find $f (0)$
50053	関数演算を解く	((((3,2-1,7))÷0,3)/(((29/35-3/7)4)÷0,2)-((33/20-1,5)1,5)/((2,44+39/25)*1/8))÷62 1/20+1 , 364÷0 , 124	$(\frac{(3, 2 - 1, 7) \div 0, 3}{(\frac{29}{35} - \frac{3}{7}) \times 4 \div 0, 2} - \frac{(\frac{33}{20} - 1, 5) \times 1, 5}{(2, 44 + \frac{39}{25}) \times \frac{1}{8}}) \div 62 \frac{1}{20} + 1$ , $364 \div 0$ , $124$
50054	関数演算を解く	Given that f(x)=x^2-5x+6 and g(x)=x-3 ; find f(x)+g(x) and express the result in standard form.	Given that $f (x) = x^{2} - 5 x + 6$ and $g (x) = x - 3$ ; find $f (x) + g (x)$ and express the result in standard form.
50055	定義域を求める	(25-a^2)/(3a-15)	$\frac{25 - a^{2}}{3 a - 15}$
50056	定義域を求める	f(x)=(6x^2+3)/(x-1)	$f (x) = \frac{6 x^{2} + 3}{x - 1}$
50057	最大公約数を求める	28 and 42	$28$ and $42$
50058	漸近線を求める	y=tan(pi/2x)	$y = \tan (\frac{π}{2} x)$
50059	関数演算を解く	Given that f(x)=x^2-6x+8 and g(x)=x-2 ; find (f*g)(x) and express the result in standard form.	Given that $f (x) = x^{2} - 6 x + 8$ and $g (x) = x - 2$ ; find $(f \cdot g) (x)$ and express the result in standard form.
50060	傾きを求める	(7/8,3/4) , (5/4,-1/4)	$(\frac{7}{8}, \frac{3}{4})$ , $(\frac{5}{4}, - \frac{1}{4})$
50061	定義域を求める	y=1/( 1-x^2)の平方根	$y = \frac{1}{\sqrt{1 - x^{2}}}$
50062	漸近線を求める	1/x+3	$\frac{1}{x} + 3$
50063	傾きを求める	Find the slope of the line passing through the points (-3,-8) and (5,6)	Find the slope of the line passing through the points $(- 3, - 8)$ and $(5, 6)$
50064	関数演算を解く	f(x)=3x Find f^-1(x)	$f (x) = 3 x$ Find $f^{- 1} (x)$
50065	関数演算を解く	f(x)=9-3x g(x)=5x-7 Find f(x)+g(x)	$f (x) = 9 - 3 x$ $g (x) = 5 x - 7$ Find $f (x) + g (x)$
50066	漸近線を求める	f(x)=((x^2-81)(2+x))/((x^2-4)(9+x))	$f (x) = \frac{(x^{2} - 81) (2 + x)}{(x^{2} - 4) (9 + x)}$
50067	定義域を求める	f(x) = log base x of 5-x	$f (x) = \log_{x} (5 - x)$
50068	関数演算を解く	Given that f(x)=x^2-10x+16 and g(x)=x-8 ; find (f-g)(x) and express the result in standard form.	Given that $f (x) = x^{2} - 10 x + 16$ and $g (x) = x - 8$ ; find $(f - g) (x)$ and express the result in standard form.
50069	定義域を求める	f(x)＝x-の平方根x+2の平方根	$f (x) = \sqrt{x - \sqrt{x + 2}}$
50070	関数演算を解く	For what value of x is the expression (2x-6)/(x-3) undefined?	For what value of $x$ is the expression $\frac{2 x - 6}{x - 3}$ undefined?
50071	漸近線を求める	(3(2x+7)(x+8))/(x+1)	$\frac{3 (2 x + 7) (x + 8)}{x + 1}$
50072	関数演算を解く	f(x)=(x^(1/3))/6+7 ; find f^-1(x)	$f (x) = \frac{x^{\frac{1}{3}}}{6} + 7$ ; find $f^{- 1} (x)$
50073	関数演算を解く	Given that f(x)=x^2-13x+30 and g(x)=x-3 ; find (f-g)(x) and express the result in standard form.	Given that $f (x) = x^{2} - 13 x + 30$ and $g (x) = x - 3$ ; find $(f - g) (x)$ and express the result in standard form.
50074	関数演算を解く	f(x)=(x^(1/3))/5+7 ; find f^-1(x)	$f (x) = \frac{x^{\frac{1}{3}}}{5} + 7$ ; find $f^{- 1} (x)$
50075	傾きを求める	What is the slope of the line through (-1,-7) and (3,9) ?	What is the slope of the line through $(- 1, - 7)$ and $(3, 9)$ ?
50076	漸近線を求める	f(x)=(10x^3+2x^2+5x+6)/(5x^3+x^2+9x+11)	$f (x) = \frac{10 x^{3} + 2 x^{2} + 5 x + 6}{5 x^{3} + x^{2} + 9 x + 11}$
50077	漸近線を求める	y=(x-10)/(x^3-125)	$y = \frac{x - 10}{x^{3} - 125}$
50078	頂点を求める	1/4y^2=x	$\frac{1}{4} y^{2} = x$
50079	最大公約数を求める	-(n+6)^4 , -3(n+6)^3 , -3(n+6)^6	$- {(n + 6)}^{4}$ , $- 3 {(n + 6)}^{3}$ , $- 3 {(n + 6)}^{6}$
50080	関数演算を解く	(1/2)(10t)=50 , 0	$(\frac{1}{2}) (10 t) = 50$ , $0$
50081	関数演算を解く	h(x)=-9-x , h(2k-5)	$h (x) = - 9 - x$ , $h (2 k - 5)$
50082	定義域を求める	f(x) = square root of 2x-a+b+3	$f (x) = \sqrt{2 x - a} + b + 3$
50083	最大公約数を求める	18 and 12	$18$ and $12$
50084	関数演算を解く	g(x)=x^2-3x h(x)=2x-2 Find (g-h)(-9)	$g (x) = x^{2} - 3 x$ $h (x) = 2 x - 2$ Find $(g - h) (- 9)$
50085	傾きを求める	(4,5) and (-3,8)	$(4, 5)$ and $(- 3, 8)$
50086	定義域を求める	(3x+5)/(35x)+(x-3)/(21x)	$\frac{3 x + 5}{35 x} + \frac{x - 3}{21 x}$
50087	関数演算を解く	Given that f(x)=x^2-12x+27 and g(x)=x-9 ; find f(x)*g(x) and express the result in standard form.	Given that $f (x) = x^{2} - 12 x + 27$ and $g (x) = x - 9$ ; find $f (x) \cdot g (x)$ and express the result in standard form.
50088	傾きを求める	(-1,-7) and (-2,-5)	$(- 1, - 7)$ and $(- 2, - 5)$
50089	関数演算を解く	f(x)=x^3 , (f(a+h)-f(a))/h	$f (x) = x^{3}$ , $\frac{f (a + h) - f (a)}{h}$
50090	定義域を求める	F(x) = square root of x^2+2	$F (x) = \sqrt{x^{2} + 2}$
50091	関数演算を解く	If P(x)=x^2+x+5 ; find P(7)	If $P (x) = x^{2} + x + 5$ ; find $P (7)$
50092	傾きを求める	x+y-1=0	$x + y - 1 = 0$
50093	定義域を求める	1/(( x)/(x^2-4))の平方根	$\frac{1}{\frac{\sqrt{x}}{x^{2} - 4}}$
50094	定義域を求める	f(x)=( 2-x)/(x^2-4x+3)の平方根	$f (x) = \frac{\sqrt{2 - x}}{x^{2} - 4 x + 3}$
50095	定義域を求める	(5a)/(a-b)+(5b)/(b-a)	$\frac{5 a}{a - b} + \frac{5 b}{b - a}$
50096	傾きを求める	(3,5) and (2,0)	$(3, 5)$ and $(2, 0)$
50097	漸近線を求める	((2x+1)(x-2))/(x(2x+1))	$\frac{(2 x + 1) (x - 2)}{x (2 x + 1)}$
50098	定義域を求める	( x+1-1)/xの平方根	$\frac{\sqrt{x + 1} - 1}{x}$
50099	関数演算を解く	What number a is 0.4% of 40 ?	What number a is $0.4 %$ of $40$ ?
50100	関数演算を解く	f(x)=6x^5-1 ; find f^-1(x)	$f (x) = 6 x^{5} - 1$ ; find $f^{- 1} (x)$