高等学校学習指導要領解説　数学編

5 10 15 20 25 30 35

5 1 1 10 1 1 2 4 16 15 18 18 18 19 19 20 19 19 20 1 20 2 22 25 3 23 4 24 5 26 28 28 30 28 28 1 28 2 30 3 31 35 4 33 5 34 36 36 36 40 36 1 36 2 39 3 41 4 42

45 45 45 46 5 1 46 2 48 3 49 4 50 5 51 10 52 52 52 53 1 53 15 2 55 3 57 4 58 59 59 20 59 59 1 59 2 62 3 64 25 66 66 67 69 69 30 69 70 70 70 71 35

5 10 21 15 20 17 21 25 30 30 10 20 35 40 60 21 45-1-

5 10 20 28 21 15 25 22 24 20 20 25 30 35 40 45-2-

5 10 30 49 62 15 20 25 30 35 40 45-3-

5 10 15 20 25 30 35 40 45-4-

5 10 15 20 25 30 35 40 45-5-

5 10 15 20 25 3 2 4 3 5 4 A 2 3 30 B 2 A 2 2 B 2 C 2 35 40 45-6-

5 10 15 20 25 30 35 40 45-7-

5 10 15 20 25 30 35 40 45-8-

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5 10 15 20 25 30 35 40 45-16-

5 10 15 20 25 30 35 40-17-

5 10 15 20 25 30-18-

5 10 1 2 3 4 15 20 1 2 25 3 4 30 1 35 4 40 2 45 3-19-

5 1 10 15 20 25 1 1 30 35 40 45-20-

5 10 a A 15 x x x x x x 20 1 25 30 a b 2 a 2 2ab b 2 a b 2 a 2 2ab b 2 a b a b a 2 b 2 x a x b x 2 a b x ab 35 ax b cx d acx 2 ad bc x bd 40 45 x -21-

a b a c b c a b a c b c a b a b m ma mb m m a 5 a b m ma mb m 40 10 2 15 20 25 sin cos tan b m 30 2 2 0 90 180 35 40 45-22-

5 sina cos 90 A cosa sin 90 A sin A tan A = sin 2 A cos 2 A cos A 90 180 90 10 sina sin 180 A cosa cos 180 A sin A tan A = sin 2 A cos 2 A cos A 15 a b c = = = 2R sin A sin B sinc a 2 b 2 c 2 2bc cosa b 2 c 2 a 2 2ca cosb 20 c 2 a 2 b 2 2ab cosc 3 25 30 3 35 3 40-23-

5 y ax 2 y ax 2 10 y ax 2 y ax 2 2 y = ax + bx + c 15 y ax 2 2 y = ax + bx + c -24-2 y = ax + bx + c y ax 2 20 y a x p 2 q x p p q y ax 2 f x 25 30 20cm xcm y cm 2 2 2 35 ax + bx + c = 0 y = ax + bx + c x x 2 y = ax + bx + c x 40 4 45

5 10 15 20 25 30 35 40 45 100-25-

5 1 2 3 4 10 3 15 20 25 30 35 1 + 5 (1: ) 2 (1: 2 ) 40 36 18 72 45-26-

5-27-

5 1 2 3 4 5 10 15 1 2 20 3 4 5 25 1 30 1 35 40 45 1-28-

5 10 15 i 20 1 1 1 25 30 35 3 3 2 2 3 ( a + b) = a + 3a b + 3ab + b 3 3 2 2 3 ( a b) = a 3a b + 3ab b 2 2 3 3 ( a + b)( a ab + b ) = a + b 2 2 3 3 ( a b)( a + ab + b ) = a b 40 1 3 ncr 1 45-29-

x + 1 x x 6 1 1 2 2 + 2 x + x 2 x + 4x + 3 x 1 x + x+ 1 5 10 15 x 4 2 20 x + x 2= 0 2 25 30 35 40 O ax + by + c = 0 b 0 y = ax 2 y 45-30-

5 10 ax + by + c = 0 b 0 15 20 25 30 35 3 40 45-31-

log a x 2 3 5 10 15 20 x y = 2 x 1 y = 2 25 30 2 x = 4 x 2 x = 3 x 2 x = 3 x log log 2 3 35 2 10 2 y = log x y a x = a 40 y = x -32-

5 4 10 15 3 4 20 2 180 25 30 35 40 45 3-33-

2 2 asinθ + bcosθ = a + b sin( θ + α) 5 5 10 15 20 lim 25 4 5 30 y = ax 2 35 40 f () x 4 45 4-34-

f ( x) 5 10 4 15 20 a x b f x y f x x a x t a t b x t S () t f t 25 30-35-

5 1 2 3 4 10 15 1 2 3 4 20 5 1 25 4 30 3 35 40 1 45-36-

5 10 15 1 3 4 20 2 25 1 30 35 p l x p 40 y px l c F c a 2 2 x y 1 b a c 2 + 2 = a b b 45 F a y a -37-

c F c a -38- = 1 b c a F 5 t x f t y g t 10 x a t sin t y a 1 cos t x a cos 3 t y a sin 3 t 0 t 2 1 15 P O r O OP 20 r θ r, θ x y x = r cos θ y = r sin θ 25 30 z r θ z z r cosθ isinθ z z r r cos θ θ isin θ θ z1 r1 35 cos θ θ isin θ θ z2 r2 z i 90 40 cosθ isinθ n cos nθ i sin nθ z n a x a 2 2 b y 2 2

5 2 10 15 20 25 5 30 2 35 40 r r r ( 2n + 1)( n 1) ( ) n n + 2 2-39-

a a n n 1 = + 2 a = + 1 2 n 1 a a n 2 5 n 10 15 x 1 y = x 2 20 y = x + 1 x = y 2 1 y 0 25 y 1 = + 1 1 1 u = x+ y = x u x y y = x 30 5 f () ( a+ h) f( a) f a = lim h 0 h 35 x a f x x f x sin θ lim = 1 θ 0 θ 40 2-40-

5 3 10 15 e 20 3 3 25 5 30 35 x n '=nx n-1 n n 40 45 x n '=nx n-1 n -41-

sin x sin x 1 co s h lim = 1 lim = 0 x 0 x h 0 h 5 e h ( 1 + h 1 )h e n n 1 + 1 e 10 lim ( 1 + h ) h = e 0 h 1 15 5 20 y >0 y 25 3 30 3 35 n 40-42-

5 10 4 ax b t x a θ 15 5 20 25 30 35 4 ax + b = t x = a sin θ 40 3 45-43-

5 a b y=f x x x 10 15 20-44-

5 1 2 3 10 15 20 1 3 3 25 2 3 30 2 35 40 45-45-

5 10 15 20 25 n r n r n! 30 35 40 45-46-

n A B n A n B n A B A B n A B n A n B 5 n r n! 10 5 2 n r n r n n-r n r 15 20 A A 25 30 35 40 A P ( ) ( A B) P A B P( A ) 45 A -47-

5 2 10 15 20 25 30 a b a 0 b aq r r a 35 40 45 n -48-

1 0.1 3 3 5 10 3 15 20 25 30 35 40 45-49-

5 10 15 20 25 1 2 3 2 30 35 40 45-50-

23 51 1173 23 2 3 5 51 5 1 6 5 6 30 3 0 3 1173 1 1 7 3 12 1 2 3 5 3 10 15 1 20 1 1 3 1 3 25-51-

5 1 2 3 10 15 20 1 2 3 25 2 n 30 35 40 45-52-

5 1 10 15 20 25 4 1 30 1 35 40 45-53-

5 1 1 1 4 2 4 10 15 p q p q p p n B n p k k n k p k q n k k n 20 B n p np npq X X k 5 k 1 1 5 B 5 k P( X = k ) = 5 C k 6 6 6 25 X f x a X b a b y f x x X f x 30 X X x ) 1 f ( x) = e 2 x ) f ( x) = 1 e 2 e 35 X X N 2 Y= Y N Y y Y y a X b X X 2 X 2 3 X 3-54-

n n p q p n p 5 X k n kp k q n-k k n n X N np npq X n 400 100 10 15 20 m n 1 2 X 1 X 2 X 3 X 25 n n n n X 1 X 2 X 3 X n nm m m n n n N 30 95 35 2 40-55-

5 10 n 15 an n an 20 n n n 2 25 10 15 n n 2 n n 2n 2 n 30 35 40 n 45 an + 1 = 3an + 2 a 2 3 n-1 1 = 1-56-

3 5 10 15 20 25 30 35 40 OH OA OB OC AH BC 0-57-

5 10 15 1 1 1 3 20 1 3-58-

5 1 2 10 15 20 1 25 30 35 1 40 45-59-

2 1 5 10 2 15 20 2 10 25 60 30 35 40-60-

90 5 90 10 15 20 25 30 35 40 45-61-

5 10 15 2 20 25 30 3 2 35 40 45-62-

5 10 3 15 20 19 12 14 http://www.npa.go.jp/koutsuu/kikaku84/502_shiryou. pdf 25 30 35 40-63-

A B C D E F G H A B C D E F G H 5 10 15 20 n 30 25 30 1 1 35-64-

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5 10 1, 2 15 3 1 20 2 25 3 30 35 2 2 40-66-

5 1 10 2 1 15 20 2 25 30 35 1 2 3 40 45-67-

1 5 10 2 15 3 20 1 2 2 3 25 1 3 30-68-

5 10 15 20 25 30 35 40 45-69-

5 10 15 20 25 30 35 40 3 45-70-

5 10 15 20 25 30 35 40 3 45-71-

5 10-72-