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4 xy 2 C : y = (x a) 2 + b D : y = x 2 (1) C D 2 2 x 1 a, b C (a, b) (2) a, b (1) C D 2 y = x (18 1) 2 n 2 a 1 1 n 1 n 1 a a n p(a) (1) p(1) p(n) (2) p(2) (3) p(n 1) 3 a 0 < a < 4 xy l : y = ax { x 2 + 4x (x < 4 ) C : y = 9a(x 4) (x 4 ) C l S(a) (1) C l (2) S(a) (3) S(a) (18 2) (18 3) 4 ABCD AB M CD N t 0 G GA + GB + (t 2) GC + t GD = 0 (1) DG DA DB DC (2) G N (3) NG MC (18 4)

5 xy x, y (x, y) m y = x 2 2mx + m 2 x y D (1) D L m m (2) D T m m (3) T m m 3 L m m 2 k 2 < k 3 {a n }, {b n } a 1 = b 1 = 2 n 1 x x 4 a n x 2 b n + k = 0 a n+1 b n+1 (1) 2 < k < 3 a 2, b 2, a 3, b 3 (2) {a n }, {b n } ( ) (1) 2 (2) 3 (3) 3 4 (a, b, c) a 2 + b 2 = c 2

6 2018 (1) a, b, c (2) a, b, c (18 4)

7 s ABC AB s : 1 D BC s : 3 E CD AE F (1) AF = α AB + β AC α β (2) F AC FG FG s 2 p, q f(x) = x 2 + px + q 1 x 2 0 (p, q) D (1) pq D (2) D (p, q) q 5 3 a 3 a 3 b c (1) c = 2 2a + 1 = as + 3t s, t b (2) n n 2a 2 n = as + 3t s, t 4 A B (1) A B 0 3 (2) A B

8 xy 1 C a b D : y = x 2 + ax + b (p, q) C (1) (p, q) = (cos θ, sin θ) (0 θ < 2π) a b θ (2) D x = 1 C 2 a, b (a, b) (3) D C 2 a, b (a, b) 2 a z = x + yi (x, y ) z = x yi z 3 = z + a ( ) i (1) a = 0 ( ) z (2) ( ) z 5 a 3 n, k 3 k < n k (n k) p(n, k) (1) p(n, k) (2) n 3 6 n k 3 k < n p(n, k) k 4 n (1) 2x + 2y + z = n x, y, z n = 4 n = 5 (2) 2x + 2y + z = n x, y, z n (3) 2x + 2y + z n x, y, z n

9 O 3 A(3, 1) B(1, 2) C( 1, 1) s, t P OP = s OA + t OB (1) s, t 1 s 1, 1 t 1, 1 s + t 1 P(x, y) D (2) P (1) D OP OC P 2 C : y = 1 2 x2 (16 1) (1) y = 2 x + k C k (2) a, b y = 2 x a + b C 4 (a, b) D xy (3) (2) D 3 A B C A B C l, m, n (l, m, n) 4 ABC A B C AD BE CF H (1) BCEF AFHE (2) ADE = ADF

10 a, b, c abc = 1 (1) (2) (1) a 2 + b 2 + c 2 1 a + 1 b + 1 c a + b + c (2) a + b + c 3 2 { x 2 + y 2 1 y x 2 1 D (1) D (2) y = k(x + 2) 2 D k A 6 B B A 4 xy O(0, 0) A(1, 0) B ( 0, 3 ) C( 1, 0) 0 < t < 1 AB t : 1 t P BC t : 1 t Q θ = POQ (1) T = t(1 t) cos θ T (2) t 0 < t < 1 θ

11 {a n } a 1 = 3 a n+1 > a n (n = 1, 2, 3, ) a n 2 2a n a n+1 + a n+1 2 = 3(a n + a n+1 ) (n = 1, 2, 3, ) (1) n = 1, 2, 3, a n + a n+2 a n+1 (2) b n = a n+1 a n (n = 1, 2, 3, ) {b n } (3) {a n } 2 t > 0 3 A( 2, 0) B(2, 0) P ( t, 3t ) ABP (1) ABP t (2) ABP (3) AB BP PA M Q R t (1) ABP MQ QR RM t 3 3 p 1, p 2, p 3 x 2 2p 1 x 2 + p 2 x + 2p 3 = 0 ( ) (1) ( ) (2) ( ) 2 α, β αβ = 1 4 a > 0 f(t) = 4t 3 + (a + 3)t 0 t 1 M(a) (1) M(a) (2) x > 0 g(x) = M(x) 2 xy y = g(x) (s, g(s)) s > 0 (3) a k = M(a) a

12 a, b, c ( O(0, 0, 0), A(2, 1, 1), B(1, 2, 3), C(a, b, c), M 1, P 4 OP 2 + AP BP CP 2 = 30 ) 1 2, 1 M a, b, c 2 a xy y = x 2 y = x 2 + 2ax a C 1, C 2 (1) C 1 C 2 a (2) a (1) C 1 C 2 2 (3) a (1) C 1 C a, b, c, d (1) ab + cd = 6 (2) ab cd = 1 4 xy D y x 2 1, x y 6 5 (1) D (2) D

13 C : y = x 2 P ( a, a 2) l 1 Q ( b, b 2) l 2 a < b l 1 l 2 R PR QR C S (1) R a b (2) S a b (3) l 1 l 2 S 2 1, 2, 3, 4, (1) (2) (3) t OAB OA 2 : 1 M OB t : 1 N AN BM P (1) OP OA, OB t (2) OP BM AOB OA OB t 4 x, y A = 2 sin x + sin y, (1) cos(x y) A, B B = 2 cos x + cos y (2) x, y A = 1 B sin x, cos x

14 xy log 10 ( 10 x 10 y 10 2 a, b x 103x y y A(6, 0, 0), B(0, 6, 0), C(0, 0, 3), P(2a, 0, 1 + 2a), Q(0, 2b, 1 4b) ) 0 PQ M ABC G (1) ABC MG a, b (2) MG a, b 3 1 : C : y = x 2 2 l ( i ) C l 2 (ii) C l 36

15 a (1) 2 x 2 2(a + 1)x + 3a = 0 1 x 3 2 a (2) a (1) y = x 2 2(a + 1)x + 3a y 2 OABC OA = OB = OC = 1 AOB = 60 BOC = 45 COA = 45 a = OA, b = OB, c = OC C OAB H (1) OH a b (2) CH (3) OABC 3 A B A (1) B 1 B (2) B 2 B (3) B 2 4 t 0 t 1 y = x 2 x = 1 x A y = 4(x t) 2 y = 1 B A B S(t) (1) S(t) (2) 0 t 1 S(t)

16 a 1 a 2 C : y = x 2 ax a D : y = ax 2 + ax (1) 2 C D 2 a (2) a (1) C D 2 m m a m 2 2 4x 2 + 2x 1 = 0 2 α, β (α > β) (1) α = cos θ θ π 3 θ π 1 2 (2) (1) θ β = cos 2θ (3) (1) θ 3 1, 2, 3, 4, n p n (1) p 1, p 2 (2) n 3 p n n OABC OA 3 : 1 D OB 2 : 1 E AC 2 : 1 F 3 D, E, F α α BC G (1) OG OB OC (2) EFG

17 a a \= 1 ( ) 2 C : y = x2 2 P 1 2, 1 4 Q ( a, a 2) P P C l Q Q C m l m C (1) a (2) 2 l, m C y 2 f(x) f(x) = 2 cos 2 x 2 3 sin x cos x sin x + 3 cos x 5 4 (1) t = sin x + 3 cos x f(x) t (2) x 0 x 90 t (3) x 0 x 90 f(x) f(x) x 60 < x < 75 3 A B 1 N N (1) N = 4 A, B 1 4 X X = 1, X = 2, X = 3, X = 4 X (2) N = 3 n A, B 1 n p n n q n p n q n 4 a, b a = b = 1, a b = 1 2 a b a b (1) p, q c = p a + q b c = 1, a c = 0, p > 0 p, q

18 2012 (2) x 1 a x 1, 1 b x 2 x (1) x, y 4 x 4 2 x + 9 y 2 3 y 1 2 x + 3 y (2) x, y 4 x 2 2 x + 2 y 0 x + y 2 x f(x) f(x) = (1) x 0 f(x) x x 2 2x + 3 (2) x f(x) p, q f(x) = q p q 3 x 3 1, 2, 3, 4, , 2, 3, 4, 5 (1) 2 (2) (3) A(0, 0, 1) B(3, 1, 1) C(1, 4, 4) D(1, 1, 2) A AD L 2 B, C M (1) M L L H H (2) P L PB PC 2 PB 2 + PC 2

19 (1) x { x x + a 3 x 1 a (2) x 1 x 3 x + a 3 x a a 2 OAB AB 1 : 2 C D OD = x OA (x 1) CD OB E (1) y OE = y OB 2 x + 1 y = 3 (2) OAB S ODE T S T x 3 3 A B C A 2 3 B C (1) 2 A 2 (2) 2 B 1 4 y = x 2 2 l, m (1) l (a, a 2 ) l, m a (2) l, m y l, m y = x

20 f(x) = x 3 (1) 0 a < x < y a, x, y f(x) f(a) x a < f(y) f(x) y x (2) y < x < b x, y f(x) > (x y)f(b) + (b x)f(y) b y b 2 C : y = x 2 (1) C P ( a, a 2) P C l (2) l (1) a \= 0 x = a l m (3) (2) m a F F 3 P 2 2 P 1 2 P 1 P O n S n (1) S 2 = 1 (2) S 3 = 1 (3) n i S n (4) k S n = k 4 ABCD AB M CD N (1) PA + PB = PC + PD P (2) Q QA + QB = QC + QD Q

21 2010 (3) R RA 2 + RB 2 = RC 2 + RD 2 MN MR R (4) (2) Q (3) R AB = CD n 2 x 1,, x n, y 1,, y n x 1 > x 2 > > x n, y 1 > y 2 > > y n z 1,, z n y 1,, y n n (x i y i ) 2 n (x i z i ) 2 i=1 i=1 2 OAB OA 1 : 1 M OB 2 : 1 N AN BM P (1) OP OA OB (2) OA = 1 OA l OB m ABP l, m OA OB 3 n n 2 (1) 1 (0 1 ) (2) k (1 k n) t k a k = t k k 1 m n 1 a 1 a 2 a m, a m > a m+1 p m (3) n 1 mp m m=1 4 xy ( 1, 0) (0, 1) (1, 4) y = f(x) 1 1 {f(x) (a x + b)} 2 dx a, b

22 x 2 2x x a + 1 a > 0 a 2 AB 1 A ABC BC C B D AD AB t (1) t (2) AD AC = CD CA t (1) 4 (2) 8 (3) 8 4 2y > x x 1 D a C y = x 2 2ax + a 2 + a + 2 C D a

23 P (x) x 3 x 3 1 a < b c < d a, b, c, d P (x) (x a)(x b) P (x) (x c)(x d) a = c, b = d (1) 3 (2) (3) (4) 3 a y = a C 2 (1) C 1 C 2 (2) C 1 C 2 S (3) a (2) S x C 1 y = a + 1 4a x t t 0 x 2 + y 2 + 2y 1 0 A x 2 + y 2 2(t + 1)x 2t 2 y + t 4 + t 2 + 2t 1 0 B x 2 + y 2 + 2(t + 1)x 2t 2 y + t 4 + t 2 + 2t 1 0 C (1) t = 0 A, B, C A B C (2) B C 1 t (3) t (2) B C A (4) A B C t

24 a f(x) = x 3 + (2a 4)x 2 + (a 2 4a + 4)x f(x) = 0 2 (1) a (2) y = f(x) (3) a (1) y = f(x) x (x, f(x)) xy 2 a, b, c, d, e f(x) = ax 4 + bx 3 + cx 2 + dx + e ( i ) (ii) (iii) a, b, c, d, e ( ) ( i ) x 4 f 1 = f(x) x (ii) f(1 x) = f(x) (iii) f(1) = 1 3 OA 1 A 2 OA 2 A 1 = 90 OA 1 = 1 OA 2 = 1 3 A 2 OA 1 A 3 A 3 OA 2 A 4 k = 4, 5, A k OA k 1 A k+1 A 5, A 6, (1) A k A k+1 (k = 1, 2, ) (2) h k = A k A k+1 n h k h k+1 h k h k+1 n k=1 h k h k+1 4 P ( i ) (ii) ( i ) 1, 2, 3, 4, 5, 6 k P a a > 0 a k a < 0 a + k (ii) ( i ) (1) P 1, 2,, 6 2 (2) P 1, 2,, 6 3 (3) P 7 n

25 a 0 a 1 y = x a + x 1 y = x 2 a b C : y = x 2 + 2ax + b 4 O(0, 0) P(2, 4) Q(2, 5) R(0, 1) OP C OP C OPQR S(a) (1) b a a (2) C OR a S(a) a (3) a (1) S(a) 3 P A P A (1) P O 5 A (2) P O 6 2 B (3) P O < θ < π 4 m π 2 4θ cos θ sin 2mθ

26 n 2 x n x 2 6x 12 a n x + b n (1) a 2 b 2 (2) a n+1 b n+1 a n b n (3) n a n b n 2 C ABC A BC D AD DC CA A = θ (1) sin θ (2) θ < 5 12 π 2 = = xy 3 A(0, 0) B(2, 0) C ( 1, 3 ) ABC (1) 0 a 3 a P(x, a) ABC x (2) (1) a (1) x AP 2 +BP 2 +CP 2 x (3) P(x, y) ABC AP 2 + BP 2 + CP 2 P (x, y) 4 f(x) f(x) = x 2 x 2 0 f(t) dt f(x)

27 (1) sin 3 x + cos 3 x 1 (2) 0 x < 2π sin 3 x + cos 3 x + sin x = 2 x 2 ABCD ADB D AC AC E AD = a AB = b a = 1 b = 13 (1) a b (2) DE a b D C a A B b (07 ( ) 2) 3 xy 3 (0, 0) (1, 0) (0, 1) A 3 (0, 0) (b, 0) (0, 1) B (a 1, a 2 ) A (b 1, b 2 ) B (a 1 + b 1, a 2 + b 2 ) A + B (1) b = 2 A + B (2) b > 0 A + B A + B A + B A B A + B, A, B (07 ( ) 3) 4 p 0 p 1 2n a n (p) (1) a 2 (p) p p 2 (2) a 2 (p) a 1 (p) p

28 a, b, c, p, q x y P = (x + a) 2 9c 2 (y + b) 2 Q = (x + 11) (x + 11)y + 36y 2 R = x 2 + (p + 2q)xy + 2pqy 2 + 4x + (11p 14q)y 77 (1) P, Q, R (2) P Q Q R R P x, y 1 a, b, c, p, q X, Y, Z X, Y, Z AB = BC = CD = DA = AC = 1 ABCD ABCD AC 2 B C D P 2 CB CD α, α = BCD 0 < α < 120 (1) 2 A P P H AH CA CB CD α (2) AH α (3) H 2 BCD α A A B C D D P B H α C 1 2

29 x 2, y 0 xy D a y x 2 3ax + 2a 2 xy E (1) D E a (2) (1) a D E S(a) (3) (2) S(a) F (x) G(x) R(x) (1) F (x) = 0 G(x) = 0 R(x) = 0 (2) a G(x) = x 4 ax 3 2x 2 + 2(a 2)x + 4a R(x) = x 3 + x 2 (a 2 + 3a + 6)x + 2a(a + 3) G(x) R(x) S(x) F (x) = 0 G(x) = n 39 n n 6 n log 10 2 = , log 10 3 = (a, b) xy (a, b) y = x 3 x 2 2 (a, b) (1) 2 (2) 3 7 (3) S 1 S S

30 < t < 1 2 a, b e ( i ) (1 t) a + t b = e (ii) (1 t)( a + e ) = t( b + e ) x x a x b t : 1 t x e t ABCD AB = BC = r, AD = 2r CD E 3 ABC, ACE, ADE α = BAC, β = CAD (1) α = β (2) cos DAB = 3 5 sin CAE D E C β α B A (1) (2)

31 C : y = x 2 D : y = (x a) 2 + b 1 D E : y = 1 2 (x 1)2 + 1 S a, b S a 0 C : y = x 2 A(0, a) (1) 2 a (2) a (1) A 2 P Q AP AQ C (05 1) 2 m \= 0 m l l P : y = a(x b) 2 + c (1) c b m (2) l l P l b m A B 1 A B 4 ABC AB M AC N MN ABC G MG : GN = 3 : 2 (1) MG : MB AN : NC (2) D BC MD AC E AC : CE ( tex)

32 C : y = x 2 2 L : y = x D : y = (x a) 2 + b L C L 2 D L (1) b a a (2) 2 C D S(a) (3) a (2) S(a) (04 1) 2 OABC OA CB AOC OAB a = OA c = OC m = OA OC (1) m < a2 2 (2) OABC S a c m (3) OB AC D OD OA OC 3 z, w 1 z i + 1 z + i = 1 w z ±i, w 0 z x, y w u, v (1) (z w) 2 u v (2) u = 0 x = 0 (3) u > 0, v > 0, w 2 1 x u 4 A B C (1) 1 (2) 2 (3) 3 (4) n 4 n

33 C(θ) y = x 2 2 x sin 2θ cos θ 1 + cos 2θ C(θ) P(θ) C(θ) y R(θ) θ 90 < θ < 90 (1) P(θ) (2) P(θ) Q(θ) 2 a, b, c, d a a = 1, b b = 1, a b = k ( 1 < k < 1) b c = 0, c c = 1, a c > 0 a d = 0, d d = 1, b d > 0 (1) f = p a + q b f p q f, a, b k (2) c d a, b, k (3) g g = r c + s d (1) f f g k, p, q, r, s < θ < 180 z = cos θ + i sin θ w 1 (1 + z) 2 w x, y (1) x cos θ (2) x 2 + y 2 cos θ (3) x y a b c d e f g 7 (1) 2 (2) 7 a b c (3)

34 a A, B { } A = x x 2 + (1 a 2 )x + a 3 2a 2 + a 0, x { } B = x x 2 + (2a 7)x + a 2 7a + 10 < 0, x A B a 2 ABC AB = 1, AC = 2, A = 60 m, n BC CA AB m : n D E F (1) DE EF m : n (2) m, n AD EF 3 A A B B B C C 5 1. A B B C 3 2. A B C 4. A B B C A C n P (n) (03 3)

35 t = cos θ + 3 sin θ, y = 4 cos 3θ + cos 2θ 3 sin 2θ + 2 cos θ sin θ (1) cos 3θ t (2) y t (3) 0 θ 180 y θ O A B C O (1) 4 A B C (2) n C O B A C 2 C a, b : y = (x a) 2 + b y = x 2 S (1) S = 9 b a 8 (2) C : y = mx 2 + nx + p (m 0) (1) C a, b 1 C (03 2)

36 O(0, 0, 0), A(1, 0, 0), B(1, 2, 0), C(0, 2, 0), D(1, 0, 1), E(1, 2, 1), F(0, 2, 1), G(0, 0, 1) 6 P, Q, R, S, T, U (i), (ii) ( i ) t = 0 P, Q O R, S E T A U F (ii) P A Q, U C R F S, T D t = 1 A, C, F, D (1) R P, T, U (2) t PURT (3) Q, S P, T, U t (0 < t < 1) z G F R S U D E O Q P y T C x A B 4 P(s, t) O 1 Q(u, v) (1, 0) 1 P Q PQ = 1 (1) s \= 1 u v s t (2) PQ

37 a, b x 4 + (a + 2)x 3 (2a + 2)x 2 + (b + 1)x + a 3 = 0 x = 1 + i i = 1 a, b 2 0 θ 180 x f(x) 3 f(x) = x cos θ 3 x 2 sin θ x f(x) m(θ) 3 (1) θ cos θ m(θ) θ 2 (2) m(θ) θ (02 2) C B A A n 7 A n 6 B B n C 4 t 1 f(t) = 1 1 (02 3) (x t + 2)(x + t) dx t (02 4)

38 a 2 xy A(1, 0), B( 1, 0), C( 1, 1), D(1, 1) 2 2y = x 2 a S 1, S 2 (1) S 1 (2) a 1 2 a 2 S S 2 2 a m A θ θ > m 2θ 100 m 4θ (1) cos θ (2) (3) A m 3θ (02 2) (1) 4 (2) 1 5 (3) C 1 : y = x 2, C 2 : y = (x a) 2 + b (a \= 0) 1 C : y = p(x q) 2 + r (p \= 1) C i C P i (x i, y i ) x 1 P 1 P 2 a b \= x 2

39 C : y = (x + 1) 2 D : y = (x 1) C, D 2 C (01 1) 2 y = (x p) (0, 0) (1, 2) (0, 2) p (1) (2) OABC a = OA, b = OB, c = OC OA, OB, OC, BC, CA, AB L, M, N, P, Q, R p = LP, q = MQ, r = NR (1) LP, MQ, NR 1 (2) a, b, c, p, q, r (3) LP, MQ, NR X AX = LP XABC p, q, r ( tex)

40 C : y = 2x 2 + ax, D : y = 1 2 x2 + bx + c (0, 0) (2, 2) y = x a, b, c C x 0 D y = x 2 a 90 < t < 90 2 ( ) P 1 2 sin t + cos 2t, tan t, Q(sin 2t + a cos t, 3 sin t 2 cos t + a + 2) t a t 3 a b f(x) = x 2 2a x + b f(x) = 1 x N (1) a 0 N (2) N = 6 (a, b) ab 4 n n 1 1 n (1) 1 (2) M n n M n 1 (3) n = 4, (01 3)

41 ( ) x 2 + (i 2)x + 2ab + b 2 2a i = 0 a b x i = 1 2 x 2 3x + 1 > x 2 1 2x 1 x 3 a b xy 3 A( a, 0) B(0, b) C(a, 0) 0 < t < 1 t AB BC t : 1 t P(t) Q(t) P(t)Q(t) t : 1 t R(t) R(t) 0 t 1 R R(0) = A R(1) = C (1) R x y (2) 2 P(t) Q(t) l(t) l(t) R(t) R (3) ABC l(t) 0 t 1 S l(0) A B l(1) B C 4 O A 1 A A (00 4)

42 ABC = ACB = 15 ABC AB A D AD = BC (1) sin 15, cos 15, tan 15 (2) ADC = θ sin θ 2 3 x 3 (p 3)x 2 3x + p 1 = 0 3 p ( ) 3 a, b, c a 2 3b 2 = c 2 (1) a, b (2) a, b 4 (3) a b 4 4 P ( 1, 5) A, B 2 A x 1, x 1 P B y 1 y 1 P A, B 2 8 P (1) {(x, y) y = 1} (2) {(1, 1)} (3) {(x, y) x = 1, y > 1} (4) {(x, y) x > 1, y > 1}

43 α, β, γ ( 90 < α, β, γ < 90 ) tan α + tan β + tan γ = tan α tan β tan γ α + β + γ 2 a f(x) = ax {f(t)} 2 dt f(x) 1 a f(x) 3 xy x y 0 P(x y) N(P) N(P) = 2 x (2y + 1) (1) 2000 (2) n n + 1 n + 2 A B C 2 a n = 2 a (2 a + 1) ABC a 4 p 0 2 x 2 + px + 5p = 0 (1) x 2 px + 5p = 0 α, β α 5 + β 5 = p 5 p (2) x 2 px + 5p = 0 5 p

44 α β (0 < α < 90 0 < β < 90 ) tan α + 2 tan β = 3 (1) T = 1 cos 2 α + 4 cos 2 β (2) L = 1 cos α + 2 cos β 2 xy + 4 cos(α β) cos α cos β α β y x 3 3p 2 (x 2) q D 1 x 2, y 0 E E D p, q (p, q) pq ABCD G BCD H ACD AG BH O (1) AO AB AC AD (2) AO + BO + CO + DO (3) P AP 2 + BP 2 + CP 2 + DP 2 4 u 1 = (1, 0) u 2 = (0, 1) u 3 = ( 1, 1) (1) (l, m) l u 1 + m u 2 + u 3 3 (2) l + m + n 6 (l, m, n) l u 1 + m u 2 + n u 3 3

45 y = x 2 y = 1 2 x2 + 3 x + 3 S 2 S (1) S (2) y = x + k S k 2 0 < a < b m, n f(m) = log am + b m 2, g(m) = log(am ) + log(b m ) 2 f(m + n) f(m) + f(n) g(m + n) g(m) + g(n) 3 2 A (4, 0) B (0, 2) AB P x Q OPB = QPA (O : ) OP m Q x m (1) 7 2 A B 7 1 (2) {a n } a 3n = a n, a n+5 = a n, a 1 + a 2 + a 3 + a 4 + a 5 = 4, a 1 a 3 a 5 = 8 (1) a 1 a 5 (2) a 1 + a a n ( [5].tex)

46 O A B C OA = (2, 2, 2) OB = (a, 2, 1) OC = (x, y, z) OC OA OB OC l AC BC (1) l a (2) l = 1 OC 2 ABC r r = sin B sin A = sin C sin B (1) r 3 cos A + r 2 cos B + r cos C r (2) cos A cos B cos C r 3 k y = x 2 + k y = x(x 2 1) 4 (1) 6 (2) n 2 (1) a 1, a 2,, a n+1 2 j n j (A) a j a j 1 + a j k n k (B) a k a 1 + (k 1)a k+1 k (2) 1 j n + 1 j b j = 1 + j 1 n(n + 1) a j = log 2 b j a 1, a 2,, a n+1 (A) (3) ( ) n ( n n 1 ) n 1

47 x 2 + ax + b = (1) b a (2) 2 y = x 2 + ax + b 2x + y < 0 a (97 1) 2 (1) (1 + sin θ + cos θ) 2 = 2(1 + sin θ)(1 + cos θ) (2) θ (1 + sin θ)(1 + cos θ) 0 θ < 360 (97 2) 3 (1) y = x y = x(x 1) y = x 2 3x + 3 (2) y = x y = x(x 1) y = x 2 3x + 3 ( [3].tex) 4 1 n n log 10 2 = log 10 3 = (97 4A) 5 (1) 2 x 2 + ax + b = 0 2 α, β p, q x 0 = p + q, x n = pα n + qβ n (n = 1, 2, 3, ) x n+2 + ax n+1 + bx n = 0 (n = 0, 1, 2, ) (2) x 0 = 2, x 1 = 3, x n+2 = x n+1 + x n (n = 0, 1, 2, ) x n = 2 + ( ) n ( ) n (97 4B)

48 (1) θ 0 < θ < 90 sin θ 2 (log 2 32)x 2 + (log 3 9)x log 4 64 = 0 cos θ (2) θ (1) cos(2θ + 60 ) (97 1) 2 OAB 2 OA OB 3 : 1 4 : 1 C D BC AD P CD OP Q OA OB a b (1) OP a b (2) OQ a b 3 a 0 < a < 1 (1) f(x) = x x a (2) g(a) = 1 0 (97 2) x x a dx a (0 ) 2 (12 ) 1 3 ( [4-A].tex) 5 a r (r \= 1) a n = ar n 1 (n = 1, 2, 3, ) 3 a 1, a 2, a 3 ( i ) (ii) ( i ) a 1 + a 2 + a 3 = 6 (ii) a 1, a 2, a 3 a r (97 4B)

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