{"id":336,"date":"2026-05-05T04:40:16","date_gmt":"2026-05-05T04:40:16","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/bo-de-on-tap-kiem-tra-giua-hoc-ki-2-mon-toan-11-theo-cau-truc-moi-4-phan\/"},"modified":"2026-05-05T07:13:00","modified_gmt":"2026-05-05T07:13:00","slug":"bo-de-on-tap-kiem-tra-giua-hoc-ki-2-mon-toan-11-theo-cau-truc-moi-4-phan","status":"publish","type":"post","link":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/bo-de-on-tap-kiem-tra-giua-hoc-ki-2-mon-toan-11-theo-cau-truc-moi-4-phan\/","title":{"rendered":"B\u1ed9 \u0111\u1ec1 \u00f4n t\u1eadp ki\u1ec3m tra gi\u1eefa h\u1ecdc k\u00ec 2 m\u00f4n To\u00e1n 11 theo c\u1ea5u tr\u00fac m\u1edbi (4 ph\u1ea7n) 3 b\u1ed9 s\u00e1ch"},"content":{"rendered":"

B\u1ed9 \u0111\u1ec1 \u00f4n t\u1eadp ki\u1ec3m tra gi\u1eefa h\u1ecdc k\u00ec 2 m\u00f4n To\u00e1n 11 theo c\u1ea5u tr\u00fac m\u1edbi (4 ph\u1ea7n)<\/strong>\u00a0s\u1ebd gi\u00fap c\u00e1c b\u1ea1n h\u1ecdc sinh 11 h\u1ec7 th\u1ed1ng l\u1ea1i ki\u1ebfn th\u1ee9c To\u00e1n gi\u1eefa h\u1ecdc k\u1ef3 2 v\u00e0 r\u00e8n luy\u1ec7n k\u1ef9 n\u0103ng gi\u1ea3i b\u00e0i t\u1eadp theo t\u1eebng chuy\u00ean \u0111\u1ec1. V\u1edbi n\u1ed9i dung b\u00e1m s\u00e1t ch\u01b0\u01a1ng tr\u00ecnh h\u1ecdc \u0111\u01b0\u1ee3c bi\u00ean so\u1ea1n b\u1edfi th\u1ea7y gi\u00e1o Ph\u1ea1m L\u00ea Duy, \u0111\u00e2y l\u00e0 b\u1ed9 t\u00e0i li\u1ec7u h\u1eefu \u00edch gi\u00fap b\u1ea1n t\u1ef1 tin \u0111\u1ea1t \u0111i\u1ec3m cao trong b\u00e0i ki\u1ec3m tra. C\u00f9ng t\u00ecm hi\u1ec3u v\u1edbi tailieuonthi<\/a><\/strong> qua b\u00e0i vi\u1ebft sau \u0111\u00e2y n\u00e0o!<\/p>\n

N\u1ed9i dung B\u1ed9 \u0111\u1ec1 \u00f4n t\u1eadp ki\u1ec3m tra gi\u1eefa h\u1ecdc k\u00ec 2 m\u00f4n To\u00e1n 11 theo c\u1ea5u tr\u00fac m\u1edbi (4 ph\u1ea7n)<\/strong><\/h2>\n

N\u1ed9i dung B\u1ed9 \u0111\u1ec1 \u00f4n t\u1eadp ki\u1ec3m tra gi\u1eefa h\u1ecdc k\u1ef3 2 m\u00f4n To\u00e1n 11 theo c\u1ea5u tr\u00fac m\u1edbi (4 ph\u1ea7n)<\/strong> d\u00e0i 71 trang bao g\u1ed3m c\u00e1c t\u1eadp \u0111\u1ec1 \u00f4n t\u1eadp ki\u1ec3m tra To\u00e1n 11 gi\u1eefa k\u1ef3 2 theo c\u1ea5u tr\u00fac m\u1edbi \u0111\u01b0\u1ee3c tr\u00edch t\u1eeb 3 b\u1ed9 s\u00e1ch l\u1edbn. Ki\u1ebfn th\u1ee9c tr\u1ea3i d\u00e0i t\u1eeb c\u00e1c d\u1ea1ng b\u00e0i t\u1eadp d\u1ec5 \u0111\u1ebfn n\u00e2ng cao v\u1edbi ki\u1ebfn th\u1ee9c \u0111\u1ea1o h\u00e0m, gi\u1ea3i t\u00edch, x\u00e1c su\u1ea5t t\u1ed5 h\u1ee3p, h\u00ecnh h\u1ecdc kh\u00f4ng gian,\u2026C\u1ea5u tr\u00fac \u0111\u1ec1 \u00f4n t\u1eadp chi ti\u1ebft nh\u01b0 sau:<\/p>\n

+ Ph\u1ea7n 1. Tr\u1eafc nghi\u1ec7m nhi\u1ec1u l\u1ef1a ch\u1ecdn<\/strong><\/span><\/p>\n

Tham kh\u1ea3o m\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi trong \u0111\u1ec1 nh\u01b0 sau:<\/p>\n

C\u00e2u 1.<\/strong> Cho hai bi\u1ebfn c\u1ed1 A v\u00e0 B l\u00e0 hai bi\u1ebfn c\u1ed1 xung kh\u1eafc. Bi\u1ebft P(A) = 1\/4 , P(A cup B) = 1\/2 . T\u00ednh P(B) <\/p>\n

A.<\/strong> 1\/8 \u00a0 \u00a0 \u00a0 \u00a0 B.<\/strong> 1\/4 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 C.<\/strong> 1\/3 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 D.<\/strong> 3\/4 <\/p>\n

C\u00e2u 2.<\/strong> M\u1ed9t chi\u1ebfc m\u00e1y c\u00f3 hai chi\u1ebfc \u0111\u1ed9ng c\u01a1 I v\u00e0 II ch\u1ea1y \u0111\u1ed9c l\u1eadp nhau. X\u00e1c su\u1ea5t \u0111\u1ec3 \u0111\u1ed9ng c\u01a1 I v\u00e0 II ch\u1ea1y t\u1ed1t l\u1ea7n l\u01b0\u1ee3t l\u00e0 0,8 v\u00e0 0,7 . X\u00e1c su\u1ea5t \u0111\u1ec3 c\u1ea3 hai \u0111\u1ed9ng c\u01a1 ch\u1ea1y t\u1ed1t l\u00e0:<\/p>\n

A.<\/strong> 0,24 \u00a0 \u00a0 \u00a0 \u00a0 B.<\/strong> 0,94 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0C.<\/strong> 0,14 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 D.<\/strong> 0,56 <\/p>\n

C\u00e2u 3.<\/strong> Cho a > 0 ; a \u2260 1 ; m, n in mathbbZ ; n \u2260 0 . Ch\u1ecdn \u0111\u1eb3ng th\u1ee9c \u0111\u00fang.<\/p>\n

A.<\/strong> (a^m)\u207f = a^m+n \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B.<\/strong> a^m\/n = \u221a[n]a^m <\/p>\n

C.<\/strong> a^m a\u207f = \u221a[n]a^m \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D.<\/strong> a^m a\u207f = a^m+n <\/p>\n

C\u00e2u 4<\/strong>. Bi\u1ec3u th\u1ee9c T = \u221a[5]a \u221aa v\u1edbi a > 0 . Vi\u1ebft bi\u1ec3u th\u1ee9c T d\u01b0\u1edbi d\u1ea1ng l\u0169y th\u1eeba v\u1edbi s\u1ed1 m\u0169 h\u1eefu t\u1ec9 l\u00e0:<\/p>\n

A.<\/strong> a^3\/5 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B.<\/strong> a^2\/15 <\/p>\n

C.<\/strong> a^4\/15 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 D.<\/strong> a^3\/10 <\/p>\n

C\u00e2u 5.<\/strong> V\u1edbi m\u1ecdi s\u1ed1 th\u1ef1c a d\u01b0\u01a1ng kh\u00e1c 1 , log_a \u221a[3]a b\u1eb1ng:<\/p>\n

A.<\/strong> 1\/3 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B.<\/strong> 3 <\/p>\n

C.<\/strong> -1\/3 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D.<\/strong> -3 <\/p>\n

C\u00e2u 6.<\/strong> T\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c P = 2 log_a a + log_a (a^b) v\u1edbi a > 0, a \u2260 1 .<\/p>\n

A.<\/strong> P = 2^a + b \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B.<\/strong> P = a – b <\/p>\n

C.<\/strong> P = 2a + b \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D.<\/strong> P = a + b <\/p>\n

+ Ph\u1ea7n 2. Tr\u1eafc nghi\u1ec7m \u0111\u00fang sai<\/strong><\/span><\/p>\n

C\u00e2u 1.<\/strong> Cho x, y l\u00e0 hai s\u1ed1 th\u1ef1c d\u01b0\u01a1ng v\u00e0 m, n l\u00e0 hai s\u1ed1 th\u1ef1c t\u00f9y \u00fd. C\u00e1c m\u1ec7nh \u0111\u1ec1 sau \u0111\u00fang hay sai?<\/p>\n

a) (x^m)\u207f = (x\u207f)^m .<\/p>\n

b) x^m\u00b3 = (x^m)\u00b3 .<\/p>\n

c) log\u2083 9x = 3 + log\u2083 x .<\/p>\n

d) log_\u221a2 x + log_1\/2 (2x\u00b2y) + log\u2084 (2y\u00b2) = 1 .<\/p>\n

C\u00e2u 2.<\/strong> Cho h\u00ecnh ch\u00f3p S.ABCD c\u00f3 SA perp (ABCD) , ABCD l\u00e0 h\u00ecnh vu\u00f4ng t\u00e2m O , c\u1ea1nh AB = a , SA = a . G\u1ecdi H l\u00e0 h\u00ecnh chi\u1ebfu vu\u00f4ng g\u00f3c c\u1ee7a A tr\u00ean c\u1ea1nh SD .<\/p>\n

a) BC perp SA .<\/p>\n

b) G\u00f3c gi\u1eefa SB v\u00e0 CD b\u1eb1ng widehatSAB .<\/p>\n

c) AC perp (SBD) .<\/p>\n

d) AH perp (SCD) .<\/p>\n

+ Ph\u1ea7n 3. Tr\u1eafc nghi\u1ec7m tr\u1ea3 l\u1eddi ng\u1eafn<\/strong><\/span><\/p>\n

C\u00e1c b\u1ea1n h\u1ecdc sinh c\u00f3 th\u1ec3 tham kh\u1ea3o qua c\u00e2u h\u1ecfi sau \u0111\u1ec3 bi\u1ebft d\u1ea1ng b\u00e0i trong \u0111\u1ec1 thi th\u1eadt nh\u00e9:<\/p>\n

C\u00e2u 3.<\/strong> Trong n\u00f4ng nghi\u1ec7p, b\u00e8o hoa d\u00e2u \u0111\u01b0\u1ee3c d\u00f9ng l\u00e0m ph\u00e2n b\u00f3n, n\u00f3 r\u1ea5t t\u1ed1t cho c\u00e2y tr\u1ed3ng. M\u1edbi \u0111\u00e2y, c\u00e1c nh\u00e0 khoa h\u1ecdc Vi\u1ec7t Nam \u0111\u00e3 ph\u00e1t hi\u1ec7n ra b\u00e8o hoa d\u00e2u c\u00f3 th\u1ec3 d\u00f9ng \u0111\u1ec3 chi\u1ebft xu\u1ea5t ra ch\u1ea5t c\u00f3 t\u00e1c d\u1ee5ng k\u00edch th\u00edch h\u1ec7 mi\u1ec5n d\u1ecbch v\u00e0 h\u1ed7 tr\u1ee3 \u0111i\u1ec1u tr\u1ecb b\u1ec7nh ung th\u01b0. B\u00e8o hoa d\u00e2u \u0111\u01b0\u1ee3c th\u1ea3 nu\u00f4i tr\u00ean m\u1eb7t n\u01b0\u1edbc. M\u1ed9t ng\u01b0\u1eddi \u0111\u00e3 th\u1ea3 m\u1ed9t l\u01b0\u1ee3ng b\u00e8o hoa d\u00e2u chi\u1ebfm 4% di\u1ec7n t\u00edch m\u1eb7t h\u1ed3. Bi\u1ebft r\u1eb1ng c\u1ee9 sau \u0111\u00fang m\u1ed9t tu\u1ea7n b\u00e8o ph\u00e1t tri\u1ec3n th\u00e0nh 3 l\u1ea7n s\u1ed1 l\u01b0\u1ee3ng \u0111\u00e3 c\u00f3 v\u00e0 gi\u1ea3 s\u1eed t\u1ed1c \u0111\u1ed9 ph\u00e1t tri\u1ec3n c\u1ee7a b\u00e8o \u1edf m\u1ecdi th\u1eddi \u0111i\u1ec3m nh\u01b0 nhau. H\u1ecfi sau \u00edt nh\u1ea5t bao nhi\u00eau ng\u00e0y b\u00e8o s\u1ebd v\u1eeba ph\u1ee7 k\u00edn m\u1eb7t h\u1ed3?<\/p>\n

+ Ph\u1ea7n 4. T\u1ef1 lu\u1eadn<\/strong><\/span><\/p>\n

Ph\u1ea7n n\u00e0y th\u01b0\u1eddng chi\u1ebfm kh\u00e1 nhi\u1ec1u th\u1eddi gian c\u1ee7a c\u00e1c b\u1ea1n h\u1ecdc sinh, c\u00e1c c\u00e2u h\u1ecfi t\u1ef1 lu\u1eadn \u0111\u00f2i h\u1ecfi t\u01b0 duy nh\u1ea1y b\u00e9n, kh\u1ea3 n\u0103ng gi\u1ea3i \u0111\u1ec1 t\u1ed1t. B\u1ea1n c\u00f3 th\u1ec3 xem qua d\u1ea1ng c\u00e2u h\u1ecfi t\u1ef1 lu\u1eadn sau \u0111\u00e2y:<\/p>\n

C\u00e2u 1.<\/strong> C\u01b0\u1eddng \u0111\u1ed9 \u00e2m thanh L (\u0111\u01a1n v\u1ecb: decibel, dB) \u0111\u01b0\u1ee3c t\u00ednh b\u1eb1ng c\u00f4ng th\u1ee9c L = 10 \u00b7 log ( (I)\/(I\u2080) ).
\nTrong \u0111\u00f3:<\/p>\n

\u2013 I l\u00e0 m\u1ee9c c\u01b0\u1eddng \u0111\u1ed9 \u00e2m thanh \u0111o \u0111\u01b0\u1ee3c (\u0111\u01a1n v\u1ecb: W\/m \u00b2 ).<\/p>\n

\u2013 I\u2080 l\u00e0 m\u1ee9c c\u01b0\u1eddng \u0111\u1ed9 \u00e2m thanh chu\u1ea9n (th\u01b0\u1eddng l\u00e0 10\u207b\u00b9\u00b2 W\/m \u00b2 ). Gi\u1ea3 s\u1eed b\u1ea1n \u0111\u1ee9ng g\u1ea7n m\u1ed9t ngu\u1ed3n \u00e2m thanh v\u00e0 \u0111o \u0111\u01b0\u1ee3c c\u01b0\u1eddng \u0111\u1ed9 \u00e2m thanh l\u00e0 80 dB. N\u1ebfu b\u1ea1n di chuy\u1ec3n xa h\u01a1n ngu\u1ed3n \u00e2m thanh l\u00e0m m\u1ee9c c\u01b0\u1eddng \u0111\u1ed9 \u00e2m thanh gi\u1ea3m \u0111i 10 l\u1ea7n, h\u00e3y t\u00ednh c\u01b0\u1eddng \u0111\u1ed9 \u00e2m thanh m\u1edbi m\u00e0 b\u1ea1n nghe \u0111\u01b0\u1ee3c.<\/p>\n

C\u00e2u 2<\/strong>. \u0110\u1ea1i Kim t\u1ef1 th\u00e1p Giza c\u00f3 chi\u1ec1u cao 138,5 m v\u00e0 \u0111\u1ed9 d\u00e0i c\u00e1c c\u1ea1nh \u0111\u00e1y l\u00e0 230,33 m. Xem Kim t\u1ef1 th\u00e1p n\u00e0y l\u00e0 m\u1ed9t h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u S.ABCD c\u00f3 O l\u00e0 t\u00e2m c\u1ee7a \u0111\u00e1y. M\u1ed9t \u0111o\u00e0n th\u00e1m hi\u1ec3m \u0111\u00e3 \u0111i \u0111\u1ebfn \u0111\u01b0\u1ee3c t\u00e2m O c\u1ee7a Kim t\u1ef1 th\u00e1p v\u00e0 nh\u1eadn th\u1ea5y \u1edf m\u1ed7i m\u1eb7t b\u00ean c\u1ee7a kim t\u1ef1 th\u00e1p \u0111\u1ec1u c\u00f3 m\u1ed9t \u00f4 c\u1eeda tr\u1ed1ng, v\u00e0 t\u1eeb v\u1ecb tr\u00ed c\u1ee7a h\u1ecd \u0111\u1ebfn v\u1edbi \u00f4 c\u1eeda \u0111\u00f3 th\u00ec s\u1ebd vu\u00f4ng g\u00f3c v\u1edbi c\u00e1c m\u1eb7t b\u00ean c\u1ee7a kim t\u1ef1 th\u00e1p. V\u1eady kho\u1ea3ng c\u00e1ch t\u1eeb v\u1ecb tr\u00ed \u0111ang \u0111\u1ee9ng c\u1ee7a \u0111o\u00e0n th\u00e1m hi\u1ec3m \u0111\u1ebfn \u00f4 c\u1eeda l\u00e0 bao nhi\u00eau?(K\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n \u0111\u1ebfn h\u00e0ng th\u1eadp ph\u00e2n)<\/p>\n

T\u1ea3i B\u1ed9 \u0111\u1ec1 \u00f4n t\u1eadp ki\u1ec3m tra gi\u1eefa h\u1ecdc k\u00ec 2 m\u00f4n To\u00e1n 11 theo c\u1ea5u tr\u00fac m\u1edbi (4 ph\u1ea7n)<\/strong><\/h2>\n

B\u1ed9 \u0111\u1ec1 \u00f4n t\u1eadp ki\u1ec3m tra gi\u1eefa h\u1ecdc k\u00ec 2 m\u00f4n To\u00e1n 11 theo c\u1ea5u tr\u00fac m\u1edbi (4 ph\u1ea7n) l\u00e0 t\u1eadp h\u1ee3p c\u00e1c d\u1ea1ng b\u00e0i t\u1eadp chi ti\u1ebft theo c\u1ea5u tr\u00fac m\u1edbi nh\u1ea5t, gi\u00fap h\u1ecdc sinh d\u1ec5 d\u00e0ng \u00f4n t\u1eadp v\u00e0 r\u00e8n luy\u1ec7n m\u1ed7i ng\u00e0y tr\u01b0\u1edbc k\u1ef3 thi. T\u1ea3i ngay B\u1ed9 \u0111\u1ec1 \u00f4n t\u1eadp ki\u1ec3m tra gi\u1eefa h\u1ecdc k\u00ec 2 m\u00f4n To\u00e1n 11 theo c\u1ea5u tr\u00fac m\u1edbi (4 ph\u1ea7n)<\/strong> qua \u0111\u01b0\u1eddng link sau. V\u00e0 \u0111\u00e2y c\u0169ng ch\u00ednh l\u00e0 ch\u00eca kh\u00f3a gi\u00fap b\u1ea1n chinh ph\u1ee5c t\u1ed1t k\u1ef3 thi h\u1ecdc gi\u1eefa k\u1ef3 2 s\u1eafp t\u1edbi.<\/p>\n