TRƯỜNG ĐẠI HỌC HÙNG VƯƠNG
KHOA TOÁN TIN
-----------------------

ĐẶNG NGỌC TÂN

XÂY DỰNG KẾ HOẠCH BÀI HỌC CHỦ ĐỀ
MẶT NÓN, MẶT TRỤ, MẶT CẦU
THEO ĐỊNH HƯỚNG TĂNG CƯỜNG TRẮC NGHIỆM
KHÁCH QUAN

KHÓA LUẬN TỐT NGHIỆP ĐẠI HỌC
Ngành: Sư phạm Toán

Phú Thọ, 2018


TRƯỜNG ĐẠI HỌC HÙNG VƯƠNG
KHOA TOÁN TIN

-----------------------

ĐẶNG NGỌC TÂN

XÂY DỰNG KẾ HOẠCH BÀI HỌC CHỦ ĐỀ MẶT
NÓN, MẶT TRỤ, MẶT CẦU THEO ĐỊNH HƯỚNG
TĂNG CƯỜNG TRẮC NGHIỆM KHÁCH QUAN

KHÓA LUẬN TỐT NGHIỆP ĐẠI HỌC
Ngành: Sư phạm Toán

NGƯỜI HƯỚNG DẪN: TS. Đặng Thị Phương Thanh

Phú Thọ, 2018


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6
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9

3. +ӑFVLQKWӵOjPFiFEjLWұSVDXWUrQOӟS
D%jLWұSWӵOXұQ
Bài WӵOX\ӋQVӕ1JѭӡLWDPXӕQWXVӱD[XQJTXDQKPӝWWzDWKjQKFәKuQK
WUөFDR


bán kính

EҵQJFiFKWKD\JҥFKӕS[XQJTXDQKErQQJRjL

WzD WKjQK ÿy &iF Nƭ Vѭ WtQK ÿѭӧF GLӋQ WtFK FiF FәQJ Fj Eӡ WUrQ WzD WKjQK
NK{QJFҫQWKD\JҥFKӕSNKRҧQJGLӋQWtFKFҫQWKD\PӛLPpWYX{QJFҫQ
YLrQJҥFK7tQKVӕYLrQJҥFKFҫQVӱGөQJÿӇWXVӱDWzDWKjQKÿy
ĈiSV͙ : .KR̫QJYLrQJ̩FK
Bài WӵOX\ӋQVӕ0ӝWEӗQFKӭDQѭӟFKuQKWUөFyFKLӅXFDR
ÿѭӡQJ WUzQ ÿi\

bán kính

1JѭӡL WD PXӕQ VѫQ EҧR YӋ [XQJ TXDQK Yj SKLD WUrQ

EӗQFKӭDQѭӟFĈӇVѫQ[RQJEӗQFKӭDQѭӟFQj\QJѭӡLWDFҫQPXDEDRQKLrX
WKQJVѫQ "%LӃWPӛLWKQJ VѫQÿѭӧFNKRҧQJ
ĈiSV͙ 9 thùng
Bài WӵOX\ӋQVӕ &KRNKӕLQyQEiQNtQKÿi\

YjFyJyFӣÿӍQKOj

+m\WtQKGLӋQWtFKFӫDWKLӃWGLӋQÿLTXDKDLÿѭӡQJVLQKYX{QJJyF
YӟLQKDX
ĈiS V͙
%jLWӵOX\ӋQVӕ7tQKGLӋQWtFK[XQJTXDQKYjWKӇWtFKNKӕLQyQWUzQ[RD\
WҥRWKjQKNKLTXD\WDPJLiFÿӅXFҥQKDTXDQKWUөFOjPӝWÿѭӡQJWUXQJWX\ӃQ
ĈiSV͙
b. Bài tұSWUҳFQJKLӋP
Câu 1. .KLTXD\PӝWWDPJLiFYX{QJTXDQKWUөFOjPӝWFҥQKJyFYX{QJWDWKX

ÿѭӧFKuQKJu"
A. Hình nón.

%+uQKWUө

C. Hình chóp.

'+uQKFҫX


10
Câu 2. Cho hình thang

ÿi\ OӟQ

.ҿ ÿѭӡQJ FDR

4XD\KuQKWKDQJTXDQKWUөF

thang,

FӫD KuQK

WDÿѭӧF

$0ӝWKuQKWUө

%0ӝWKuQKQyQFөW

&0ӝWKuQKFҫX


'0ӝWKuQKQyQ

Câu 3. 1ӃXWăQJFKLӅXFDRFӫDKuQKWUөOrQEӕQOҫQÿӗQJWKӡLJLҧPEiQNtQK
ÿi\FӫDNKӕLWUөÿy[XӕQJKDLOҫQWKuWKӇWtFKNKӕLWUө
$*LҧPKDLOҫQ

%.K{QJÿәL

&7ăQJKDLOҫQ

'7ăQJEӕQOҫQ

Câu 4. 1ӃX WăQJ EiQ NtQK ÿi\ FӫD PӝW KuQK QyQ OrQ 3 OҫQ ÿӗQJ WKӡL JLҧP
FKLӅXFDRFӫDKuQKQyQÿyÿL3 OҫQWKuWKӇWtFKFӫDNKӕLQyQ
$*LҧPOҫQ

%.K{QJÿәL

&7ăQJOҫQ

'7ăQJOҫQ
Fyÿi\OjWDPJLiFYX{QJWҥL

Câu 5. Cho hình chóp

vng góc

YӟLÿi\7kPPһWFҫXQJRҥLWLӃSOj
$7UXQJÿLӇPFҥnh


$7UXQJÿLӇPFҥnh

$7UXQJÿLӇPFҥQh

'7UӑQJWkPKuQKFKyS

&%¬,7Ұ39ӄ1+¬
%jLWұSWӵOXұQ
%jLWұSVӕTính EiQNtQKYjWKӇWtFKPһWWUөQJRҥLWLӃSKuQKOăQJWUөWDP
JLiFÿӅXFҥQK

&KLӅXFDROăQJWUөOj

ĈiSV͙
%jL WұS Vӕ . 7URQJ PһW SKҷQJ
*ӑL
YӟL

WҥL

FKR ÿѭӡQJ WUzQ

OjPӝWÿLӇPGLÿӝQJWUrQÿѭӡQJWUzQ.ҿ
'ӵQJ ÿѭӡQJ WKҷQJ YX{QJ JyF YӟL

WKҷQJÿyOҩ\ÿLӇP

sao cho


PһWFҫXQJRҥLWLӃSWӭGLӋQ
ĈiSV͙ %iQNtQKOͣQQK̭WOj

WҥL

ÿѭӡQJ NtQK
vuông góc
7UrQ ÿѭӡQJ

Tính gii WUӏOӟQQKҩWFӫDEiQNtQK


11
%jLWұSVӕ&ҳWKuQKQyQÿӍQK

EӣLPһWSKҷQJÿLTXDWUөFWDÿѭӧFPӝWWDP

JLiFYX{QJFkQFyFҥQKKX\ӅQEҵQJ
a) Tính GLӋQWtFK[XQJTXDQKGLӋQWtFKÿi\YjWKӇWtFKFӫDNKӕLQyQÿy.
b) Cho dây cung

FӫD ÿѭӡQJ WUzQ ÿi\ KuQK QyQ VDR FKR PһW SKҷQJ

WҥRYӟLPһWSKҷQJFKӭDÿi\KuQKQyQPӝWJyF

TíQKGLӋQWtFKWDP

giác
ĈiSV͙
a)

b)
%jL WұS Vӕ  4. 7URQJ NK{QJ JLDQ FKR KDL ÿLӇP
*ӑL

OjPӝWÿѭӡQJWKҷQJWKD\ÿәLOX{QOX{QÿLTXD

PӝWNKRҧQJEҵQJ

cách

Fӕ ÿӏQK Yj Fy ÿӝ GjL

&KӭQJWӓUҵQJÿѭӡQJWKҷQJ

và

luôn ln

QҵPWUrQPӝWPһWQyQKm\[iFÿӏQKWUөFÿѭӡQJFDRvà bán kinh hình QyQÿy
ĈiSV͙

, 0̿WQyQFyWUͭFOj

ÿ˱ͥQJFDR

%jLWұSWUҳFQJKLӋP
Câu 1. &KRPһWWUө
ĈѭӡQJWKҷQJ

YjPӝWÿLӇP


WKD\ÿәLÿLTXD

FyWKӇWUQJQKDX
*ӑL

(
ÿLӇP

FӕÿӏQKQҵPErQQJRjLPһWWUө

YjOX{QFҳWPһWWUө

WҥLKDLÿLӇP

OjWUXQJÿLӇPÿRҥQWKҷQJ

7ұSKӧSFiF

là

$0ӝWPһWSKҷQJÿLTXD

%0ӝWPһWFҫXÿLTXD

&0ӝWPһWQyQFyÿӍQKOj

D. 0ӝWKuQKFKӳQKұW.

Câu 2. Trong không gian, cho hai ÿLӇP

VDRFKRGLӋQWtFKWDPJLác

SKkQELӋWĈLӇP

WKD\ÿәL

NK{QJÿәL.KLÿyWұSKӧSWҩWFҧFiFÿLӇP

OjPӝW
A. MһWSKҷQJ

B. MһWWUө

C. MһWQyQ

D. MһWFҫX


12
Câu 3. &KRPӝWKuQKFҫXQӝLWLӃSWURQJPӝWKuQKQyQYjPӝWKuQKWUөQJRҥL
WLӃSKuQKFҫXFyÿi\GѭӟLQҵPWURQJPһWSKҷQJÿi\FӫDKuQKQyQ*ӑL
OҫQOѭӧWOjWKӇWtFKFӫDKuQKQyQYjKuQKWUө*LiWUӏQKӓQKҩWFӫDWӍVӕ
B.

A.

là

D.


C.

Câu 4. 7URQJWҩWFҧFiFKuQKQyQFyGLӋQWtFKWRjQSKҫQOj

hình nón có

WKӇWtFKOӟQQKҩWEҵQJ
B.

A.

Câu 5. &KRWDP JLiF ÿӅX
JҩSNK~F

D.

C.
FҥnK EҵQJ

TXD\ TXDQK FҥQh

ÿѭӡQJ

WҥRWKjQKPӝWKuQKQyQFyWKӇWtFKEҵQJ

A.

B.

D.


C.

'ĈÈ3È175Ҳ&1*+,ӊ0
%jLWұSWUrQOӟS
Câu

1

2

3

4

5

ĈiSiQ

A

B

B

D

A

Câu


1

2

3

4

5

ĈiSiQ

D

B

A

A

B

%jLWұSYӅQKj


13
1.2 .ӃKRҥFKEjLKӑF 0Һ71Ï175Đ1;2$<
A. /é7+8<ӂ775Ӑ1*7Ỉ0
1. .KiLQLӋPPһWQyQWUzQ[RD\

7URQJ PһW SKҷQJ P
 FKR KDL ÿѭӡQJ
WKҷQJ

và d FҳWQKDXWҥLS WҥRWKjQKJyF

YӟL

0һWWUzQ[RD\VLQKra

EӣL ÿѭӡQJ WKҷQJ
(P) xung quanh

NKL TXD\ PһW SKҷQJ
sao cho góc

khơng

ÿәLJӑLOjP̿WQyQWUzQ[RD\ÿ͑QK2 JӑL
WҳWOjP̿WQyQ


: WUөFFӫDPһWQyQ



:ÿӍQKFӫDPһWQyQ

Hình 1.2


 ÿѭӡQJVLQKFӫDPһWQyQ


: JyFӣÿӍQKFӫDPһWQyQ.

2. +uQKQyQYjNKӕLQyQ
&KR PһW QyQ

YӟL WUөF

Yj JyF ӣ ÿӍQK Oj

*ӑL

SKҷQJYX{QJJyFYӟL

WҥL

ÿӍQK
Oj PһW
khác

FҳW

PһW QyQ WKHR WKLӃW GLӋQ Oj ÿѭӡQJ WUzn
OjPһWSKҷQJYX{QJJyFYӟL
WҥL

.KLÿySKҫQFӫDPһWQyQ


JLӟL KҥQ EӣL KDL PһW SKҷQJ
FQJ YӟL ÿѭӡQJ WUzQ

ÿѭӧF JӑL Oj

hình nón.
9ӟLKuQKQyQ


OjÿӍQKYj

ta có:
OjWUөFFӫDKuQKQyQ

 *yFӣÿӍQKFӫDKuQKQyQOj


OjFKLӅXFDRFӫDKuQKQyQ

Hình 1.3


14


OjEiQNtQKFӫDKuQKQyQ



OjÿѭӡQJVLQKFӫDKuQKQyQ

.K͙LQyQ OjSKҫQNK{QJJLDQJLӟLKҥQEӣLKuQKQyQNӇFҧKuQKQyQÿó.

3. 'LӋQWtFKKuQKQyQYjWKӇWtFKNKӕLQyQ
Cho hình nón

FyFKLӅXFDR

EiQNtQKÿi\ YjÿѭӡQJVLQK

ta có:

 'LӋQWtFK[XQJTXDQKFӫDKuQKQyQ
 'LӋQWtFKWRjQSKҫQFӫDKuQKQyQ
 7KӇWtFKNKӕLQyQ
%+2Ҥ7ĈӜ1*75Ç1/Ӟ3
1.KӣLÿӝQJ
ĈLӅQÿ~QJ

sai

YjRFӝWWUѭӟFEjLKӑFFӫDEҧQJGѭӟLÿk\

7UѭӟFEjL

&iFPӋQKÿӅ

KӑF

Sau bài
KӑF


&ҳWPһWQyQWUzQ[RD\EҵQJPӝWPһWSKҷQJVRQJ
VRQJYӟLWUөFFӫDQyQWKXÿѭӧFPӝWÿѭӡQJWUzQ
7KLӃWGLӋQTXDWUөFFӫDKuQKQyQOjPӝWWDPJLiF
cân.
+uQKQyQOX{QOX{QFKӭDPӝWÿѭӡQJWKҷQJ
1ӃXWăQJÿӝGjLEiQNtQKÿi\OrQOҫQWKuWKӇ
WtFKNKӕLQyQWѭѫQJӭQJVӁWăQJOҫQ
7ұSKӧSFiFÿѭӡQJWKҷQJÿLTXDPӝWÿLӇPFӕ
ÿӏQKWKXӝFPӝWPһWSKҷQJYjWҥRYӟLPһWSKҷQJ
ÿyPӝWJyFNK{QJÿәL

OjPӝWPһWQyQ

2. Giáo viên KѭӟQJGүQKӑFVLQKOjPEjL
9tGө 7tQKGLӋQWtFK[XQJTXDQKGLӋQWtFKWRjQSKҫQYjWKӇWtFKFӫDNKӕL
QyQFyÿѭӡQJNtQKÿi\EҵQJ
+˱ͣQJG̳Q

YjÿѭӡQJVLQKEҵQJ


15
Ta có:
%iQNtQKÿi\
&KLӅXFDRKuQKQyQ
'LӋQWtFKÿi\
'LӋQWtFK[XQJTXDQK
'LӋQWtFKWRjQphҫQ


7KӇWtFKNKӕLQyQ
9tGө2: &KRKuQKFKӳQKұW

7tQKGLӋQWtFKWRjQ

có

SKҫQFӫDNKӕLWUzQ[RD\khi quay tam giác

quanh

+˱ͣQJG̳Q
Tam giác

YX{QJWҥL

có:

.KӕLWUzQ[RD\OjNKӕLQyQFy

'LӋQWtFKWRjQSKҫQNKӕLQyQOj

9tGө &ҳWKuQKQyQÿӍQK

EӣLPӝWPһWSKҷQJÿLTXDWUөFWDÿѭӧFPӝWWDP

JLiFYX{QJFkQFyFҥQKKX\ӅQEҵQJ

7tQKWKӇWtFKNKӕLQyQÿy


+˱ͣQJG̳Q
7KLӃWGLӋQFӫDPһWSKҷQJYӟLKuQKFKySOjWDPJLiFYX{QJFkQ

nên


16
7KӇWtFKNKӕLQyQOj
9tGө &KRKuQKQyQFyEiQNtQKÿѭӡQJWUzQÿi\

FKLӅXFDR

0ӝWWKLӃWGLӋQÿLTXDÿӍQKKuQKQzQFyNKRҧQJFiFKWӯWkPFӫDÿi\ÿӃQPһW
SKҷQJFKӭDWKLӃWGLӋQOj

7tQKGLӋQWtFKWKLӃWGLӋQÿy

+˱ͣQJG̳n:
*ӑLWkPÿѭӡQJWUzQÿi\YjJLDRWX\ӃQFӫDWKLӃW
GLӋQYӟLÿi\OҫQOѭӧWOj

và

WUXQJÿLӇPFӫD

*ӑL là
'ӵQJ

Trong tam giác
YX{QJWҥL


có:

9tGө 7tQKWKӇWtFKNKӕLQyQQJRҥLWLӃSNKӕLWӭGLӋQÿӅXYӟLOjÿӍQKQyQ
ÿѭӡQJWUzQQJRҥLWLӃSWDPJLiFOjÿѭӡQJWUzQÿi\FӫDNKӕLQyQ
+˱ͣQJG̳Q
&KLӅXFDRFӫDNKӕLWӭGLӋQEҵQJFKLӅXFDRFӫDNKӕLFKySOj
WUzQÿi\NKӕLFKySOjÿѭӡQJWUzQQJRҥLWLӃSWDPJLiF
ÿi\FӫDNKӕLQyQOj

ĈѭӡQJ
.KLÿyEiQNtQK

.

7KӇWtFKNKӕLQyQOj
3+ӑFVLQKtӵOjPFiFEjLWұSVDXWUrQOӟS
a. %jLWұSWӵOXұQ
'ҥQJ7tQKGLӋQWtFK[XQJTXDQKFӫDKuQKQyQYjWKӇWtFKFӫDNKӕLQyQ
'ҥQJ&KӭQJPLQKÿѭӡQJWKҷQJ

OX{QWKXӝFPӝWPһWQyQWUzQ[RD\

'ҥQJ7tQKGLӋQWtFKWKLӃWGLӋQFӫDKuQh nón


17
%jLOX\ӋQ Vӕ 1. Trong không gian cho tam giác vuông
Yj FҥQK
JҩSNK~F


Khi quay tam giác

YX{QJWҥL
quanh

góc

WKu ÿѭӡQJ

WҥRWKjQKPӝWKuQKQyQ

D