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第十章 数的开方·培优卷
2024
120
120
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___________
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#!$% 24 $&'( 10 $&)* 6 $&+, 8 $& 120 &- 120 &#!$./0123&45
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JⅠ!
KL(M$N% 10 O$& 30 &PO$ 3 Q
1LN3 QN2025·RSTU·VWQXYZ[\&]^_`[Da N Q
AL 2
BL0.4
CL0
DL−1
2LN3 QN24-25 bc d·efgh·i\QXYjk\&lmDaN Q
AL 25=±5
BL± 9=3
CL (−2)2=−2
DL
3 −1=−1
3LN3 QN24-25 nc X·opqrs·tuvwQXYxylmDaN Q
AL 9Djz{|}a3
BL−16D{|}a−4
CL0Djz{|}a0
DL0.1D~|}a0.001
4LN3 QN2025·opp·WQ&[
d;−3DaN Q
AL A
BL B
CL C
DL D
5LN3 Q
1
81D{|}aN Q
AL
1
9
BL±1
9
CL
1
3
DL±1
3
6LN3 QN24-25 nc X··iQ2−aD~|64&aDN Q
AL−6
BL−610
CL−2
DL−26
7LN3 QN24-25 bc X·7·iQ a−3+|2−b|=0&a+bDN Q
AL−1
BL1
CL5
DL6
8LN3 QN24-25 nc X··i\Qa≠0& a&b [&XY0[\[DK
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aN Q
AL a b
BL a2
b2
CL
3 a
3 b
DL a3
3 (−b)3
9LN3 QN24-25 nc X·ef·iQ ¡D¢£¤j&¥¦§¨DxDa 27&§©
DyDaN Q
AL 2
BL 3
CL
3 2
DL
3 3
10LN3 QN24-25 nc X·ªU·tuvwQO«¬O®¯°±K²¡Dl|F³´&
O«¯°Dl|F³´D6µ96cm2&¶O¯°Dl|F³´DFµ·O«¯°Dl|F³´D
Fµ61cm3&O¯°Dl|F³´D6µN Q
AL64cm2
BL150cm2
CL157cm2
DL216cm2
¸L)*$N% 6 O$& 18 &PO$ 3 Q
11LN3 QN23-24 nc X·efp¹·tuvwQ 5−2D[a
&
3 −8Dº[a
L
12LN3 QN24-25 nc X·»U·i\Q 9+|1−2|×(−1)2024−
3 125=
L
13LN3 QN24-25 nc X·7¼½·iQK²[D{|}¾D~|}¿À&Á²[a
L
14LN3 QN24-25 nc X·ÂÃSÄÅÆ·tuvwQÇ[k (x−2)2DÈOa
L
15LN3 QN24-25 nc X·ÉpÊ·iQË“*”KÌÍÎj
0^ÏÐlZ[m,n&Ñ8m∗n= n+
m&Ò2∗9= 9+2=5&ÓÔ6∗81=
L
16LN3 QN23-24 nc X·7ÕoÖ·iQ×Z[ |kØÙ8ÚÛÜY&J 19 ÙDJ 37 ²
[a
L
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JⅡ!
VL+,$N% 8 O$& 72 Q
17LN6 QN24-25 bc d·efgh·i\Q+|¢
(1)4(2x−1)2=36Ý
(2)2(x−1)3+16=0L
18LN6 QN24-25 nc X·77U·i\Q
K²l[ a DÞ²ßÀ{|}®ax+5¬4x−10.
(1)à x a DÝ
(2)àa−9D~|}L
19LN8 QN22-23 nc X·áÕâp·iQãäå&aK²æçãäDåèLééOê¬ëëOìí
îï¯åè³ðñòãäLOìﯱKó6µ100cm2Dl|ôõö&OêﯱK²6µ200cm2D
÷|ôø&ù÷úû·5:4LOìï¯Dõößüýþ¿ÿ¨Oêï¯Dø\ĀāĂ㥤jxą
ĆDćĈL
20LN8 QN24-25 nc X·opĉĊ·i\QċČXY¤jĄ¢&čĎ~|}L
13=1&23=8&33=27&43=64&53=125&63=216&73=343&83=512&93=729Ý
(1)ďĐnc [ ĐđJ 59 Ē&ēĔ [ ĕĖė¤j~|}D|yòOą±KĘę&OąaÁ
Ěà© 19683 D~|}D
ěĜ¤ 19683 D~|}D²ĝ[&čĎ¾D²ĝ[ 7&Ğ203<19000<303&
čĎ 19683 D~|}Dğĝ[a &ĠġĢ 19683 D~|}a L
(2)ĂĆ}ģN1Q\OąD|y&¿ĤX)*
①
3 −373248= L
②
3 0.531441= L
21LN10 QN24-25 nc X·7Õpĥ·iQēĦħ w±{|}¬~|}Lx2=a&xĨaD¸ĩ
|}N{|}Q&;± aLx3=a&xĨaDVĩ|}N~|}Q&;
3 aL{|}E81Ī
l[8Þ²{|}&¾Ħ[
0 D{|}a 0Ýī[Ĭ8{|}LĂĭĮđį&ċČX&İ·d
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x4
…
1
16
81
…
x
…
±1
±2
±3
…
IJijN1Qx4=a&xĨaD________①_________&;______②______Ý
1ĪN2QĂĶķ①D1ĪÝ
ĸËN3Qx4=5&ĹĺĻ©xD
ļĽN4Q+|¢
1
2x4−8=0L
22LN10 QN24-25 nc X·SÕdľ·tuvwQ}ģXĿ,XYĵ$
x
15
15.1
15.2
15.3
15.4
15.5
15.6
15.7
15.8
15.9
x2
225
228.01
231.04
234.09
237.16
240.25
243.36
246.49
249.64
252.81
(1) 243.36=______& 23716=______& 0.023104=______Ý
(2) 25000ŀ²Ł[Èĺłāà 2.3DłŃNńŅņmŇ 0.01QÝ
(3)153< n<154& ňʼnŊDŁ[n8______²L
23LN12 Q&KŋŌōŎ A ŏ[
ŐőŒ± 2 ²'ĝ÷:Ňœ B& A −2&Ŕ B ¡
D[ mL
(1)à|m+1|+|m−1|DÝ
(2)ŕ[
dŖ8 CŗD Þ®Z[ c ¬ d&8|2c+d| d+4[&à2c−3dD{|}L
24LN12 QN24-25 nc X·ÕŘř·i\QĭĮŚ
ĂśŜĭĮXYđį&ŝ¿ĤĸDÏŞL
ÏÐK²Z[Ŕx&ß^xDÈŁ[[x]&Ò[3.15]=3&[4]=4LşŚO
DÀ }ģdıIJij&à[ 2×3]DL
+,Ą¢X
∵22<2×3<32&
∴22< 2×3< 32L
∴2< 2×3<3L
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∴[ 2×3]=2L
Šš¤j&ĢŇ[ 3×4]=3&[ 4×5]=4&[ 5×6]=5&[ 6×7]=6LĞŢşŚOĢ©ńţ
nlŁ[&
n(n+1) =nL
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(1))*
[−2.1]=____&
8
7 =____L
(2)à[
3 300]DL
(3)a=
1×2]+[ 2×3]+⋯+[ 2024×2025 &s=
a
1012&à[ s]DL
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