2026北师大七年级数学上举一反三：专题03 与数轴有关的数形结合思想(专项训练)(原卷版)

专题03与数轴有关的数形结合思想（举一反三专项训练）



2024



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【题型1利用数轴确定数的范围】

?1

@2025·ABC·DEFGHIJKLM>AIBICIN1CO78AB1>IPQ>ORS

@F

ATRU78ACJIVWXA>BTRU78ACJIVWXC>

CTRU78BCJIVWXB>DTRU78BCJIVWXC>

YZ1-1

@24-25[\]J·^_`a·bcFdaeJ&f>RSGHghIPiha+4>e

@F

AT78ABJBT78CDJCT78DEJDT78FGJ

YZ1-2

@24-25[\]J·Ajk·b1FGHIiha>e78ABJIPiha#$

>ge78O@F

ATABBTBOCTOCDTCD

YZ1-3

@2023[\]J·lm·n

opFGHIJKAIB6M>IGq>CreJIV

AC+BC=3Ist>CgeRSuve@wwF

AT>AxyBT>A9>Bz{

CT>B|yDT}~

【题型2数轴与距离】

?2

@24-25[\]J·^_€·8opFGH1I>AIBICOJ‚xƒ|„…LM>I<†

&f‡−5IbI4Iˆ‰

Š‹ŒGH2ŽSI‹ŒJ0&‘J>AI’“>B&f‹

Œ1.8cmI>C&‘‹Œ5.4cmTPJ>Bg&fb‡@F

AT−2BT−1CT3DT−3.2

YZ2-1

@24-25[\]”·^_•–—·b1FGHI˜™Mš›œžŸ

™¡Wš¢T>P

š¢!"PP′‡@F

AT1BT2CT3DT4

YZ2-2

@24-25[\]”·£¤·8opFGHI>AO¥¦§¨J™>I>A2g&f>£

©Tª«¥¦¬­‡1M®R¯ŒIdŠ¥¦°GHgh±²³=@}´=F™µI>A¶·

J>A′£©IP>A′&f¸O@F

ATπ−2BT−π+2CT−2π−2DT−2π+2

YZ2-3

@2025·A¹º»·™EFGHIJ6M#¼‹Œ!"O™M®R¯ŒI>A½B½C½D

&fRSGHghI¾¿gih<†Oa½b½c½dIVd−b+c=10IP>CihO@F

AT−6BT−3CT0DT3

【题型3数轴与相反数】

?3

@2025·AÀÁ·DEFGHIJ>P>NihO™&#$IPQ>!"0X>O

@F

AT>PBT>QCT>MDT>N

YZ3-1

@24-25[\]J·^_}÷8opFdihć#$6M>A½BeJ!"

‡16M®R¯ŒI>AÅƲ|Ç=2ÈIɲxÇ=5ȃÊ>CI«>AÇ=ˌ‡ÌÈ2M

®R¯ŒIP>CeJih#$‡T

YZ3-2

@2024[\]J·lm·n

opF>A½B½DeJRSGHghI>A½BihÄ

‡#$Id>Bgih‡2IVAB=BDIP>Dgih‡@F

AT2BT4CT6DT8

YZ3-3

@24-25[\]J·^_•–—·8opFÍÎJMINIPIQœ>gih<†‡mI

nIpIqVm<n<p<qIN1K6M9‡0IVÏÐmnpq>0TdMN=1,NP=4,PQ=5TPќM1uvÄ

‡#$OT

【题型4数轴与绝对值】

?4

@24-25[\]J·ÒÓÔÕ·bcFKÖaIbIceJ&f>RSGHghIdab

%&'#×IP”…Ø~ÙO@F

AT|a|>cBTa>−cCT|b|<−aDT|b−c|=b−c

YZ4-1

@24-25[\]J·^_ÚÔ·8opFKÖaIbIcIdeJ&f>GHghIќ

M1%&'0*OT

YZ4-2

@23-24[\]J·AÛÜÝ·8opFGHI*ÞeßàáâãäŠ6åæçåeJI

&UèéⅠ9ⅡI”…êëÙO@F

èéⅠ

æçìíî%&'ãU3gKïðèéⅡ

æçìíïz9‡3

ATⅠ9Ⅱñ&BTⅠ9Ⅱñã&CTⅠ&Ⅱã&DTⅠã&Ⅱ&

YZ4-3

@24-25[\]J·òóôõ·bcFœMKÖmInIpIqeJRSGHghIdm+p

=0IPmInIpIqœMKÖ1I%&'0OT

【题型5利用数轴比较大小】

?5

ÍÎKÖaIbeJRSGHghIPaI−bI−aIb‚ƒ*ö÷‡@F

ATb>a>−a>−bBT−a>−b>a>b

CTb>−a>a>−bDT−a>a>−b>b

YZ5-1

@24-25ø\]J·kùúû·bcFüeGHgh“ýK®R¯Œ9Ù±²IþÿĀāQ>”

Jih”…ĂIă°Ą‚ƒ*ö÷ŠÑą“>”•ĆćĈT

11

I5III

−42−22|−1.5|−(−2.5)

YZ5-2

@24-25[\]J·ĉÓĊa·b1FċāIeJĀāih”…Ă>I㰂ƒ*

ö÷“>”˜Ñą•ĆćĈ

1

−||,0,−(),+3,()201,−22T

−5.5−27−1

YZ5-3

@23-24[\]J·ČčĎď9Đđ·bcFKÖa½bgih>eJRSGHghI

Ša½b½|a|½−b°‚ƒ*ö÷„…Iă“>”•ĆIèq‡T

【题型6利用数轴的几何意义求最值】

?6

@23-24[\]J·£¤·b1F>A½BeJ<†iha½bIdA½B6>z{!"ih‡

ABIPeJA½B6>z{!"AB=|a−b|T

Jihx½−26>z{!"ih‡|x+2|ð

①d|x−3|+|x+1|=8IPx=−3ð

②dĒeïxI|x−2|+|x+1|'0*âIPx=−1I0I2ð

③d|x−1|+|x+a|0*'O2IPa=−3T

PJēØ~IÙK@wwFMT④

AT4BT3CT2DT1

YZ6-1

@24-25[\]J·ČčĎĔĕ·b1F‰

¿ñÎĖ|5−(−2)|ih5(−2)z:%&'IruÖ

ė‡5−26eJg&6>z{!"IP&UĘ,KÖxI|x+1|+|x−1|+|x−2|ę0*'âI#f

x'OT

YZ6-2

@24-25[\]J·Ě·b1Fě¿ÎĖ|x|ihxeJ&f>ƒQ>!"I|x−a|ihx

aeJ&f>z{!"T?

|x−1|=2ihx1eJih>!"O2M®R¯ŒI

GHghIĜuĝāx'‡−1Ğ3T

ğĠġJĢģIėĤ”…3

(1)d|x−2|=4IPx'‡__________ð

(2)dJiha>RUih−326>z{IP/|a+3|+|a−2|ĥĦèqð

(3)ÍÎKÖbIP|b+5|+|b−3|ĥĦèqOħK0*'ĨdKIü/ā0*'ðdĩKIüØāÖĪT

YZ6-3

@24-25[\]J·īĬĭ·8opFJ6>{!"×UÑ6>g&f:%&

'T?

>A½BeJ<†&f‡aIbIPA½B6>{!"ih‡AB=|a−b|IğĠġJÎĮė

įİZ|x+1|+|x−1|ę0*'âIxę'OI0*'‡T

①/|x−1|+|x−2|+|x−3|++|x−24|0*'‡T

②7⋯

【题型数轴中的相遇问题】

?7

@24-25[\]J·AÛÜÝ·b1FÍÎaO0ıïIb=−|−5|IcO−4#$IVaIbI

c<†O>AIBICeJ&fT

(1)/aIbIc'IăeGHJĀā>AIBICð

(2)eJId>Dƒ>A!"IJ·O5IP>DijĴ>A“ĵĶ>”T/>AĵĶ>Dgihð

(3)d=>P‚>Bā’Ųı±²Ç=I=>Q‰â‚>Aā’rŲı±²Ç=I>Pˌ

OÌÈ1M®R¯ŒI>QˌOÌÈ3M®R¯ŒI/Ç=+ÈķI>QuġĸJ>PĨ

YZ7-1

@2024[\]J·^_·n

opFÍÎIGHA½B<†‡J6>IA>&f‡

−10IB>&f‡90T

(1)A½B6>!"#×M>&fOð

(2)“eK™ýĹĺĻļP‚B>ā’âIġ5M®R/Èˌ²xÇ=I‰âĽ™ýĹĺĻļQ¶·‚A

>ā’Iġ3M®R/Èˌ²|Ç=I«6ýĹĺĻļeJC>#2IPC>&fOð

YZ7-2

@22-23[\]J·kùľ»·bcFJ>Aih−8I>Bih6I>Cih12I>Dih

18TGHIŠeQ>O9>BICĿĂ4™”Iĝƒ™ŀ“47”Te“47”JI=>M‚>A

ā’Iġ4M®R/ÈËŒÅŁ47Ù±²Ç=I‚>OÇ=ƒ>Cb{ˌY‡QĈ™łIŃ

>CķńŅġQĈˌ²ņ>DÇ=ð>M‚>Aā’‰âI>N‚>Dā’I™¬ġ3M®R/È

ËŒÅŁ“47”ı±²²ņ>AÇ=TN1™>ƒÊņ>âI6>ñŇňÇ=T«Ç=â{‡tÈI

t=âIM½N6>#2@èqʼn‡*FT

YZ7-3

@24-25[\]J·kÓŊŋ·bcFÍÎaO0ıïIbO−5#$IVa,b<†O>A,B

eJ&fT

(1)/a,b'IăeJĀā>A,Bð

(2)d=>P‚>Aā’ÅÙ±²Ç=I=>Q‰â‚>Bā’rÅÙ±²Ç=I>PˌÌÈ5M

®R¯ŒI>QˌOÌÈ3M®R¯ŒIdÇ=tÈķI>PuġĸJ>QI/t'T

【题型8数轴中的折返问题】

?8

@23-24[\]J·^_}÷8opFœM>A½B½C½DeJRSGHghIÍÎCD=2I

BC=3IAC=15Id>C‡Q>I>P½Q<†‚A½D6>‰âā’I>PġÌÈ3M®R¯Œˌ²|Ç=I

ƒÊC>ķŌĜ°Q˲A45ð>QġÌÈ1M®R¯Œˌ²xÇ=TįP½QñƒÊ>AâÇ=ŇňI

«Ç=â{‡t@®R

ÈFT

(1)įt=3âI/>P>Qz{!"ð

(2)įt=âI>PƒÊ>BIōâ>QihOð

(3)įt‡,'âIP½Q6>#!2M®RĨ

YZ8-1

@23-24[\]J·ī·bcFGHIA>eJ&fKÖO24ð=>M‚Q>O>ā

’ġ1®R/Èˌ²|Ç=I=>N‚A>ā’ġ2®R/Èˌ²xÇ=I6M=>‰âā’I«Ç

=â{‡tÈT

(1)üŎtZĺih

=>M&f‡__________I=>N&f‡__________ð

(2)GqeÇ=Ńŏ1IM½N6>#!6M®R¯I/t'ð

(3)M½NeÇ=Ńŏ1IŐK™=>p‚Q>O>őŒġ3®R/Èˌ²|Ç=@M½N‰âā’FI

į#2>NâŌĜ5œI5œŔ12ƒM>âŐŌĜ45IGōŕ5IįM½N#2â>pŇňIōâ>p

™ŖÇ=î__________M®R¯ŒT

YZ8-2

@23-24[\]J·^_ŗa·8opFGHIÍÎJA½B6>&fO−20I40I

=>M½N‰â‚>Aā’²>BÇ=I>Mˌ‡3M®R¯Œ/ÈI>Nˌ‡2M®R¯Œ/ÈI

ƒÊ>Bķ45²>AńŅÇ=IN1ˆ>œƒ>AâIlŘŇňIřŃÈ>Aƒ>N!"IJ·

×U>Bƒ>M!"T

YZ8-3

@24-25[\]J·īÀ¯Ś·8opFÍÎJAIB6>&f<†‡aIbIVaIb

ÏÐ|a+18|+(b−10)2=0I>C&f‡14I>D&f‡−10T

(1)/aIb'ð

(2)>AIBʼnâā’#²śËÇ=I>Aˌ‡4M®R/ÈI>Bˌ‡1M®R/ÈIdtÈ

â>AƒQ>!"9>BƒQ>!"#×I/t'ð

(3)e@2FŀŜ”I>AIB‚ćŒRS‰âā’IįA>Ç=ƒ>CâIŝËġQĈˌ5œIƒÊ

ā’>ķIŐ45²>CÇ=TB>Ç=ŞD>ķŇňÇ=TįBŇňÇ=â>ArŇňÇ=T/eōŃ

ŏ1IAIB6>‰âřŃ>eJ&fT

【题型9数轴中两线段和差倍分问题】

?9

@23-24[\]J·^_şa·bcFÍÎJA>İi−8IB>İi4I=>P½Q<†‚A½B

‰âā’I²|Ç=I>Pˌ‡ÌÈ2M®R¯ŒI>Qˌ‡ÌÈ1M®R¯ŒI«Ç=â{‡t

ÈIįt=âI2OP−OQ=3T@į>P>Q£©âIP½Q6>ŇňÇ=F

YZ9-1

@24-25[\]J·AÀŠa·bcFGHI>A9BeJih<†O−698I=>P‚A

ā’Iġ1M®RÌÈˌŚ7AB±²²|Ç=I‰â=>Q‚>Bā’Iġ3M®RÌÈˌÅ

š7BA±²²xÇ=IÇ=â{‡tÈ(t>0)Iį>AIPIQÑL>1¶·K™>OġĽŢ6>‡ţ>

781>âIt'‡T

YZ9-2

@24-25[\]J·AÀŠa·bcFÍÎ>AIBeJ&f<†‡aIbIV|a+6|+(b−4)2

=0Id=>PeJ&f‡xIįPAŤPBť16âIx'‡T

YZ9-3

@23-24Ŧ\]J·ŧŨũa·b1FJKAIBICL>IŪāG”.

dN1™M>ƒ

Nū6M>z{!"#×âIPŬŭ>ONū6M>“1>”IÑL>‡“1>Ů>”T

?GJ>AIBICgih<†‡1I3I5Iōâ>BO>AIC1>T

(1)d>Aih−2I>Bih1Id>BO>A>C1>I/>Cgihð

(2)>Aih−10I>Bih15IP‡J™M=>Id>A½B½PO“1>Ů>”I/ōâ>Pi

hT

【题型10数轴动点中的定值问题】

?10

@23-24[\]J·īůŰ·bcFGHIJ>AIB@>Ae>BxFg&faIbÏÐ

|a+3|+(b−5)2=0TP‡J™=>IN&f‡xIO‡Q>T

(1)dBP=1I/x'ð

(2)dPB=3PAI/x'ð

PAPB

d>C‡78AB1>Iį>e78ABű¯7JÇ=âI'Oħ‡'@Ĝ'IãŲ

(3)PPC

+

>PRSYʼnųYʼnFĨGOIü/āÑM'ðGãOIrüØÞÖĪT

YZ10-1

@23-24[\]J·œŴŵñ·b1FGH

eJ>AihaI>BihbI>Cih

c,bO0ıïIVa,cÏÐ|a+3|+|c−5|=0T

(1)a=______Ib=_______Ic=______ð

(2)Gq>Pih‡xIįP>ƒB½C6>!"z9‡8âIx=________T

(3)>A,B,CőŒeJÇ=Id>AġÌÈ1M®R¯Œˌ²xÇ=I‰âI>B9>C<†ġÌÈ