北师大二附理科学霸高中数学笔记02_2014高考状元笔记
北京高考理科状元高中数学笔记02
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高考状元笔记数学
b a ≠ ． a b
[对症下药] B
方法 1：运用特值法，如 a=-，b=-3．
1 1 0 ，则 b<a<0，故而判断． a b 1 a 1 a
方法 2：运用性质由
3．(典型例题)对于 0<a<1，给出下列四个不等式
1 ①loga(1+o)<loga(1+ ) a 1 ②1oga(1+o)>loga(1+ ) a
4 的最小值是 sin x
2．(典型例题)设 x∈(0，π)，则函数 f(x)=sinx+ A．4 C．3 [考场错解] 是 4．故选 A B．5 D．6 因为 x∈(0，π)4 2 sin x >0， f(x)=sinx+ =4，因此 f(x)的最小值 sin x sin x sin x
2 2
D． ( ) n ( ) b
答案： C 又 0<
解析：利用特值法可看出某些选择不能成立，而事实上，∵|a|，|b|>0，
2
1 <1，∴10g |a|<log 1 |b|，由此也可直接得结论，应选 C 2
2 已知 a、b 为不等正数，s<t<0，M=
s ( a b) 2t ，N= ，则 M、N 的大小关系是_________. ab 2ab
1 1 ” a b 1 1 ” a b
．不能弱化条件变成“ a b
1 1 ” a b
考场思维训练 1 若，|a|>，|b|>0，且 ab>0，则下列不等式中能成立的是 A．
1 1 a b
(
)
B．
1 2
1 1 a b a 1 2
高二数学北师大版笔记
高二数学北师大版笔记一1.抛物线是轴对称图形。
对称轴为直线x=-b/2a。
对称轴与抛物线的交点为抛物线的顶点P。
特别地，当b=0时，抛物线的对称轴是y轴(即直线x=0)2.抛物线有一个顶点P，坐标为P(-b/2a，(4ac-b^2)/4a)当-b/2a=0时，P在y轴上；当Δ=b^2-4ac=0时，P在x轴上。
3.二次项系数a决定抛物线的开口方向和大小。
当a>0时，抛物线向上开口；当a<0时，抛物线向下开口。
|a|越大，则抛物线的开口越小。
4.一次项系数b和二次项系数a共同决定对称轴的位置。
当a与b同号时(即ab>0)，对称轴在y轴左；当a与b异号时(即ab<0)，对称轴在y轴右。
5.常数项c决定抛物线与y轴交点。
抛物线与y轴交于(0，c)6.抛物线与x轴交点个数Δ=b^2-4ac>0时，抛物线与x轴有2个交点。
Δ=b^2-4ac=0时，抛物线与x轴有1个交点。
Δ=b^2-4ac<0时，抛物线与x轴没有交点。
X的取值是虚数(x=-b ±√b^2-4ac的值的相反数，乘上虚数i，整个式子除以2a)二直线、平面、简单几何体：1、学会三视图的分析：2、斜二测画法应注意的地方：(1)在已知图形中取互相垂直的轴Ox、Oy。
画直观图时，把它画成对应轴o'x'、o'y'、使∠x'o'y'=45°(或135°)；(2)平行于x轴的线段长不变，平行于y轴的线段长减半.(3)直观图中的45度原图中就是90度，直观图中的90度原图一定不是90度.3、表(侧)面积与体积公式：⑴柱体：①表面积：S=S侧+2S底；②侧面积：S侧=；③体积：V=S底h⑵锥体：①表面积：S=S侧+S底；②侧面积：S侧=；③体积：V=S底h：⑶台体①表面积：S=S侧+S上底S下底②侧面积：S侧=⑷球体：①表面积：S=；②体积：V=4、位置关系的证明(主要方法)：注意立体几何证明的书写(1)直线与平面平行：①线线平行线面平行；②面面平行线面平行。
–2– Received accepted
VERY HIGH ENERGY GAMMA RAYS FROM THE VELAPULSAR DIRECTIONT.Yoshikoshi1,2,T.Kifune2,S.A.Dazeley3,P.G.Edwards3,4,T.Hara5,Y.Hayami1, F.Kakimoto1,T.Konishi6,A.Masaike7,Y.Matsubara8,T.Matsuoka8,Y.Mizumoto9, M.Mori10,H.Muraishi11,Y.Muraki8,T.Naito12,K.Nishijima13,S.Oda6,S.Ogio1, T.Ohsaki1,J.R.Patterson3,M.D.Roberts2,G.P.Rowell3,T.Sako8,K.Sakurazawa1, R.Susukita7,14,A.Suzuki6,T.Tamura15,T.Tanimori1,G.J.Thornton2,3,S.Yanagita11and T.Yoshida11Received;accepted1Department of Physics,Tokyo Institute of Technology,Meguro-ku,Tokyo152,Japan 2Institute for Cosmic Ray Research,University of Tokyo,Tanashi,Tokyo188,Japan 3Department of Physics and Mathematical Physics,University of Adelaide,Adelaide, South Australia5005,Australia4Institute of Space and Astronautical Science,Sagamihara,Kanagawa229,Japan5Faculty of Management Information,Yamanashi Gakuin University,Kofu,Yamanashi 400,Japan6Department of Physics,Kobe University,Kobe,Hyogo637,Japan7Department of Physics,Kyoto University,Kyoto,Kyoto606,Japan8Solar-Terrestrial Environment Laboratory,Nagoya University,Nagoya,Aichi464,Japan 9National Astronomical Observatory of Japan,Mitaka,Tokyo181,Japan10Department of Physics,Miyagi University of Education,Sendai,Miyagi980,Japan11Faculty of Science,Ibaraki University,Mito,Ibaraki310,Japan12Department of Earth and Planetary Physics,University of Tokyo,Bunkyo-ku,Tokyo 113,Japan13Department of Physics,Tokai University,Hiratsuka,Kanagawa259,Japan14Institute of Physical and Chemical Research,Wako,Saitama351-01,Japan15Faculty of Engineering,Kanagawa University,Yokohama,Kanagawa221,JapanABSTRACTWe have observed the Vela pulsar region at TeV energies using the3.8m imagingˇCerenkov telescope near Woomera,South Australia between January1993and March1995.Evidence of an unpulsed gamma-ray signal has been detected at the5.8σlevel.The detected gamma-rayflux is(2.9±0.5±0.4)×10−12photons cm−2sec−1above2.5±1.0TeV and the signal is consistent with steady emission over the two years.The gamma-ray emission region is offset from the Vela pulsar position to the southeast by about0.◦13. No pulsed emission modulated with the pulsar period has been detected and the95%confidenceflux upper limit to the pulsed emission from the pulsar is (3.7±0.7)×10−13photons cm−2sec−1above2.5±1.0TeV.Subject headings:gamma rays:observations—ISM:individual(Vela SNR)—ISM:magneticfields—pulsars:individual(Vela pulsar)—supernova remnants1.IntroductionIt is highly likely that high energy particles are accelerated by non-thermal processes in the vicinity of pulsars,and extensive searches have been made for very high energy(VHE; typically at the TeV energy)gamma rays from this class of objects(Kifune1996;references therein).Positive evidence has been obtained for the Crab(e.g.Weekes et al.1989;Vacanti et al.1991;Tanimori et al.1994)and PSR B1706−44(Kifune et al.1995)using the technique of imagingˇCerenkov light from extensive air showers which VHE gamma rays initiate in the upper atmosphere.The Vela pulsar,PSR B0833−45,is one of the100MeV gamma-ray pulsars detected by EGRET of the Compton Gamma Ray Observatory,together with the Crab and PSR B1706−44(e.g.Ramanamurthy et al.1995).There have been some claims for VHE gamma-ray emission from the Vela pulsar so far (Grindlay et al.1975;Bhat et al.1987).However,no positive evidence has been found in later observations(Bowden et al.1993;Nel et al.1993;Edwards et al.1994).In these observations,period analyses were used to reduce cosmic-ray background counts and to search for pulsed gamma-ray emission.On the contrary,VHE emission from the Crab and PSR B1706−44is apparently unpulsed.Therefore,it is important to look for the unpulsed VHE gamma-ray signal also from the Vela pulsar.For the Crab pulsar,intense X-ray emission is observed as an X-ray synchrotron nebula of which the inverse Compton counterpart is the source of VHE gamma rays.The energy injection,which is close to the spindown luminosity of the Crab pulsar(PSR B0531+21),is through aflow of relativistic electrons and positrons,i.e.a“pulsar wind”(Kennel&Coroniti1984).The shock generated when the pulsar wind collides with circumstellar matter is likely to be the site of particle acceleration.It is likely that a similar process takes place at the Vela pulsar.The Vela pulsar is relatively close to us,at a distance of about500pc,and we can expect to resolve the structure of the pulsar wind and nebula better than in the case of theCrab(at a distance of∼2kpc).In the X-ray energy band,a compact nebula was detected by the Einstein satellite with fainter extended emission(Harnden et al.1985),which was later identified as an X-ray jet by the ROSAT satellite extending from the pulsar to the south-southwest direction and which Markwardt&¨Ogelman(1995)argued may be evidence of a pulsar wind from the Vela pulsar.The“head”of the Vela jet has been observed also by the ASCA satellite and the authors explored the possibility that the jet emission is non-thermal(synchrotron)radiation rather than thermal(Markwardt&¨Ogelman1997). If the X-ray emission is of non-thermal origin,the detection of Compton-boosted VHE gamma rays would provide direct and clear evidence of non-thermal electrons.2.Instruments and ObservationsThe3.8m telescope of the CANGAROO collaboration(Hara et al.1993)detectsˇCerenkov photons from extensive air showers generated by primary gamma rays or cosmic rays,and has an imaging camera of256Hamamatsu R2248square photomultiplier tubes. One photomultiplier tube views an angular extent of0.◦12×0.◦12,and the totalfield of view of the camera is about3◦across.The tracking accuracy of the telescope has been checked by monitoring the tracks of bright stars in thefield of view.Monte Carlo simulations show the accuracy of calibrating the target position using star tracks to be better than0.◦02(Yoshikoshi1996).At least four bright stars of visual magnitude5∼6are in the3◦field of view around the Vela pulsar and the telescope pointing has been checked night by night.The Vela pulsar has been observed by the3.8m telescope from January1993to March 1995.The on-source data amount to about174hours in total with a cosmic-ray event rate of about1Hz.Almost the same amount of off-source data has been taken,in pairedon-source and off-source runs each night.About119hours usable on-source data remain after rejecting the data affected by clouds.Only the data taken without cloud are used in the following analyses.3.Analyses and ResultsTheˇCerenkov imaging analysis is based on parameterization of the shape,location and orientation of approximately ellipticalˇCerenkov images detected by an imaging camera.The commonly used parameters are“width”,“length”,“conc”(shape),“distance”(location)and“alpha”(orientation)(Hillas1985;Weekes et al.1989;Reynolds et al.1993) and the gamma-ray selection criteria in the present analysis are0.◦01<width<0.◦09, 0.◦1<length<0.◦4,0.3<conc,0.◦7<distance<1.◦2and alpha<10◦.Monte Carlo simulations show that more than99%of background events are rejected after the above selections are made,while∼50%of gamma-ray images from a point source remain.First,we searched for a gamma-ray signal from the pulsar position and found a significant excess of on-source events above the background(off-source)level.However,the peak profile of the excess distribution against the orientation angle“alpha”was broader than expected from a point source.Next,the assumed position of gamma-ray emission was shifted from the pulsar position,to scan a2◦×2◦area around the pulsar within thefield of view.The position of the maximum excess counts was searched for and found to be offset from the pulsar by about0.◦13.Figure1shows the alpha distributions for the position of the maximum excess counts after the other selection criteria have been applied.EDITOR:PLACE FIGURE1HERE.The statistical significance of the excess after including the selection of alpha is at the5.2σlevel,where the statistical significance is calculated by(N on−N off)/√N on+N off,and N onand N offare the numbers of gamma-ray-like events in the on-source and off-source data, respectively.In the usual image analysis,the image parameters are calculated from the mean and second moments of light yield,i.e.assuming gamma-ray images to have a simple elliptical shape.Gamma-ray images,however,are asymmetrical along their major axes,havingan elongated,comet-like shape with the“tail”pointing away from the source position. This feature can be characterized and quantified by another image parameter called the “asymmetry”,which is the cube root of the third moment of the image along the major axis normalized by“length”(Punch1993).Figure2(a)shows the asymmetry distributions for gamma-ray images for a point source and background(proton)images,inferred from Monte Carlo simulations.EDITOR:PLACE FIGURE2HERE.About80%of gamma-ray images have positive values of“asymmetry”in the simulation, while the distribution of background images is almost symmetrical because of their isotropic arrival directions.The asymmetry analysis has been applied assuming the source lies at the position of the maximum excess counts,to examine the gamma-ray-like feature of the excess events.The on-source distribution appears nearly symmetrical as shown in Figure2(b). However,after subtracting the off-source distribution,the distribution of the excess events in Figure2(c)is asymmetrical with the peak on the positive side as expected from the simulation.This result gives clear corroborative evidence that the detected excess events of Figure1are truly due to gamma rays.The significance of5.2σfor the excess counts in the alpha distribution of Figure1increases to5.8σby adding asymmetry>0to the gamma-ray selection criteria.As an alternative method to calculating the alpha parameter,it is possible to infer andassign the true direction of a gamma ray from the location and orientation of its observed ˇCerenkov image.We have calculated a probability density for the true direction for each observed gamma-ray image using Monte Carlo simulations(Yoshikoshi1996).Thus,a density map of gamma-ray directions can be obtained by adding up all of the probability densities of the gamma-ray-like images.The contribution of the gamma-ray source in the field of view can then be found as an event excess in the on-source map over the background (off-source)map.Figure3shows the density map of the excess events for the Vela pulsar data plotted as a function of right ascension and declination.EDITOR:PLACE FIGURE3HERE.The significant excess due to a gamma-ray source near the pulsar exists in this map.The position of maximum emission is offset from the pulsar,which is indicated by the“star”mark in the map,to a position southeast by about0.◦13.The alpha distribution of Figure1 is plotted for the position of maximum emission.The gamma-ray integralflux calculated for the position of the maximum excess counts is(2.9±0.5±0.4)×10−12photons cm−2sec−1above2.5TeV,where thefirst and second errors are statistical and systematic respectively.Theflux from the pulsar position is1.4×10−12photons cm−2sec−1above2.5TeV.However,the excess counts which are calculated for the positions of the maximum excess counts and the pulsar are not independent of each other and all of theflux measured from the pulsar position is possibly contamination by the events from the position of the maximum excess counts. The threshold energy is defined as the energy of the maximum differentialflux of detected gamma-ray-like events and has been estimated from Monte Carlo simulations to be2.5TeV, assuming a power law spectrum with a photon index of−2.5.The systematic error for this threshold energy is about±1.0TeV,which is due to uncertainties in the photon index, the trigger conditions and the reflectivity of the mirror.The data have been divided tocalculate year-by-yearfluxes and thefluxes are consistent with no variation having been detected on the time scale of two years.The periodicity of the events detected from the Vela pulsar direction and the direction of the maximum excess counts has been investigated using our1994and1995data for which a global positioning system(GPS)was available.A derivative of the TEMPO programs(Taylor&Weisberg1989)has been used to transform the event arrival timesto solar system barycentric(SSB)arrival times.The solar system ephemeris used in the analysis comes from the Jet Propulsion Laboratory(JPL)and is based on epoch2000(DE 200)(Standish1982).We have applied the Z22test(Buccheri et al.1983)to the data set after the gamma-ray selection with the period of the Vela pulsar using ephemerides from the Princeton data base(Arzoumanian et al.1992),and the test has been done coherently for each year.No significant value of the Z22statistic has been found for either the excess direction nor the pulsar direction.The95%confidence upper limit to the pulsedflux has been calculated for the pulsar position as(3.7±0.7)×10−13photons cm−2sec−1above 2.5TeV from the values of Z22using the method of Protheroe(1987).4.DiscussionThe luminosity of VHE gamma rays from the position of the maximum excess counts near the Vela pulsar is calculated to be∼6.0×1032erg sec−1,assuming that the distance to the gamma-ray emission region is500pc,the photon index of the power law spectrum is−2.5,the maximum gamma-ray energy is10TeV and the emission is isotropic. The VHE luminosity corresponds to∼8.6×10−5of the pulsar’s spindown energy of 6.9×1036erg sec−1,and is smaller by an order of magnitude than the luminosity of pulsed emission in the range from100MeV to2GeV(Kanbach et al.1994).The luminosity of VHE gamma rays from the pulsar position is estimated to be∼2.9×1032erg sec−1,whichshould rather be interpreted as an upper limit because a majority of the excess events at the pulsar position are common with the events of the maximum excess position.The emission region of VHE gamma rays appears to differ by about0.◦13to the southeast from the Vela pulsar position.We have investigated whether the effect of statisticalfluctuations could cause a change in the observed source position,using Monte Carlo simulations.The position error derived for a point source of this strength is estimated to be about0.◦04,and so the observed offset of the detected peak position from the pulsar corresponds to a significance of more than3σ.In this estimation,we ignored the effect due to the source extent and,in fact,the peak profile which appears in Figure3seems to be rather more extended than the point spread function(HWHM∼0.◦18).We note also that separate maps of each year’s data show consistent offsets.The3.8m mirror has recently been recoated and the Vela pulsar region has been observed with a better reflectivity (∼90%)again in1997further to confirm the offset.We have found a gamma-ray-like event excess from the1997data with a significance of more than4σand the position of maximum excess counts,indicated by the“cross”in Figure3,agrees with that from the 1993to1995data within the statistical error.The southeast offset of0.◦13corresponds to about1pc for the distance of500pc,much larger than the size of the light cylinder,and thus,we can exclude the possibility that the detected signal is from the pulsar magnetosphere or from the X-ray jet.This conclusion is consistent with there being no pulsation detected at the pulsar period.Unpulsed VHE emission at a distance of∼1pc from the pulsar may suggest that the mechanism for generating relativistic particles and inverse Compton gamma rays in the Vela pulsar and nebula is similar to the case of the Crab pulsar and nebula.A shock due to the confinement of the pulsar wind by the nebula may exist or have formed at the position southeast of the Vela pulsar by about0.◦13.This position of the VHE emission agrees with the birthplaceof the Vela pulsar(¨Ogelman et al.1989;Bailes et al.1989).Accelerated electrons could survive longer than the pulsar age if the magneticfield is not strong,and the VHE emission may be due to such long-lived electrons as pointed out by Harding&de Jager(1997). Recent X-ray observations show that a number of young pulsars are accompanied by possible synchrotron nebulae(Kawai&Tamura1996),which are offset from the pulsars. The existence of relativistic electrons in a region displaced from the pulsar may be rather a common feature observed in pulsar/nebula systems.VHE gamma rays could well be produced by electrons in such displaced regions as we observe in the case of the Vela pulsar and nebula.In the ROSAT X-ray image(Markwardt&¨Ogelman1995),a“bright spot”can be found where we have detected the VHE gamma-ray signal.Assuming that the X-rays originate in synchrotron emission from the same electrons that,through inverse Compton scattering,produce the VHE gamma rays,we can estimate the magneticfield fromthe relation L syn/L iC=U B/U ph of inverse Compton luminosity L iC and synchrotron luminosity L syn,where U B=B2/8πand U ph are the energy densities of the magneticfield and the photonfield,respectively.The X-ray luminosity from the bright spotat the pulsar birthplace is estimated from the ROSAT image to be smaller than that from the1 X-ray nebula around the pulsar,1.3×1033erg sec−1per decade of energy (¨Ogelman et al.1993),while the VHE gamma-ray luminosity is∼1.0×1033erg sec−1per decade.An upper limit for the magneticfield at the bright spot is then estimated to be B∼<4×10−6(U ph/0.24eV cm−3)1/2G,where0.24eV cm−3is the energy density of the microwave background photons.As for the compact X-ray nebula,a lower limit for the magneticfield can be estimated from the upper limit for the VHE gamma-ray luminosity from the pulsar position,i.e.B∼>5×10−6(U ph/0.24eV cm−3)1/2G.This limit is compatible with an estimate obtained by de Jager et al.(1996)from a confinement condition for the progenitor electrons.A plausible scenario is thus that the VHE gamma-ray emission occursfrom the X-ray bright spot offset0.◦13from the pulsar to the southeast where there issufficient density of relativistic electrons,but a smaller magneticfield.This work is supported by International Scientific Research Program of a Grant-in-Aid in Scientific Research of the Ministry of Education,Science,Sports and Culture,Japan,and by the Australian Research Council.T.Kifune and T.Tanimori acknowledge the support of the Sumitomo Foundation.The receipt of JSPS Research Fellowships(P.G.E.,T.N., M.D.R.,K.S.,G.J.T.and T.Yoshikoshi)is also acknowledged.REFERENCESArzoumanian,Z.,Nice,D.&Taylor,J.H.1992,GRO/radio timing data base,Princeton UniversityBailes,M.,et al.1989,ApJ,343,L53Bhat,P.N.,et al.1987,A&A,178,242Bowden,C.C.G.,et al.1993,Proc.23rd Int.Cosmic Ray Conf.(Calgary),1,294 Buccheri,R.,et al.1983,A&A,128,245de Jager,O.C.,Harding,A.K.&Strickman,M.S.1996,ApJ,460,729Edwards,P.G.,et al.1994,A&A,291,468Grindlay,J.E.,et al.1975,ApJ,201,82Hara,T.,et al.1993,Nucl.Inst.Meth.Phys.Res.A,332,300Harding,A.K.&de Jager,O.C.1997,Proc.32nd Rencontres de Moriond,in press Harnden,F.R.,et al.1985,ApJ,299,828Hillas,A.M.1985,Proc.19th Int.Cosmic Ray Conf.(La Jolla),3,445Kanbach,G.,et al.1994,A&A,289,855Kawai,N.&Tamura,K.1996,Proc.IAU Colloquium160,“Pulsars:Problems and Progress”,ed.S.Johnston,M.A.Walker and M.Bailes,p.367Kennel,C.F.&Coroniti,F.V.1984,ApJ,283,694Kifune,T.,et al.1995,ApJ,438,L91Kifune,T.1996,Proc.IAU Colloquium160,“Pulsars:Problems and Progress”,ed.S.Johnston,M.A.Walker and M.Bailes,p.339Markwardt,C.B.&¨Ogelman,H.1995,Nature,375,40Markwardt,C.B.&¨Ogelman,H.1997,ApJ,480,L13Nel,H.I.,et al.1993,ApJ,418,836¨Ogelman,H.,Koch-Miramond,L.&Auri´e re,M.1989,ApJ,342,L83¨Ogelman,H.,Finley,J.P.&Zimmermann,H.U.1993,Nature,361,136 Protheroe,R.J.1987,Proc.Astron.Soc.Aust.,7(2),167Punch,M.1993,Ph.D.thesis,National University of Ireland Ramanamurthy,P.V.,et al.1995,ApJ,447,L109Reynolds,P.T.,et al.1993,ApJ,404,206Standish,E.M.1982,A&A,114,297Tanimori,T.,et al.1994,ApJ,429,L61Taylor,J.H.&Weisberg,J.M.1989,ApJ,345,434Vacanti,G.,et al.1991,ApJ,377,467Weekes,T.C.,et al.1989,ApJ,342,379Yoshikoshi,T.1996,Ph.D.thesis,Tokyo Institute of Technology This manuscript was prepared with the AAS L A T E X macros v4.0.Fig.1.—Distributions of the image orientation angle“alpha”with respect to the direction of the maximum excess counts,which is offset by about0.◦13to the southeast from the Vela pulsar and corresponds to the peak position in Figure3:(a)on-source(solid line)and off-source(dashed line)distributions;(b)distribution of the excess counts of the on-source above the background(off-source)level.For gamma-ray-like events,one expects this angle to be close to zero.Fig.2.—Distributions of the“asymmetry”parameter for simulated and observedˇCerenkov images:(a)distributions of gamma-ray images for a point source(solid line)and background (proton)images(dashed line)inferred from Monte Carlo simulations;(b)on-source(solid line)and off-source(dashed line)distributions of gamma-ray-like events for the direction of the maximum excess counts,which is the same as in Figure1;(c)distribution of the excess counts of the on-source above the background.This parameter measures the pointing of the images toward the source,as indicated by positive values.Fig. 3.—A density map of excess counts around the Vela pulsar plotted as a function of right ascension and declination;north is up and east is to the left.The gray scale at the right is in counts degree−2.The“star”at the origin of the map indicates the position of the Vela pulsar.We have observed the samefield of view also in1997with a reduced energy threshold,to confirm the offset of the source from the pulsar.The position of the maximum excess counts from the1997data is indicated by the“cross”in the map.Alpha (degrees)C o u n t s0200400600800100012001400160002004006008001000-2-1012Asymmetry C o u n t s(a)100200300400500600AsymmetryC o u n t s20406080100120140160AsymmetryE x c e s s C o u n t s-1-0.50.51-200020040060080010001200Right Ascension (degrees)D e c l i n a t i o n (d e g r e e s )。
【北京高考状元笔记】人大附中高中部学霸的数学笔记,清晰手写体-模块1必修1部分共82页
QQ ：178********高考状元笔记介绍高考状元有着好的学习方法、学习习惯，他们善于思考、善于总结。
而《高考状元笔记》是他们学习的综合体现，也是他们为战胜高考所打造的最好武器。
笔记中涵盖了应对各地高考都必须拥有的各种能力。
可以说，只要认真使用《高考状元笔记》，一定会让你有一个很大的提升和意想不到的收获。
本系列笔记适合各省市高中同学使用，是广大考生及家长首选的必备高考资料。
高一同学：《高考状元笔记》可以帮你从一开始就养成良好的高中学习习惯。
更好更透彻的掌握各学科知识！高二同学：对于马上开始的一轮复习，《高考状元笔记》可以帮你在复习的过程中更具规律性、系统性，使你的高考复习计划更加完美！高三同学：《高考状元笔记》可以帮你高考最后阶段进行更加有力的冲刺！借鉴清华北大状元对高考的理解、清华北大状元总结归纳的各科知识点及梳理的知识架构，为你在接下来的复习阶段里达到迅速提分的效果！同学们可认真利用《高考状元笔记》，熟悉状元总结的考点，进行有针对性的复习，以达到用最短的时间，最高效的取得更多的优势，从而为决胜高考增加一份筹码。
每个人都有自己的学习方法，但一本好的笔记确实能带给你很大用处。
你可以借鉴上面的学习方法，也可以填补自己笔记上的漏洞。
他山之石，可以攻玉！相互借鉴才能自我提高！若你能理解高考状元笔记的内容及思路，那对你的学习一定大有帮助！《高考状元笔记》是从高中生的角度去看待高考、分析高考、理解高考，相对于其他高考教辅资料，《高考状元笔记》让考生更容易理解，更容易消化，也更容易把握！读完本册，如果需要另外几本，现在免费送上数学科目的所有内容（共6册），北京高考状元，人大附中的学霸状元笔记之数学笔记（共六册）免费获取地址：点击进入，留下QQ 邮箱完成订阅，即可收到！加QQ ：1784867209在空间关注更多精品资源信息个人推荐（也算是广告吧，不过真的不同于一般产品）：英语学习新利器：。
历年高考状元“私房”复习笔记：数学篇
历年高考状元“私房”复习笔记：数学篇养兵千日，用兵一时，高考尽管只有两天，但考前的预备却是一场持久战。
作为跨入高三门槛的学生，就应做好充分的预备，让自己赢在起点，更赢在终点。
具体而言，需要做好心理、方法和状态上的三大预备。
第一做好心理上的预备。
走进高三，每一位同学应当保持健康的心理。
高三是辛劳的，但决非痛楚不堪的人间地狱。
准高三学生第一要克服对高三的惧怕心理，以主动的心态，以积极的行动，去迎接高三的到来。
刚迈入高三的同学还应克服一种“急功近利”的焦躁心理，有的同学一认识到自己已进入高三，就迫不及待地想证明自己的实力，想在第一轮高考复习中立竿见影。
这种激进的念头假如操纵不行，反而会造成严峻的心理负担，一旦某一次考试发挥失利会造成庞大的心理压力。
这时考生就需要客观评估自己的实力，凝视自己的基础，检讨自己的方法，反思自己的状态，不要被好高骛远的方法牵引自己步入泥潭。
第二是做好方法上的预备。
方法对头，事半功倍。
每一个优秀的高考考生都有其独到的学习方法，对刚刚进入高三的学生而言，把握一套科学而有效的学习方法是专门有必要的。
需要指出的是，看书，听课，反思，作业，考试是一个学习的综合系统，看明白不等于心领神会，听明白也不等于真正把握，对知识要实现真正的领会和内化离不开后面三个环节。
知识要过手，要从教师的大脑移植入我们细胞，知识要堂堂清、天天清，决不留一点一滴的遗漏。
反思和作业能够利用晚自习和周末时刻进行综合归纳，强化经历巩固，达到准确、灵活、高效。
第三是做好状态上的预备。
学习状态是指学习者在学习过程中表现出来的形象、形状。
一个学生在跨过高三的门槛时，应当有更用心、更投入、更高效的冲刺状态。
“学习求成才，考试求成功”是指学习的目的在于成才，考试的目标在于成功。
在中国当今的高考制度下，通过读书改变命运，通过高考实现青春跨过是众多学生的共同选择。
一个成功的学习者，对失败的回答是重新站起，对困难的回答是迎难而上，对高考角逐的回答是夺取最后胜利。
全国高考状元手写笔记合集理科数学
全国高考状元手写笔记合集理科数学在中国的教育领域，高考无疑是每个学生最重要的考试之一。
每年的高考状元，他们的成功经验和学识备受。
今天，我们整理了一份全国高考状元的手写笔记合集，特别是针对理科数学这一重要科目。
理科数学，一直是高考中的重头戏。
它不仅考验学生的基础知识，还考察学生的逻辑推理、空间想象和数据处理等多种能力。
对于许多学生来说，理科数学是一个难以攻克的难关。
但高考状元们却能在这一科目上脱颖而出，他们的秘诀是什么呢？状元们有一个共同点，那就是他们都有扎实的基础知识储备。
在他们的手写笔记中，我们可以看到他们对概念的理解和掌握程度非常深。
他们不仅知道如何解题，还知道这些题背后的原理和方法。
状元们非常注重解题方法的积累。
在他们的笔记中，我们可以看到他们记录了各种解题方法，从常规的代数、几何到更复杂的概率统计、微积分等。
他们能够灵活运用这些方法，使他们在解题时能够游刃有余。
再者，状元们善于总结和反思。
每次做完题目后，他们都会进行总结，找出自己的不足之处，并及时进行改进。
这种反思和总结的习惯，让他们能够不断提高自己的学习效率。
状元们都有良好的学习习惯。
他们不会临时抱佛脚，而是注重平时的积累和学习。
他们有规律的学习计划，以及科学的学习方法，这让他们在学习中能够事半功倍。
在这份全国高考状元的手写笔记合集中，我们可以看到他们的思考过程、解题思路和知识点整理。
这些笔记不仅为其他学生提供了学习的参考，也让我们看到了高考状元的努力和智慧。
要想在理科数学这一科目上取得好成绩，我们需要有扎实的基础知识、灵活的解题方法、深刻的总结和反思以及良好的学习习惯。
在这份手写笔记合集中，我们看到了这些要素的完美结合，也感受到了高考状元的学术智慧和人格魅力。
这份手写笔记合集不仅是对高考状元们学术成果的肯定，更是对所有热爱学习、追求梦想的学生的鼓励和激励。
让我们从中汲取智慧和力量，为我们的学习之路照亮前行的方向。
中班数学比多少教案反思，本课的教学设计首先了学生的学习状态。