劍橋STEP 2021的官方更新自2021年起取消STEP 1、僅保留STEP 2和STEP 3考試。2021版STEP大綱內(nèi)容與2020版一致，原STEP 1要求的知識(shí)點(diǎn)仍將在STEP 2和3中出現(xiàn)。STEP 2021考試相關(guān)日期已于3月8日公布。STEP 2021面向所有考生開放，沒有offer的學(xué)生同樣可以參加考試。劍橋官方保留變更STEP 2021考試政策的權(quán)利。關(guān)鍵日期劍橋STEP 2021考試關(guān)鍵日期2021年3月15日 注冊(cè)報(bào)名開放2021年5月07日 注冊(cè)報(bào)名截止2021年6月14日 STEP 2考試日2021年6月17日 STEP 3考試日2021年8月10日 STEP成績(jī)公布注意：劍橋官方保留調(diào)整上述日期的權(quán)利。特別提醒STEP考試時(shí)間可能與A Level相關(guān)考試時(shí)間沖突，注意提前做好準(zhǔn)備，如有時(shí)間沖突請(qǐng)務(wù)必提前做好相關(guān)考試科目的調(diào)整。報(bào)名方式劍橋STEP 2021考試如何報(bào)名？考生需通過授權(quán)考試中心報(bào)名參加STEP考試： 考生所在學(xué)校是授權(quán)考試中心，則可通過學(xué)校報(bào)名和參加STEP考試。學(xué)校不是授權(quán)考試中心，可以社會(huì)考生的身份登錄BC官網(wǎng)報(bào)名。還有部分城市有校外機(jī)構(gòu)，可以代社會(huì)考生報(bào)名并組織STEP考試。報(bào)名時(shí)需提交給考試中心以下信息：姓名、性別、出生日期及UCAS編號(hào)。所申請(qǐng)大學(xué)的名稱、專業(yè)及專業(yè)代碼。如因身體原因需要特殊照顧，需一并提交相關(guān)證明材料。報(bào)名資格哪些學(xué)生可以報(bào)考STEP 2021？所有人均可報(bào)名參加STEP 2021考試。不再像2020年那樣要求必須是offer holder才能參加。全面解讀｜劍橋STEP數(shù)學(xué)考試【2021】考試簡(jiǎn)介什么是劍橋STEP數(shù)學(xué)考試？由劍橋大學(xué)招生考試委員會(huì)組織的STEP考試是為測(cè)試申請(qǐng)者數(shù)學(xué)能力而舉行的筆試，其全稱為Sixth Term Examination Paper，直譯過來就是“第六學(xué)期考試”。STEP成績(jī)通常作為英國幾所頂尖高等院校，包括劍橋大學(xué)、帝國理工學(xué)院、倫敦大學(xué)學(xué)院、華威大學(xué)等院校的數(shù)學(xué)、計(jì)算機(jī)等相關(guān)專業(yè)錄取條件之一。盡管牛津大學(xué)數(shù)學(xué)、計(jì)算機(jī)相關(guān)專業(yè)不要求提供STEP成績(jī)，但牛津官網(wǎng)上也明確建議申請(qǐng)者參加STEP考試。需考專業(yè)哪些大學(xué)和專業(yè)需要考劍橋STEP？劍橋大學(xué)Courses 專業(yè)名稱 UCAS代碼Mathematics 數(shù)學(xué) G100Mathematics with Physics 數(shù)學(xué)物理 G100Economics 經(jīng)濟(jì) L100Engineering 工程 H100通常劍橋大學(xué)在條件錄取中要求考生的STEP成績(jī)達(dá)到等級(jí)1及以上。其中，數(shù)學(xué)專業(yè)通常要求STEP 2、3等級(jí)1、1甚至等級(jí)1、S的成績(jī)。自2018年起劍橋大學(xué)以下專業(yè)不再要求考STEP：化學(xué)工程 Chemical Engineering via Engineering (H810)，但要求考ENGAA。自然科學(xué) Natural Sciences (BCF0)，但要求考NSAA。自2019年起劍橋大學(xué)以下專業(yè)不再要求考STEP：計(jì)算機(jī) Computer Science with Mathematics (G400 BA/CS)，但要求考CTMUA。華威大學(xué)Courses 專業(yè)名稱 UCAS代碼Mathematics 數(shù)學(xué) G100Mathematics (Master of MATH) 數(shù)學(xué)(四年) G103Mathematics and Philosophy 數(shù)學(xué)和哲學(xué) GV15Mathematics andStatistics 數(shù)學(xué)與統(tǒng)計(jì) GG13Mathematics and Statistics (MMathStat) 數(shù)學(xué)和統(tǒng)計(jì)(四年) GGC3MORSE (Mathematics, Operational Research, Statistics and Economics) 數(shù)學(xué)運(yùn)籌學(xué)統(tǒng)計(jì)與經(jīng)濟(jì)(四年) G0L0MORSE(Mathematics, Operational Research, Statistics andEconomics) 數(shù)學(xué)運(yùn)籌學(xué)統(tǒng)計(jì)與經(jīng)濟(jì) GLN0Data Science (Mathematics, Statistics and Computer Science) 數(shù)據(jù)科學(xué) G103一般華威大學(xué)要求STEP成績(jī)達(dá)到等級(jí)2及以上。盡管華威大學(xué)接受考生用MAT或TMUA代替STEP成績(jī)，但很多考生因?yàn)楦鞣N原因錯(cuò)過每年10月底或11月初的MAT和TMUA考試，不得不選擇參加次年6月的STEP考試。華威大學(xué)官方給出的TMUA最低要求為(滿分分)，而MAT因?yàn)槊磕瓿煽?jī)會(huì)有所變化，無法在考試成績(jī)統(tǒng)計(jì)結(jié)果出來以前給出MAT對(duì)應(yīng)的最低分?jǐn)?shù)。自2018年起華威大學(xué)以下專業(yè)不再要求考STEP：數(shù)學(xué)與商學(xué) Mathematics and Business Studies (G1NC)數(shù)學(xué)與經(jīng)濟(jì)學(xué) Mathematics and Economics (GL11)帝國理工Courses 專業(yè)名稱 UCAS代碼Computing 計(jì)算 G400Computing 計(jì)算 G401 Computing(International Programme of Study） 計(jì)算(國際項(xiàng)目) G402 Computing (Management and Finance） 計(jì)算(管理和金融) G501Computing(Software Engineering） 計(jì)算(軟件工程) G600Computing(Security and Reliability) 計(jì)算(安全和可靠性) G610Computing(Artificial Intelligence and Machine Learning） 計(jì)算(人工智能和機(jī)器學(xué)習(xí)) G700 Computing(Visual Computing and Robotics) 計(jì)算(視覺計(jì)算和機(jī)器人) GG47Mathematics and Computer Science 數(shù)學(xué)與計(jì)算機(jī)科學(xué) GG14Mathematics and Computer Science 數(shù)學(xué)與計(jì)算機(jī)科學(xué) GG41一般帝國理工在條件錄取中要求STEP 2或3達(dá)到等級(jí)2或1以上，或者STEP 2和3同時(shí)達(dá)到等級(jí)2甚至等級(jí)1以上。其他大學(xué)其他要求STEP(或MAT、TMUA)的大學(xué)包括：倫敦大學(xué)學(xué)院(UCL)布里斯托大學(xué)巴斯大學(xué)倫敦國王學(xué)院上述大學(xué)的相關(guān)專業(yè)會(huì)在官網(wǎng)或錄取條件中明確提出具體STEP考試和成績(jī)等級(jí)要求。帝國理工的計(jì)算機(jī)專業(yè)必須要STEP，而數(shù)學(xué)專業(yè)通常要求MAT，如果沒有MAT成績(jī)則可以用STEP替代。通常帝國理工要求STEP 2或3等級(jí)2以上的成績(jī)。牛津大學(xué)的數(shù)學(xué)、計(jì)算機(jī)等相關(guān)專業(yè)則要求考生必須參加自家組織的MAT(Mathematics Admissions Test數(shù)學(xué)入學(xué)考試）。盡管STEP成績(jī)不作為牛津大學(xué)錄取的必要條件之一，但牛津也鼓勵(lì)考生參STEP考試并提供成績(jī)，以全面評(píng)估考生的學(xué)術(shù)能力?？荚囆问絼騍TEP考試形式是怎樣的？考試題型自2021年起取消STEP 1考試后，STEP僅提供STEP 2和STEP 3兩種考試。題型均為計(jì)算題，不必做答所有題目，考生只需從試卷中選擇6道題作答。自2019年改革以后，STEP 2和3試卷題量由13道減少為12道，見下表?？荚?Section A Section B Section C 合計(jì)STEP 2 純數(shù)8道 力學(xué)2道 統(tǒng)計(jì)2道 12道STEP 3 純數(shù)8道 力學(xué)2道 統(tǒng)計(jì)2道 12道答題方式筆試考試時(shí)長(zhǎng)3小時(shí)公式表考試不提供公式表，大綱中涉及的公式要求學(xué)生全部掌握，如果有超過大綱給出的公式，試題中會(huì)給出。計(jì)算器不允許使用計(jì)算器詞典允許使用紙質(zhì)雙語詞典試卷樣題劍橋STEP試卷樣以下為2020年STEP 2真題：Section A: Pure Mathematics[STEP 2, 2020Q1](i) Use the substitution ，where , to find in terms of the integral(where ).(ii) Find in terms of the integral (where ).(iii) Show that[STEP 2, 2020Q2]The curves and both satisfy the differential equation,where .All points on have positive and co-ordinates and passes through (1, 1). All points on have negative and co-ordinates and passes through (?1, ?1).(i) Show that the equation of can be written as .Determine a similar result for curve .Hence show that is a line of symmetry of each curve.(ii) Sketch on the same axes the curves and , for . Hence show that lies between the lines and .Sketch curve .(iii) Sketch curve .[STEP 2, 2020Q3]A sequence of positive real numbers is said to be unimodal if there is a value such thatandSo the sequences ; ; and are all unimodal, but is sequence of positive real numbers is said to have property if for all with .(i) Show that, in any sequence of positive real numbers with property L,Prove that any sequence of positive real numbers with property is unimodal.(ii) A sequence of real numbers satisfies for , where is a positive real constant. Prove that, for ,and, for ,Hence show that the sequence consists of positive terms and is unimodal, provided .In the case and , prove by induction that . Let , where is an integer with .In the case and , prove that ur is largest when .[STEP 2, 2020Q4](i) Given that , and are the lengths of the sides of a triangle, explain why , and .(ii) Use a diagram to show that the converse of the result in part (i) also holds: if , and are positive numbers such that , and then it is possible to construct a triangle with sides of length , and .(iii) When , and are the lengths of the sides of a triangle, determine in each case whether the following sets of three lengths canalwayssometimes but not alwaysneverform the sides of a triangle. Prove your claims.(A) , , .(B) , , .(C) , , .(D) , , .(iv) Let f be a function defined on the positive real numbers and such that, whenever ,but .Show that, whenever , and are the lengths of the sides of a triangle, then , and can also be the lengths of the sides of a triangle.[STEP 2, 2020Q5]If is a positive integer, the value of the function is the sum of the digits of in base 10. For example, d(249) = 2 + 4 + 9 = -digit positive integer is written in the form , where for all and .(i) Prove that is non-negative and divisible by 9.(ii) Prove that is a multiple of 9 if and only if is a multiple of that . Show that if has n digits, then and , and hence that .Find a value of for which . Show that there are no further values of satisfying this equation.(iii) Find a value of for which . Show that there are no further values of satisfying this equation.[STEP 2, 2020Q6]A matrix is real if it can be written as , where , , and are this case, the trace of matrix is defined to be tr and det() is the determinant of matrix . In this question, is a real 2 × 2 matrix.(i) Prove thattr() = tr ? 2det().(ii) Prove thatbut andand thatand(iii) Use part (ii) to prove thatFind a necessary and sufficient condition on and so that .(iv) Give an example of a matrix for which , but which does not represent a rotation or reflection. [Note that the matrices are both rotations.][STEP 2, 2020Q7]In this question, .(i) Let be the complex number , where . Show that is independent of . Hence show that, if is a complex number on the line in the Argand diagram, then lies on a circle in the Argand diagram with centre be the line , where is a real constant not equal to 2. Show that, if lies on , then lies on a circle whose centre and radius you should give in terms of . For which on is ?(ii) Let be the line , where is a non-zero real constant. Show that, if lies on H, then lies on a circle whose centre and radius you should give in terms of . For which on is ?[STEP 2, 2020Q8]In this question, is a quartic polynomial where the coefficient of is equal to 1, and which has four real roots, 0, , and , where .is defined by .The area enclosed by the curve and the -axis between 0 and is equal to that between and , and half that between and .(i) Sketch the curve , showing the co-ordinates of its turning points. Explain why must have the form , where . Find, in factorised form, an expression for in terms of , and .(ii) If , explain why and why if . Hence show that or .By considering also , show that and that .(iii) Find an expression for in terms of and only. Show that the points of inflection on lie on the B: Mechanics[STEP 2, 2020Q9]Point is a distance above ground level and point is directly below at ground level. Point is also at ground level, a distance horizontally from . The angle of elevation of from is . A particle is projected horizontally from , with initial speed . A second particle is projected from B with speed at an acute angle above the horizontal. The horizontal components of the velocities of the two particles are in opposite directions. The two particles are projected simultaneously, in the vertical plane through , and .Given that the two particles collide, show thatand also that(i) ;(ii) ;(iii) .Show that the particles collide at a height greater than if and only if the particle projected from is moving upwards at the time of collision.[STEP 2, 2020Q10]A particle of mass m moves freely and without friction on a wire circle of radius , whose axis is horizontal. The highest point of the circle is , the lowest point of the circle is and angle . A light spring of modulus of elasticity λ is attached to and to . The natural length of the spring is , which is less than the diameter of the circle.(i) Show that, if there is an equilibrium position of the particle at , where , thenShow also that there will only be such an equilibrium position if .When the particle is at the lowest point of the circular wire, it has speed .(ii) Show that, if the particle comes to rest before reaching , it does so when , where satisfieswhereShow also that this will only occur if .Section C: Probability and Statistics[STEP 2, 2020Q11]A coin is tossed repeatedly. The probability that a head appears is and the probability that a tail appears is .(i) A and B play a game. The game ends if two successive heads appear, in which case A wins, or if two successive tails appear, in which case B that the probability that the game never ends is that the first toss is a head, show that the probability that A wins is .Find and simplify an expression for the probability that A wins.(ii) A and B play another game. The game ends if three successive heads appear, in which case A wins, or if three successive tails appear, in which case B thatP(A wins | the first toss is a head) = P(A wins | the first toss is a tail) and give a similar result for P(A wins | the first toss is a tail).Show thatP(A wins) =(ii) A and B play a third game. The game ends if a successive heads appear, in which case A wins, or if successive tails appear, in which case B wins, where and are integers greater than the probability that A wins this that your result agrees with part (i) when .[STEP 2, 2020Q12]The score shown on a biased -sided die is represented by the random variable which has distribution for , where not all the are equal to 0.(i) Find the probability that, when the die is rolled twice, the same score is shown on both rolls. Hence determine whether it is more likely for a fair die or a biased die to show the same score on two successive rolls.(ii) Use part (i) to prove that, for any set of positive numbers ,(ii) Determine, with justification, whether it is more likely for a fair die or a biased die to show the same score on three successive rolls.計(jì)分方式劍橋STEP考試計(jì)分方式是怎樣的？STEP考試計(jì)分方式考生作答6道題，每題均為20分，全卷滿分120分。盡管只需要做6道題，但不限制考生的答題數(shù)量?？忌痤}超過6道時(shí)，每道題都會(huì)判分，但只取得分最高的6道題計(jì)入總分。需要注意的是STEP計(jì)分采用鼓勵(lì)性原則：STEP強(qiáng)調(diào)考生能在解題過程中完整做答，如果使用的解題方法非常巧妙、且答題過程完整，考官會(huì)酌情給出bonus mark。也即有考生一道題能得分超過20分！STEP考試成績(jī)等級(jí)等級(jí) 含義 占比S Outstanding (優(yōu)秀) 約前5~15%1 Very Good (非常好) 約前15~30%2 Good (好) 約前30~50%3 Satisfactory (合格) 約前50~80%U Unclassified (不合格) _需要注意的是，盡管STEP 2、3的滿分、等級(jí)都一樣，但每種考試每年各個(gè)等級(jí)對(duì)應(yīng)的分?jǐn)?shù)閾值都不一樣。STEP考試成績(jī)等級(jí)劃分標(biāo)準(zhǔn)以下為2020年官方給出的STEP 2和3的等級(jí)劃分標(biāo)準(zhǔn)和統(tǒng)計(jì)圖。STEP 2等級(jí)劃分標(biāo)準(zhǔn)和統(tǒng)計(jì)圖Grade boudaries (STEP 2, 2020)等級(jí)劃分標(biāo)準(zhǔn)Maximum Mark S 1 2 3 U120 77 55 42 25 0Cumulative percentage achieving each grade (STEP 2, 2020)達(dá)到各等級(jí)的累積百分比Maximum Mark S 1 2 3 U120 100Distribution of scores (STEP 2, 2020)分?jǐn)?shù)分布全面解讀｜劍橋STEP數(shù)學(xué)考試【2021】 STEP 3等級(jí)劃分標(biāo)準(zhǔn)和統(tǒng)計(jì)圖Grade boudaries (STEP 3, 2020)等級(jí)劃分標(biāo)準(zhǔn)Maximum Mark S 1 2 3 U120 80 67 53 30 0Cumulative percentage achieving each grade (STEP 3, 2020)達(dá)到各等級(jí)的累積百分比Maximum Mark S 1 2 3 U120 100Distribution of scores (STEP 3, 2020)分?jǐn)?shù)分布全面解讀｜劍橋STEP數(shù)學(xué)考試【2021】考試范圍劍橋STEP考試范圍有哪些變化？STEP考試的考查范圍見下表。考試 考察范圍STEP 1(已取消，但仍作為STEP 2和3的知識(shí)點(diǎn)) A Level數(shù)學(xué)的純數(shù)、力學(xué)、概率統(tǒng)計(jì)部分，附加2021大綱要求的內(nèi)容STEP 2(同樣作為STEP 3的知識(shí)點(diǎn)) AS進(jìn)階數(shù)學(xué) (高數(shù)) 的純數(shù)、力學(xué)、概率統(tǒng)計(jì)部分，附加2021大綱要求的內(nèi)容STEP 3 A level進(jìn)階數(shù)學(xué)(高數(shù))的純數(shù)、力學(xué)、概率統(tǒng)計(jì)部分，附加2021大綱要求的內(nèi)容為了適應(yīng)近幾年的A Level課程改革，STEP考試在2019年做了重大調(diào)整，最主要的變化是對(duì)STEP 2、3的考試范圍和試卷結(jié)構(gòu)進(jìn)行了調(diào)整，但題型沒有變化。主要變化簡(jiǎn)述如下：按照A Level數(shù)學(xué)和進(jìn)階數(shù)學(xué)(高數(shù))改革對(duì)應(yīng)的修訂考試大綱；STEP 2和3試卷的題量由13道減少為12道；出題風(fēng)格不變，意味著往年的STEP真題可以用于備考；考試的鼓勵(lì)性計(jì)分原則不變。最新的2021年大綱已經(jīng)出爐，與2020年的大綱相比幾乎沒有變化。考試難度劍橋STEP考試有多難？一句話概括難度STEP有少量題比較簡(jiǎn)單，但大多數(shù)題都是高考?jí)狠S題難度，尤其是每道題的最后一問非常有挑戰(zhàn)性。近幾年STEP考試越來越難嗎？是的，經(jīng)過牛劍課程教學(xué)和研發(fā)團(tuán)隊(duì)的對(duì)比分析，發(fā)現(xiàn)最近幾年STEP試題難度有明顯提升。一個(gè)明顯的變化是劃分等級(jí)S和等級(jí)1的分?jǐn)?shù)線上有大幅下降的趨勢(shì)，另一方面考慮到越來越多數(shù)學(xué)成績(jī)優(yōu)秀的中國學(xué)生參加STEP考試，無疑會(huì)在一定程度上提高各個(gè)等級(jí)的分?jǐn)?shù)線。STEP考試難在哪兒？強(qiáng)調(diào)邏輯推理的完備性；計(jì)算量大且不能用計(jì)算器；要求基本數(shù)學(xué)運(yùn)算相當(dāng)熟練；注重?cái)?shù)學(xué)基本知識(shí)和基本定理、公式的推導(dǎo)方法所蘊(yùn)含的基本數(shù)學(xué)思想；通過已知與未知知識(shí)的并行使用考查學(xué)生的領(lǐng)悟能力和知識(shí)遷移能力。STEP和數(shù)學(xué)競(jìng)賽相比哪個(gè)難？試題難度：總體來說STEP的難度沒有大多數(shù)數(shù)學(xué)競(jìng)賽最后幾道題難；側(cè)重考查點(diǎn)：STEP更強(qiáng)調(diào)對(duì)基本數(shù)學(xué)知識(shí)、思想方法的運(yùn)用，而數(shù)學(xué)競(jìng)賽強(qiáng)調(diào)巧思妙解、是對(duì)智商和數(shù)學(xué)技巧的雙重考驗(yàn)；答題策略：取決于題型，多數(shù)數(shù)學(xué)競(jìng)賽的初賽以選擇題為主，相對(duì)于STEP所有的題都是解答題而言會(huì)更容易得分；備考方式：STEP有考綱和明確的考試范圍，題型和解答套路相對(duì)比較固定，所以更容易備考，而競(jìng)賽沒有考綱、也沒有明確的考試范圍，有些難題不能按常規(guī)套路求解、不容易準(zhǔn)備。參加數(shù)學(xué)競(jìng)賽對(duì)考STEP有幫助嗎？雖然STEP和數(shù)學(xué)競(jìng)賽試題存在諸多差異，但在備考數(shù)學(xué)競(jìng)賽過程中學(xué)到的數(shù)學(xué)知識(shí)、方法和思想對(duì)于備考STEP考試也是非常有幫助的，建議學(xué)有余力的學(xué)生在備考STEP的同時(shí)參加數(shù)學(xué)競(jìng)賽，比如美國數(shù)學(xué)競(jìng)賽AMC 10/12、英國數(shù)學(xué)競(jìng)賽BMO系列賽事等。MAT跟STEP相比難度如何？MAT比STEP簡(jiǎn)單。MAT僅考查純數(shù)知識(shí)，考查范圍比原STEP 1考試的純數(shù)部分考查的知識(shí)還要少。MAT有選擇題，且選擇題大部分都比較容易，通常只有2-3道選擇題比較難或容易丟分。MAT考試這樣設(shè)置的原因一方面是要兼顧申請(qǐng)帝國理工和華威大學(xué)的考生數(shù)學(xué)水平，另一方面也是為了不讓考生的MAT成績(jī)太難看，鼓勵(lì)更多的學(xué)生參加MAT考試，并通過MAT考試測(cè)評(píng)其數(shù)學(xué)實(shí)力。而STEP考試全是大題，且大題之間的難度差異比較大。所以STEP考試不全是考查數(shù)學(xué)水平，也不像考MAT的選擇題會(huì)有一定的運(yùn)氣成分，STEP考試中會(huì)挑題比會(huì)解題更重要！題目挑得好就會(huì)更容易得高分。STEP準(zhǔn)備多久才能考到等級(jí)1以上？不同學(xué)生的數(shù)學(xué)基礎(chǔ)差別較大，劍橋官方建議備考STEP時(shí)間不少于6個(gè)月。沒有學(xué)高數(shù)和數(shù)學(xué)競(jìng)賽基礎(chǔ)的學(xué)生，建議備考時(shí)間9個(gè)月以上。學(xué)過高數(shù)且有數(shù)學(xué)競(jìng)賽基礎(chǔ)的學(xué)生如果準(zhǔn)備STEP 2和3，建議不少于6個(gè)月。熱門國際競(jìng)賽輔導(dǎo)/報(bào)名-ALevel/AP/IB/IG課程輔導(dǎo)請(qǐng)?zhí)砑覯olly微信【hupowayy】咨詢！本文由 EDITOR 發(fā)布在 國際競(jìng)賽，轉(zhuǎn)載此文請(qǐng)保持文章完整性，并請(qǐng)附上文章來源（國際競(jìng)賽）及本頁鏈接。原文鏈接：