A-Level考试刷题必备：新航道alevel分类真题训练合集

A-Level考试备考有什么好的学习资料?有不少刷题的alevel考生喜欢在网络上、线下书店寻找alevel资料，市面上那么多A-Level考试资料，哪家的资料更好，性价比高?下面我们推荐由新航道重庆学校A-Level教研团队出品的《alevel分类真题训练合集》。

新航道alevel刷题资料包含了数学、进阶数学、物理、化学、生物、心理学等主要科目，资料从多角度分析历次的A-Level考试题型，配合教材，精挑细选，全方位覆盖alevel考试真题，是alevel考生们勤思勤练的好助手。

建议大家拿到这套资料后，分门别类，按照主题练习，下面我们就先睹为快这套资料的真容(部分)。

一、算法

dijkstra 最短路径

Figure 1 represents a network of roads between ten villages, A, B, C, D, E, F, G, H, J and K. The number on each edge represents the length, in kilometres, of the corresponding road. The local council needs to find the shortest route from A to J.

(a) Use Dijkstra’s algorithm to find the shortest route from A to J. State the route and its length.

(6)

During the winter, the council needs to ensure that all ten villages are accessible by road even if there is heavy snow. The council wishes to minimise the total length of road it needs to keep clear.

(b) Use Prim’s algorithm, starting at A, to find a minimum connector for the five villages A, B, C, D and E. You must clearly state the order in which you select the edges of your minimumconnector.

(2)

(c) Use Kruskal’s algorithm to find a minimum connector for the five villages F, G, H, J and K.You must clearly show the order in which you consider the edges. For each edge, state whether or not you are including it in your minimum connector.

(2)

(d) Calculate the total length of road that the council must keep clear of snow to ensure that all tenvillages are accessible.Figure 3 models a network of roads. The number on each edge gives the time taken, in minutes, to travel along the corresponding road.

(a) Use Dijkstra’s algorithm to find the shortest time needed to travel from A to J. State the quickest route.

(6)

Alan needs to travel along all the roads to check that they are in good repair. He wishes to complete his route as quickly as possible and will start at his home, H, and finish at his workplace, D.

(b) By considering the pairings of all relevant nodes, find the arcs that will need to be traversed twice in Alan’s inspection route from H to D. You must make your method and working clear.

(5)

For Alan’s inspection route from H to D (c) (i) state the number of times vertex C will appear,

(ii) state the number of times vertex D will appear.

(2)

(d) Determine whether it would be quicker for Alan to start and finish his inspection route at H,instead of starting at H and finishing at D. You must explain your reasoning and show all your working.

Figure 3 represents a network of roads. The number on each arc represents the time taken, in minutes, to drive along the corresponding road.Malcolm wishes to minimise the time spent driving from his home at A to his office at H. The delays from roadworks on two of the roads leading in to H vary daily, and so the time taken to drive along these roads is expressed in terms of x, where x is fixed for any given day and x > 0

(a) Use Dijkstra’s algorithm to find the possible routes that minimise the driving time from A to H. State the length of each route, leaving your answer in terms of x where necessary.

(7)

On Monday, Malcolm needs to check each road. He must travel along each road at least once. He must start and finish at H and minimise the total time taken for his inspection route.

Malcolm finds that his minimum duration inspection route requires him to traverse exactly four roads twice and the total time it takes to complete his inspection route is 307 minutes.

(b) Calculate the minimum time taken for Malcolm to travel from A to H on Monday. You must make your method and working clear.

以上是本套ALEVEL资料部分内容，更多A-Level真题内容请在线咨询重庆新航道学校官网领取。