Maths › Flashcards › Decision 1: lesson checks, part 1

Decision 1: lesson checks, part 1 flashcards

This deck has 6 check-yourself questions and 6 spot-the-error cards. The misconception each lesson corrects, and its check-yourself question with the worked answer. Rate each answer, and the card comes back sooner or later depending on how you rated it.

Further Maths · all 584 maths cards

How the five kinds differ

Standard results ask you to recall a formula or a value. Definitions ask you to state a mathematical term precisely. Recall prompts ask for a rule, condition or method. Check yourself cards are a short question with its answer. Spot the error cards ask you to correct a statement that is wrong.

Every card in this deck

Choose any card to try it in the player above. Each card links to the lesson that teaches it.

• A good algorithm is one that always finds the best possible answer.Spot the error
• Items of size 6, 3, 5, 4, 2 are packed into bins of size 8. Find the lower bound and pack them by first fit decreasing.Check
• A graph with an even number of odd nodes has an Eulerian circuit.Spot the error
• A connected graph has nodes of order 2, 3, 3, 4 and 4. Is it Eulerian, semi-Eulerian or neither?Check
• Prim's and Kruskal's algorithms can give trees of different total weight, so it is worth trying both.Spot the error
• A network has 8 nodes. How many edges does its minimum spanning tree have, and what happens if you take one more?Check
• Dijkstra's algorithm finds the shortest route by choosing the smallest edge at each node along the way.Spot the error
• In a Dijkstra solution the final labels are P 0, Q 4, R 9 and S 11, and the edge RS has weight 2. Is RS on the shortest route to S?Check
• In route inspection you repeat the shortest edges in the network until every node has even order.Spot the error
• A network of total weight 80 has odd nodes P, Q, R, S with shortest paths PQ 6, PR 9, PS 11, QR 8, QS 5, RS 7. Find the shortest closed route.Check
• Loading the items with the greatest profit per kilogram first fills a knapsack for the greatest profit.Spot the error
• A rucksack carries 9 kg. The items are F at 3 kg for £18, G at 5 kg for £35 and H at 6 kg for £39. Load by profit per kilogram, and say whether that load is the best there is.Check

The lessons these cards come from

• Algorithms, sorting and bin packing
• Further packing and the knapsack problem
• Graphs: order, Eulerian paths and planarity
• Minimum spanning trees: Prim and Kruskal
• Route inspection
• Shortest paths: Dijkstra and Floyd

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