Year 12 Maths Standard Checkpoint 2 ~25 min

Checkpoint 2: Network Optimisation

Covers Lessons 7–12: minimum spanning trees, shortest paths, maximum flow, and mixed network problems.

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Know

Key Facts

Kruskal's and Prim's steps
Dijkstra's process
Max-flow min-cut theorem

Understand

Concepts

When to use each algorithm
Why MST ≠ shortest path
Flow conservation

Can Do

Skills

Apply all algorithms
Identify problem types
Solve multi-part questions

Multiple Choice

Revision Multiple Choice

10 questions drawn from Lessons 7–12

Short Answer

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Extended Questions

ApplyBand 4

1. Network: AB=5, AC=2, BC=3, BD=4, CD=1, CE=6, DE=3. (a) Find MST using Kruskal's. (b) Find shortest path A→E using Dijkstra's. (c) If directed A→B(5), A→C(2), B→C(3), B→D(4), C→D(1), C→E(6), D→E(3), find max flow A→E. 4 MARKS

Answer in your workbook</div><div class="autosave-indicator" id="save-cp2-q1"></div></div>
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      <div class="question-meta"><span class="bloom-badge bloom-analyse">Analyse</span><span class="band-badge band-5">Band 5</span></div>
      <p>2. (a) Explain why Prim's and Kruskal's always find MSTs with the same total weight. (b) A student finds an MST of weight 20 and claims the shortest path between two vertices in this MST is also 20. Explain the error. (c) In a max flow problem, if all edge capacities are integers, must the max flow be an integer? Explain. <span class="marks">3 MARKS</span></p>
      <div class="answer-wrap"><textarea class="answer-textarea" data-key="maths-std-y12-m5-cp2-q2" style="min-height:200px" placeholder="(a) Both are proven correct algorithms for MST. The MST total weight is unique (though the specific edges may not be). So both find a tree with that unique minimum weight.
(b) MST total weight is the sum of ALL n-1 edges. The shortest path between two vertices uses only some of those edges, so is much smaller.
(c) Yes — with integer capacities, the Ford-Fulkerson algorithm (and inspection method) only adds integer flows, so max flow is integral.">

Answer in your workbook

Comprehensive Answers

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Short Answer Model Answers

Q1 (4 marks): (a) MST edges and total = 9 [1.5]. (b) Shortest path = 6 [1]. (c) Max flow = 7 [1.5].

Q2 (3 marks): (a) Explanation [1]. (b) Error explained [1]. (c) Yes with reason [1].

Mark checkpoint as complete

Tick when you have finished all questions and checked your answers.

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