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Question bank

Original exam-style questions, mapped to your syllabus. Answers are checked for mathematical equivalence and every attempt updates your mastery.

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2450 questions · page 45 of 123 · choose a topic above to narrow them down

SA-DM-GR-0011 markL1 FoundationNon-calculatorTypes of graph
How many edges does K6K_6 have?

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Salam Academy Original Practice · Proposed mark scheme
SA-DM-GR-0021 markL1 FoundationNon-calculatorTypes of graph
How many edges does K3,4K_{3,4} have?

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Salam Academy Original Practice · Proposed mark scheme
SA-DM-GR-0041 markL1 FoundationNon-calculatorTypes of graph
How many edges does a tree with 1010 vertices have?

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Salam Academy Original Practice · Proposed mark scheme
SA-DM-GR-G011 markL1 FoundationNon-calculatorTerminology
A graph has vertex degrees 3,3,2,2,43,3,2,2,4. How many edges does it have?

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Salam Academy Original Practice · Proposed mark scheme
SA-DM-GT-G011 markL1 FoundationNon-calculatorSaddle points
Pay-offs to A: R1(3,−1,2)R_1(3,-1,2), R2(4,1,3)R_2(4,1,3), R3(−2,0,1)R_3(-2,0,1). Find A's play-safe value (maximin).

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Salam Academy Original Practice · Proposed mark scheme
SA-DM-LP-0021 markL1 FoundationNon-calculatorSimplex
How many slack variables are needed to put the constraints x+y≤4x+y\le4, x+3y≤6x+3y\le6 into simplex form?

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Salam Academy Original Practice · Proposed mark scheme
SA-DM-MS-G011 markL1 FoundationNon-calculatorKruskal
How many edges are in a spanning tree of a network with 88 vertices?

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Salam Academy Original Practice · Proposed mark scheme
SA-DM-RI-0021 markL1 FoundationNon-calculatorRoute inspection
How many ways can six odd vertices be paired?

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Salam Academy Original Practice · Proposed mark scheme
SA-DM-RI-G011 markL1 FoundationNon-calculatorRoute inspection
Find the total weight of the network AB4AB4, AC3AC3, BC2BC2, BD5BD5, CD6CD6, CE7CE7, DE3DE3.

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Salam Academy Original Practice · Proposed mark scheme
SA-DM-SP-G011 markL1 FoundationNon-calculatorDijkstra
In the network AB4AB4, AC3AC3, BC2BC2, BD5BD5, CD6CD6, CE7CE7, DE3DE3, which value does BB get as its final label from AA?

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Salam Academy Original Practice · Proposed mark scheme
SA-DM-TP-G011 markL1 FoundationNon-calculatorNorth-west corner
A problem has 2 supply points and 3 demand points. How many occupied cells must a non-degenerate solution have?

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Salam Academy Original Practice · Proposed mark scheme
SA-FM-C1-G011 markL1 FoundationNon-calculatorWalls
A ball hits a wall at 88 m s−1^{-1} with e=0.25e=0.25. Find its rebound speed.

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Salam Academy Original Practice · Proposed mark scheme
SA-FM-C2-G011 markL1 FoundationCalculatorOblique wall
A smooth ball hits a smooth wall at 1010 m s−1^{-1} at 60∘60^\circ to the wall. Find the velocity component parallel to the wall after impact.

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Salam Academy Original Practice · Proposed mark scheme
SA-FM-CL-G012 marksL1 FoundationNon-calculatorParticles
Masses of 22 kg and 66 kg are at x=0x=0 and x=4x=4. Find xˉ\bar x.

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Salam Academy Original Practice · Proposed mark scheme
SA-FM-EL-0022 marksL1 FoundationCalculatorElastic energy
Find the elastic potential energy in a spring of natural length 0.50.5 m and modulus 4040 N compressed by 0.10.1 m.

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Salam Academy Original Practice · Proposed mark scheme
SA-FM-EL-G012 marksL1 FoundationCalculatorHooke's law
An elastic string has natural length 22 m and modulus 3030 N. Find the tension when it is stretched to 2.52.5 m.

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Salam Academy Original Practice · Proposed mark scheme
SA-FM-FK-G012 marksL1 FoundationNon-calculatorVectors
r=t2i+(4t−t2)j\mathbf r=t^2\mathbf i+(4t-t^2)\mathbf j. Find the time when the particle moves parallel to i\mathbf i.

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Salam Academy Original Practice · Proposed mark scheme
SA-FM-RB-G012 marksL1 FoundationNon-calculatorConditions
A uniform rod ABAB of length 44 m and weight 6060 N rests horizontally on supports at AA and BB. Find the reaction at BB.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-CE-0011 markL1 FoundationNon-calculatorEccentricity
For the same ellipse, find the positive xx-coordinate of a focus.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-CP-0011 markL1 FoundationNon-calculatorFocus–directrix
The directrix of y2=8xy^2=8x is x=kx=k. Find kk.

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Salam Academy Original Practice · Proposed mark scheme