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Practise

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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12 questions

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-LP-Q011 markL1 FoundationNon-calculatorGraphical
In a linear programme with a bounded feasible region, the optimum always occurs
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-DM-LP-X031 markL1 FoundationNon-calculatorGraphical
For the same problem, find PP at the vertex (0,4)(0,4).

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Salam Academy Original Practice · Proposed mark scheme
SA-DM-LP-X041 markL1 FoundationNon-calculatorGraphical
How many vertices does the feasible region of that problem have (including the origin)?

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Salam Academy Original Practice · Proposed mark scheme
SA-DM-LP-X051 markL1 FoundationNon-calculatorFormulating
"At least twice as many chairs (xx) as tables (yy)" is written as
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-DM-LP-0012 marksL2 StandardNon-calculatorGraphical
Maximise P=2x+3yP=2x+3y subject to x+y≤4x+y\le4, x+3y≤6x+3y\le6, x,y≥0x,y\ge0. Find the maximum value of PP.

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Salam Academy Original Practice · Proposed mark scheme
SA-DM-LP-0032 marksL2 StandardNon-calculatorFormulating
Chairs need 2 h and tables 3 h of labour; 60 h are available. What is the largest number of tables that could be made?

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Salam Academy Original Practice · Proposed mark scheme
SA-DM-LP-G012 marksL2 StandardNon-calculatorGraphical
Find the xx-coordinate where x+y=4x+y=4 meets x+3y=6x+3y=6.

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Salam Academy Original Practice · Proposed mark scheme
SA-DM-LP-X012 marksL2 StandardNon-calculatorGraphical
Find the yy-coordinate where x+2y=8x+2y=8 meets 3x+y=93x+y=9.

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Salam Academy Original Practice · Proposed mark scheme
SA-DM-LP-X022 marksL2 StandardNon-calculatorGraphical
Maximise P=3x+4yP=3x+4y subject to x+2y≤8x+2y\le8, 3x+y≤93x+y\le9, x,y≥0x,y\ge0. Find Pmax⁡P_{\max}.

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Salam Academy Original Practice · Proposed mark scheme
SA-DM-LP-X062 marksL2 StandardNon-calculatorSimplex
For P−3x−4y=0P-3x-4y=0 with x+2y+s1=8x+2y+s_1=8 and 3x+y+s2=93x+y+s_2=9, find the value of the first pivot element.

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Salam Academy Original Practice · Proposed mark scheme
SA-DM-LP-0042 marksL3 ExamNon-calculatorGraphical
For the region x+y≤4x+y\le4, x+3y≤6x+3y\le6, x,y≥0x,y\ge0, the objective is changed to P=x+kyP=x+ky. Find the largest kk for which (4,0)(4,0) is still optimal.

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Salam Academy Original Practice · Proposed mark scheme