Salam Academy
Sign inCreate account
Practise

Question bank

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

Sign in to check answers. Your attempts build your mastery and error book.

2730 questions · page 111 of 137 · choose a topic above to narrow them down

SA-DM-GR-0032 marksL2 StandardNon-calculatorEuler
A connected planar graph has 66 vertices and 99 edges. How many faces does it have?

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-DM-GT-0012 marksL2 StandardNon-calculatorSaddle points
For the same game, find B's play-safe value (minimax of column maxima).

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-DM-GT-0031 markL2 StandardNon-calculatorMixed strategies
Find the value of that game to A.

Sign in or create a free account to check answers, get hints and track your progress.

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.

Sign in or create a free account to check answers, get hints and track your progress.

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?

Sign in or create a free account to check answers, get hints and track your progress.

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.

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-DM-MS-0013 marksL2 StandardNon-calculatorKruskal
Network edges: AB4AB4, AC3AC3, BC2BC2, BD5BD5, CD6CD6, CE7CE7, DE3DE3. Find the weight of the minimum spanning tree.

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-DM-MS-0021 markL2 StandardNon-calculatorPrim
Using Prim's algorithm from AA on the same network, what is the weight of the first edge chosen?

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-DM-MS-0031 markL2 StandardNon-calculatorPrim
Using Prim from AA, what is the weight of the third edge added?

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-DM-RI-0012 marksL2 StandardNon-calculatorRoute inspection
Find the length of the shortest closed route that traverses every edge of that network.

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-DM-RI-0032 marksL2 StandardNon-calculatorTSP bounds
For a TSP, deleting vertex AA leaves an MST of weight 1010. The two shortest edges from AA are 33 and 44. Find the lower bound.

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-DM-SP-0012 marksL2 StandardNon-calculatorDijkstra
Find the shortest distance from AA to DD.

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-DM-SP-0022 marksL2 StandardNon-calculatorDijkstra
Find the shortest distance from AA to EE.

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-DM-SP-0031 markL2 StandardNon-calculatorFloyd
In Floyd's algorithm, dBE=∞d_{BE}=\infty, dBD=5d_{BD}=5, dDE=3d_{DE}=3. After the iteration using DD, what is dBEd_{BE}?

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-DM-TP-0012 marksL2 StandardNon-calculatorNorth-west corner
Supplies A30A30, B20B20; demands X10X10, Y25Y25, Z15Z15. Unit costs: AA: X4X4, Y6Y6, Z8Z8; BB: X5X5, Y3Y3, Z7Z7. Find the cost of the north-west corner solution.

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-DM-TP-0022 marksL2 StandardNon-calculatorImproving
With RA=0R_A=0, find the shadow cost KZK_Z.

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-DM-TP-0031 markL2 StandardNon-calculatorImproving
Find the improvement index for cell AZAZ.

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-FM-C1-0013 marksL2 StandardNon-calculatorRestitution
Sphere A (22 kg, 55 m s−1^{-1}) hits sphere B (33 kg, at rest) directly with e=12e=\frac12. Find B's speed afterwards.

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-FM-C1-0022 marksL2 StandardNon-calculatorEnergy loss
In the last question, find the kinetic energy lost in joules.

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-FM-C1-0032 marksL2 StandardNon-calculatorWalls
A ball is dropped and hits the floor at 1010 m s−1^{-1}, rebounding at 66 m s−1^{-1}. Find ee.

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme