School / IB / MATH AA HL / Number and algebra Question practice
Number and algebra About this practice HL-only depth: counting principles, complex numbers in Cartesian and polar forms, proof, and linear systems.
Mathematics AA: Higher Level Number and algebra
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23 An infinite geometric series has first term 8 and common ratio 0.5. Calculate the sum to infinity, stating the condition required for this sum to exist. Paper 2 style Easy 3 marks Calculator + 24 Marking analysis: A learner attempts the following task: “An infinite geometric series has first term 8 and common ratio 0.5. Calculate the sum to infinity, stating the condition required for this sum to exist.” Their response addresses only this point: “States that the condition |r| < 1 is required for the sum to infinity to exist.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Easy 3 marks Calculator + 25 The quadratic equation 2x² − 7x + 3 = 0 has roots α and β. Without solving for the roots directly, calculate the value of α + β and αβ. Paper 2 style Easy 3 marks Calculator + 26 Marking analysis: A learner attempts the following task: “The quadratic equation 2x² − 7x + 3 = 0 has roots α and β. Without solving for the roots directly, calculate the value of α + β and αβ.” Their response addresses only this point: “States that for ax² + bx + c = 0, the sum of roots α + β = −b/a.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Easy 3 marks Calculator + 29 Find the number of ways in which 5 people can be seated around a circular table, where rotations of the same arrangement are considered identical. Paper 2 style Easy 3 marks Calculator + 30 Marking analysis: A learner attempts the following task: “Find the number of ways in which 5 people can be seated around a circular table, where rotations of the same arrangement are considered identical.” Their response addresses only this point: “States that for circular arrangements, one person's position can be fixed to remove rotational duplicates, leaving (n − 1)! distinct arrangements.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Easy 3 marks Calculator + Self-assessed Not marked yet
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