General Rules and nth Terms
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General Rules and nth Terms — Free MYP3 Mathematics Practice Questions

1QuestionSolving Problems with nth Term in ContextConcept Practice
2 marks~3 minCriterion B
The diagram shows rows of unit squares placed side by side.

Arrangement 1: perimeter =4= 4 cm
Arrangement 2: perimeter =6= 6 cm
Arrangement 3: perimeter =8= 8 cm
a
Write down the nthnth term formula for the perimeter of arrangement nn. [1]
b
Calculate the perimeter of the 10th arrangement. [1]
Question diagram

Solutions

2QuestionEvaluating Terms Using nth Term RuleAssessment Practice
7 marks~11 minCriterion D
A conservation agency monitors a reintroduced bird species. The predicted population after nn years is given by the rule P=3n+50P = 3n + 50.
a
Calculate the predicted population for years 1, 5, and 10. Show your working. [3]
b
Explain why a linear model may not accurately predict the population after many years. [2]
c
The agency observes that the actual population in year 10 is 74 birds. Interpret what this difference tells you about the model's predictions. [2]
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Solutions

3QuestionEvaluating Terms Using nth Term RuleConcept Practice
2 marks~3 minCriterion A
A sequence of regular pentagons has side lengths defined by the nth term rule Tn=2n+1T_n = 2n + 1 cm.

Calculate the side length of the 5th pentagon in this sequence. [2]
Question diagram

Solutions

4QuestionEvaluating Terms Using nth Term RuleAssessment Practice
4 marks~6 minCriterion C
The nnth term of a sequence is given by 4n−34n - 3.
a
Calculate the 5th term of the sequence. [1]
b
A student claims the 10th term is 43. Calculate the correct value and explain the error the student made. [2]
c
Another sequence has nnth term 4n+54n + 5. Analyse how the two sequences are related and justify which sequence will always produce greater values. [1]

Solutions

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