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General Term nth Term of a Sequence — Free MYP4 Mathematics (Extended) Practice Questions
1QuestionFinding Term Position Given ValueConcept Practice
2 marks~3 minCriterion C
A lighting technician programs a theatre spotlight to increase in brightness by a fixed amount each second. The brightness at second 1 is 12 lumens, and the brightness increases by 8 lumens per second.
Deduce the position of the term in this arithmetic sequence that has value , expressing in terms of , , and . Show all algebraic steps clearly. [2]
Deduce the position of the term in this arithmetic sequence that has value , expressing in terms of , , and . Show all algebraic steps clearly. [2]
Solutions
2QuestionApplications in Tables and GraphsAssessment Practice
2 marks~3 minCriterion D
Outline one real-world context where the nth term of a linear sequence is used to make predictions. The scenario involves a student saving money each week. The savings are recorded in the following rows: Week: 1, 2, 3, 4 Savings (dollars): 5, 10, 15, 20
a
Determine the nth term rule for the sequence.
b
Use the rule to predict the savings at Week 12.
c
Discuss one limitation of using this linear model for long-term savings predictions.
Solutions
3QuestionApplications in Tables and GraphsAssessment Practice
6 marks~9 minCriterion A
A scientist records the temperature of a cooling liquid every minute. The temperatures in degrees Celsius are: 90, 82, 74, 66, 58.
a
Find the nth term rule for this sequence.
b
Use your rule to predict the temperature after 10 minutes.
c
The liquid becomes unsafe at temperatures below 10°C. Use your model to determine when the temperature will first drop below 10°C.
d
Evaluate the appropriateness and impact of using this linear model for the cooling process. In your response, compare the predicted temperature at 10 minutes with the actual temperature if the cooling slows over time. Discuss at least two limitations of the model and explain the real-world impact of relying on this model for safety decisions.
Solutions
4QuestionApplications in Tables and GraphsAssessment Practice
4 marks~6 minCriterion B
A city's two water-storage tanks are monitored over time.
Tank A — volume recorded at hourly intervals:
(hours): 1, 2, 3, 4, 5
(litres): 3, 7, 11, 15, 19
Tank B — volume recorded at hourly intervals:
(hours): 1, 2, 3, 4, 5
(litres): 2, 6, 12, 20, 30
Tank A — volume recorded at hourly intervals:
(hours): 1, 2, 3, 4, 5
(litres): 3, 7, 11, 15, 19
Tank B — volume recorded at hourly intervals:
(hours): 1, 2, 3, 4, 5
(litres): 2, 6, 12, 20, 30
a
Calculate the first differences for Tank A. Justify whether the relationship between and is linear or quadratic. [1]
b
Deduce an expression for in terms of for Tank A. [1]
c
Calculate the first and second differences for Tank B. Justify whether the relationship between and is linear or quadratic. [1]
d
Deduce an expression for in terms of for Tank B. [1]
(e) Both tanks have a maximum capacity of 115 litres. Using your expressions, determine at which integer hour each tank first reaches or exceeds this capacity. Advise the city's water management team which tank requires priority monitoring, and why. [1]
(e) Both tanks have a maximum capacity of 115 litres. Using your expressions, determine at which integer hour each tank first reaches or exceeds this capacity. Advise the city's water management team which tank requires priority monitoring, and why. [1]
Solutions
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