You're viewing free preview questions — 4 questions previewing here — subscribe to unlock 83 more, plus the Full Question Bank, Mock Papers & Worksheets.Upgrade
General Term nth Term of a Sequence — Free MYP5 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
4 marks~6 minCriterion D
A student records the battery percentage of a smartphone during continuous video playback.
The student models battery drain using:
where is the battery percentage and is the time in hours.
| Time (hours) | 0 | 2 | 4 | 6 | 8 |
|---|---|---|---|---|---|
| Battery (%) | 100 | 75 | 50 | 25 | 0 |
The student models battery drain using:
where is the battery percentage and is the time in hours.
a
Calculate the predicted battery percentage after 3 hours. [1]
b
The student claims the model can be used to schedule a 90-minute video call starting at hours. Using the model, determine whether the battery will last the full call, then advise the student whether the linear model is reliable for this scheduling decision. [3]
Solutions
3QuestionFinding Term Position Given ValueAssessment Practice
7 marks~11 minCriterion A
A student opens a savings account with an initial deposit of 500 dollars. Each month, exactly 25 dollars is added, forming an arithmetic sequence.
a
Show that the account balance first reaches 875 dollars in month 16. [2]
b
The student considers making an additional one-off deposit of 200 dollars at the start of month 10. Deduce the new month in which the balance would first reach 875 dollars under this revised plan. [2]
c
The arithmetic model assumes a constant monthly increase of 25 dollars. Advise the student whether this model is reliable for predicting their long-term account balance, discussing at least two real-world factors in your response. [3]
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
That's every free question here — 4 of 87.
+83 more questions, plus Mock Papers & Worksheets, are waiting in Premium.