Estimation Rounding and Significant Figures
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Estimation Rounding and Significant Figures — Free MYP4 Mathematics (Extended) Practice Questions

1QuestionApproximations in Scientific and Everyday ContextsConcept Practice
2 marks~3 minCriterion A
State the formula for percentage error, where AA is the approximate value and EE is the exact value. [2]

Solutions

2QuestionUse of Estimation in Checking ResultsAssessment Practice
2 marks~3 minCriterion C
A surveyor is mapping a triangular plot of land, triangle ABCABC. The angle at vertex AA measures ∠BAC=110°\angle BAC = 110°. The diagram shows that ∠ABC\angle ABC is visibly smaller than ∠ACB\angle ACB.
a
Deduce the combined size of ∠ABC\angle ABC and ∠ACB\angle ACB, showing your working. [1]
b
Estimate the size of ∠ABC\angle ABC, justifying your answer using the diagram and your result from part (a). [1]
Question diagram

Solutions

3QuestionRounding Large and Small NumbersAssessment Practice
6 marks~9 minCriterion D
A city's population is currently estimated at 2.36 million. Planners use the exponential growth model

P(t)=P0 ektP(t) = P_0 \, e^{kt}

where P(t)P(t) is the population after tt years, P0P_0 is the initial population, kk is the annual growth rate, and tt is time in years. The city's annual growth rate is 3.8\%.
a
Calculate the projected population after 50 years. Round your answer to three significant figures. [2]
b
Explain how rounding P0P_0 to the nearest million and kk to the nearest whole percent each affect the 50-year projection, and describe one consequence for resource planning. [2]
c
The city council must decide whether to begin construction of three new hospitals now, each designed to serve 1.5 million people. Using your projection and the limitations of the model, advise the council whether to proceed with all three, fewer, or more hospitals. [2]
Question diagram

Solutions

4QuestionApproximations in Scientific and Everyday ContextsAssessment Practice
2 marks~3 minCriterion B
A student rounds each grocery item to the nearest dollar before totalling the bill.

Estimated price (dollars)25324118
Actual price (dollars)25.4531.5039.8017.75
Rounding error (dollars)−0.450.501.200.25
Percentage error−1.8%1.6%3.0%1.4%


Analyse the data to identify the relationship between the magnitude of the rounding error and the percentage error, and explain why this relationship exists using the percentage error formula. [2]

Solutions

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