Positive and Negative Numbers Integers
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Positive and Negative Numbers Integers — Free MYP3 Mathematics Practice Questions

1QuestionComparing and Ordering IntegersConcept Practice
2 marks~3 minCriterion A
A thermometer shows three temperatures: −5°C-5°C, 0°C0°C, and 3°C3°C.
a
Compare the three temperatures and identify the coldest and the warmest. [1]
b
List all three temperatures in ascending order. Explain how you know which temperature is least. [1]
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Solutions

2QuestionOpposites and Zero on the Number LineAssessment Practice
4 marks~6 minCriterion C
A weather station records daily high temperatures:

Monday: +8°C+8°C
Tuesday: −3°C-3°C
Wednesday: 0°C0°C
Thursday: +5°C+5°C
Friday: −7°C-7°C

A student claims: "0°C0°C means no temperature, so Wednesday had no heat energy."
a
Explain how 0°C0°C acts as a reference point on the number line, using at least two temperatures from the data to support your answer. [2]
b
Explain one real-world problem that arises from treating 0°C0°C as "nothing," and refer to +8°C+8°C and −3°C-3°C as opposites in your response. [2]
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Solutions

3QuestionAbsolute Value of an IntegerAssessment Practice
6 marks~9 minCriterion D
A city planner checks whether five buildings comply with a height limit of 50 m.

Building 1: 47 m
Building 2: 53 m
Building 3: 49 m
Building 4: 52 m
Building 5: 48 m

The planner measures total deviation by calculating ∣height−50∣|\text{height} - 50| for each building and summing the results.
a
Calculate the total deviation from the height limit. [2]
b
Explain one limitation of using absolute value to measure compliance in this situation. [2]
c
A revised model only penalises buildings that exceed the limit. Analyse whether this revised model is more useful to the city planner, using the data above to support your answer. [2]
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Solutions

4QuestionAbsolute Value of an IntegerAssessment Practice
4 marks~6 minCriterion B
The absolute value of an integer is its distance from zero on the number line.

Integer: +3, −3, +7, −7, +10, −10+3,\ -3,\ +7,\ -7,\ +10,\ -10
Absolute value: 3, 3, 7, 7, 10, 103,\ 3,\ 7,\ 7,\ 10,\ 10
a
Describe a general rule for the absolute value of any integer nn, writing your rule using nn. [2]
b
Apply your rule to show that ∣−15∣=15|-15| = 15, stating which part of your rule you used. [1]
c
A student claims: "Because ∣−20∣|-20| and ∣+20∣|+20| give the same result, absolute value tells us nothing useful about the original integer." Justify whether this claim is correct or incorrect. [1]

Solutions

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