Comparing and Ordering Numbers
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Comparing and Ordering Numbers — Free MYP2 Mathematics Practice Questions

1QuestionInequalities and SymbolsConcept Practice
2 marks~3 minCriterion A
The number line below shows points marked at −3-3, 00, and 55.
a
Identify the inequality symbol needed when an open circle is used on a number line. [1]
b
Write the inequality that represents the shaded region shown on the number line. [1]
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Solutions

2QuestionInequalities and SymbolsAssessment Practice
4 marks~6 minCriterion D
A student measures a plant's height using a ruler marked in whole centimetres only and records it as 12 cm. The actual height lies somewhere in the range 11.5≤height≤12.511.5 \leq \text{height} \leq 12.5 (in cm).
a
State what the notation ≤\leq means in the inequality above. [1]
b
Explain why the inequality 11.5≤height≤12.511.5 \leq \text{height} \leq 12.5 is a more honest record of the measurement than writing "height = 12 cm." [2]
c
Identify one real-world limitation of using this inequality to describe the plant's height. [1]
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Solutions

3QuestionInequalities and SymbolsConcept Practice
3 marks~5 minCriterion C
A number line shows points at −3-3 and 44. The inequality x<−3x < -3 is shown to the left of −3-3, and x>4x > 4 is shown to the right of 44. Both regions are shaded.
a
Identify one value of xx that satisfies x<−3x < -3 and one value that satisfies x>4x > 4. [1]
b
Explain why no single value of xx can satisfy both x<−3x < -3 and x>4x > 4 at the same time. [1]
c
Compare the two shaded regions and describe what this tells you about the solution set for both inequalities together. [1]
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Solutions

4QuestionInequalities and SymbolsAssessment Practice
5 marks~8 minCriterion B
Given a=−3a = -3, b=1b = 1, and c=4c = 4, where a<ba < b and b<cb < c.
a
Identify the positions of aa, bb, and cc on the number line below by labelling each point. [1]
b
Explain why a<ca < c is true for these values, using the number line. [2]
c
Compare the statement "if a<ba < b and b<cb < c, then a<ca < c" with what your number line shows. Does this pattern hold for any real numbers? Give a reason. [2]
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Solutions

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