Rational and Irrational Numbers
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Rational and Irrational Numbers — Free MYP2 Mathematics Practice Questions

1QuestionDefining Irrational NumbersConcept Practice
2 marks~3 minCriterion A
The diagram shows a right triangle with legs measuring 2 cm and 3 cm.
a
Calculate the length of the hypotenuse. [1]
b
State whether this length is rational or irrational, and explain how the definition of an irrational number supports your answer. [1]
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Solutions

2QuestionRational Numbers as Terminating and Repeating DecimalsAssessment Practice
3 marks~5 minCriterion B
The table shows five fractions and whether their decimal form is terminating (T) or repeating (R).

Fraction: 12, 13, 14, 16, 17\dfrac{1}{2},\ \dfrac{1}{3},\ \dfrac{1}{4},\ \dfrac{1}{6},\ \dfrac{1}{7}

Decimal type: T, R, T, R, R
a
Identify the prime factors of the denominator 6. [1]
b
Explain why 14\dfrac{1}{4} gives a terminating decimal but 16\dfrac{1}{6} gives a repeating decimal. [1]
c
Compare the denominators that give terminating decimals with those that give repeating decimals, and state the rule that predicts which type will occur. [1]
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Solutions

3QuestionRational Numbers as Terminating and Repeating DecimalsAssessment Practice
4 marks~6 minCriterion C
A student measures a table and records its length as 1.333...1.333... m.
a
Explain why the fraction 43\dfrac{4}{3} is equal to the repeating decimal 1.333...1.333... [2]
b
The student claims the table's length is exactly 43\dfrac{4}{3} m. Explain whether this claim can be justified, given that the ruler has millimetre markings. [2]
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4QuestionIrrational Numbers in Square Roots and PiAssessment Practice
4 marks~6 minCriterion D
A student measures the circumference of a circular garden as C=15.7C = 15.7 m (precision: ±0.1\pm 0.1 m) and uses C=2πrC = 2\pi r to calculate the radius as r=2.5r = 2.5 m.
a
State whether the calculated radius is exact or approximate. [1]
b
Calculate the radius using π≈3.1416\pi \approx 3.1416 instead of 3.143.14, and explain how this affects the result. [2]
c
Compare the reliability of the measured circumference with the reliability of the calculated radius. [1]
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Solutions

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