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Andhra Pradesh SSC (Class 10) Mathematics — practice by topic

Browse 634 questions across 16 Mathematics topics. Choose what you want to revise, then open a question to check its answer and worked solution.

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Mathematics topics

Real Numbers and Polynomials (115)Arithmetic Progression (95)Statistics and Probability (71)Quadratic Equations (63)Linear Equations in Two Variables (51)Triangles and Circles (50)Introduction to Trigonometry (46)Surface Areas and Volumes (32)Areas Related to Circles (31)Circles (23)Value Added Tax (20)Some Applications of Trigonometry (16)Coordinate Geometry (12)Mensuration: Surface Areas & Volumes (7)Polygons (1)Trigonometric Identities (1)

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Which of the following fractions will have a non-terminating recurring decimal expansion?Read the answer and worked solution →Which of the following rational numbers has a terminating decimal expansion?Read the answer and worked solution →Let $r$ be a non-zero rational number and $x$ be an irrational number. Which of the following must be irrational?Read the answer and worked solution →Which statement is always true about the sum of a rational number and an irrational number?Read the answer and worked solution →

Worked practice questions

Which of the following fractions will have a non-terminating recurring decimal expansion?

  1. $\frac{3}{40}$
  2. $\frac{7}{125}$
  3. $\frac{11}{24}$
  4. $\frac{9}{20}$
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Correct answer: C. $\frac{11}{24}$

A rational number has a recurring decimal if, in lowest terms, the denominator contains a prime factor other than 2 or 5. Since $24=2^3\times 3$ contains 3, $\frac{11}{24}$ is non-terminating recurring. The others have denominators made only of 2s and 5s.

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Which of the following rational numbers has a terminating decimal expansion?

  1. $\frac{7}{12}$
  2. $\frac{13}{25}$
  3. $\frac{11}{18}$
  4. $\frac{5}{21}$
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Correct answer: B. $\frac{13}{25}$

A rational number terminates when, in lowest terms, its denominator has only 2s and/or 5s as prime factors. Here $25=5^2$, so $\frac{13}{25}$ terminates. The other denominators contain 3 or 7, so they are recurring decimals.

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Let $r$ be a non-zero rational number and $x$ be an irrational number. Which of the following must be irrational?

  1. Only $r+x$
  2. Only $rx$
  3. Both $r+x$ and $\frac{x}{r}$
  4. Neither $r+x$ nor $rx$
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Correct answer: C. Both $r+x$ and $\frac{x}{r}$

The notes state that the sum of a rational and an irrational number is irrational. They also state that the product and quotient of a non-zero rational number and an irrational number are irrational. **Hence both $r+x$ and $x/r$ are irrational.**

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