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Karnataka SSLC (Class 10) Mathematics — practice by topic

Browse 145 questions across 25 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

Binomial Theorem (55)Geometry (55)Probability & Statistics (55)Sequences (55)Sequences and Series (55)Vectors & 3D Geometry (55)Correlation and Regression (38)Linear Programming (38)Mean (38)Median (38)Permcomb (38)Permutations and Combinations (38)Probability (38)Algebra (29)Logarithms (29)Number Theory (29)Quadratic Equations (28)Probability Density Function (26)Probability Distribution (26)Arithmetic Progressions (21)Coordinate Geometry (12)Introduction to Trigonometry (12)Real Numbers (12)Pair of Linear Equations in Two Variables (11)Polynomials (11)

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A list of numbers in which each term is obtained by adding a fixed number to the preceding term is calledRead the answer and worked solution →For an AP with first term $a$ and common difference $d$, the general form isRead the answer and worked solution →The common difference of the AP $3,\ 7,\ 11,\ 15,\ \ldots$ isRead the answer and worked solution →The formula for the $n$th term of an AP with first term $a$ and common difference $d$ isRead the answer and worked solution →

Worked practice questions

A list of numbers in which each term is obtained by adding a fixed number to the preceding term is called

  1. a geometric progression
  2. a harmonic progression
  3. an arithmetic progression
  4. a Fibonacci sequence
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Correct answer: C. an arithmetic progression

1. In such a list the difference between any term and the one before it is constant. 2. This list is an **arithmetic progression (AP)**. 3. The fixed number added is called the common difference d. _Source: Karnataka SSLC (KSEEB) Class 10 Mathematics, Ch1 'Arithmetic Progressions' (definition)_

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For an AP with first term $a$ and common difference $d$, the general form is

  1. $a,\ ad,\ ad^2,\ \ldots$
  2. $a,\ a-d,\ a-2d,\ a-3d$ only
  3. $a,\ 2a,\ 3a,\ \ldots$
  4. $a,\ a+d,\ a+2d,\ \ldots$
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Correct answer: D. $a,\ a+d,\ a+2d,\ \ldots$

1. Each term is the previous term plus the common difference d. 2. Starting from a: a, a+d, a+2d, a+3d, …, which is the **general form of an AP**. 3. (Geometric progressions multiply by a fixed ratio instead.) _Source: Karnataka SSLC (KSEEB) Class 10 Mathematics, Ch1 'Arithmetic Progressions' (general form)_

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The common difference of the AP $3,\ 7,\ 11,\ 15,\ \ldots$ is

  1. 4
  2. 3
  3. 7
  4. 11
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Correct answer: A. 4

1. The common difference is d = (any term) − (previous term). 2. d = 7 − 3 = 4 (and 11 − 7 = 4, 15 − 11 = 4). 3. So d = 4. _Source: Karnataka SSLC (KSEEB) Class 10 Mathematics, Ch1 'Arithmetic Progressions' (common difference)_

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