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ICSE Class 10 Mathematics — practice by topic

Browse 1,044 questions across 11 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

Algebra: Equations, Inequations & Matrices (212)Commercial Mathematics: GST, Banking & Shares (152)Geometry: Similarity, Circles & Loci (121)Statistics and Probability (112)Arithmetic & Geometric Progressions (81)Coordinate Geometry (77)Quadratic Equations (74)Mensuration: Surface Areas & Volumes (65)Algebra: Expansions, Factorisation & Indices (50)Algebra: Simultaneous Linear Equations & Quadratics (50)Trigonometry (50)

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Standard form of a quadratic equation isRead the answer and worked solution →Which of the following is a quadratic equation?Read the answer and worked solution →The quadratic formula gives the roots of ax^2 + bx + c = 0 asRead the answer and worked solution →The quantity b^2 - 4ac is called theRead the answer and worked solution →

Worked practice questions

Standard form of a quadratic equation is

  1. ax^2 + bx + c = 0 with a not 0
  2. ax + b = 0 with a not 0 only
  3. ax^3 + bx + c = 0 of degree three
  4. ax^2 + bx + c = a non-zero number
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Correct answer: A. ax^2 + bx + c = 0 with a not 0

1. A quadratic is a polynomial equation of degree two. 2. Its general form has a, b, c with a not equal to zero. 3. If a = 0 the equation reduces to linear. 4. So the standard form is ax^2 + bx + c = 0. _Source: Selina Concise Mathematics Class 10, Ch 5 Quadratic Equations (Mistral OCR'd PDF), section on standard form_

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Which of the following is a quadratic equation?

  1. 2x + 7 = 0 of degree one
  2. x^2 - 5x + 6 = 0
  3. x^3 + 4x = 0 of degree three
  4. 1/x = 7 of fractional form
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Correct answer: B. x^2 - 5x + 6 = 0

1. A quadratic has its variable's highest power equal to 2. 2. Option A is x^2 - 5x + 6 = 0 with a = 1. 3. Options B is linear, C is cubic, D is rational. 4. So only option A is quadratic. _Source: Selina Concise Mathematics Class 10, Ch 5 Quadratic Equations (Mistral OCR'd PDF), section on identification_

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The quadratic formula gives the roots of ax^2 + bx + c = 0 as

  1. x = (b plus or minus sqrt(b^2 - 4ac)) / (4a)
  2. x = (b plus or minus sqrt(b^2 + 4ac)) / (2a)
  3. x = (-b plus or minus sqrt(b^2 - 4ac)) / (2a)
  4. x = (-b plus or minus sqrt(b^2 + 4ac)) / a
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Correct answer: C. x = (-b plus or minus sqrt(b^2 - 4ac)) / (2a)

1. Start from ax^2 + bx + c = 0 and complete the square. 2. Rearranging gives x = (-b plus or minus sqrt(b^2 - 4ac)) / (2a). 3. This is Sridharacharya's rule mentioned in the chapter. 4. So option A is correct. _Source: Selina Concise Mathematics Class 10, Ch 5 Quadratic Equations (Mistral OCR'd PDF), section on quadratic formula_

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