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ICSE Class 10 Algebra: Expansions, Factorisation & Indices — practice questions

Explore 50 free Algebra: Expansions, Factorisation & Indices questions in ICSE Class 10 Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Algebra: Expansions, Factorisation & Indices questions and exercises with answers

Showing questions 1–30 of 50.

In an isosceles right triangle each equal side is 10 cm. The hypotenuse isRead the answer and worked solution →Express 4 x - 5 y + 20 = 0 with y as the dependent variable.Read the answer and worked solution →The point (3, -2) lies in which quadrant?Read the answer and worked solution →If a point lies on the x-axis, its y-coordinate isRead the answer and worked solution →Expand the algebraic expression (3x + 2y)^2.Read the answer and worked solution →Given that a + b = 7 and ab = 10, evaluate a^2 + b^2.Read the answer and worked solution →Cutting a square of side a + b gives two squares and how many rectangles?Read the answer and worked solution →Which algebraic expression is identically equal to (a - b)^2?Read the answer and worked solution →Find the numerical value of (a - b)^2 when a + b = 9 and ab = 14.Read the answer and worked solution →When x + 1/x equals 3, compute the fourth power sum x^4 + 1/x^4.Read the answer and worked solution →Expand the trinomial (a + b + c)^2.Read the answer and worked solution →If a + b + c = 9 and ab + bc + ca = 23, find a^2 + b^2 + c^2.Read the answer and worked solution →How many rectangular boxes are formed when a cube of side a + b is cut?Read the answer and worked solution →Factorisation expresses a polynomial as a product of what factors?Read the answer and worked solution →An irreducible polynomial cannot be factored into two what?Read the answer and worked solution →Up to sign, the content of an integer polynomial is what of coefficients?Read the answer and worked solution →An integer polynomial is primitive if the GCD of its coefficients equals:Read the answer and worked solution →Content-primitive factorisation writes an integer polynomial as a:Read the answer and worked solution →According to Gauss's lemma, the product of two primitive polynomials is:Read the answer and worked solution →A primitive polynomial is irreducible over rationals if irreducible over:Read the answer and worked solution →If two factors of a polynomial match, it is a multiple of their:Read the answer and worked solution →Any multiple factor of a polynomial must also be a factor of its:Read the answer and worked solution →Which test finds all rational linear factors of an integer polynomial?Read the answer and worked solution →Factoring a reducible cubic completely yields three linear factors or:Read the answer and worked solution →Kronecker's polynomial factorisation method relies on evaluation at:Read the answer and worked solution →A polynomial GCD of two polynomials is a common factor polynomial of:Read the answer and worked solution →Every common divisor of two polynomials p and q must also divide their:Read the answer and worked solution →Multiply (3 * 10^4) by (2 * 10^5) in standard scientific form.Read the answer and worked solution →The distance between (0, 0) and (3, 4) isRead the answer and worked solution →In an equation written as y = 3 x - 6, the dependent variable isRead the answer and worked solution →

Worked practice questions

In an isosceles right triangle each equal side is 10 cm. The hypotenuse is

  1. 5 sqrt(2) cm
  2. 20 cm
  3. 10 sqrt(3) cm
  4. 10 sqrt(2) cm
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Correct answer: D. 10 sqrt(2) cm

1. Two legs equal 10 cm each. 2. c^2 = 100 + 100 = 200. 3. c = sqrt(200) = 10 sqrt(2) cm. 4. So option A is correct. _Source: Selina Concise Mathematics Class 9, Ch on Pythagoras Theorem (Mistral OCR'd PDF), section on isosceles right triangle_

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Express 4 x - 5 y + 20 = 0 with y as the dependent variable.

  1. y = (4 x + 20) / 5
  2. y = (5 x - 20) / 4
  3. y = (4 x - 20) / 5
  4. y = 4 x - 5 + 20
Show answer and solution

Correct answer: A. y = (4 x + 20) / 5

1. Start with 4 x - 5 y + 20 = 0. 2. Move y terms: 5 y = 4 x + 20. 3. Divide by 5: y = (4 x + 20)/5. 4. Matches Example given in the chapter. _Source: Selina Concise Mathematics Class 9, Ch 26 Co-ordinate Geometry (Mistral OCR'd PDF), Example in section 26.2_

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The point (3, -2) lies in which quadrant?

  1. First quadrant
  2. Fourth quadrant
  3. Second quadrant
  4. Third quadrant
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Correct answer: B. Fourth quadrant

1. x = 3 > 0 and y = -2 < 0. 2. Positive x with negative y locates a point below the x-axis to the right. 3. That region is the fourth quadrant. 4. So option A is correct. _Source: Selina Concise Mathematics Class 9, Ch 26 Co-ordinate Geometry (Mistral OCR'd PDF), section on quadrants_

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