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ICSE Class 10 Algebra: Expansions, Factorisation & Indices — practice questions — page 2

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 31–50 of 50.

In Cartesian co-ordinates, the two perpendicular reference lines are calledRead the answer and worked solution →Express 4 x - 5 y + 20 = 0 with y as the dependent variable.Read the answer and worked solution →Distance between two points (x1, y1) and (x2, y2) is given byRead the answer and worked solution →If a point lies on the x-axis, its y-coordinate isRead the answer and worked solution →The distance between (1, 2) and (4, 6) isRead the answer and worked solution →Match each algebraic theorem with its mathematical statement:Read the answer and worked solution →Match each cubic identity with its algebraic expansion:Read the answer and worked solution →Match each special conditional cubic identity with its result:Read the answer and worked solution →Match each binomial product with its expansion:Read the answer and worked solution →Match each sum or difference of cubes with its factored binomial-trinomial form:Read the answer and worked solution →Match each polynomial with its complete factorisation:Read the answer and worked solution →Match each quadratic trinomial with its factored binomials:Read the answer and worked solution →Match each three-variable identity with its expanded polynomial:Read the answer and worked solution →In an isosceles right triangle each equal side is 10 cm. The hypotenuse isRead the answer and worked solution →The co-ordinates of a point are written in the orderRead the answer and worked solution →If a point lies on the y-axis, its x-coordinate isRead the answer and worked solution →The point (3, -2) lies in which quadrant?Read the answer and worked solution →The point of intersection of the x-axis and the y-axis is called theRead the answer and worked solution →The point (-4, 5) lies onRead the answer and worked solution →Zero slope, undefined slope, or neither?Read the answer and worked solution →

Worked practice questions

In Cartesian co-ordinates, the two perpendicular reference lines are called

  1. x-axis and y-axis
  2. Number line and origin only
  3. Vertical line and slope only
  4. Slope and intercept only
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Correct answer: A. x-axis and y-axis

1. Section 26.1 introduces co-ordinate geometry. 2. A point is located using two perpendicular number lines. 3. These lines are the x-axis (horizontal) and y-axis (vertical). 4. So option A is correct. _Source: Selina Concise Mathematics Class 9, Ch 26 Co-ordinate Geometry (Mistral OCR'd PDF), section 26.1_

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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
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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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Distance between two points (x1, y1) and (x2, y2) is given by

  1. (x1 + y1)(x2 + y2) overall
  2. (x2 - x1) + (y2 - y1) directly
  3. sqrt(x1 * x2 + y1 * y2) only
  4. sqrt((x2 - x1)^2 + (y2 - y1)^2)
Show answer and solution

Correct answer: D. sqrt((x2 - x1)^2 + (y2 - y1)^2)

1. Form a right triangle with the segment as hypotenuse. 2. Legs are |x2 - x1| and |y2 - y1|. 3. By Pythagoras the distance squared is (x2 - x1)^2 + (y2 - y1)^2. 4. So option A is correct. _Source: Selina Concise Mathematics Class 9, Ch 26 Co-ordinate Geometry (Mistral OCR'd PDF), section on distance formula_

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