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Completing the Square · CSEC Mathematics

18 past-paper questions on Completing the Square, part of ALGEBRA, from every CSEC Mathematics paper on Quelpr.

Practise Completing the Square
  1. 9(c)5 marks· CSEC Mathematics · 2003 (Specimen) · Paper 2Write 3x^2 + 12x + 25 in the form a(x + h)^2 + k where a, h and k are real numbers. Hence, or otherwise, solve the equation 3x^2 + 12x + 25 = 40.
  2. 2(e)2 marks· Mathematics Q2 2(e)Given that x² + ax + b = (x + 2)² – 3, work out the values of a and b.
  3. 8(b)(i)3 marks· Mathematics Q8 8(b)(i)Express f(x) in the form a(x + h)^2 + k, where a, h and k are constants.
  4. 9(a)4 marks· Mathematics Q9 9(a)Write 5x² + 2x - 7 in the form a(x + b)² + c, where a, b, and c are real numbers.
  5. 9(b)3 marks· Mathematics Q9 9(b)Express 2x² - 3x + 1 in the form a(x + h)² + k, where a, h and k are real numbers.
  6. 9(b)3 marks· Mathematics Q9 9(b)Express 4x^2 - 12x - 3 in the form a(x + h)^2 + k, where a, h and k are real numbers.
  7. 9(b)(i)3 marks· Mathematics Q9 9(b)(i)Express y = x^2 - 3x - 12 in the form y = (x - h)^2 + k, where h and k are constants.
  8. 9(b)(i)3 marks· Mathematics Q9 9(b)(i)Express the function f(x) = 2x² - 4x - 13 in the form f(x) = a(x + h)² + k.
  9. 9(b)(i)2 marks· Mathematics Q9 9(b)(i)Express the function f(x) = 4x² - 8x - 2 in the form a(x + h)² + k, where a, h and k are constants.
  10. 9(b)(i)2 marks· Mathematics Q9 9(b)(i)Write f(x) = 3x^2 – 5x + 1 in the form a(x – h)^2 + k where a, h and k are constants to be determined.
  11. 9(b)(i)3 marks· Mathematics Q9 9(b)(i)Write g(x) in the form a(x + b)^2 + c, where a, b and c ∈ R.
  12. 9(b)(i)3 marks· Mathematics Q9 9(b)(i)Express the quadratic function 1 - 6x - x² in the form k - a(x + h)², where a, h and k are constants.
  13. 9(b)(i)3 marks· Mathematics Q9 9(b)(i)Express the quadratic function f(x) = 3x² + 6x - 2, in the form a(x + h)² + k, where a, h and k are constants.
  14. 9(b)(i)3 marks· Mathematics Q9 9(b)(i)Write 3x² - 12x + 8 in the form a(x + h)² + k where a, h and k are constants.
  15. 9(b)(iii)3 marks· Mathematics Q9 9(b)(iii)Write x² - 6x + 8 in the form a(x + h)² + k where a, h and k are constants.
  16. 9(c)(i)5 marks· Mathematics Q9 9(c)(i)Write 3x² + 8x - 25 in the form a(x + h)² + k where a, h and k are real numbers.
  17. 9(c)(i)3 marks· Mathematics Q9 9(c)(i)Write f(x) in the form f(x) = a(x + b)^2 + c where a, b, c ∈ R.
  18. 10(c)(i)7 marks· Mathematics Q10 10(c)(i)Write f(x) = 4x² - 7x + 3 in the form f(x) = a(x + b)² + c, where a, b and c are constants.

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