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CAIE A Level Mathematics 9709

Algebra questions

Exam-style questions on Algebra, ordered from foundation to challenge. Pick one, write your answer the way you would in the exam, and it comes back marked against the mark scheme, point by point.

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Written by Markquill to follow the Cambridge International syllabus. Markquill is independent and is not affiliated with or endorsed by Cambridge International.

  1. 3 marksFoundationSolve the inequality x - 6 < 1.
  2. 3 marksFoundationSolve the inequality x - 1 < 4.
  3. 4 marksStandardExpress the following in partial fractions: ( 2(x+2)(x+1) + 4(x+3)(x+1) + 3(x+3)(x+2) )/((x+3)(x+2)(x+1))
  4. 3 marksStandardThe polynomial P(x) = x^3 + kx^2 + 5x + 10 has a factor (x - 2). Find the value of the constant k.
  5. 3 marksStandardThe polynomial f(x) = 2x^3 + px^2 - 5x + 6 has a factor (x - 2). Find the value of p.
  6. 3 marksStandardFind the coefficient of x^2 in the expansion of (1 + 2x)^(1)/(2), where 2 is a positive integer, given that the expansion is valid for 2x < 1.
  7. 4 marksStandardExpress the following fraction in partial fractions.
  8. 3 marksStandardFind the coefficient of x^2 in the binomial expansion of (1+2x)^0.5.
  9. 4 marksChallengeFind the remainder when f(x) = x^3 - 3x - 1 is divided by x + 1.