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CAIE A Level Mathematics 9709

Integration (AS) questions

Exam-style questions on Integration (AS), 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. 4 marksStandardA curve has gradient function (dy)/(dx) = 2x + 1. Given that the curve passes through the point (1, 15), find the value of the constant of integration C.
  2. 4 marksStandardThe curve y = (x - 1)(7 - x) intersects the x-axis at x = 1 and x = 7. Find the exact area of the region enclosed by the curve and the x-axis.
  3. 3 marksStandardEvaluate the definite integral ∫1^2 ( 9x^2 + 1 ) dx.
  4. 4 marksStandardThe gradient of a curve is given by (dy)/(dx) = 2x + 4 . The curve passes through the point (3, 11) . Find the constant of integration, C .
  5. 4 marksStandardA curve has equation y = x^2 + 2.
  6. 3 marksStandardEvaluate the definite integral ∫1^4 (c x + d) dx.
  7. 4 marksChallengeConsider the definite integral ∫ 1 ^ 3 (3x + 3)^ 3 \,dx.