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Practise

Question bank

Original exam-style questions, mapped to your syllabus. Answers are checked for mathematical equivalence and every attempt updates your mastery.

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14 questions

SA-9709-P1-IN5-G013 marksL1 FoundationCalculatorAbout the x-axis
The region under y=xy=x from x=0x=0 to x=3x=3 is rotated through 360∘360^\circ about the xx-axis. Find the exact volume.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-IN5-Q011 markL1 FoundationCalculatorAbout the x-axis
The line y=2y=2 from x=0x=0 to x=5x=5 is rotated through 360∘360^\circ about the xx-axis. The volume is
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-IN-Q021 markL1 FoundationCalculatorAbout the x-axis
The volume when a region is rotated 360∘360^\circ about the xx-axis is
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-IN-0103 marksL2 StandardCalculatorAbout the x-axis
The region under y=xy=\sqrt{x} from x=0x=0 to x=4x=4 is rotated through 360∘360^\circ about the xx-axis. Find the exact volume.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-IN5-0013 marksL2 StandardCalculatorAbout the x-axis
The region under y=x2y=x^2 from x=0x=0 to x=2x=2 is rotated through 360∘360^\circ about the xx-axis. Find the exact volume.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-IN5-0023 marksL2 StandardCalculatorAbout the x-axis
The region under y=2xy=\dfrac2x from x=1x=1 to x=4x=4 is rotated through 360∘360^\circ about the xx-axis. Find the exact volume.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-IN5-0033 marksL2 StandardCalculatorAbout the x-axis
The region under y=2x+1y=\sqrt{2x+1} from x=0x=0 to x=4x=4 is rotated through 360∘360^\circ about the xx-axis. Find the exact volume.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-IN-0114 marksL3 ExamCalculatorAbout the x-axis
The region under y=x2+1y=x^2+1 from x=0x=0 to x=1x=1 is rotated through 360∘360^\circ about the xx-axis. Find the exact volume.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-IN-0174 marksL3 ExamCalculatorAbout the y-axis
The region bounded by y=x2y=x^2 (for x≥0x\ge0), the yy-axis and the line y=4y=4 is rotated through 360∘360^\circ about the yy-axis. Find the exact volume.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-IN5-0043 marksL3 ExamCalculatorAbout the y-axis
The region bounded by y=x2y=x^2 (x≥0x\ge0), the yy-axis and the line y=9y=9 is rotated through 360∘360^\circ about the yy-axis. Find the exact volume.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-IN5-0054 marksL3 ExamCalculatorAbout the y-axis
The region bounded by y=x3y=x^3 (x≥0x\ge0), the yy-axis and the line y=8y=8 is rotated through 360∘360^\circ about the yy-axis. Find the exact volume.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-IN5-0064 marksL4 ChallengingCalculatorAbout the x-axis
The semicircle y=9−x2y=\sqrt{9-x^2}, −3≤x≤3-3\le x\le3, is rotated through 360∘360^\circ about the xx-axis to form a sphere. Use integration to find its exact volume.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-IN-0126 marksL5 ExtensionCalculatorBetween graphs
The region enclosed by the curve y=9−x2y=9-x^2 and the line y=5y=5 is rotated through 360∘360^\circ about the xx-axis. Find the exact volume of the solid formed.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-IN5-0075 marksL5 ExtensionCalculatorBetween graphs
The region enclosed by y=xy=x and y=x2y=x^2 is rotated through 360∘360^\circ about the xx-axis. Find the exact volume.

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Salam Academy Original Practice · Proposed mark scheme