IB Mathematics Analysis and Approaches Topic AHL 5.17—areas Under Curve Onto Y-axis, Volume of Revolution Questionbank (HL)

IB Mathematics Analysis and Approaches Topic AHL 5.17—areas Under Curve Onto Y-axis, Volume of Revolution Questionbank (HL) | RevisionDojo

Practice IB Mathematics Analysis and Approaches (AA) Topic AHL 5.17—areas Under Curve Onto Y-axis, Volume of Revolution with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for AHL 5.17—areas Under Curve Onto Y-axis, Volume of Revolution and mirrors Paper 1, 2, 3 style where relevant.

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Paper

Level

Question 1

HLPaper 1

Consider the function $f (x) = sec (x - \frac{π}{3})$ , for $0 \leq x \leq \frac{2 π}{3}$ . The region bounded by the graph of $y = f (x)$ , the $x$ -axis and the lines $x = 0$ and $x = \frac{2 π}{3}$ is rotated $2 π$ radians about the $x$ -axis.

Determine the range of $f$ .

[3]

Find the volume of revolution generated.

[4]

Question 2

HLPaper 1

Let $f (x) = \frac{18}{x ^{2} + 9}$ , for $x \in R$ . Consider the region $R$ bounded by the graph of $y = f (x)$ , the x-axis, and the lines $x = 0$ and $x = 3$ .

Sketch the graph of $y = f (x)$ for $0 \leq x \leq 3$ , clearly indicating the coordinates of any intercepts and the maximum point.

[3]

Find the area of region $R$ .

[3]

The region $R$ is rotated $2 π$ radians about the x-axis to form a solid of revolution. Find the volume of the solid formed, giving your answer in the form $π (a + b arctan c)$ , where $a, b, c \in Z$ .

[6]

Question 3

HLPaper 1

Consider $f (x) = \frac{l n x}{x}$ , for $1 \leq x \leq e^{2}$ . Let $R$ be the region bounded by the graph of $y = f (x)$ , the x-axis, and the lines $x = 1$ and $x = e^{2}$ .

Find the area of region $R$ .

[4]

Find the volume of the solid formed when region $R$ is rotated about the $y$ -axis, giving your answer in terms of $π$ .

[4]

Question 4

HLPaper 1

Let $f (x) = x ln x$ , for $1 \leq x \leq e$ . Consider the region $R$ bounded by the graph of $y = f (x)$ , the x-axis, and the lines $x = 1$ and $x = e$ .

Find the area of region $R$ .

[4]

Find the volume of the solid formed when region $R$ is rotated about the x-axis, giving your answer in terms of $π$ .

[5]

Question 5

HLPaper 1

The function $f$ is given by $f (x) = 16 - x^{2}$ , with $x \geq 0$ . The shaded region is bounded by the graph of $f$ , the $x$ -axis, and the $y$ -axis.

Find the $x$ -coordinate at which the graph of $f$ crosses the $x$ -axis.

[2]

Find the area of the shaded region.

[2]

Find the volume of the solid obtained when the shaded region is rotated $36 0^{\circ}$ about the $x$ -axis.

[4]

IB Mathematics Analysis and Approaches AHL 5.17—areas Under Curve Onto Y-axis, Volume of Revolution Questionbank

IB Mathematics Analysis and Approaches AHL 5.17—areas Under Curve Onto Y-axis, Volume of Revolution Questionbank

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IB Mathematics Analysis and Approaches AHL 5.17—areas Under Curve Onto Y-axis, Volume of Revolution Questionbank

IB Mathematics Analysis and Approaches AHL 5.17—areas Under Curve Onto Y-axis, Volume of Revolution Questionbank

IB Mathematics Analysis and Approaches (AA) Topic AHL 5.17—areas Under Curve Onto Y-axis, Volume of Revolution Questionbank

Unlock all 19 questions with a free account