IB Mathematics Analysis and Approaches Topic SL 5.5—integration Introduction, Areas Between Curve and x Axis Questionbank (SL/HL)

IB Mathematics Analysis and Approaches Topic SL 5.5—integration Introduction, Areas Between Curve and x Axis Questionbank (SL/HL) | RevisionDojo

Practice IB Mathematics Analysis and Approaches (AA) Topic SL 5.5—integration Introduction, Areas Between Curve and x Axis with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 5.5—integration Introduction, Areas Between Curve and x Axis and mirrors Paper 1, 2, 3 style where relevant.

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Paper

Level

Question 1

SL & HLPaper 1

Let $g (x) = \frac{s i n ( 2 x )}{2} (\frac{1}{t a n ( x )} + 2) - sin^{2} (x)$ .

Show that $g (x) = sin (2 x) + cos (2 x)$ .

[5]

Show that $g^{''} (x) = - 4 g (x)$ .

[3]

Hence, using your answer from Part 2, find $\int g (x) d x$ in terms of $g^{'} (x)$ .

[4]

Question 2

SLPaper 1

Define $g (x) = sin^{- 1} (\frac{x}{3}) + cos^{- 1} (\frac{x}{3})$ for $x \in [- 3, 3]$ , and $h (x) = e^{g (x)}$ .

Show that $g (x) = \frac{π}{2}$ for all $x \in [- 3, 3]$ .

[2]

Find the exact coordinates of the intersection of $h$ and the line $y = 2 x + 1$ .

[3]

Find the exact coordinates of the point where the normal to the curve $y = h (x)$ at $x = 1$ intersects the $x$ -axis.

[4]

Find the exact area of the region bounded by $h, y = 2 x + 1$ , and the $y$ -axis.

[5]

Question 3

SLPaper 1

Find $\int (4 x^{2} - 3 x + 2) d x$ .

[3]

Given $f^{'} (x) = 4 x^{2} - 3 x + 2$ and $f (2) = 5$ , find $f (x)$ .

[3]

Calculate the area under the curve $y = 4 x^{2} - 3 x + 2$ from $x = 0$ to $x = 1$ .

[4]

Question 4

SLPaper 2

The expression $2 x + \frac{3}{x}$ can be written as $2 x^{p} + 3 x^{q}$ . Write down the values of $p$ and $q$ .

[2]

Find $\int (2 x + \frac{3}{x}) d x$ .

[3]

Sketch the curve $y = 2 x + \frac{3}{x}$ for $0.5 \leq x \leq 2$ , indicating the approximate shape and the coordinates of at least one point on the curve.

[3]

Question 5

SLPaper 1

Let $g (x) = x^{3} - 4 x + 5$ .

Find $\int g (x) d x$ .

[3]

Given $f^{'} (x) = g (x)$ and $f (2) = 5$ , find $f (x)$ .

[3]

Calculate the area under the curve $y = g (x)$ from $x = - 1$ to $x = 1$ .

[4]

IB Mathematics Analysis and Approaches SL 5.5—integration Introduction, Areas Between Curve and x Axis Questionbank

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IB Mathematics Analysis and Approaches SL 5.5—integration Introduction, Areas Between Curve and x Axis Questionbank

IB Mathematics Analysis and Approaches (AA) Topic SL 5.5—integration Introduction, Areas Between Curve and x Axis Questionbank

Unlock all 13 questions with a free account