IB Mathematics Applications & Interpretation Topic SL 5.5—introduction to Integration Questionbank (SL/HL)

IB Mathematics Applications & Interpretation Topic SL 5.5—introduction to Integration Questionbank (SL/HL) | RevisionDojo

Practice IB Mathematics Applications & Interpretation (AI) Topic SL 5.5—introduction to Integration with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 5.5—introduction to Integration and mirrors Paper 1, 2, 3 style where relevant.

Get instant solutions, detailed explanations, and build confidence with questions aligned to IB examiner expectations.

Paper

Level

Question 1

SLPaper 2

A farmer is planning a new orchard. The shape of one section is defined by the region bounded by the curve $g (t) = t^{2} + t$ , the $t$ -axis, and the vertical line $t = 4$ , where $t$ and $g (t)$ are measured in metres.

Divide the interval $[0, 4]$ into 4 equal sub-intervals and state the $t$ -values of the endpoints.

[3]

Calculate the value of $g (t)$ at each endpoint.

[4]

Use the trapezoidal rule with these 4 sub-intervals to approximate the area of the orchard section, giving your answer in $m^{2}$ .

[5]

Calculate the exact area of the orchard section by integrating $g (t)$ from 0 to 4, giving your answer in $m^{2}$ .

[5]

Compare the approximation with the exact value and explain the difference.

[3]

Question 2

SLPaper 1

Let $g (x) = - x^{2} + 4 x + 2$ .

Determine the indefinite integral $\int g (x) d x$ .

[2]

Calculate the area enclosed between the graph of $y = g (x)$ and the $x$ -axis for $0 \leq x \leq 3$ .

[4]

Question 3

SLPaper 1

For all real $x$ , the curve $y = f (x)$ passes through the points $(- 1, - 5)$ and $(2, 7)$ , and its second derivative is $f^{''} (x) = 12 x^{2} - 8$ . Determine an expression for $f (x)$ .

[5]

Question 4

HLPaper 2

The velocity of a particle, $v$ m s $^{- 1}$ , is modelled by the function $v (t) = - 3 t^{2} + 18 t - 24$ for $t \geq 0$ , where $t$ is the time in seconds.

Find the values of $t$ for which the velocity is zero.

[2]

Find $∣ v^{'} (4) ∣$ .

[3]

Find $max_{0 \leq t \leq 4} ∣ v (t) ∣$ .

[2]

Assuming the particle is at the origin at $t = 0$ , find an expression for the displacement $s$ (in metres) of the particle at time $t$ seconds.

[4]

Calculate the total distance travelled, including both forward and backward motion, in the interval $0 \leq t \leq 3$ .

[3]

Question 5

SLPaper 2

An architect is designing a glass panel. The shape of the panel is defined by the region bounded by the curve $g (x) = x^{2} + 2 x$ , the $x$ -axis, and the vertical line $x = 4$ , where $x$ and $g (x)$ are measured in metres.

Divide the interval $[0, 4]$ into 4 equal sub-intervals and state the $x$ -values of the endpoints.

[3]

Calculate the value of $g (x)$ at each endpoint.

[4]

Use the trapezoidal rule with these 4 sub-intervals to approximate the area of the panel, giving your answer in $m^{2}$ .

[5]

Calculate the exact area of the panel by integrating $g (x)$ from 0 to 4, giving your answer in $m^{2}$ .

[5]

Compare the approximation with the exact value and explain the difference.

[3]

IB Mathematics Applications & Interpretation SL 5.5—introduction to Integration Questionbank

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IB Mathematics Applications & Interpretation SL 5.5—introduction to Integration Questionbank

IB Mathematics Applications & Interpretation (AI) Topic SL 5.5—introduction to Integration Questionbank

Unlock all 27 questions with a free account