IB Mathematics Applications & Interpretation Topic SL 5.1—introduction to Limits Questionbank (SL/HL)

IB Mathematics Applications & Interpretation Topic SL 5.1—introduction to Limits Questionbank (SL/HL) | RevisionDojo

Practice IB Mathematics Applications & Interpretation (AI) Topic SL 5.1—introduction to Limits with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 5.1—introduction to Limits and mirrors Paper 1, 2, 3 style where relevant.

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Paper

Level

Question 1

SLPaper 1

Given $f (x) = x^{3} - 5 x^{2} + 6 x$

Find the derivative of $f (x)$ .

[4]

Determine the coordinates of the turning points of $f (x)$ .

[6]

Question 2

SLPaper 2

The volume of water in a storage tank is modeled by the function $V (t) = 2 t^{2} + 5 t + 4$ , where $t$ represents the number of hours since filling began and $V (t)$ is the volume of water in litres.

Find the derivative $V^{'} (t)$ that represents the rate at which the volume of water changes over time.

[2]

Find the gradient of the volume curve at $t = 3$ .

[2]

Determine the equation of the tangent line to the volume curve at the point where $t = 3$ hours. Give your answer in the form $y = m t + c$ .

[5]

Interpret the meaning of the gradient of the tangent line in the context of the volume of water in the tank.

[3]

Question 3

SLPaper 2

The growth of a plant species is modeled by the function $f (x) = 3 x^{2} + 2 x + 5$ , where $x$ represents the number of weeks since planting and $f (x)$ is the height of the plant in cm.

Find the derivative $f^{'} (x)$ that represents the rate of growth of the plant over time.

[2]

Find the gradient of the growth curve at $x = 4$ .

[2]

Determine the equation of the tangent line to the growth curve at the point where $x = 4$ weeks. Give your answer in the form $y = m x + c$ .

[5]

Interpret the meaning of the gradient of the tangent line in the context of the plant's growth rate.

[3]

Question 4

SLPaper 2

The total cost, in dollars, of producing $t$ items can be modeled by the function $h (t) = 3 t^{2} + 2 t + 5$ , where $t$ is the number of items produced.

Find the derivative $h^{'} (t)$ , which represents the rate of change of the cost as production increases.

[2]

Calculate the rate of change of the cost at $t = 4$ .

[2]

Determine the equation of the tangent to the curve at the point where $t = 4$ .

[4]

Interpret the meaning of the gradient of the tangent line in this context. Explain why this information is valuable for monitoring production costs.

[2]

Question 5

SLPaper 2

The concentration index $g (t)$ of a solution after $t$ minutes is modelled by $g (t) = \frac{5 t - 1}{2 t + 3}$ , where $t > - \frac{3}{2}$ .

Evaluate the limit:

$t \to \infty lim \frac{5 t - 1}{2 t + 3}$

[3]

Find the derivative ( $g^{'} (t)$ )

[5]

Find $g^{'} (1)$ .

[1]

Interpret $g^{'} (1)$ as a rate of change of $g$ at $t = 1$ .

[2]

IB Mathematics Applications & Interpretation SL 5.1—introduction to Limits Questionbank

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IB Mathematics Applications & Interpretation SL 5.1—introduction to Limits Questionbank

IB Mathematics Applications & Interpretation (AI) Topic SL 5.1—introduction to Limits Questionbank

Unlock all 7 questions with a free account