IB Mathematics Analysis and Approaches Topic SL 5.4—tangents and Normal Questionbank (SL/HL)

IB Mathematics Analysis and Approaches Topic SL 5.4—tangents and Normal Questionbank (SL/HL) | RevisionDojo

Practice IB Mathematics Analysis and Approaches (AA) Topic SL 5.4—tangents and Normal with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 5.4—tangents and Normal and mirrors Paper 1, 2, 3 style where relevant.

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Paper

Level

Question 1

SLPaper 1

Consider the polynomial function

f (x) = x^{3} - 6 x^{2} + 9 x + k

, where

k

is a constant. The normal to the graph of

y = f (x)

at the point where

x = 2

is perpendicular to the line

y = - 3 x - 3

Find $f^{'} (x)$ .

[2]

Determine the gradient of the normal at $x = 2$ .

[3]

Find the value of $k$ .

[3]

Question 2

SLPaper 1

Let $h (x) = x^{3} - 3 x + 2$ and $j (x) = 2 x - k$ , where $k$ is a constant. The line $y = j (x)$ is a normal to the graph of $y = h (x)$ at the point where $x = a$ .

Find $h^{'} (x)$ .

[2]

Show that $a = \pm \frac{5}{6}$ .

[3]

If $a = \frac{5}{6}$ , find the value of $k$ .

[3]

Question 3

SLPaper 1

The function $f$ is differentiable for all $x \in R$ . The line with equation $y = 12 - 5 x$ is tangent to the graph of $f$ at the point where $x = 3$ .

State the value of $f (3)$ .

[1]

State the value of $f^{'} (3)$ .

[1]

Let $g$ be a function defined by $g (x) = 2 x^{2} - 5 x$ and $h (x) = (f \circ g) (x)$ . Evaluate $h (3)$ .

[3]

Determine the equation of the tangent line to the graph of $h$ at $x = 3$ .

[5]

Question 4

SLPaper 1

The curve $C$ is defined by the function $g (x) = 2 x^{4} - 8 x^{2} + 5$ . Let $P$ be the point on $C$ where $x = 1$ .

Find the gradient of the tangent to $C$ at $P$ .

[3]

Determine the equation of the tangent at $P$ .

[3]

Question 5

SLPaper 1

The curve $C$ is defined by the function $h (x) = x^{3} - 6 x + 1$ . Let $A$ be the point on $C$ where $x = 2$ .

Find the gradient of the tangent to $C$ at $A$ .

[3]

Determine the equation of the tangent at $A$ .

[3]

IB Mathematics Analysis and Approaches SL 5.4—tangents and Normal Questionbank

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IB Mathematics Analysis and Approaches SL 5.4—tangents and Normal Questionbank

IB Mathematics Analysis and Approaches (AA) Topic SL 5.4—tangents and Normal Questionbank

Unlock all 20 questions with a free account