IB Maths AA HL Sl 2 10 Solving Equations Questions

Practise solving polynomial, exponential, logarithmic, trigonometric and composite equations, using graphs or technology when needed and rejecting roots outside the stated…

Exam points

Solve polynomial, exponential, logarithmic, trigonometric or composite equations by an appropriate analytic method, showing the valid roots.
Use graphs or technology to find intersections, count solutions or locate a root when no suitable closed-form method is available.
Solve an equation or inequality with parameters, domain restrictions or multiple branches, and reject roots that violate the stated conditions.
Apply an equation to a real model to determine a time, threshold, position or rate, then report the result with suitable units and interpretation.

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Study SL 2.10—Solving equations conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

[Maximum number: 3]

Consider the function f defined by $f(x)=90 \mathrm{e}^{-0.5 x}$ for $x \in \mathbb{R}^{+}$ .
The graph of f and the line y=x intersect at point P .

(a) attempt to find the point of intersection of the graph of f and the line y=x (M1)
$x=5.56619 \ldots$
=5.57

(a)

Find the x-coordinate of P .

The line L has a gradient of -1 and is a tangent to the graph of f at the point Q .

[ 2 ]

attempt to find the point of intersection of the graph of f and the line y=x (M1)
$x=5.56619 \ldots$
=5.57

(b)

Find the x-coordinate of the point where L intersects the line y=x.

[ 1 ]

$x=\ln 45+1(=4.81)$

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IB Maths AA HL Sl 2 10 Solving Equations Questions question 1

Question (a)

Question (b)