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 conditions.

Exam points

Solve equations algebraically and graphically, including equations involving multiple function types.
Select valid solutions and verify them using complete mark-scheme evidence.

[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)