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Date November 2014 Marks available 2 Reference code 14N.1.sl.TZ0.11
Level SL only Paper 1 Time zone TZ0
Command term Solve Question number 11 Adapted from N/A

Question

Consider the functions \(f(x) = x + 1\) and \(g(x) = {3^x} - 2\).

Write down

(i)     the \(x\)-intercept of the graph of \(y = {\text{ }}f(x)\);

(ii)     the \(y\)-intercept of the graph of \(y = {\text{ }}g(x)\).

[2]
a.

Solve \(f(x) = g(x)\).

[2]
b.

Write down the interval for the values of \(x\) for which \(f(x) > g(x)\).

[2]
c.

Markscheme

(i)     \(( - 1,{\text{ }}0)\)     (A1)

Note: Accept \( - 1\).

 

(ii)     \((0,{\text{ }} - 1)\)     (A1)     (C2)

Note: Accept \( - 1\).

a.

\((x = ){\text{ }} - 2.96{\text{ }}( - 2.96135 \ldots )\)     (A1)

\((x = ){\text{ }}1.34{\text{ }}(1.33508 \ldots )\)     (A1)     (C2)

b.

\( - 2.96 < x < 1.34\;\;\;{\mathbf{OR}}\;\;\;\left] { - 2.96,{\text{ }}1.34} \right[\;\;\;{\mathbf{OR}}\;\;\;( - 2.96,{\text{ }}1.34)\)     (A1)(ft)(A1)     (C2)

Notes: Award (A1)(ft) for both correct endpoints of the interval, (A1) for correct strict inequalities (or correct open interval notation).

Follow through from part (b).

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

Syllabus sections

Topic 6 - Mathematical models » 6.2 » Linear models.
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