IB Mathematics Applications & Interpretation Topic SL…

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SLPaper 1

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The severity of rockbursts in a mine is measured on a local magnitude scale, with values usually ranging from $0$ to $4$ , where $4$ represents the highest severity.

For one mining site, the annual number, $R$ , of rockbursts reaching at least magnitude $m$ is modeled by $\log_{10} R = p - 2m$ , where . At this site, there are on average rockbursts per year with a magnitude of or greater.

The model is alternatively written as $R = \frac{d}{100^m}$ .

The expected return period in years between rockbursts with magnitude at least $m$ is $\frac{1}{R}$ .

The largest rockburst ever recorded at this site had magnitude $3.8$ .

(a)

the value of $p$ .

[2]

(b)

the value of $d$ .

[2]

(c)

Assuming $0 < m$ , the possible interval of values for .

SLPaper 1

The area covered by an invasive plant in a pond is modelled by the function, $A(w)=c\times 2^w$ , where is a constant and represents the time in weeks since the beginning of the survey. It is observed that the area covered is 384 m after 6 weeks.

SLPaper 2

A candle maker uses a hemispherical mould to form a decorative candle. The mould has radius 9 cm and is filled exactly with molten wax. Before melting, the same wax was shaped as a right circular cone with base radius 7 cm.

After the filled mould is removed from a warming cabinet, the temperature, $W$ , of the wax in degrees Celsius (°C), is modeled by the function:

$W(t)=a(1.28)^{-t}+22,\ t \geqslant 0$

SLPaper 1

The pH, $p$ , of a solution depends on its hydrogen ion concentration, $c$ , expressed in mol dm $^{-3}$ . This relationship is defined by the equation: , for .

HLPaper 1

(a)

The graph of the function $f(x) = x^3$ is reflected in the -axis and then translated by the vector to form the graph of the function .

Practice IB Mathematics Applications & Interpretation (AI) Topic SL 1.5—exponents and Logarithms with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 1.5—exponents and Logarithms and mirrors Paper 1, 2, 3 style where relevant.

Get instant solutions, detailed explanations, and build confidence with questions aligned to IB examiner expectations.

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IB Mathematics Applications & Interpretation SL 1.5—exponents and Logarithms Questionbank

IB Mathematics Applications & Interpretation SL 1.5—exponents and Logarithms Questionbank

IB Mathematics Applications & Interpretation SL 1.5—exponents and Logarithms Questionbank

IB Mathematics Applications & Interpretation SL 1.5—exponents and Logarithms Questionbank

IB Mathematics Applications & Interpretation (AI) Topic SL 1.5—exponents and Logarithms Questionbank