IB Mathematics Applications & Interpretation Topic AHL 1.9—log Laws Questionbank (HL)

IB Mathematics Applications & Interpretation Topic AHL 1.9—log Laws Questionbank (HL) | RevisionDojo

Practice IB Mathematics Applications & Interpretation (AI) Topic AHL 1.9—log Laws with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for AHL 1.9—log Laws and mirrors Paper 1, 2, 3 style where relevant.

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Paper

Level

Question 1

HLPaper 1

Let $lo g 25 + lo g 4 = lo g c$ . Now consider base- $5$ logarithms: let $lo g_{5} 500 - lo g_{5} 4 = lo g_{5} d$ .

Find the value of $c$ .

[2]

Hence, or otherwise, find the value of $lo g 25 + lo g 4$ .

[2]

Find the value of $d$ .

[3]

Hence, or otherwise, find the value of $lo g_{5} 500 - lo g_{5} 4$ .

[2]

Question 2

HLPaper 1

Let $lo g_{10} p = m$ , $lo g_{10} q = n$ and $lo g_{10} r = k$ .

Write $lo g_{10} \frac{p ^{3} 3 q ^{2}}{r ^{4}}$ in terms of $m$ , $n$ and $k$ .

[3]

Hence write $\frac{p ^{3} 3 q ^{2}}{r ^{4}}$ in terms of $m$ , $n$ and $k$ .

[2]

Question 3

HLPaper 1

Find the value of the integer $k$ in each of the following cases:

$lo g (3 k) = lo g 3 + lo g 5$

[1]

$lo g 21 = lo g 3 + lo g k$

[1]

$ln 21 = ln 3 + ln k$

[1]

$lo g (14 k) = lo g 2 + lo g 7 + lo g k$

[1]

$ln (8 k) = ln 2 + ln 4 + ln k$

[1]

Question 4

HLPaper 1

Lengths in this problem are measured in centimetres. Consider the function $r (x) = 1 + x$ , defined for $0 ⩽ x ⩽ 4$ . A candle is formed by rotating the region between the curve $y = r (x)$ and the $x$ -axis through $36 0^{\circ}$ about the $x$ -axis.

Calculate the total volume of the candle.

[3]

As the candle burns, the volume $W$ cm $^{3}$ of wax remaining after $t$ hours is modeled by $W = \frac{68 π}{3} e^{- 0.25 t}$ . Determine the time elapsed until half the candle remains.

[3]

Question 5

HLPaper 2

A flare's height is modelled by $h (t) = - t^{3} + 7 t^{2} + 2 t + 1$ , where $h$ is in metres and $t$ is in seconds. In the first two parts, use technology where appropriate.

Find the time when the flare hits the ground, giving your answer correct to three significant figures.

[4]

A signal reading is modelled by $P (u) = u^{3} - 4 u^{2} - 11 u + 20$ . Write down an equation whose solutions are the $u$ -values for which the signal reading is $8$ , and solve it.

[4]

The cost of a subscription is modelled by $C (t) = 240 (1.09)^{t}$ , where $C$ is in dollars and $t$ is in years. Find the value of $t$ when the cost reaches $600$ .

[4]

Hence determine the first whole year for which the cost exceeds $600$ .

[2]

IB Mathematics Applications & Interpretation AHL 1.9—log Laws Questionbank

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IB Mathematics Applications & Interpretation AHL 1.9—log Laws Questionbank

IB Mathematics Applications & Interpretation (AI) Topic AHL 1.9—log Laws Questionbank

Unlock all 33 questions with a free account