IB Maths AI HL AI 1.3 Exponents, logarithms and equations questions

Exam-style questions in the shape of Paper 1 and Paper 2, with full markschemes. Read the markscheme, or type, photograph or draw your answer and get it marked.

Paper

Paper 1 Paper 2

Difficulty

Easy Medium Hard

Question 1

Paper 1Easy6 marks

A laboratory compares the hydrogen ion concentrations of two aqueous solutions. Figure 1 shows the measured concentrations. For these solutions, the one with the greater hydrogen ion concentration is more acidic.

For the pH calculations, use

\mathrm{pH}=-\log_{10}(C),

where $C$ is the numerical value of the hydrogen ion concentration in $\mathrm{mol\,dm^{-3}}$

(a)

Write down the hydrogen ion concentration of solution B in standard form, including its unit.

[1]

(b)

Calculate the pH of solution A, giving your answer to 2 decimal places.

[2]

(c)

Determine the ratio of the hydrogen ion concentration of solution A to that of solution B, giving your answer in standard form.

[2]

(d)

Hence state which solution is more acidic.

[1]

Question 2

Paper 1Medium6 marks

A fountain jet is modelled, for $0\leq x\leq 6$ by

h=ax^2+bx+c,

where $x$ is the horizontal distance from the nozzle, in metres, and $h$ is the height above the ground, in metres. The model passes through the points shown.

$x$	0	3	6
$h$	1.20	4.80	5.10

(a)

Use technology to determine the values of $a$ $b$ and $c$ giving each to at least three significant figures.

[3]

(b)

Hence determine the horizontal distance(s), in the interval $0\leq x\leq 6$ at which the model gives $h=3.00$ Give your answer to the nearest $0.01$ m.

[3]

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