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SL 1.6—Approximating and estimating - IB Questionbank | RevisionDojo

Practice SL 1.6—Approximating and estimating with authentic IB Mathematics Applications & Interpretation (AI) exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like core principles, advanced applications, and practical problem-solving. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of IB examiners.

Paper

Level

Question 1

SLPaper 2

The diameter of Earth is $1.274 \times 10^{7}$ , correct to four significant figures. The circumference of Mars is $2.134 \times 10^{7}$ , correct to four significant figures

Modelling Earth and Mars as perfect spheres, find the difference between the volume of Earth and the volume of Mars, giving your answer in the form $a \times 10^{k}$ , where $1 \leq a \leq 10$ and $k \in \mathbf{Z}$

[5]

Question 2

SLPaper 2

A cylinder has radius of 12.7 and height of 14.4

Calculate volume of the cylinder correct to one decimal place.

[2]

Calculate volume of the cylinder correct to three significant figures.

[1]

Calculate volume of the cylinder correct to the nearest integer.

[1]

Write your answer to part 2 . in the form $a \times 10^{k}$ , where $1 \leq a \leq 10$ and $k \in \mathbf{Z} \quad$

[1]

Question 3

SLPaper 2

Lucy has found exact answer for $S$ is $\frac{45}{16}$

Write down the exact answer as a decimal.

[1]

Lucy rounds her exact answer so that the percentage error is $6.67 \%$ . State the number of significant figures Lucy rounded the exact answer to and write down the approximate value of $S$ used in calculating the percentage error.

[2]

Question 4

SLPaper 2

Let $S=\left(a^{2} \sin ^{2} 4 b\right)\left(c^{2} \tan ^{2} 12 d\right)^{-1}(\sqrt{a}+c-\cos 48 b)$ , where $a=16, b=7.5^{\circ}, c=3, d=5^{\circ}$ .

Find the value of $S$ , giving your answer as a fraction.

[3]

Let $X=\frac{\sqrt{a}+c^{2}-2 \sin 54 d}{\sqrt{a^{3}}-a-c}$ . Find the value of $X$ , giving your answer as a fraction.

[3]

John estimates the value of $S X$ to be 0.3. Calculate the percentage error in John's estimate.

[3]

Question 5

SLPaper 2

Let $P=\frac{30 \sin 2 a}{8 b}$ , where $a=45^{\circ}$ and $b=2$

Calculate exact value of $P$ .

[2]

Give your answers from part 1 correct to two significant figures.

[1]

Allen estimates the value of $P$ to be 2 . Calculate the percentage error in Allen's estimate.

[2]

Question 6

SLPaper 2

Consider the numbers $a=4.14 \times 10^{6}$ and $b=2.54 \times 10^{-7}$

Calculate $C=\sqrt[10]{\left(\frac{a}{b}\right)^{3}}$ . Give your answer correct to the nearest integer.

[2]

Give your answer to part 1 . in the form $a \times 10^{k}$ , where $1 \leq a \leq 10$ and $k \in \mathbf{Z}$ .

[1]

Question 7

SLPaper 2

Let $Q=\frac{4 x}{6 \cos 5 y}$ , where $x=1.25$ and $y=36^{\circ}$

Calculate exact value of $Q$ in fractions.

[2]

Give your answers from part 1 correct to three significant figures.

[1]

Luna estimates the value of $Q$ to be -1 . Calculate the percentage error in Luna's estimate.

[2]

Question 8

SLPaper 2

A shop sells bags of potatoes labelled as " 5 ". The shop owner weighs five bags, in kilograms, at random and recorded the following : 4.96, 4.89, 5.07, 5.11, 5.02

Find the mean of the shop owner's recorded weights.

[2]

Calculate the percentage error between the mean and the stated weight of 5 kg .

[2]

Find the interval for the values of $X$ such that the percentage error from the five bags that the supplier weighed is less than 1%.

[6]

Question 9

SLPaper 2

Calculate the following, giving your answers in the form $a \times 10^{k}$ , where $1 \leq a \leq 10$ and $k \in \mathbf{Z}$

$4 \times\left(6.2 \times 10^{-5}\right)$

[2]

$\left(4 \times 10^{5}\right)-\left(5 \times 10^{4}\right)$

[2]

$(4321)^{-1}\left(1.2 \times 10^{-1}\right)$

[2]

Question 10

SLPaper 2

Let $W=\frac{(2 \cos 2 x+y)\left(\tan \frac{x}{2}-z\right)}{10\left(5 \sin x+z^{2}\right)}$ , where $x=90^{\circ}, y=-1$ and $z=2$

Calculate exact value of $W$ .

[3]

Louis estimates the value of $W$ to be 0.03 . Calculate the percentage error in Louis's estimate.

[2]

SL 1.6—Approximating and estimating Questionbank