SL 1.1—Using standard form Questionbank

Practice SL 1.1—Using standard form with authentic IB Mathematics Analysis and Approaches (AA) exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like functions and equations, calculus, complex numbers, sequences and series, and probability and statistics. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of IB examiners.

Paper

Level

Question 1

SL & HLPaper 1

A large forest contains $20$ million trees.

Write down, in standard form, the number of trees in this forest.

[1]

Each tree produces an average of $50$ kilograms of oxygen per year. Find the total amount of oxygen produced by this forest in one year. Give your answer in tonnes using standard form. $(1 \, \text{tonne} = 1000 \, \text{kilograms})$

[3]

Question 2

SL & HLPaper 1

Write the number $0.0078 \times 10^4$ in standard form.

[1]

Arrange the following numbers in order, starting with the smallest: $0.0078 \times 10^4$ , $0.92 \times 10^5$ , $85.1 \times 10^2$ .

[1]

Question 3

SL & HLPaper 1

It is given that $p = 4.8 \times 10^9$ and $q = 2 \times 10^3$ . Expressing your answers in standard form, find:

$p \div q$

[2]

$q^2 + p$

[2]

Question 4

SL & HLPaper 1

Write the number $820 \, 000$ in standard form.

[1]

Giving your answer in standard form, evaluate $(6.9 \times 10^5) \div 200$ .

[2]

Question 5

SL & HLPaper 2

The mass of Jupiter is $2 \times 10^{27}$ kg.

The mass of Saturn is $5 \times 10^{26}$ kg.

Find the total mass, in grams, of Jupiter and Saturn. Give your answer in standard form.

[3]

Question 6

SLPaper 1

A water company delivers $7.2 \times 10^5$ liters in January. Each month delivery increases by $4.8 \times 10^4$ liters.

Write down the amount delivered in April in scientific notation.

[2]

Find the total amount delivered from January to December.

[3]

In which month does delivery first exceed $1.0 \times 10^6$ liters?

[3]

Question 7

SLPaper 1

A reforestation project plants $6.0 \times 10^2$ trees in the first season. Each season, $4.5 \times 10^1$ more trees are planted than in the previous season.

Find the number of trees planted in the 7th season in scientific notation.

[2]

Find the total number of trees planted in the first 8 seasons.

[3]

In which season does the planting first exceed $1.0 \times 10^3$ trees?

[3]

Question 8

SLPaper 2

In microbiology, understanding bacterial growth is essential for various applications, including medicine and biotechnology. A certain bacterium divides every 20 minutes. Starting with one bacterium, the population after ${n}$ divisions is given by ${N = 2^n}$ .

Calculate the bacterial population after 8 hours. Express your answer in standard form.

[3]

If each bacterium has a mass of ${1 \times 10^{-12}}$ grams, calculate the total mass of the bacterial population. Express your answer in grams using standard form.

[3]

Express the total mass of the bacterial population in milligrams using standard form.

[1]

Question 9

SLPaper 2

Computer Processing Capacity

In the field of computational science, supercomputers play a crucial role in processing vast amounts of data for research in areas such as climate modeling, genomics, and artificial intelligence. One such supercomputer can perform $(1.5 \times 10^{15})$ calculations per second (1.5 petaflops).

Calculate how many calculations this supercomputer can perform in one day. Express your answer in standard form.

[3]

Express this number in exaflop-days, where 1 exaflop $(=1 \times 10^{18})$ calculations.

[2]

If another supercomputer performs $(2.0 \times 10^{17})$ calculations in a day, compare the performance by calculating the ratio of their daily calculations. Express your answer in standard form.

[4]

Question 10

SLPaper 2

Meteorites can contain precious metals like platinum, which are of great interest for both scientific research and potential economic value on Earth. A particular meteorite is estimated to contain a substantial amount of platinum, which could be worth immense amounts if extracted.

Given Information:

Estimated value of platinum in the meteorite: 57,320 quadrillion euros (EUR).
Assume the meteorite is spherical with a radius of 55 km.

Express the estimated value of the platinum in standard form.

[3]

Calculate the estimated volume of the meteorite using the formula for the volume of a sphere: $V=\frac{4}{3} \pi r^3$ where $r$ is the radius in kilometers.

[3]

The actual volume of the meteorite has been measured to be $7.1 \times 10^4 \mathrm{~km}^3$ . Calculate the percentage error between your estimated volume and the actual volume. Give your answer to two significant figures.

[3]