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

SL & HLPaper 2

The total number of animals in a wildlife reserve is estimated to be $7.5 \times 10^4$ . The number of mammals is $3 \times 10^3$ .

The number of birds is $4.2 \times 10^4$ .

What fraction of the total number of animals are mammals? Give your answer in its simplest form.

[1]

Find the number of animals that are neither mammals nor birds. Give your answer in standard form.

[2]

If the number of birds is expected to increase by $20\%$ over the next five years, and the total number of animals increases by $10\%$ , find the new number of animals that are neither mammals nor birds after five years. Give your answer in standard form.

[3]

Question 9

SL & HLPaper 2

A spacecraft travels at a speed of $8 \times 10^3$ m/s. Calculate the time it takes for the spacecraft to travel $2400$ km. Give your answer in standard form.

[3]

One molecule of methane is made up of one atom of carbon and four atoms of hydrogen. The mass of one atom of carbon is $1.99 \times 10^{-23}$ g. The mass of one atom of hydrogen is $1.67 \times 10^{-24}$ g. Calculate the mass of one molecule of methane. Give your answer in standard form.

[3]

Question 10

SL & HLPaper 2

An atom of carbon has a mass of $1.99 \times 10^{-26}$ kilograms.

Express this mass in grams. Give your answer in standard form.

[2]

A sample contains $3 \times 10^{20}$ atoms of carbon. Find the mass of carbon in the sample. Give your answer in grams as a normal decimal number.

[2]