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: $0.0078 \times 10^4$ , $0.92 \times 10^5$ , $85.1 \times 10^2$ .

[2]

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

(No specification provided)

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 $7.2 \times 10^5$ litres in January. Each month delivery increases by $4.8 \times 10^4$ litres.

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 $1.0 \times 10^6$ litres?

[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 ${1.00 \times 10^{-12}}$ 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 exa-operations, where 1 exa-operation represents $1 \times 10^{18}$ calculations.

[2]

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

[4]

Question 10

SLPaper 2

In the context of space exploration, understanding distances between celestial bodies is crucial. The average distance from Earth to the Sun is defined as one astronomical unit (AU), approximately $1.496 \times 10^{11}$ meters. The distances from Earth to Mars vary significantly depending on their positions in their respective orbits.

Calculate the distance from Earth to Mars at its closest approach, given as $5.46 \times 10^7$ km, in astronomical units (AU), using standard form.

[3]

Determine the distance from Earth to Mars at its farthest, given as $4.01 \times 10^8$ km, in AU, using standard form.

[2]

Calculate the ratio of the farthest distance to the closest distance between Earth and Mars. Express your answer in standard form.

[3]