Math for IGCSE biology

That's how you 'should' simplify a fraction. Find the highest common factor and divide both numbers by this. However, as you're allowed a calculator in all your exam, I'll show you how to simplify using one

EXAM TIPS! • ALWAYS make sure you cannot simplify a fraction anymore. The fraction may look small enough...but if it can be smaller...it's not! You will lose marks if you do not simplify! • Remember to simplify to 1 if both the top and bottom number are the same.

STEP 4: Write x 10 after your answer. Add the number from step 3 as a power to the 10. Make it negative / have a minus sign. 6.24 x 10 to the power of -5

EXAM TIPS! • •

In the exam it's unlikely you'd be asked to convert a difficult percentage into a fraction. You're most likely to see this in biology (genetics) and the conversion will be simple.

For example, 25% is 1/4 or 50% is 1/2.

Ratios show how much of one thing there is compared with another.

For example, there might be 32 people with blue eyes and 48 with brown. Stick both numbers next to each other with a colon in the middle. The ratio of blue to brown eyes is 32:48. Then (as you did with fractions) simplify the numbers in the ratio if needed. To do this, find the largest number that both numbers in the ratio divide by (highest common factor) and divide both numbers by this!

When do you round a number up?

If the number after is 5 or more.

You may think you're tall. Your mum might think she's short. If you measured the height of everyone in the world and found the height exactly in the middle this would be the average height of humans. Taking averages is very useful. You may feel tall, but you may just be tall compared to your family. Taking the average height of a country ...or even the world... can tell you if you are tall compared to everyone else.

If we wanted to know how tall people are in China compared to the UK, but only measured one person in both countries, we might pick a tall person in China and small in the UK. We use averages all the time in science. If we didn't, our results might end up being just one offs or odd balls(we call these anomalies). Taking an average gives a better result we can trust.

MEAN

- ADD UP ALL THE NUMBERS AND DIVIDE BY HOW MANY NUMBERS THERE ARE

How do we use significant figures to make estimates (quick calculations in your head to check your answer is correct).

1. Round all numbers in your calculation to 1 sf in your head. 2. Complete the calculation. 3. Round the estimate to 1 sf.

PERCENTAGE TO A FRACTION

1. change the percentage to a fraction 2. reduce the fraction EX: 35% = 35/100 = 7/20

What is 191,000,000 in standard form?

1.91 × 10 to the power of 8

Estimate the following 8901 + 10,789 =

20,000

Estimate the following 340 + 2678 =

3000

STEP 2: Look at the power (the small number next to the 10). If it's positive, add that many zeros after your number. If the power is negative (has a minus sign) add that many zeros before your number minus one. You'll need to add a decimal place before your number in this case.

600

How many sig figs 111.11101

8

What is 91,000,000 in standard form ?

9.1 x 10 to the power of 7

CONVERT A PERCENTAGE TO A DECIMAL CONVERT A

Divide by 100.

CONVERT A FRACTION TO A DECIMAL

Divide the top number by bottom number

Standard form is another important skill to know well for your exams! There are epic numbers in science. • • •

The number of cells in the human body is around 37 200 000 000 000.

There are around 43 000 000 000 000 000 000 atoms in a grain of sand.

The number of stars in the universe is estimated to be 1,000,000,000,000,000,000,000.

What are the 2 main ways we round a number.

The two main ways we round a number is to decimal places or significant figures.

Look for a button on your calculator like xy .

The x represents your big number. The y your little superscript number (the power).

We use fractions all the time. Maybe you've taken half (1/2) a cake and only given your sister a third (1/3). Maybe you've paid for something half (1/2) each or told someone the time is quarter (1/4) past five. Fractions tell us how much of something there is.

There are 9 vegetarian guests and 30 guests in total what fraction are vegetarian

9/30 guests are vegetarian. This is the right answer......but wouldn't get you the mark in an exam. We need to simplify it.

This means to make the numbers as small as possible whilst still being whole (an integer). To do this find the largest number that both numbers in the fraction divide by to give a whole number (highest common factor). In this example both 9 and 30 divide by 3. If we divide both sides by 3 we get 3/10. This is now simplified.

The large number at the front must always be between 1 and 10.

This must always be multiplied by 10. That never changes.

Roots are the opposite of powers.

Two squared is 4 and the square root of 4 is 2.

MEDIAN -

WHEN ALL THE NUMBERS ARE LINED UP IT'S THE ONE IN THE MIDDLE

You can show probability as a fraction, decimal or percentage. You learnt how to convert between these forms earlier.

We could show this probability as 1/6 , 0.166 ... or 16.67% (2dp)

It can be hard to read off numbers this size (and boring to write) ......so we don't!

We write them in something called standard form. Standard form makes long numbers, with lots of zeros, easier to read.

EXAM TIP: One of the main tricks in the exam (especially chemistry) is to ask you to calculate a mean from some experimental results. You should not count any anomalies in your calculation e.g. any oddball answers that don't match the rest.

When giving averages it is often useful to know the range of numbers the average was taken from. What were the highest and lowest numbers (maximum and minimum)? To find the range (or difference) subtract the smallest number from the largest.

Significant figures

all the digits in a measurement that are directly measured, plus the last digit, which is estimated

1,000,000,000,000,000,000,000,000

becomes 1 x 10 to the power of 24

What are the 3 ways to work out averages

mode, median and mean

CONVERT A DECIMAL TO A PERCENTAGE

multiply by 100 Ex. 0.426 x 100 = 42.6 %

To work out 9 to the power of 2

press 9 then xy button, then 2. This saves you multiplying 9 by itself lots of times.

Why are the zeros not counted if there is no decimal place

they might just be place holders.

When are the zeros significant?

zeros between nonzeros digits, zeros after the decimal point and a nonzero number are significant

The small number at the top (the power) is how many times the decimal place would need to move to get it back to its place in the original number.

• If you had to move the decimal place right the small number is negative (-). If you had to move the decimal place left the small number is positive (+).

MODE -

THE MOST COMMON NUMBER

You can write ratios as a fraction. 2:3 becomes 2/3 Using this knowledge, we can simplify a ratio with a calculator

The area of something is how much space it covers. It's easy to work out, but how you do it depends on the shape of the object. For something that's a square or rectangle, multiply how long it is by how wide it is. Maths folk like to write it like this:

There are 10 numbers after the decimal point. STEP 4: Write x 10 after your answer.

Add the number from step 3 as a power to the 10.

Significant figures

All the digits that can be known precisely in a measurement, plus a last estimated digit

Pronounced 12 to the power of 24.

It means multiply 12 by itself 24 times.

9 to the power of 4.

It means multiply 9 by itself 4 times. 9 x 9 x 9 x 9 1224

I bet you love a 70% sale in your favourite shop or having 100% health in your favourite game. Percentages, decimals, and fractions are just different ways of writing a number.

It's important that you can convert numbers between these different formats.

The exams can be very picky about how you round your answers! The rounding rule is especially important for physicists. Almost every question will expect you to do this. Biologists and chemists have more freedom (and some exceptions that we shall learn later), but it's still a good rule to follow when in doubt.

Obviously, if you are told to round in a specific way then do that. If you aren't given instructions, then round to the lowest number of significant figures in the question text.

Here is a basic formula for calculating the percentage of something.

Part/ whole x 100

Common powers are 'the power of 2' and 'the power of 3'. They're so common they have their own names. WHat are they called?

Powers of 2, such as 42 , are called 4 squared. Powers of 3, such as 43 , are called 4 cubed. They have their own calculator buttons.

What is the probability of rolling a 6 on a dice?

Probability = 1/6

The likelihood of a certain thing happening is called its probability. To calculate probability, divide the likelihood of one or more events happening by the number of possible outcomes.

Probability = events/ outcomes

Now, for small numbers. Write the 0.0000624 in standard form.

STEP 1: Take the numbers that are not zero and write them down. 624

How do you change Change 6 x 10 to the power of 2 to normal.

STEP 1: Write down the number before the x 10. 6

STEP 2: If the number is 10 or greater put a decimal place after the first digit. 6.24

STEP 3: Count how many numbers are after this (after the decimal point if present) in the original number

STEP 2: If the number is 10 or greater put a decimal place after the first digit. 6.24

STEP 3: Count how many numbers are before this (before the new dp if present) in the original number. Don't include zeros before the original dp. 1 2 3 4 5 6 7 8 9 10 You need to move the decimal point 10 times to get it to the end. 16 0.0000624 There are 5 numbers before.

How do we figure out standard form?

Write the large number 62,400,000,000 in standard form. STEP 1: Take the numbers that are not zero and write them down. 624