NATIONAL 5 BIOLOGY

CALCULATION PRACTISE

Average (Mean!)

• Add up all the numbers/how many numbers you added up
• Example: In a class the heights of the pupils in cm were 148, 153, 147 and 160
• Step 1:
• Step 2:

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148+ 153+ 147 + 160 =

608

608 ÷ 4=

152cm

36

30

Average Change/Rate

• Change/time
• Example: A pupil’s height increased from 152cm in 2008 to 176cm in 2016. What was the average increase in height per year?
• Step 1:
• Step 2:

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176 -152 =

24

24 ÷ 8=

3cm

Change = 15 - 5 = 10

10 ÷ 5 = 2

Change/time

Change= 64 -10 = 54

54 ÷ 60 = 0.9 mm/minute

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______mm/minute

Change/time

Percentage

• The formula for calculating a percentage is (number ÷ total) x 100
• Example: 14 out of 20 pupils have brown eyes. What percentage have brown eyes?

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• Step 1:
• Step 2:

14 ÷ 20 =

0.7

0.7 x 100 =

70%

Hint:

7 have high mutation = 13 do not

Hint:

32g dry mass = 18g of water

Number when given a Percentage

• (Percentage/100) x total
• Example: There are 150 kids in the park. 20% have an ice cream. Calculate the number of pupils with an ice cream

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• Step 1:
• Step 2:

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20 ÷ 100 =

0.2

0.2 x 150 =

30 kids

20 ÷ 100 = 0.2

0.2 x 95

(percentage/100) x total

(percentage/100) x total

Hint:

95% not used = 5% captured

Percentage Change

• Percentage increase or percentage decrease:

(change ÷ start) x 100

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Example: If a pupil has a height of 155 cm in August and measures 160 cm by December, what is the percentage change?

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Step 1.

Step 2.

Step 3.

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Change =

160 cm – 155 cm =

5 cm

5 (change) ÷ 155 (start value) =

0.032258

0.032258 x 100 =

3 % increase in height

25 – 30 = 5

5 ÷ 25 = 0.2

0.2 x 100 = 20 %

67.5 – 54 = 13.5

(change/start) x 100

13.5 ÷ 54 = 0.25

0.25 x 100 = +25 %

35 to 42 = 7

7 ÷ 35 = 0.2

0.2 x 100 = 20%

2 to 7 = 5

5 ÷ 2 = 2.5

2.5 x 100 = 250%

5 – 20 = - 15 *ignore the minus

15 ÷ 5 = 3

3 x 100 = 300%

(change/start) x 100

90 – 45 = 45

45 ÷ 45 = 1

1 x 100 = 100%

Because the starting populations weren’t all the same number

Ratios

1. Write the numbers in the correct order
2. Simplify by dividing both numbers by the same number until both in their simplest terms.
1. Example: If 40 girls and 30 boys, what is the ratio of boys to girls?
2. Step 1:
3. Step 2:

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30 : 40

Divide both by 5 =

6: 8

Divide both by 2 =

3: 4

165 : 105

Divide both by 5

= 33 : 21

Divide both by 3

= 11 : 7

OR

divide both by 15

= 11 : 7

13 : 5

65 : 25

Straight Hitchhiker

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Divide both by 5

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= 13 : 5

90. : 4.5 X 2

180 : 9

20 : 1

Cell Size

• length or width/ number of cells

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2mm

Length is 2mm

5 cells across

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2 ÷ 5 = 0.4mm

Cells Dividing

• Always double your number

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Example: Cells divide every 20 minutes. If you start with 5 cells, how many will you have after 1 hour?

0 minutes = 5 cells

20 minutes = 10 cells

40 minutes = 20 cells

1 hour = 40 cells

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2

Start = 1000 cells/cm3

30 mins = 2000

60 = 4000

90 = 8000

120 = 16000

Other types of question

2.5 = 8

4.5 = 2

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8 ÷ 2 = 4

26mm ÷ 20 minutes =

Non-resistant = 250

Resistant = 425

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425 – 250 = 175

1975 = 4000 (millions), 2000 = 6000

1975 – 2000 = difference of 2000

6000 + 2000 = 8000

difference = 8000

8^OC is the difference

Drop of 1000 per 1^OC

32^OC to 35^OC = 3^OC

3 x 1000 = 3000

1600 – 3000

= 1300

Validity

• Only 1 variable should be changed

Only one variable should be altered to ensure valid results.

Reliability

• Repeat the experiment several times at each altered variable and calculate an average

Answer: the measurements have not been repeated enough times for each type of stem to ensure reliable results.

• AVERAGE (MEAN): add up all the numbers/how many numbers you added up
• AVERAGE CHANGE/RATE: change/time
• PERCENTAGE: (number / total) x 100
• NUMBER WHEN GIVEN A PERCENTAGE: (percentage/100) x total
• PERCENTAGE CHANGE: (change/start) x 100
• CELL SIZE: length or width/number of cells
• RELIABILITY: repeat the experiment several times several times and calculate an average

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