CAMBRIDGE IGCSE™ BIOLOGY: MATHS SKILLS WORKBOOK
Exam-style questions and sample answers have been written by the author. In examinations, the way marks are awarded
may be different.
aths Skills
M
Workbook answers
Chapter 1
1
2
their mass
b kilograms
The numbers would be too small and not
very accurate.
b centimetres or millimetres
3 a cm3
b mm
c °C
d s
4 Learners’ own responses
5 a g / cm3
b m/s
3
6 cm / s
7 a 5 × 104
b 6.7 × 103
8
c 2.75 × 10
8 a 208
b 925 000
c 100 600 000
9 1.7 × 107
10 a 3 × 10−3
b 6.08 × 10−5
c 4.108 × 10−8
11 a 0.0006
b 0.000 000 722
c 0.005 008
12 1.05 × 10−4 metres
13 Learners’ own responses
14
1
a
a
105
10 × 10 × 10 × 10 × 10
100 000
106
10 × 10 × 10 × 10 × 10 × 10 1 000 000
15 a
16 a
c
103
b 109
100 000
b 100 000 000
10 000 000 000
17
10−3 1 ÷ (10 × 10 × 10)
0.001
one thousandth
10−4 1 ÷ (10 × 10 × 10 × 10)
0.0001
one ten
thousandth
18 a 10−2
b 10−10
19 a 0.1
b 0.0001
20 a (given) b 1 kg
d 1 ms
e 1 nJ
21 0.000 000 01 = 10−8
10−9 metres = 1 nm
so 10−8 metres = 10 nm
22 a 1 × 1000 = 1000 mm
c
1200
= 1.2 mm
1000
8
Exam-style questions
1
a
b
80
= 0.32 mg / cm3 [1]
250
(0.315 + 0.423 + 0.345 + 0.478 + 0.278)
i
= 0.368 s
5
[1]
c
one
million
107
14
= 0.014 kg
1000
23 1000 = 0.008 mm
one
hundred
thousand
c
b
c 10−7
c 0.000 000 01
c 1 cm3
2
d
a
b
ii 0.368 × 1000 = 368 ms [1]
cm3 [1] because the size of the number
will not be too big or too small [1]
Caffeine decreases reaction times. [1]
1 litre = 1 000 000 µl [1]
9856 × 5 000 000 [1] = 49 280 000 000 [1]
4.928 × 1010 [1]
Cambridge IGCSE™ Biology – Young © Cambridge University Press 2022
CAMBRIDGE IGCSE™ BIOLOGY: MATHS SKILLS WORKBOOK
Chapter 2
1
2
Temperature of mixture
Independent variable
pH of mixture
Dependent variable
Time taken to break down the starch
Control variable (variable they kept the same)
a
14 a
b
Independent: the year; Dependent:
the number of measles cases
b Independent: concentration of salt
solution; Dependent: change in mass
c Independent: light intensity of
area; Dependent: the number of
dandelion plants
3 Learners’ own responses
4 a discrete
b continuous
c categorical
d discrete
e continuous
f categorical
5 a Independent: volume of water;
Dependent: height of seedling
b Both are continuous because they are
measured and so can take any value
within a range.
6 C, a 25 cm3 measuring cylinder, because it
would give the most accurate measurement.
7 a 20 cm
b 0.5 cm
c It has a higher resolution, of 1 mm.
8 a 21 °C
b 38 °C
c −7 °C
d 6 °C
9 a 6.6 cm3 b 20.5 cm3 c 38 cm3
10 Put the measuring cylinder on a flat,
level surface.
Put her eyes level with the meniscus.
Take the measurement from the bottom
of the meniscus.
11 a 2 b 3 c 4
d 1 e 4 f 5
12 Learners’ own responses
13 a 3
b Use a balance that has greater precision,
for example 0.01 kg.
c There would be a greater number of
significant figures.
2
type of seeds
They have not given the unit for
temperature.
c 45 − 21 = 24 °C
15 First column heading is independent variable
plus unit used (if applicable)
One row for each value of independent
variable used
Second column heading is dependent variable
plus unit
Columns for each repeat
Column for mean
16
Volume of oxygen used in
Glucose
5 minutes / cm3
concentration
Reading Reading Reading Mean
/ g per cm3
1
2
3
0.2
0.4
0.6
0.8
17 41, 60, 90, 76
18 5.5 g
Exam-style questions
1
a
b
i
ii
Independent: type of fruit juice [1]
Dependent: number of drops of juice
required to decolourise 1 cm3
of DCPIP [1]
So the results are accurate/reduce the
number of errors [1]
Cambridge IGCSE™ Biology – Young © Cambridge University Press 2022
CAMBRIDGE IGCSE™ BIOLOGY: MATHS SKILLS WORKBOOK
Chapter 2 continued
2
a
i
ii
iii
25 cm3 [1]
10 cm3 [1]
50 cm3 [1]
b
Concentration of
hydrogen peroxide
/ vol.
Volume of oxygen produced after 30 s / cm3
Reading 1
Reading 2
Reading 3
Mean
10
15
20
25
30
5 rows with correct measurements [1]
Three columns for repeats [1]
Column for mean [1]
Correct headings with units [1]
c
(12.6 + 13.2)
[1] = 12.9 cm3 [1]
2
The 7.2 value is being ignored, as it is an
anomalous result.
3
Cambridge IGCSE™ Biology – Young © Cambridge University Press 2022
CAMBRIDGE IGCSE™ BIOLOGY: MATHS SKILLS WORKBOOK
Chapter 3
1
2
3
4
5
6
7
8
4
Scale B
a The y-axis only goes up to 20.
The highest number of plants is 38.
The bar for 38 plants will not fit on
the chart.
b Either have each large square as 20 (rather
than 10) or extend the y-axis up to 40.
The y-axis drawn should:
• have large squares with a value of 2
(Number of girls)
• start at 0, and end at 8
• have tick lines drawn extending away from
the large squares
• be labelled ‘Number of girls’.
a Year
b 7/Year 7
The bar graph should have:
• two bars drawn of equal width
• the first bar labelled ‘Right’, the second
bar labelled ‘Left’
• bars of correct height
• a gap in between each bar
• a title on the x-axis ‘Handedness’.
The bar graph should have:
• five bars drawn of equal width
• the bars labelled correctly
• bars of correct height
• a gap in between each bar
• a title on the x-axis ‘Number of siblings’.
Learners’ own answers
Length of middle finger/cm
Frequency
6.0–6.4
1
6.5–6.9
3
7.0–7.4
1
7.5–7.9
7
8.0–8.4
3
9
a
Mass of tortoise / g
Frequency
100–114
115–129
130–144
145–159
b
10
The zookeeper chose it because it created
four bars, which is neither too few nor
too many.
Length of leaf / mm
Frequency
50–54
3
55–59
2
60–64
3
65–69
2
70–74
6
11 Learners’ own answers
12 The histogram should have:
• bars of correct height
• no gaps in between the bars.
13 a ‘Foot length / mm’. Scale should start at
200. Each large square has a value of 10.
b The histogram should have:
• five bars drawn of equal width,
one large square each
• the bars labelled correctly
• bars of correct height
• no gaps in between the bars
• a title on the x-axis
‘Foot length / mm’.
14 The histogram should have:
• the y-axis labelled ‘Frequency’ with one
large square for 2
• the x-axis labelled ‘Resting heart rate/
beats per minute’. Each large square has
a value of 10
• six bars drawn of equal width
• the bars labelled correctly
• bars of correct height
• no gaps in between each bar.
15 Learners’ own answers
16 Learners’ own answers
Cambridge IGCSE™ Biology – Young © Cambridge University Press 2022
CAMBRIDGE IGCSE™ BIOLOGY: MATHS SKILLS WORKBOOK
Chapter 3 continued
5
Rate of photosynthesis / arbitrary units
23
Distance of light from plant / cm
Rate of photosynthesis / arbitrary units
24
Temperature / °C
25
Rate of photosynthesis / arbitrary units
D Concentration of carbon dioxide
i
Volume of oxygen produced in
1 minute
ii Concentration of carbon dioxide
18 The axes are labelled incorrectly. Time is
the independent variable and should be on
the x-axis. Light intensity is the dependent
variable and should be on the y-axis.
19 The graph should have:
• lines drawn with a ruler to show axes
• label of y-axis: Number of oxygen
bubbles produced in 1 minute
• label of x-axis: Temperature / °C
• suitable scales chosen for each axis, e.g.
one large square = 10 units
• both scales starting at 0
• tick marks and numbers added.
20 The points plotted for 0.04, 0.06 are incorrect.
21 a The dots used to plot the points are
too big.
The axes are the wrong way around (the
independent variable, Distance of lamp,
should be on the x-axis).
b He should use smaller dots, so just the
middle is on the correct coordinate/point,
or draw crosses, so just the middle is on
the correct point. This will make it clear
what the data points show to make it
easier to interpret his results.
Change so that Distance of lamp from
plant / cm is on the x-axis and Number
of bubbles produced in 1 minute is on
the y-axis. This is important so that the
line on the graph shows the relationship
between the variables; for example,
as distance increases, the number of
bubbles decreases.
22 The points plotted should be with small dots
or crosses, where the middle of the cross or
dot is at the correct point.
17 a
b
Carbon dioxide concentration / %
Cambridge IGCSE™ Biology – Young © Cambridge University Press 2022
CAMBRIDGE IGCSE™ BIOLOGY: MATHS SKILLS WORKBOOK
Chapter 3 continued
26 Put the independent variable on the x-axis and
the dependent variable on the y-axis.
Make sure the axes are labelled (use the
column headings from the table).
Choose an appropriate scale so all data can be
plotted and the graph is not too small.
Make sure each large square has the
same value.
Plot the points using a small cross or dot.
Draw a best-fit line using a ruler if it is a
straight line, or by eye if it is curved.
Make sure there is an even number of points
on either side of the line.
Use a sharp pencil to draw one thin, clear line;
do not sketch.
Exam-style questions
1
2
6
a
The bar chart should have:
• y-axis with a suitable scale and
correctly labelled ‘highest pulse rate/
beats per minute’ [1]
• bars plotted to correct height [1]
• bars labelled correctly and x-axis title
given ‘activity’. [1]
b Answer between 76 and 97 beats
per minute. [1]
The graph should have:
• both axes labelled correctly (x-axis:
fertiliser added / kg per hectare. y-axis:
amount of wheat / tonnes per hectare) [1]
• both axes appropriate scale [1]
• plotting correct [1]
• best-fit line drawn. [1]
Cambridge IGCSE™ Biology – Young © Cambridge University Press 2022
CAMBRIDGE IGCSE™ BIOLOGY: MATHS SKILLS WORKBOOK
Chapter 4
1
2
3
4
5
6
7
8
9
7%
a 14
b 16 + 31 = 47
D
Strong negative correlation
As the ethanol concentration increased the
heart rate decreased.
Learners’ own responses
C
After Arun drunk the cola, his heart rate
began to increase for about 11 minutes,
reaching a maximum of 86 beats per minute.
a
Resting heart rate / beats per minute
85
80
75
70
65
60
55
c
d
The graph shows a weak correlation,
showing that in countries where people
eat a lot of saturated fat, there are fewer
deaths from CHD. This weakly supports
the hypothesis. However, there may be
other factors that are not taken into
account. For example, if people are less
stressed and take more exercise, the risk
of developing CHD decreases. Also, it
shows deaths from CHD, not how many
people develop the disease. In some
countries, health care may be successful in
treating CHD, thus reducing the number
of people who die from it. The graph
only shows death in men; the relationship
might be different in women.
b Learners’ own responses
11 3.6 billion
12 10 000
13 a 52
b Learners’ own responses
14 a
10
9
8
7
6
5
4
3
2
1
0
50
45
1
b
10 a
2
3
4
5
6
7
Hours of exercise per week
8
9
The correlation is very strong because the
points are close to the best-fit line.
The more hours of exercise a person
10
does per week, the lower their resting
9
heart rate.
8
7
Learners’ own answers
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10
10
9
8
7
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10
b
0 1 2 3 4 5 6 7 8 9 10
10
9
8
7
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10
10
9
8
7
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10
c
10
9
8
7
6
5
4
3
2
1
0
7
0 1 2 3 4 5 6 7 8 9 10
10
9
8
7
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10
10
9
8
7
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10
Cambridge IGCSE™ Biology – Young © Cambridge University Press 2022
10
9
8
7
6
5
4
3
2
1
0
0
CAMBRIDGE IGCSE™ BIOLOGY: MATHS SKILLS WORKBOOK
Chapter 4 continued
3
15 24
16 a 6
b Day 14
Exam-style questions
1
a
b
c
2
a
b
8
a
b
c
10 minutes [1]
25 − 13 [1]
= 12 breaths per minute [1]
The breathing rate decreased. [1]
The student slowed down. [1]
She used interpolation. [1]
Or a description of this, for example, she
drew a line up from 4 years and across
to 27 000.
The population is not following a trend/
the population fluctuates (goes up
and down). [1]
Positive (correlation) [1]
Best-fit line drawn correctly [1]
The data points are all close to the line of
best fit. [1]
As the diameter of the neurone
increases the speed of electrical impulse
also increases. [1]
Cambridge IGCSE™ Biology – Young © Cambridge University Press 2022
CAMBRIDGE IGCSE™ BIOLOGY: MATHS SKILLS WORKBOOK
Chapter 5
1
2
a
a
48
3
b
a
Learners’ own responses
12
b
4
b
( )
43.2
11
× 100 = 55%
20
c
1140
17 a 50%
b 100%
18 There are two possible combinations out
of four that result in XY (a boy). This is a
probability of 2 in 4, which is simplified to
1 in 2.
(123 ) × 100 = 25%
Exam-style questions
1928 − 954 = 974
1
( )
974
× 100 = 50.5% increase
1928
5
Learners’ own responses
6
a
b
c
7
8
9
6000 − 50 000 = −44 000
2
000
× 100 = –88 = 88%
(–44
50 000 )
1200 − 6000 = −4800
× 100 = –80 = 80%
( –4800
6000 )
3
40
= 0.4 mm [1]
100
b
0.4 × 1000 = 400 µm [1]
c
8
= 0.2 μm [1]
40
a
100 − 55 − 1 = 44% [1]
b
55
= 0.55 [1]
100
a
240 − 1200 = −960
(
0.55 × 156 = 85.8 cm3 [1]
5 000 000 000 : 250 000 000 [1]
5 000 000 000
= 20 [1]
250 000 000
)
–960
× 100 = –80 = 80%
1200
Scale: 1 cm : 10 µm
Diameter of red blood cell image = 2 cm
Diameter of real red blood cell = 2 × 10 = 20 µm
Length of scale line = 1 cm
Diameter of image = 4.4 cm
Actual diameter = 44 nm
a Height of image = 54 mm
b
a
b
20 : 1 [1]
2 400 000 − 3 200 000 = −800 000 [1]
000
× 100 = −25 [1]
(−800
3 200 000)
= 25% decrease [1]
54
= 0.027 mm
2000
size of image
real size =
magnification
I needed to calculate the real height
of the cell.
10
25
= 0.00125 mm
20 000
0.00125 × 1000 = 1.25 µm (Accept an answer
derived from a diameter of +/− 2 mm)
11 size of image = 10.2 × 10 = 102 mm
102
= ×1020
0.1
size of image
12 magnification =
actual size
1 mm = 0.001 µm
34
= ×34 000
0.001
13 a 3 : 2
b 7:3
14 Learners’ own responses
15 a 2 : 1
b 1:4
c 3:1
16 a 1 : 1
b Learners’ own answers
9
d
1:3
Cambridge IGCSE™ Biology – Young © Cambridge University Press 2022
CAMBRIDGE IGCSE™ BIOLOGY: MATHS SKILLS WORKBOOK
Chapter 6
1
a
b
c
2
54
= 9 cm2
6
3
4
5
6
5 × 5 = 25 cm2
25 × 6 = 150 cm2
Learners’ own responses
√9 = 3 cm
3 × 10 = 30 mm
a Calculate the area of the two square
sides and the four oblong sides. Add
them together.
b 1.22 × 2 = 2.88
(5.5 × 1.2) × 4 = 26.4
2.88 + 26.4 = 29.28 cm2
c Calculating the surface area of a cube
requires calculating the area of one face
and multiplying by 6; for a rectangular
block, there are more calculations
involved, depending on the dimensions.
2
4.4 × π = 60.8 cm2 (3 sf)
90
= 45
2
45 mm = 4.5 cm
4.52 × π = 63.6 cm2 (3 sf)
Learners’ own answers
Exam-style questions
1
a
b
c
2
3
10
Area of one face: 2 × 2 = 4 cm2 [1]
Surface area: 4 × 6 = 24 cm2 [1]
Area of one face: 1 × 1 = 1 cm2 [1]
Surface area of one cube: 1 × 6 = 6 cm2 [1]
Total surface area of eight cubes:
6 × 8 = 48 cm2 [1]
It will increase the rate of diffusion. [1]
Because the surface area has
increased/doubled. [1]
Radius:
2.4
= 1.2 cm [1]
2
Area = π × 1.22 [1]
= 4.52 cm2 (3 sf) [1]
5100 m2 [1]
(Accept an answer between 4500 and 5500 m2.)
Cambridge IGCSE™ Biology – Young © Cambridge University Press 2022
CAMBRIDGE IGCSE™ BIOLOGY: MATHS SKILLS WORKBOOK
Applying more than one skill
1
a
b
c
2
Mother
82
= 1.9 mm / s [1]
44
Father
d
Measure the temperature of the water [1]
using a thermometer. [1]
a
8
[1]
1000
b
Correct alleles of offspring [1]
Bar drawn with a height of 122 (allow +/−
half a small square) [1]
52 s [1]
8.2 × 10 = 82 mm [1]
= 0.008 mm [1]
Diameter of image = 18 mm [1]
6
18
= 0.0045 [1]
4000
c
0.0045 × 1000 = 4.5 µm [1]
6 − 8 = –2 [1]
( –28 ) × 100 [1]
3
a
b
c
4
a
b
7
= 25% decrease [1]
270 mm2 [1]
(Accept an answer between 250 and
315 mm2.)
Use paper with smaller squares. [1]
(1 ÷ 0.001) × 5 = 5000 [1]
5000 × 525 = 2 625 000 [1]
= 2.625 × 106 [1]
(4 × 0.5) × 4 = 8, (0.5 × 0.5) × 2 = 0.5 [1]
8 + 0.5 = 8.5 cm2 [1]
0.15
× 100 [1]
1.35
8
= 11.1% [1]
There are different starting masses. [1]
Using percentage change allows you to
compare the change in mass. [1]
d Graph should have:
Correct points plotted [1]
Label on x-axis: Concentration of sugar
solution in mol / dm3 [1]
Circle drawn around point at
0.6 mol / dm3 [1]
e Best-fit line: straight line ignoring result at
0.6 mol / dm3 [1]
Genetic diagram drawn:
Correct alleles of parents [1]
5
11
9
d
d
Dd
dd
d
Dd
dd
Children with Dd will have polydactyly.
2 in 4 or 1 in 2 or 50% [1]
a Multiply it by 4 [1]
b Bar drawn correctly [1]
c 59 + (60 × 2) + (61 × 2) + (62 × 4) +
(63 × 3) + (64 × 4) + 65 + (66 × 2) + 67 = 1258
[1]
1258 ÷ 20 = 62.9 beats per minute [1]
a clock/stopwatch [1]
b It has a high precision [1] so the
measurement will be accurate. [1]
c Line: Z [1]
Reason: It shows that as temperature
increases the time taken for the methylene
blue to turn colourless decreases. [1]
This shows that more oxygen is being used
up as temperature increases [1] because
the rate of respiration increases with
temperature [1]
a 100 − 37 − 23 − 32 = 8% [1]
b
c
D
c
d
a
b
10 a
23
1.3 × 109 × ( ) [1]
100
= 2.99 × 108 [1]
1.02 billion [1]
1.55 billion (+/− 0.05 billion) [1]
Any one from: temperature/humidity/
air movement [1]
Volume = π × (0.5)2 × 6 [1]
= 4.71… mm3 in 20 minutes [1]
= 14.1 mm3 per hour [1]
Answer to three significant figures [1]
30 mm [1]
b
30
[1] = 0.6 mm [1]
50
c
Use a higher magnification. [1]
Repeat the measurement and
calculation. [1]
Cambridge IGCSE™ Biology – Young © Cambridge University Press 2022