MODUL NOTA RINGKAS & LATIHAN MATHEMATICS FORM 1

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6. Linear inequality in one variable has __________ than one possible solution. The linear

inequalities also can be solved by system of _______________________________________.
Example:
Solve the following simultaneous linear inequalities: 2 + 5 < 11 and 3 − 10 < 5

Example:
Solve the following simultaneous linear inequalities:

8 + 5 ≥ 15 − 13 and 3 − 4 > 9 + 20

7. Summary for this topic:

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8. Solve the following simultaneous linear inequalities:

a) − 1 < 3 and 3 − 2 ≤ c) 2 −5 ≤ 3 and 5− ≤ 1
2 5 3 2

b) 2(3 −1) ≥ −2 and 5 − 2 < 7 d) 8 < 3 − 1 ≤ 32, list all the integers that
7 5 satisfy the simultaneous linear inequalities.

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MODUL MATHS F1
CHAPTER 8 : LINES AND ANGLES

A) LINES AND ANGLES

1. Two line segments having the same length are known as _________________________ while
two angles having the same size are known as __________________________.

Examples of congruent line segment Examples of congruent angles

2. The length of a line segment can be measured more accurately by using a ___________ and
the size of angle can be measured more accurately using a ________________.

3. Types of angles:

Right angle Acute angle Obtuse angle Reflex angle
-angle with 90° -angle less than 90°
-angle more than 90° -angle more than
but less than 180° 180° but less than
360°

Angle on straight line Angle of one whole turn

-angle on a straight line -angle of one whole turn

is 180° is 360°

Complementary angle Supplementary angle Conjugate angle

-sum of two angles are -sum of two angles are always 180° -sum of two angles are

always 90° always 360°

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4. Examples to solve problems using angles:

5. Geometrical construction is the work of using ____________________ or
_______________________ to do drawings of accurate measurements.
a) Line Segments
i) It is a section of a straight line with a fixed length.
ii) Example how to construct a line segment AB with a length of 8 cm.

b) Perpendicular bisectors
i) It is happened when a line AB (for example) is
perpendicular to line segment CD and divide CD
_________________________________.

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ii) Example how to construct the perpendicular

bisector of line segment PQ.

c) Perpendicular line to a straight line
i) Example how to construct the perpendicular line
from point M to the straight line PQ.

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ii) Example how to construct the perpendicular line

to PQ passing through point N

d) Parallel lines
i) Parallel lines are lines _____________________ even when they are extended.
ii) Example how to construct the line that is parallel
to PQ passing through point R.

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e) Constructing an angle of 60°

i) Can be use in forming an equilateral triangle (equal length and interior angles)
ii) Example how to construct line PQ so that

∠ = 60°

f) Constructing an angle bisector
i) Angle bisector is defined if a line ___________________________________.
ii) Example how to construct the angle bisector
of ∠

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iii) Other examples of angle bisector

6. An exercise for geometrical construction skills.

The diagram above shows a quadrilateral KLMN. Using the lines LM and MN provided
below, construct the diagram using only a ruler and a pair of compasses.

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7. C) ANGLES RELATED TO D) ANGLES OF
PARALLEL LINES & ELEVATION &
B) ANGLES RELATED TO TRANSVERSALS DEPRESSION
INTERSECTING LINES

Transversal is a straight line The angle of elevation is the
that ___________________ "upwards" angle from the
_______________________. __________ to a line of sight
from the observer to some
point of interest.

Example: Example:
In the diagram, POR and TOQ In the diagram, PQ, RS and
are straight lines. Find the values TU are parallel lines. Find the
of x and y. values of a, b and c.

The angle of depression is the
___________ angle from the
horizontal to a line of sight
from the observer to some
_______________________.

a = 60°
b = 180°
b + c = 180°
118° + c = 180°

c = 180° - 118°
= 62°

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8.

In the diagram above, VQ, PQR and WTQ are straight lines.
a) Find the value of x and of y.

b) Assume UV is a horizontal line, find the angle of elevation of U from T.

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MODUL MATHS F1
CHAPTER 9 : BASIC POLYGONS

A) POLYGONS

1. A polygon is an __________________ on a plane bounded by 3 or more straight sides.

2. For a polygon,
a. The number of ____________ = the number of ___________
b. The number of ____________ can be determined according to the steps:

Identify the Minus 3 from the
number of sides number of sides.
of polygon Let the result be m.

3. The number of diagonals of a polygon having n sides also can be calculated by using
formula:

( −3)

No. of diagonals = 2

4. Fill in the table below.

Name of polygon

Number of sides
Number of vertices
Number of diagonals

Name of polygon

Number of sides
Number of vertices
Number of diagonals

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5. A polygon can be drawn according the following steps.

Identify the Join all the
number of points with
sides of the straight lines
polygon to form a
closed figure.

6. The vertices of a polygon are usually labelled in ______________________ and the polygon
is named either ______________ or ____________________ of the vertices.

B) PROPERTIES OF TRIANGLES AND THE INTERIOR & EXTERIOR ANGLES OF
TRIANGLES

1. Triangles can be classified based on the ____________________ of their interior angles or
the __________ of their sides.

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2. Besides that, for a triangle,

a. The _________ of all the interior angles is ________
b. The sum of an _______________ and its adjacent exterior angle is __________.
c. An _____________________ is the sum of two opposite interior angles.

3. Example in solving problem regarding triangles:
In the diagram, PQRS is a straight line. Calculate the value of x and y.

4. Solve the problem involving triangles.

In the diagram above, PRT and QRS are straight lines. Find the value of x.

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5. Summary for triangles:

C) PROPERTIES OF QUADRILATERALS AND THE INTERIOR & EXTERIOR ANGLES
OF QUADRILATERALS.

1. Fill in the following table below with the correct geometric properties/ number of axes of
symmetry according to the quadrilaterals.

Type of No. of axes of Geometric properties
quadrilateral symmetry
Rectangle • The opposite sides are parallel and of equal
2 length.

• The diagonals are of equal length and are
bisectors of each other.

•

Square • All the sides are of equal length.
Parallelogram • The diagonals are of equal length and are

perpendicular bisectors of each other.
•

•

None • The opposite sides are parallel and of equal
length.

•

•

Rhombus 62
Trapezium
• All the sides are of equal length.
• The opposite sides are parallel.
• The opposite angles are equal.
•

• Only one pair of opposite sides is parallel.

Kite • One of the diagonals is the perpendicular
bisector of the other.

• One of the diagonals is the angle bisector of
1 the angles at the vertices.

•
•

2. Notes to be remembered:
a. The sum of the interior angles of a quadrilateral is __________.
b. The sum of an exterior angle of a quadrilateral and its adjacent exterior angle is ___.
c. The opposite angles in parallelogram (or rhombus) are ___________.

3. Problems solving regarding quadrilaterals.

In the diagram, PQRU is a square and QRSV is a
parallelogram. PVR is a straight line. Find the values of
x and y.

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4. Problems solving involving the combinations of triangles and quadrilaterals.

In the diagram, QRTU is a parallelogram and PQRS is a
straight line. Find the values of x and y.

5. Summary for quadrilaterals:

6. Exercises for this topic:
i. Mark  for a TRUE statement and  for a FALSE statement.
a) A right-angled triangle has an axis of symmetry if one of the interior
angles is 45°
b) If the axis of symmetry of an equilateral triangle PQR passes through
vertex P, then the axis of symmetry is the angle bisector of the angle
at P.
c) A diagonal of a rectangle is the perpendicular bisector of the other
diagonal.
d) A square and a rhombus are quadrilaterals and their diagonals
intersect at right angles.

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ii. Determine the types of _______________
a. Quadrilaterals which have two axes of symmetry. _______________
b. Triangles which do not have an axis of symmetry. _______________
c. Quadrilaterals with all the sides having the same length. _______________
d. Quadrilaterals with all the interior angles being 90°.

iii. PRST is a trapezium. PQR and PTU
are straight lines. Find the value of x
and y.

iv. In the diagram below, PRST is a
rhombus and QRUT is a straight line.
Find the value of x.

v. In the diagram below, PQR and SQT
are straight lines. Find the value of x.

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MODUL MATHS F1
CHAPTER 10 : PERIMETER AND AREA

A) PERIMETER
1. Perimeter is the _______________ around an enclosed area. For example,

2. To measure a curve or besides straight line, we can use __________.

3. Besides that, to estimate the perimeter accurately, we can use _____________________ or a
_______________________.

4. The ___________ of estimated perimeter can be evaluated by comparing the
_________________ with the _______________.

5. The ___________ the difference between the values of estimated perimeter and measured
perimeter, the _______________ precise the estimated value.

Percentage error = Difference between estimated value and actual value × 100%
actual value

*The smaller the percentage error, the more precise the estimated value*

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6. Solving problems.

The diagram shows the parking area in front of a shopping mall. The shopping mall
management intends to fence up the entire parking area, except the main entrance and another
side entrance. If the cost of fencing is RM80 per metre, what will be the cost incurred by the
shopping mall?

Solution:

7. An exercise to be done for enrichment.

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B) AREA OF TRIANGLES, PARALLELOGRAMS, KITES AND TRAPEZIUM

1. To estimate the area of an irregular shape, we can use:
a. A __________________
b. Draw ____________________

2. Fill in the table below with a correct formula to find the area.

No Shape & Formula
Triangle

1
Area of triangle =

Parallelogram Area of parallelogram =
2

Kite Area of kite =
3

Trapezium Area of trapezium =
4

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C) RELATIONSHIP BETWEEN PERIMETER AND AREA

1. For rectangles with, b) The same ________
a) The same perimeter • The ____________ will increases if

• The ________ will decreases if the the difference between the ________
difference between the _______ and and the ________ decreases.
the ______ increases. • The ____________ will be the
____________ when the rectangle is
• The ______ will be the ________ a square.
when the rectangle is a square.

2. Examples to solve problems.

a) The diagram shows a rectangle plot of land PRTV. The triangular region PQW and the
trapezium-shaped region UTSX are used for planting banana trees and rambutan trees
respectively. The remaining shaded region is used to plant papaya trees. Calculate the area
of the region used to plant papaya trees.

b) Given the area of a square garden is 500 m2, find the perimeter of the garden.

69
3. Summary/ quick review for this chapter.

4. Exercises for enrichment.
i) In the diagram, the perimeter of
the shaded region is 25 cm. Find
the perimeter of the region which
is not shaded.

ii) In the diagram, PQRW is a square,
RST is a triangle and TWVU is a
trapezium. Find the area of the
whole diagram.

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MODUL MATHS F1
CHAPTER 11 : INTRODUCTION TO SET

A) SET
1. Set is a group of objects that have ______________________ .

Answer: Water Transport Air Transport
Land Transport Sampan Rocket
Car Boat
Lorry Ship Aeroplane
Van Ferry Helicopter
Bus Hot-air balloon

2. Sets can be written by using
a. Description
b. ____________
c. ___________________

For example, we can write the colours of Jalur Gemilang in set A as follows.

3. Empty set/ null set is a set that does not contain any _______________ and can be represented
with the symbol ______ or _______

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4. The elements of a set are defined according to certain ____________ which must satisfy the
conditions of the set that is defined.

5. Or we can say that elements are the things that is in/ belongs in a ________. The symbol for
element is ________

For example, Q = { }
Thus, durian is an element of set Q or we can say that durian ∈ Q

6. The number of elements in a set P can be represented by the notation n(P).
For example:
P = {1, 2, 3,4,5, 6}
n(P) = 6

7. Equality of sets happened when every element in sets A, B and C are the ___________. These
equal sets can be written as A = B = C.

8. Generally, if every element in two or more sets are the same, then
__________________________.

9. The universal set can be defined as a set that consists of ____________________ under
discussion and is commonly represented by a __________________.

Set shows the students who got participated in Mathematics quiz.
{ , , ℎ , ℎ, ℎ}
Universal set, = { , , ℎ , ℎ, ℎ}

10. ___________________________ is the elements that is not/ besides the set discussed from
the universal set.
= { 1 10}
B = { }
B’ = elements that is not/ besides the prime number
B’ = {1,4,6,8, 9}

72
11. Venn diagram or an _____________________________ will represents the relationship

between sets.

12. Here is a situation where every element in set B is also an element of set A, thus the set B is a
subset of set A and can be written as ______________.

Other example:

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13. For the number of subsets,

If a set contains n elements, then the possible number of subsets is 2n.
For example, {3, 6} = 22 = 4
The possible subsets of {3, 6} = ∅, {3}, {6}, {3,6}
= There are 4 number of subsets in {3, 6}.

SUMMARY/ QUICK REVISION

No Terms Definition Example / symbols

a) Set Group of objects that have A is the set of colours of Jalur Gemilang
common characteristics. A = { , ℎ , , }

b) Empty set/ A set that does not contain { } or ∅
null set any element

c) Element Things that in/ belongs to a Q = { }
set durian ∈ Q

d) No of How many things/ elements P = {1, 2, 3,4,5, 6}

element in a set n(P) = 6

Set shows the students who got

participated in Mathematics quiz.
A set consists of all the { , , ℎ , ℎ, ℎ}
e) Universal set elements under discussion

Universal set,

= { , , ℎ , ℎ, ℎ}

= { 1 10}

f) Complement Elements that is not / B = { }
besides the set discussed B’ = elements that is not/ besides the
of a set
from the universal set prime number

B’ = {1,4,6,8, 9}

g) Subset Every element in set X is X = {2,4, 6} and Y = {1,2,3,4,5, 6}

also an element of set Y. X⊂Y

If a set contains n elements, then the possible number of subsets is 2n.

Number of For example, {3, 6} = 22 = 4
h)
subsets The possible subsets of {3, 6} = ∅, {3}, {6}, {3,6} = There are 4 number

of subsets in {3, 6}.

74
14. Some exercises to be done for enrichment.

a) If = { : 10 ≤ ≤ 30, } and P = { 4}, find n(P’).

b) Given the universal set , A ⊂ B and C ⊂ A, draw a Venn diagram to represent sets , A,
B and C.

c) Based on the Venn diagram,
i. What is the relationship between Q and R?
ii. What is represented by the shaded region?

d) Based on the Venn diagram, write the relationship between , A, B and C.

75

MODUL MATHS F1
CHAPTER 12 : DATA HANDLING

A) DATA COLLECTION (Pengumpulan data)

1. Statistical question (soalan statistic) is a question that can be answered by
______________________ and there will be variability or diversity in the data related to
the question.

2. After generating the statistical questions, the next step is to determine the method of
_______________________.

3. Data collection method (kaedah pengumpulan data) can be in the form of:
a. __________________
b. Survey
c. __________________
d. __________________

4. After collecting the data, the next step is to ______________________ into categorical
data and _____________________.

5. Numerical Data
1. Measures ______________
Categorical Data
1. Measures characteristics

2. Cannot be measured numerically 2. Measured numerically.
but can be _________________

3. Examples: 3. Examples:
a. Gender of a person a. The number of cars in a
b. ____________________ school
c. ____________________ b. ________________________
c. The time spent on exercise

6. Numerical data consists of: __________________________
Discrete Data 1. Measured on a continuous scale.
2. Example:
1. Measures in a whole unit
2. Example: ___________________________

_____________________

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7. Examples of CONSTRUCTING A FREQUENCY TABLE

EXERCISE ON DATA COLLECTION
1. State whether each of the following data as categorical data or numerical data
Data Categorical data / numerical data
a) Colour of cars
b) Annual income
c) Number of stamps each student collects
d) Language spoken at home

2. Construct a frequency table for datas below.

Size Tally Frequency
S
M
L
XL

DATA REPRESENTATION (Perwakilan data)

1. Data can be represented in a few ways. They are:
a. Bar chart
b. Pie chart
c. _________________
d. _________________
e. Stem – and – leaf plot
f. Histogram
g. __________________

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2. Data representations help us to ________________ and ________________ data much
easier.

3. We need to represent the data ethically to avoid ________________.

4. All we need to note and be careful is that:
a) The scale must be consistent and start at 0
b) The information shown (data displayed) must be correct.

a) BAR CHART

1. Bar chart represents data by using bars. It is suitable for showing _________________
between __________________.

2. Steps to construct a bar chart:

Choose one of the Draw the bars
axes to mark a such that the
suitable scale and height of each
label the number bar corresponds
of students. Label to the frequency
the other axis with of the category
types of activities it represents.

3. There are two types of bar chart.
a. Horizontal bar chart
b. Vertical bar chart

_________________________________ _______________________________

4. A dual bar chart is suitable for comparing two sets of data. For example, the performance
of students in two tests, ___________________________________________________.

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5. Example of a dual bar chart to compare between two sets of data.

b) PIE CHART

1. A pie chart is a data representation that uses
_____________________________________ to show the
____________________________________ of the whole data.

2. Steps to construct a pie chart.

Find the angle Draw a circle
of sector for and divide it into
each category different sectors
based on the
angles
calculated

3. Example of a pie chart.

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c) LINE GRAPH

1. A line graph is a data representation used to _______________________________ over
a period of time that represented by _________________ which are connected in a straight
line.

2. Steps to construct a line graph.

Choose a suitable

and uniform scale Write down the
title of the line
for both axes. The graph.

vertical axis

represents data. The

horizontal axis

represents time.

3. Example of line graph.

d) DOT PLOT

1. A dot plot shows the ___________________________________ on a number line.

2. The data either clustered around certain values or _______________________ evenly on
a ______________________.

3. Dot plot can help us to:
a. Visualise data patterns
b. ________________________
c. ________________________
d. Detect unusual observations (extreme values) in the data.

4. Steps to construct dot plot: 80

Plot the individual
data with a dot over
their values on the
number line.

5. Example of dot plot.

e) STEM–AND–LEAF PLOT

1. A stem–and–leaf plot is a data representation that separates the data values into
_________________________ according to their _____________ value.

2. The leaf is the ____________ digit of the number while the stem is the
_____________________ or digits on the left of the number.

3. The plot retains the _________________________ and were able to do arithmetic
calculation for the purpose of ____________________________.

4. Steps to construct a stem – and – leaf plot. Write a key
and the title.
Write each The key
data one by indicates the
one and take unit for the
the tens digit stem and leaf.
of each data
values as the
team.

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5. Example of stem – and – leaf plot.

f) HISTOGRAM
1. Histogram is a data representation that displays _______________________ , that is

collected in intervals.
2. The _________ of each bar in a histogram represents a specific interval while the

____________ of each bar represents the frequency in each interval.
3. Histogram does not display the ______________________ of the data but displays values

in a certain interval
4. It can also provide a display of ___________ data sets because the data is represented in

class intervals.
5. Example of interpretation data in histogram.

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g) FREQUENCY POLYGON
1. Frequency polygon is a graph formed by joining the _____________ of the top of each

bar in ______________ with straight lines.
2. Example of a histogram converting into a frequency polygon.

3. Example of interpretation data in frequency polygon.

B) DATA INTERPRETATION (Pentafsiran data)
1. From interpretation of data, we can obtain _________________ and make
__________________ and predictions.
2. Example of interpretation data from a line graph.
The line graph shows the mass of waste, in thousand
tonnes, produced in a city from 2010 to 2015.
a) What is the mass of waste produced in 2010?
b) What can you say about the mas of waste produced
in 2011 and 2014?
c) Find the mean mass of the waste produced over a period of six years.
d) State one inference based on the line graph given.
e) Based on the trend of the line graph, predict the mass of waste produced in 2016.

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3. Example of interpretation data from a dot plot.

84
4. Exercises in interpreting data representations of a grouped and ungrouped data.

a)

A university is running a survey to find out the idols of 250 students. A pie chart shows
different types of their idols.
i) What percentage of the students choose famous people as their favourite type of idol?
ii) Find the value of x in the diagram.

b)

Mr Khurana has two kitchen appliance stores. He compares the sales of two stores during a
month and recovered as in the dual bar chart above.
i) Calculate the total sales of grill and coffee maker for both Mr Khurana’s stores.
ii) Calculate the difference between the total sales of kitchen appliances in store A and B

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MODUL MATHS F1
CHAPTER 13 : THE PYTHAGORAS’ THEOREM

A) THE PYTHAGORAS’ THEOREM

1. ________________ is the longest side opposite to the right angle.
2. The adjacent of a right-angle triangle is the length of side beside the angle ( ) while the

opposite is the length which is opposite to the angle in a right-angle triangle.

Opposite Hypotenuse (the longest side)


Adjacent

3. Pythagoras’ Theorem is the relationship between the ___________________________ on
the hypotenuse is equal to the ________________________________ on the other two
sides.

4. Some exercises to state the relationship between the lengths of sides of the given right-
angled triangle.

a) __________________ b) _____________________

5. From the formula of Pythagoras’ Theorem, we can determine the length of an
________________________ in a right-angled triangle if the lengths of two other sides are
given.

86 Working steps
6. For examples,

No Examples of questions
Calculate the value of x

1
Calculate the value of x

2

Calculate the length of PQ

3

Calculate the length of PQ

4

7. However, we also use Pythagoras’ Theorem to solve problems. For example,

87

8. Therefore, here are some exercises should be done in enhancing the formula of Pythagoras’
Theorem.

Solution: (b)
(a)

Solution:

Solution:

88
B) THE CONVERSE OF PYTHAGORAS’ THEOREM

1. There are three angles that should be recognised in this topic. They are:
a. Acute angle
b. ___________________
c. ___________________

2. Determine whether each of the following length of sides of triangle given would form a
right-angled, acute-angled or obtuse-angled triangle.
a) 6 cm, 8 cm and 10 cm

b) 9 cm, 12 cm and 16 cm

c) 12 cm, 16 cm and 18 cm

3. An ______________________ is an angle less than 90° while an obtuse angle is an
angle _________________________ but _______________________.

4. Examples to determine whether a triangle is a right-angled triangle or not are:

89

5. Example to solve a problem:

6. Try to solve this problems.
a) Lokman has three sticks of length 14 cm, 48 cm and 50 cm respectively. Determine
whether the sticks can form a right-angled triangle.

b) Gopal walked along a slope starting from P to Q. When he arrived at Q, the horizontal
distance and the vertical distance travelled by him was 120 m and 10 m respectively.
What was the actual distance travelled by him?