EM-SSLC Worksheets - Questions - John P A

c) What is the measure of angleADC?
d) Find the angles of triangle AOC
e) If the diametre of the circle is 10cm then find the length of the chord AB
3) In the figure O is the centre of the circle.If angle ADC = 140◦, angleAEC = 60◦ then

a) What is the measeure of ∠AP C and ∠AQC
b) What is the measure of angle AOC?
c) Fnd the angles of the quadrlateralP EQB
4) In the figure Ois the centre of the circle, ∠AOC = 45◦then

a) What kind of triangle is OAC?
b) What is the measure of angleABC?
c) What is the measure of angle ADC?
d) If the radius of the circle is 6cm then what is the length of the chord AC.
5) Draw a circle of radius 3cm , construct an equilateral triangle with vertices on the circle. What is the length
of the side?

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2020-21 Academic year Works

Mathematics X
Circles

24
Concepts
a) If the vertices of a qudrilateral are on a circle we call it cyclic quadrilateral.
b) The sum of the opposite angles of a cyclic quadrilateral is 180◦.
c) The converse of the above statement is also true. If the sum of the opposite angles of a quadrilateral
is 180◦ it will be a cyclic quadrilateral.
d) Square, rectangle and isosceles trapezium are cyclic .

Worksheet24
1) In the figure O is the centre of the circle, ∠DAB = 50◦

a) Find x
b) Find y
c) If BC = CDthen what is the measure of ∠ADC?
d) If BC = CDthen what is the measure of ∠ABC?

2) In the figure ∠BAC = 60◦,∠BCA = 20◦

a) Looking into the figure Riswan said: ACis the diametre of the circle .Can you agree with his opinion?

Why? 1

b) What is the measure ∠ADC
c) If ∠DAC : ∠DCA = 3 : 1 then find these angles.
3 In the figure ABCDEis a regular pentagon.Prove that ABCEis a cyclic quadrilateral.

4) Prove that the trapezium having diagonals equal is cyclic
5) ABCDis a cyclic quadrilateral. If ∠A − ∠C = 60◦ then find the measure of ∠C.What is the measure of

∠A?
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2020-21 Academic year Works

Mathematics X
Circles

25
Concepts
a) Two chords of a circle AB and CD intersect at the point P inside the circle .It can be proved that
PA×PB = PC ×PD
b) This relation can be used to construct a rectangle having equal area of another rectangle.
c) If the chords intersect outside the circle ,the same relation holds. P A × P B = P C × P D
Worksheet 25
1) In the figure two chords AB and CD intersect inside a circle at P .

.
a) Join AC and BD. Establish the similarity of triangle P AC and P BD
b) What are the equal angles of these triangles
c) Prove that P A × P B = P C × P D

2) In the figure the chord AB has length 8cm and OA = 5cm.

a) What is the length of OB?
b) IfOC = 2.5cm, what is the length of OD?

1

3) In the figure AB = 5cm, BD = 4cm, CD = 9cm.

.
a) What is the length of AD?
b) Calculate the length of DE?
c) Is CE the diameter of the circle? why?
d) Find the length of DE

4) If AB and CD are two chords of a circle which when produced meet at a point P . If P A = P C show
that AB = CD.

5) In the figure AB and CD are two chords of a circle which when produced meet at a point P

a) Draw AC and BD , complete the quadrilateral ABDC
b) Establish the similarity of the triangles P AC and P DB
c) Establish the relation P A × P B = P C × P D

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2020-21 Academic year Works

Mathematics X
Circles

25
Concepts
a) Two chords of a circle AB and CD intersect at the point P inside the circle .It can be proved that
PA×PB = PC ×PD
b) This relation can be used to construct a rectangle having equal area of another rectangle.
c) If the chords intersect outside the circle ,the same relation holds. P A × P B = P C × P D
Worksheet 25
1) The chords AB and CD intersect at O .This point divide each chord into two segments

a) What is the relation between these segments?
b) If CD = 10cm and OD = 4cm then what is the length OC?
c) If OA = 8cm , OC = 6cm and OD = 4cm then what is the length OB?
2) The chords AB and CD intersect at P inside the circle.

a) What is the relation between P A, P B, P C and P D?
b) If AB = 5cm , P B = 3cm , P D = 2cm then what is the length CD?

1

3) In the trapezium ABCD, AD = BC and AB is parallel to CD . The diagonals AC and BD intersect at
P.

a) What is the relation between ∠ADB and ∠ACB? How can we realize this relation?
b) If ∠DAC = 30◦then what is the measure of ∠DBC?
c) What is the relation between the segments made byP on the diagonals?
4) In the quadrlateral ABCD , the diagonals AC and BD intersect at P . If P A = 9cm
P B = 12cm, P C = 4cm and P D = 3cm then
a) Draw a rough diagram and mark the mesaurements
b) Is this a cyclic quadrilateral ? How can we realize this ?
c) If ∠A = 40◦ and ∠B = 70◦ find other two angles of the quadrilateral
5) Draw a rectangle of sides 4cm and 6cm . Construct another rectangle with area equal to the area of the
first rectangle and one side 7cm in length.

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2020-21 Academic year Works

Mathematics X
Circles

26
Concepts

a) In the case of the intersecting chords of a circle,if one chord AB is the diametre of the circle and
other chordCD is perpendicular to the diametre ,then P A × P B = P C2

b) This relation is used to construct a square with same area of a rectangle.It can be used to draw the
lines of irrational lengths.
Worksheet 26

1) AB is the diametre of a semicircle, P is a point on AB and P C is perpendicular to AB

a) Prove that P A × P B = P C2
b) IfP A = 9cm , P B = 4 cm then what is the length P C?
c) What is the area of the square with side P C?
2) ]AB is the diametre of a semicircle, P is a point on AB and P C is perpendicular to AB

1
a) If P C = 6cm,and P B = 3cm then what is the length of P A
b) What is the radius of the circle ?
c) What is the area of the square drawn with side P C?

√
3) In the figure AB is the diametre of the semicircle, P C is perpendicular to AB. AC = 5 29cm and

P A = 25cm.

a) What is the length of P C?
b) What is the lenght P B?
c) What is the radius of the circle?

√
4) Draw a semicircle of suitable diametre .Construct a line of length 12cm perpendicular to the diametre

whose one end is on the diameter and other end is on the semicircle.Explain the principle of construction.
5) In the figure AB is the diametre of the circle and P C is perpendicular to the diametre. P A : P B = 2 : 1

and P C = 6cm.

a) Write the relation between P A, P B and P C?
b) Find the lengths P A and P B
c) What is the radius of the circle?

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2020-21 Academic year Works

Mathematics X
Circles

26
Concepts

a) In the case of the intersecting chords of a circle,if one chord AB is the diametre of the circle and
other chordCD is perpendicular to the diametre ,then P A × P B = P C2

b) This relation is used to construct a square with same area of a rectangle.It can be used to draw the
lines of irrational lengths.
Worksheet 26

1) AB is the diametre of a semicircle.The lines P Qand RSare perpendicular to AB.If P Q = RSthen

a) What is the relation between the lengths P A, P B and P Q ?
b) What is the relation between the lenghths AR, BR and RS
c) Prove that P A = BR
2) a) Draw an equilateral triangle of altitude 3 cm
b) What is the lenght of one side ?
c) What is the radius of its incircle?
3) Draw a rectangle of sides 5cm and 3cm .Construct a square whose area is same as the area of the rectangle

1

√
4) a) Draw a semicircle of suitable diametre .Draw a line of length 12cm whose one end on AB and other

end on the semicircle.
√

b) Draw a chord of length 48 cm by make the semicircle as the circle
√√

5) ABis the diametre of a semicircle.P Q = 14cm RS = 18 cm . These lines are perpendicular to the
diametre . Find the length of AB?

6) AB is the diametre of a semicircle , P Q is parallel to the diametre
If AB = 8cm , BQ = 2 cm then find the langth P Q.

√
7) Draw an equilateral triangle of one side 18cm

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03

Mathematics of
Chance

സാധ്യതകള‍ുടെ
ഗണിതം

2020-21 Academic year Works

Mathematics X
സാധ തക െട ഗണിതം

27
Concepts

a) Probability or mathematical chance is measured as the ratio of favourable outcome and possible
outcome in a probability experiment

b) The experiments whose resut or outcome cannot be predected are called probability experiment

Worksheet 27

1) A vessel contains 3 black beads and 2 white beads. One is taken from the vessel without looking into the
vessel.

a) What is the probability of getting black bead?
b) What is the probability of getting white bead?

2) A box contains 10 cards on which one of the numbers 1, 2, 3 · · · 10 is written in each card.One card is taken
from the box at random.

a) What is the probability of getting a an even numbered card
b) What is the probability of getting an odd numbered card?
c) What is the probability of getting a card on which a prime number is written ?
d) What is the probability of getting a perfect square on the card.

3) Each of the numbers from 1 to 100 are written on small paper pieces .One is taken from the card at random.

a) How many perfect squared cards are there in the box? ത് ഇര സംഖ യായ ർ വർ ം
b) What is the probability of getting a perfect squared card?
c) What is the probability of getting an even numbered card?കി

ആകാ സാധ ത എ ?
d) What is the probability of getting an odd numbered card?
e) What is the probability of not getting a perfect numbered card?

4) A die in which the numbers 1 to 6are written on the faces is thrown

a) What is the probability of falling an even numbered face?
b) What is the probability of getting an odd numbered face ?
c) What is the probability of getting a prime numbered face?

5) Two digit numbers are written in small paper pieces and placed in a box.One is taken from the box at random

a) How many multiples of 5 are there in the box?
b) What is the probability of getting a multiple of 5?
c) What is the probability of not getting a multiple of 5?

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2020-21 Academic year Works

Mathematics X
Mathematics of Chance

28

Concepts

a) Probability or mathematical chance is measured as the ratio of favourable outcome and possible
outcome in a probability experiment

b) The experiments whose resut or outcome cannot be predected are called probability experiment

Worksheet 28
1) Numbers 1, 2, 3 · · · 17 are written in small paper cards and placed in a box.One card is taken from the box

at random.
a) What is the probability of getting odd numbered card?
b) What is the probability of getting prime numbered card?
c) What is the probability of getting a multiple of 3?
d) What is the probability of getting a multiple of 2 and 3?

2) A die numbered 1 to 6 are thrown.
a) What is the probability of falling a number less than 4?
b) What is the probability of getting a multiple of 2?
c) What is the probability of falling a multiple of both 2 and 3
d) What is the probability of not falling a prime number?

3) Integers from −4 to 4 are written in small paper pieces and placed in a box. One is drawn from the box at
random .If the outcome is denoted by x,
a) What is the probability of getting a number satisfying the condition | x |< 2 ?
b) What is the probability of getting a number satisfying the condition| x |≤ 2 ?
c) What is the probability of getting a number satisfying the condition| x |≥ 3 ?
d) What is the probability of getting a number satisfying the condition| x |≤ 3?

4) Two dice numbered 1to6 are thrown at together.
a) Write the outcomes as pairs
b) What is the probability of the occurence of equal numbers ?
c) What is the probability of the occurence of perfect squares ?
d) What is the probability of the occurence of multiple of 2 in one die and multiple of 3 in other die ?

5) What is the probability of getting 5 Sundays in the month December?
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2020-21 Academic year Works

Mathematics X
Mathematics of Chance

29

Concepts

a) Probability or mathematical chance is measured as the ratio of favourable outcome and possible
outcome in a probability experiment

b) The experiments whose resut or outcome cannot be predected are called probability experiment

Worksheet 29
1) The numbers 1, 2, 3, 4are written in small paper cards and placed in a box.

a) How many cards are there in the box?
b) If one card is taken from the box at random , what is the probability of getting an even numbered

card?
c) What is the probability of getting an odd numbered card?
d) What is the probability of getting a card with equal digits?
2) The numbers 21, 22, 23 · · · 250 are written in small paper pieces and placed in a box.
a) Write the sequence of numbers comes in the right end of these numbers ?
b) If one is taken from the box at random, then what is the probability of getting a number with 4 in ones

place?
c) What is the probability of getting a number with 8 in ones place?
d) What is the probability of getting a number with 2 in ones place?
e) what is the probability of not getting a number with 2 in ones place?
3) Two digit numbers are written in small paper pieces and placed in a box.
a) How many paper slips are there in the box?
b) If one is taken from the box, what is probability of getting a number with digits same?
c) If one is taken from the box, what is probability of getting a number in which the product of the digits

a prime number.
d) What is the probability of getting a prime number?
4) The numbers 12, 22, 32 · · · 1002are written in small slips and placed in a box.Consider the remainders
obtained by dividing these numbers by 3.
a) Write the remainders as a sequence
b) One slip is taken from the box at random. What is the probability of getting a number which gives 1

as the remainder?
c) What is the probability of getting a number which gives2 as the remainder ?
d) What is the probability of getting a number which gives0 as the remainder ?

1

5) Two dices numbered 1, 2, 3, 4, 5, 6 are thrown together.The outcome faces are written as pairs.
a) How many pairs are there ?
b) Make the list of pairs with sum 2 , 3 ,4 , 5 and 6 seperately
c) What is the probability of occuring the maximum sum
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2020-21 Academic year Works

Mathematics X
Mathematics of Chance

30
Concepts
a) Probability can be measuered as the ratio of area
b) A square is drawn inside a circle.A fine dot is placed without looking into the figure. The probability
of falling the dot into the square is the ratio of the area of the square to the area of the circle.
Worksheet 30
1) There are two circles in the picture.One is inside other.Radius of the small circle is half of the radius of the
big circle.

a) If the radius of the small circle is r then what is the area of the small circle and big circle ?
b) If a fine dot is placed into the figure, whatb is the probability of falling the dot in the small circle?
c) What is the probability of falling the dot the yellow shaded part in the figure.
2) A square is drawn by joining the mid points of the sides of another square.The inner square is shaded blue.

a) Divide the triangle into eight equal triangles by drawing two lines
b) A fine dot is placed into the figure. What is the probability of falling the dot in the inner square?

1

3) Triangle P QR is drawn by joining the mid points of the sides of triangle ABC.

a) How many equal triangles are there in the figure?
b) A fine dot is placed into the figure. What is the probability of falling the dot in triangle P QR?
c) How many parallelograms are there in the picture?
d) A fine dot is placed into the figure. What is the probability of falling the dot in the parallelogram

P QRC?
4) A triangle is drawn by joining the alternate vertices of a regular hexagon.

a) Divide the figure into 6 equal triangles
b) If a fine dot is placed into the figure , what is the probability of falling the dot in the shaded triangle?
5) A square is drawn in a circle . The vertices of the square are on the circle. A fine dot is placed into the
figure at random. What is the probability of falling the dot in the shaded square.

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2020-21 Academic year Works

Mathematics X
Mathematics of Chance

31
Concepts
a) Probability can be measuered as the ratio of area
b) A square is drawn inside a circle.A fine dot is placed without looking into the figure. The probability
of falling the dot into the square is the ratio of the area of the square to the area of the circle.
Worksheet 31
1) ACP is drawn in the square ABCD and shaded .P is the mid point of the side of the square

a) If the side of the square is a then what is the altitude to the side P C of the shaded triangle.
b) If the side of the square is a then what is the area of the shaded triangle ?
c) If a fine dot is placed into the figure then what is the probability of falling the dot in the shaded triangle

?
2) There are two squares in the figure.The perimetre of the outer square is 28cm, the perimetre of the inner

square is 20cm

a) What is the area of the outer square?
b) What is the area of inner square?
c) What is the area of the shaded triangle ?
d) If a fine dot is placed into the figure then what is the probability of falling the dot in the shaded triangle?

1

3) The mid points of the two sides and one vertex of a square are joined in such a way as to get a triangle
which is coloured in the picture.

a) If the side of the square is a, what is are of unshaded triangles ?
b) What is the area of the shaded triangle?
c) If a fine dot is placed into the figure then what is the probability of falling the dot in the coloured

traingle?
4) O is the center of the circle of diametre AB.

There is another circle with diametre OB.If r is the radius of the small circle

a) What is the radius of the big circle ?
b) Find the area of big circle and small circle.
c) If a fine dot is placed into the figure what is the probability of falling the dot in the shaded part.
5) Square ABCD is drawn in triangle P QR.Also QD = DC = CR .If the side of the square is a then

a) What is the altitude of the triangle P QR to the side P Q
b) What is the area of the triangle P QR?
c) If a fine dot is placed into the figure then what is the probability of falling the dot in the shaded square?

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2020-21 Academic year Works

Mathematics X
സാധ തക െട ഗണിതം

32

Concepts

a) There is a concept known as the Fundamental principle of counting.If a process can be completed
in m different ways, another concept can be completed in n ways then both processes can be
completed in m × n ways.

b) Let us see an example. The journey from Kochi to Mumbai can be completed in 4 ways. Journey
from Mumbai to Delhi can be completed in 3 ways.The journey fom Kochi to Delhi can be completed
in the following ways .
(Rail,Rail),(Rail ,Road), (Rail , Air)
(Road,Rail),(Road, Road), (Road, Air)
(Air,Rail),(Air ,Road), (Air , Air)
(Sea ,Rail),(Sea ,Road), (Sea, Air)
Total number of ways is 4 × 3 = 12.

Worksheet 32

1) A boc contains three paper slips carrying numbers 2, 3, 4 . Another box contains paper slips carrying

fractions 1 , 1 , 1 .One is taken from each box at random
2 3 4

a) How many pairs are possible?

b) What is the probability of getting the product of numbers in each pair a natural number?

c) Wha is the probability of not getting the numbers in the pair whose product is not a natural number?

2) Manju has three ornaments :Green , Red and Blue ear rings and chains.She ware it in different ways.

a) How many ways she can ware the ornaments?
b) What is the probability of waring ornaments of same colour?
c) What is the probability of wearing the ornaments of different colours?

3) A box contains 4 black balls and 3 white balls. Another box contains 5 black balls and 3 white balls. One
from each box is taken at random.

a) How many pair of balls are possible ?
b) What is the probability of getting both balls black?
c) What is the probability of getting both balls white?
d) What is the probability of getting balls of different colours?

1

4) A box contains four paper slips carrying numbers 1, 2, 3, 4.Another box contains paper slips carrying numbers
1, 2, 3. One from each box is taken at random and entered as pairs.
a) How many pairs are possible ?
b) What is the probability of getting a pair with the product of the digits odd?
c) What is the probability of getting a pair with the product of the digits even?

5) There are 30boys and 20girls in 10A. There are 15boys and 25girls in 10B.
One student is selected from each class at random.
a) How many ways the selections can be made ?
b) What is the probability of getting both boys?
c) What is the probability of getting both girls?
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04

Second Degree
Equations

രണ്ടാംകൃ‍തി
സമവാക്യങ്ങൾ

2020-21 Academic year Worksheets

Mathematics X
Second Degree Equations

33
Concepts

Let us learn second degree equations.This is a tool for solving problems in various mathematical
situations.Theory of second degree equation is not the scope of this unit. Here we discuss the
methods to solve equations and its applications.

Worksheet 33

1) Form the equations in the following cases.

a) The sum of a number and its square is 12

b) When a number is subtracted from its square results 20

c) The sum of the square of a number and two times that number is 63

d) Product of two consecutive odd numbers is 63.

e) The sum of a number and its reciprocal is 10 .
3

2) The square of a number is 16.

a) What are the numbers ?
b) Take the number as x and form an equation
c) Can the square of a real number −16? Explain.

3) The sum of a number and its square is 30.

a) If the number is x, form an equation.
b) What is the positive numberxന്?
c) Can more than one number satisfying this condition?

4) x is an odd number greater than 1.

a) What are the odd numbers nearer to x
b) If the product of those numbers is 45, form an equation.
c) Find the numbers.

5) If the sides of a square are reduced by 1 , the area becomes 100.

a) If the side of the first square before reducing is x, form an equation.
b) Find the side of the square.
c) What will be the perimetre of the new square.

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2020-21 Academic year Works

Mathematics X
Second Degree Equations .

34
Concepts

Let us learn second degree equations.This is a tool for solving problems in various mathematical
situations.Theory of second degree equation is not the scope of this unit. Here we discuss the
methods to solve equations and its applications.

Worksheet 34
1) The chords AB and CD meet at a point P inside the circle.

CD = 21cm, P C = 5cm.
a) What is P D?
b) If P A = x + 1 and P B = x − 1then form an equation
c) Find the lenght P A and P B.

2) The product of two consecutive even numbers is 360
a) If the odd number in between these numbers is x then write the numbers .
b) Form an equation using the given condition.
c) Find the numbers.

3) Consider the arithmetic sequence 5, 9, 13, 17, 21 · · · .
a) Write the algebraic form of this sequence.
b) What is the position of the term in the sequence whose square is 625?
c) Is 36 a term of this sequence . How can you realize it ?
d) What is the position of 49in this sequence ?

1

4) Three boxes in which dates of a calandar are given.
a) If B = x find A, C
b) If A × C = 120 form an equation.
c) Find B
d) Find the days A and C

5) Sum of the areas of two rectangles is 130. Side of one square is 2 more than the side of the other square .
a) If the side of the small square is x then what is the side of the big square ?
b) Form a second degree equation using the condition.
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2020-21 Academic year Works

Mathematics X
Second Degree Eqautions

35

Concepts

Let us learn second degree equations.This is a tool for solving problems in various mathematical
situations.Theory of second degree equation is not the scope of this unit. Here we discuss the
methods to solve equations and its applications.

Worksheet 35
1) Consider two adjacent even numbers

a) If one of them is x then what is the other?
b) If the product is 120 then write a second degree equation.
c) Convert this equation as a completed square by suitable changes
d) Find the numbers .
2) Length of a rectangle is 8 more then its breadth.
a) If the breadth is x then what is its length?
b) If the area is 240 sq.cm form a second degree equation.
c) Calculate the lenght and breadth
3) In the figure AB is the diametre of the semicircle. AB is perpendicular to P C.Also,AP = BP + 5,
P C = 6.

a) Write the relation between the lenghts P A, P B and P C

b) If P B = x then write an equation connecting the lenghts P A, P B and P C

c) What is the length of P B?

d) What is the radius of this circle. ിെ ആരെമ ?

1

4) Consider the sequence of even numbers 2, 4, 6, 8 · · · .
a) What is its algebraic form?
b) How many terms from the beginning in the order makes the sum 210?

5) The smallest side of a right angled triangle is 4 less than its hypotenuse.Third side is 2 more than the
smallest side.
a) If the smallest side is x what are the other two sides.
b) Write an equation connecting the length of the sides .
c) What is the length of the smallest side?
d) Find the length of other sides of the triangle.
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2020-21 Academic year Works

Mathematics X
Second Degree Equations

36
Concepts

Let us learn second degree equations.This is a tool for solving problems in various mathematical
situations.Theory of second degree equation is not the scope of this unit. Here we discuss the
methods to solve equations and its applications.

Worksheet 36
1) In traingle ABC, AB = AC

AD is the perpendicular from A to BD. This perpendicular distance from A to BC is 2 cm more than
BC. Area of the triangle is 60 sq.cm

a) If BC = x then what is the langth AD?
b) Form an equation connecting the lengths BC, AD and area of the rectangle
c) Find the length of BC.
d) What is the lenghth of AD?
e) Calculate the perimetre of the triangle ABC
2) Length of a rectangle is 4 more than its breadth .Area of the rectangle is 357 sq.cm
a) If the breadth is x then what is its length?
b) Write an equation connecting length , breadth and area
c) Find the lenghth and breadth of the rectangle .

1

3) Given picture is the dates marked in a calandar .
A, B, C, D denotes the dates.

a) If A = x write B, C, D?
b) If A × C = 84form a second degree equation.
c) Find the number corresponding to A.
d) Write the numbers in the boxes A, B, C, D
4) Sum of the areas of two squares is 468sq.cm.The difference between the perimetres is 24cm.
a) If the small side is x then what is the length of the big side ?
b) What is the perimetre of the gig square?
c) Write the length of the sides the squares in x
d) Form a second degree equation and find the length of the small square.
e) Find the length of the big square.
5) Hypotenuse of a right angled triangle is 1 less than twice its small side.Third side is 1 more than its small
side
a) If the small side is x what is the length of other two sides .
b) Form an equation connecting the length of the sides .
c) Calculate the length of the sides of the triangle.

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2020-21 Academic year Works

Mathematics X
Second Degree Equations.

37
Concepts

We are discussing the process of solving a second degree equation using the colpleting the square
method.As the generalization of this method we can establish a formula to solve the second degree
equation. It is not necessary to use the formula for solving the second degree equation.
In the equation ax2 + bx + c = 0

√
−b ± b2 − 4ac
x=

2a

Worksheet 37

1) The sum of the squares of two consecutive natural numbers is313.

a) If one number is x then what is the other?

b) Form an equation using this condition.

c) Find the numbers .

2) The sum of two numbers is 15. The sum of its reciprocals is 3 .
10

a) If one number is x then what is the other?

b) Form an equation.

c) Find the numbers.

3) The sum of a number and its reciprocal is 2 1 .
30

a) If one number is x what is the other.

b) Find the numbers.

4) Two chords AB and CD intersect at P inside the circle.If AB = 13cm
and P C = 12 cm ,P D = 3 cm

a) Write the relation between P A, P B, P C and P D
b) If P A = x form an equation
c) Find the lengths of P A and P B

1

5) The sum of the first n terms of the arithmetic sequence 7, 9, 11, 13 · · · is 40.

a) Form a second degree equation using this condition.
b) How many terms make the sum 40 ?
c) Find n in another method .

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2020-21 Academic year Works

Mathematics X
ര ാം തിസമവാക ൾ

38

Concepts

We are discussing the process of solving a second degree equation using the colpleting the square
method.As the generalization of this method we can establish a formula to solve the second degree
equation. It is not necessary to use the formula for solving the second degree equation.
In the equation ax2 + bx + c = 0

√
−b ± b2 − 4ac
x=

2a

Worksheet 38
1) The product of the digits of a two digit number is 18.When 63 is subtracted from the number we get the

two digit number with digits in the reversed order.
a) If the digit in the tens place is x when what will be the digit in the one’s place ?
b) Write the number using the place value of the digits.
c) Form a second degree equation using the given condition.
d) Find the number.

2) The difference between the squares of two numbers is 45.The square of the small number is 4 times the
large number.
a) Write an equation by taking x as the large number.
b) Calculate the numbers.

3) A rod of 16cm length is cut into two pieces. Two times the square of the length of the larger piece is equal
to 164 more than the square of the smaller piece.
a) If the length of the larger piece is x then what is the length of the smaller piece.
b) Form an equation using the given conditions.
c) Find the length of the pieces .

4) The sum of the squares of two positive numbers is 208.18 times the small number is equal to the square
of the large number.
a) Form an equation by taking x as the small number.
b) Find the numbers.

5) A two digit number is 4 times the sum of the digits.Also the number is 3 times the product of the digits.
a) Form an equation by taking x, y as the digits.
b) Make a second degree equation using the given condition.
c) Find the numbers.
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1 9847307721

2020-21 Academic year Works

Mathematics X
Second Degree Equations.

39

Concepts

We are discussing the process of solving a second degree equation using the colpleting the square
method.As the generalization of this method we can establish a formula to solve the second degree
equation. It is not necessary to use the formula for solving the second degree equation.
In the equation ax2 + bx + c = 0

√
−b ± b2 − 4ac
x=

2a

Worksheet 39
1) The difference between the lengths of the perpendicular sides of a right triangle is 10, area of the triangle

is 600 square cm. ആണ്.
a) One of the perpendicular sides is x then what is the length of the other?
b) Form an equation using the given condition.
c) What is the length of the perpendicular sides?
d) Calculate the perimetre of the triangle.

2) Perimetre of a rectangle is 82cm, area 400 sq.cm
a) What is the total length of the adjacent sides?
b) if one side is x then what is the length of the other side?
c) Form a second degree equation using the given condition.
d) Calculate the length of the sides.

3) In triangle ABC, AB = AC = 13cm, area of the triangle is 60 sq.cm .The perpendicular distance from A
to BC is AD.

a) If BD = xthen what is AD?

1

b) Form a second degree equation using BC, AD, and area .
c) What is the length of BC?
d) What is the perimetre of the triangle?
4) The perimetre of a right triangle is 60 cm, hypotenuse is 25cm
a) What is the total length of the perpendicular sides ?
b) If the length of one perpendicular side is x then what will be the length of the other ?
c) Form an equation using the length of the sides
d) Calculate the area of the triangle.
5) The difference between the length of the sides of two squares is 4cm. The sum of the areas is 400sq.cm
a) If the side of the small square is x then what is the side of the other square?
b) Form an equation using the given condition.
c) Calculate the side of the squares.

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2

2020-21 Academic year Works

Mathematics X
Second Degree Equations

40

Concepts

We are discussing the process of solving a second degree equation using the completing the
square method.As the generalization of this method we can establish a formula to solve the second
degree equation. It is not necessary to use the formula for solving the second degree equation.
In the equation ax2 + bx + c = 0

√
−b ± b2 − 4ac
x=

2a

Worksheet 40
1) The age of a man after 15 years would be the square of his age before 15 years.

a) If the present age is x , form a second degree equation
b) Find the present age.
c) Without using algebra find the present age .
2) Manju’s present age is the square of Laya’s age.After 5years Manju’s age become 3 times Laya’s age.
a) If Laya’s present age is x form a second degree equation.
b) Find the present age of both.
c) How many years later the age of Manju become two times Laya’s age?
3) One year ago, Ajayan’s age was 8 times his son’s age.Present age of Ajayan is the square of his son’s
present age.
a) If son’s age before 1 year is x what was Ajayans age one year ago.
b) Form a second degree equation using the given condition.
c) Calculate their present age.
4) The sum of the ages of a father and son is 45. 5 years ago the product of their ages was 124.
a) If father’s present age is x what is son’s present age?
b) Form a second degree equation using the given condition.
c) Find the their present age.
5) Nasrin’s age is two times Riswan’s age. Four years hence the product of their ages become 160.
a) If Riswan’s present age is x what is Nasrin’s present age?
b) Form a second degree equation using the given condition.
c) Calculate their present age.

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1

2020-21 Academic year Works

Mathematics X
Second Degree Equations

41

Concepts

We are discussing the process of solving a second degree equation using the completing the
square method.As the generalization of this method we can establish a formula to solve the second
degree equation. It is not necessary to use the formula for solving the second degree equation.
In the equation ax2 + bx + c = 0

√
−b ± b2 − 4ac
x=

2a

Worksheet 41
1) The speed of a boat in still water is 8 km in an hour.The boat travels 15 kilometre in upstream and 22

kilometre in downstream in5 hours.
a) If the speed of the stream is x what will be the speed attained by the boat in the downstream.
b) If the speed of the stream is x what will be the resulting speed inn the upstream?
c) Form an equation using the given condition.
d) Calculate the speed of the stream.

2) A train travels with uniform speed in 300 km.If the speed of the train is increased by 5 km per hour, the
journey would have taken 2 hours less.
a) If the usual speed is x what will be the time taken for the journey.
b) If the speed is increased by 5 km per hour what will be the time taken for the journey?
c) Form an equation using the given condition.
d) Calculate the speed of the train .

3) There are 64 small squares in a chess board.The area of one small square is 6.25 sq.cm.There is a boarder
of width 2cm around the chess board squares.
a) If the length of the board is x what will be the total area of small squares?
b) Form a second degree equation using the given condition.
c) Calculate the length of the chess board.

4) In a group of children each child gives a gift to every other child.If the total number .of gifts is 132, then
a) If the number of children is n then how many gifts each child give other children.
b) Form an equation using the given condition.
c) calculate the number of children in the group.

1

5) Teacher asked the children to draw a rectangle of area 5 sq.cm and perimetre 8 cm. Manju , a good student
made a comment that it is possible to draw such a square after some algebraic calculations.
a) If one side of the reactangle is x then what will be the other.
b) Form a second degree equatio.
c) Prove that it is not possible to construct such a rectangle.
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2020-21 Academic year Worksheets

Mathematics X
Second Degree Equations

41

Concepts

We are discussing the process of solving a second degree equation using the completing the
square method.As the generalization of this method we can establish a formula to solve the second
degree equation. It is not necessary to use the formula for solving the second degree equation.
In the equation ax2 + bx + c = 0

√
−b ± b2 − 4ac
x=

2a

Worksheet 41
1) The participants of a meeting gave hanshakes to eachother. It is found that there are 190handshakes in

total.
a) If there are n participants , what is the number of handshakes given by a participant to others?
b) Form a second degree equation using the number of participants and the number of handshakes.
c) Calculate the number of participants of the meeting.

2) If the price of a book is reduced by 5 rupees,a person can buy 5 more books for 300 rupees.
a) If the original price of the book is x, how many books can be purchased for 300 rupees?
b If the price is decreased by 5 how many books can be purchased in 300 rupees
c) Form a second degree equation using the given condition.
d) Calculate the original price of the book

3) The perimetre of a rectangle is 82cm, area 400 sq.cm
a) If the length of one side is x then what is the length of other side ?
b) form a second degree equation
c) Find the sides of the rectangle.

4) The hypotenuse of a right triangle is 25cm,the difference between other two sides is 5cm
a) If one of the perpendicular sides is x what is the length of other perpendicular side?
b) Form a second degree equation .
c) Calculate the length of its sides.
d) Calculate the area of the triangle.

1

5) The denominator of a fraction is 1 more than two times its numerator.The sum of the fraction and its reciprocal

is 2 16 .
21

a) If the numerator is x what is its denominator.

b) Write the fraction in x

c) Form a second degree equation using the given condition.

d) Find the fraction.

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2020-21 Academic year Worksheets

Mathematics X
ര ാം തിസമവാക ൾ

42

Concepts

We are discussing the process of solving a second degree equation using the completing the
square method.As the generalization of this method we can establish a formula to solve the second
degree equation. It is not necessary to use the formula for solving the second degree equation.
In the equation ax2 + bx + c = 0

√
−b ± b2 − 4ac
x=

2a

Worksheet 42
1) First term of an arithmetic sequence is 7 and common difference 3.

a) What is its algebraic form?
b) Find the sum of the first n terms
c) How many terms of this sequence beginning from the first term makes the sum 710?
2) On joining two vertices of a polygon we get either a side or a polygon.Consider a polygon of n sides.
a) How many diagonals can be drawn from a vertex?
b) How many diagonals are there in a polygon of n sides ?
c) Find the number of sides of a polygon having 35 diagonals.
d) Name the polygon having number of sides and diagonals equal.
3) The points A1, A2, A3 · · · An are marked in a circle. On joining two points we get a chord .
a) How many chords can be drawn from a given point to other points?
b) What is the total number of chords?
c) How many points should be marked on the circle to get 120 chords.
4) Consider the sequence of numbers which gives the remainder 3 on dividing by 4.
a) Write the algebraic form of this sequence ?
b) What is the sum of first n terms of this sequence ?
c) How many terms from the beginning make the sum 820?
d) Can the sum of any 25 terms of this sequence 2020?

1

5) The sum of a number and its positive square root is 6 .
25

a) If x is the number , write an equation using the given conditions.

b) Write the equation in the form ax2 + bx + c = 0

c) Find the number.

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2020-21 Academic year Worksheets

Mathematics X
ര ാം തിസമവാക ൾ

43

Concepts

We are discussing the process of solving a second degree equation using the completing the
square method.As the generalization of this method we can establish a formula to solve the second
degree equation. It is not necessary to use the formula for solving the second degree equation.
In the equation ax2 + bx + c = 0

√
−b ± b2 − 4ac
x=

2a

Worksheet 43
1) An aeroplane takes 1 hour less for a journey of 1200km. If the speed is increased by 100 km per hour,

from its usual speed.

a) If the usual speed is x then what is the time taken for the journey?
b) If the speed is increased by 100 km/h what will be the time taken for the journey?
c) Form a second degree equation using the given condition.
d) Calcualte the usual speed.

2) The length of a rectangular hall is 5m more than its width and the area of the hall is 84 sq.

a) If the length is x , what will be its width?
b) Form a second degree equation using the given condition.
c) Find the length and breadth of the rectangle.

3) A two digit number is 4 times the sum of the digits and twice the product of the digits.

a) If the digit in the one’s place is y and the digit in ten’s place is x, write two equations using the given
conditions.

b) Form a second degree equation.
c) Find the digits and write the number.

4) The area of a rectangular plot is 528 sq.m.Length of the plot is 1 more than twice its breadth.
a) If the breadth is x what will be its length?
b) Form a second degree equation with the given condition.
c) Find the length and beradth of the plot.

5) In copying a second degree equation to solve it,the term without x was written as 24 instead of −24.The
answers found were 4 and 6.
a) If the equation wrongly written is ax2 + bx + 24 = 0, write two equations using the wrong ansers
given
b) Find a and b by solving the equations.
c) Write the correct equation and find its solut1ion.
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05

Trigonometry

ത്രികോണമിതി

2020-21 Academic year Works

Mathematics X
Trigonometry

44
Concepts

a) There are some special right triangles. The diagonal of a square makes two right triangles of angles

45◦, 45◦, 90◦

b) If the si√de opposite to 45◦ is 1 then the side opposite to 90◦ will be √ The sides are in the ratio
2.

1:1: 2

c) The altitude of an equilateral triangle makes two right triangles.The angles of these triangles are

30◦, 60◦, 90◦. √

If the side opposite to 30◦ is 1, the side opposite to 90◦ will be 2, side opposite tos 60◦ will be 3

Worksheet 44

1) Consider a square of perimetre 40cm

a) What is the length of its side?
b) What is the length of its diagonal
c) What is the area of the square drawn on its diagonal?

2) The area and perimetre of a square are equal in number.

a) What is the length of its side?
b) What is the length of its diagonal?
c) What is the area of the square drawn on its diagonal?
3) A bridge of length 600m is built across a river making 45◦ angle with the direction of flow.

a) Draw a rough diagram.
b) What is the width of the river?
4) In traingle ABC ,∠A = 30◦, BC = 10cm

a) What is the length AB? 1

b) What is the length of the side AC?
c) What is the length of the diagonal of the square drawn on AC?
d) What is the perimetre of the square?

5) Consider an equilateral triangle of side 10cm

a) What is its altitude?
b) Draw a rough diagram of the square drawn on the altitude
c) What is the area of this square.
d) What is the length of its diagonal?

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2020-21 Academic year Works

Mathematics X
Trigonometry

45
Concepts

a) There are some special right triangles. The diagonal of a square makes two right triangles of angles

45◦, 45◦, 90◦

b) If the si√de opposite to 45◦ is 1 then the side opposite to 90◦ will be √ The sides are in the ratio
2.

1:1: 2

c) The altitude of an equilateral triangle makes two right triangles.The angles of these triangles are

30◦, 60◦, 90◦. to 30◦ is 1, the side opposite to 90◦ will be 2, side opposite tos 60◦ will be √
If the side opposite 3

Worksheet 45
1) In the parallelogram ABCD ,∠A = 60◦., AB = 12cm , AD = 10cm

a) What is the perpendicular distance from D to AB.
b) Find the area of the parallelogram

2) In the rhombus ABCD,∠D = 150◦

1

a) What is the measure of ∠A?
b) What is the diatance between AB and CD
c) Find the area of the rhombus.
3) In the figure O is the centre of the circle.∠ACB = 30◦

a) What is the measure of ∠AOB?
b) What kind of triangle is OAB?
c) If the radius of the circle is 12cm then what is the altitude of triangle OAB?
d) What is the area of triangle OAB?
4) The diagonal of the rectangle ABC is 12cm , ∠BAC = 30◦

a) What is the length of the side AB?
b) What is the length of the side BC?
c) Calculate the area of the rectangle
5) ABCD is a quadrilateral .AC = CD = AD,∠BAD = 120◦, ∠B = 90◦ ,The perpendicular distance
from D to the diagonal AC is 12cm .

a) What is the length of AC?
b) What are the angles of triangle ABC ?

2

c) What are the length AB and BC
d) Find the area of triangle ABC.
e) Find the area of triangle ADC.
f) Find the area of the quadrilateral ABCD

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3

2020-21 Academic year Works

Mathematics X
Trigonometry

46
Concepts

a) There are some special right triangles. The diagonal of a square makes two right triangles of angles

45◦, 45◦, 90◦

b) If the si√de opposite to 45◦ is 1 then the side opposite to 90◦ will be √ The sides are in the ratio
2.

1:1: 2

c) The altitude of an equilateral triangle makes two right triangles.The angles of these triangles are

30◦, 60◦, 90◦. to 30◦ is 1, the side opposite to 90◦ will be 2, side opposite tos 60◦ will be √
If the side opposite 3

Worksheet 46
1) In triangle ABC , the line AD is perpendicular to BC, AB = 12cm

a) What is the length of AD?
b) What is the length of AC?
c) What is the length of BC?
d) Calculate the area of triangle ABC?

2) In the fogure O is the centre of the circle. ∠BAC = 60◦,BC = 10 then

a) Draw the diametre from B which meet the circle at P

b) Draw triangle BP C, write the measure of ∠BP C?

c) What is the diametre of the circle? What is its radius?
d) Calculate the area of triangle BP C? 1