vikas mathematics practical book 9th class answers with formula

🔷 VIKAS MATHEMATICS PRACTICAL BOOK

STANDARD IX — COMPLETE EXPLAINED ANSWERS

🟣 SECTION 1 — HOME ASSIGNMENTS

🔵 MATHEMATICS PART – I

🔵 CHAPTER 1

🟦 Activity 1(A)

🟢 Answer

{2}, 2, 2, ∅

🟡 Explanation

This activity is based on the basic concept of sets.

2 is a number.
{2} is a set containing the element 2.
∅ represents the empty set.

An empty set contains no elements.

🟣 Important Rule

A number and a set containing that number are different:

2 ≠ {2}

For example:

A = {5}

Here, 5 is an element of A, while {5} is the complete set.

🟦 Activity 1(B)

🟢 Answer

n(B), n(A ∩ B), 29, 7, 8, 21

🟡 Explanation

This activity deals with cardinality and intersection of sets.

n(B) represents the number of elements in set B.

The symbol:

A ∩ B

represents the intersection of A and B.

It means the elements that are common to both sets.

🟣 Example

A = {1, 2, 3, 4}

B = {3, 4, 5, 6}

Therefore:

A ∩ B = {3, 4}

So:

n(A ∩ B) = 2

🟦 Activity 2(A)

🟢 Answer

n(A ∪ B), 36, 36, 12

🟡 Explanation

The symbol ∪ represents the union of two sets.

The union contains all elements from both sets, but common elements are counted only once.

🟣 Formula

n(A ∪ B) = n(A) + n(B) − n(A ∩ B)

The intersection is subtracted because common elements have already been counted twice.

🟢 Example

Suppose:

n(A) = 20
n(B) = 28
n(A ∩ B) = 12

Then:

20 + 28 − 12

= 36

🟦 Activity 2(B)

🟢 Answer

1, 2, 3, 4, 5, 6, 7, 8, 9, 10

🟡 Explanation

This activity involves identifying elements and forming sets or subsets.

A set is not affected by the order of its elements.

For example:

{1, 2, 3} = {3, 2, 1}

Both represent the same set.

🔵 CHAPTER 2

🟦 Activity 3(A)

🟢 Answer

25, 5, 9 − 4 + 5, 10

🟡 Explanation

The numerical expression:

9 − 4 + 5

is evaluated from left to right.

First:

9 − 4 = 5

Then:

5 + 5 = 10

Therefore, the final value is:

🟢 10

🟦 Activity 3(B)

🟢 Answer

10, 0.7, 7.7, 0.7, 7, 7/9

🟡 Explanation

The activity involves decimal and rational-number calculations.

For example:

0.7 = 7/10

because one digit occurs after the decimal point.

Similarly:

0.07 = 7/100

🟣 Rule

A decimal can be converted into a fraction by using a denominator of:

10, 100, 1000, etc., depending on the number of decimal places.

🟦 Activity 4(A)

🟢 Answer

+1, 6, 4, 4/3

🟡 Explanation

These are the required numerical/algebraic values obtained from the activity.

The fraction:

4/3

can also be written as:

1 1/3

🟦 Activity 4(B)

🟢 Answer

The activity includes expressions involving:

√(5 − √3)

(√3)²

(8 − 2√15)/2

🟡 Explanation

This activity deals with square roots and surds.

One of the most important rules is:

🟣 Rule

(√a)² = a

Therefore:

(√3)² = 3

Square-root expressions must be simplified according to the structure of the expression.

🔵 CHAPTER 3

🟦 Activity 5(A)

🟢 Answer

x³ + 2x² + 2, 1, x⁸, 2

🟡 Explanation

This activity involves algebraic expressions, polynomials and powers.

🟣 Important Law of Exponents

When powers having the same base are multiplied:

xᵃ × xᵇ = xᵃ⁺ᵇ

For example:

x³ × x⁵ = x⁸

because:

3 + 5 = 8.

🟦 Activity 5(B)

🟢 Answer

1, 5, −2, 2, y² − 2y + 3, 2

🟡 Explanation

This involves substitution and simplification of algebraic expressions.

For example, if:

y = 1

then:

y² − 2y + 3

= 1² − 2(1) + 3

= 1 − 2 + 3

= 2

🟦 Activity 6(A)

🟢 Answer

−1, −2, 2, 7

🟡 Explanation

These values are obtained through algebraic substitution and numerical operations.

When working with negative numbers, the signs must be handled carefully.

For example:

−2 + 5 = 3

while:

−2 − 5 = −7

🟦 Activity 6(B)

🟢 Answer

3x, x, √3, √3, 1, √(3x + 1)

🟡 Explanation

The activity involves algebraic expressions and square-root expressions.

Expressions such as 3x contain a variable, while √3 is a radical expression.

🔵 CHAPTER 4

🟦 Activity 7(A)

🟢 Answer

√35, √81, <, <

🟡 Explanation

A square root is the number which, when multiplied by itself, gives the original number.

For example:

√81 = 9

because:

9 × 9 = 81

Square-root expressions can also be compared by considering their numerical values.

🟦 Activity 7(B)

🟢 Answer

c, b, b, c + d, a − b, d

🟡 Explanation

These answers involve identifying and using algebraic variables and expressions.

For example:

If:

a = 10
b = 4

then:

a − b = 6

🟦 Activity 8(A)

🟢 Answer

36, 22, 16, 2a − 2b + 2c

🟡 Explanation

Consider:

2a − 2b + 2c

The common factor is 2.

Therefore:

2a − 2b + 2c = 2(a − b + c)

🟣 Important Rule

Taking a common factor is a basic method of factorisation.

🟦 Activity 8(B)

🟢 Answer

m², x + y, x − y, (x + y)², x²y², (x + y)

🟡 Explanation

This activity uses algebraic expressions and identities.

🟣 Important Identity

(x + y)² = x² + 2xy + y²

Another important identity is:

(x − y)² = x² − 2xy + y²

These identities help us expand and simplify algebraic expressions.

🔵 CHAPTER 5

🟦 Activity 9(A)

🟢 Answer

10, (−3, 10), (−5), (−5, 12)

🟡 Explanation

The ordered pair:

(−3, 10)

represents a point on the coordinate plane.

Here:

x-coordinate = −3

y-coordinate = 10

The first number represents the horizontal position and the second represents the vertical position.

🟦 Activity 9(B)

🟢 Answer

8y, 16, (x + y), 2, −2, −1

🟡 Explanation

These are algebraic values obtained from the activity through substitution or simplification.

🟦 Activity 10(A)

🟢 Answer

y − x = 7

x + y = 53

60, 30

🟡 Explanation

These are linear equations involving variables.

For:

y − x = 7

y is 7 greater than x.

For:

x + y = 53

the sum of x and y is 53.

Such equations can be solved using substitution or elimination.

🟦 Activity 10(B)

🟢 Answer

7x, 21, 3, 15, −6, −2

🟡 Explanation

These are the required algebraic values obtained by applying the appropriate operations to the expressions.

🔵 CHAPTER 6

🟦 Activity 11(A)

🟢 Answer

6000, 10000, 6000, 4000

🟦 Activity 11(B)

🟢 Answer

520000, 400000, 120000, 48000, 120000, 72000

🟡 Explanation

For example:

520000 − 400000

= 120000

and:

120000 − 48000

= 72000

These calculations involve large numerical values.

🟦 Activity 12(A)

🟢 Answer

10000, 15000, 10000, 15000

🟦 Activity 12(B)

🟢 Answer

N, 100, 220000, 2200, 2200, 24200

These are the numerical values given for the activity.

🔵 CHAPTER 7

🟦 Activity 13(A)

🟢 Answer

15, 20, 35, 17.5

🟦 Activity 13(B)

🟢 Answer

12, 10 − 15, 24, 8, 8, 42

🟦 Activity 14(A)

🟢 Answer

Σfᵢ, 525, 25, 21

🟡 Explanation

The symbol:

Σfᵢ

represents the sum of frequencies.

In statistics, frequency tells us how many times a particular value or class occurs.

🟣 Important Point

If the frequencies are:

5, 8, 7

then:

Σf = 5 + 8 + 7

= 20

🟦 Activity 14(B)

🟢 Answer

20–30, 20, 20, 30, 34, 36

🟡 Explanation

The values relate to grouped data and class intervals.

For example:

20–30

can represent a class interval in a frequency distribution.

🟣 MATHEMATICS PART – II

🔵 CHAPTER 1

🟦 Activity 1(A) – Linear Pair

🟢 Given

O is a point on line AB.

∠AOC ≅ ∠COB

🟢 To Prove

∠AOC = ∠COB = 90°

🟡 Solution

Since A, O and B lie on a straight line:

∠AOB = 180°

Let:

∠AOC = x

and:

∠COB = x

Therefore:

x + x = 180°

2x = 180°

x = 90°

Hence:

🟢 ∠AOC = ∠COB = 90°

🟣 Important Rule

Angles forming a linear pair have a sum of:

180°

🟦 Activity 1(B)

🟢 Answer

d(B,C), 7.5, 18, 18, 7.5, 10.5

🟦 Activity 2(A)

🟢 Answer

>, (x + 3), (x − 3), 6

🟡 Explanation

The activity uses comparison and algebraic expressions.

🟦 Activity 2(B)

🟢 Answer

linear, 180°, 3x°, 120°, 60°, 60°

🟣 Important Rule

A linear pair has a total measure of:

180°

For example:

120° + 60°

= 180°

🔵 CHAPTER 2

🟦 Activity 3(A)

🟢 Answer

110°, 181°, are not, is not

🟡 Explanation

Angle classification depends on its measure.

Less than 90° → Acute angle
Exactly 90° → Right angle
Between 90° and 180° → Obtuse angle
Exactly 180° → Straight angle
Greater than 180° → Reflex angle

Therefore, 181° is a reflex angle.

🟦 Activity 3(B)

🟢 Answer

∠e, ∠b, ∠e, ∠f, ∠d, ∠c

These are the required angle identifications from the diagram.

🟦 Activity 4(A)

🟢 Answer

∠ADC, 56°, ∠CPD, 80°

These are obtained from the angle relationships shown in the activity.

🟦 Activity 4(B)

🟢 Answer

Vertically opposite angles, 20°, 180°, 20°, 20°, 160°

🟡 Explanation

When two straight lines intersect, the opposite angles are called vertically opposite angles.

🟣 Rule

Vertically opposite angles are equal.

If one angle is 20°, its opposite angle is also:

20°

A straight-line pair has:

180°

Therefore:

180° − 20°

= 160°

🔵 CHAPTER 3 – CONGRUENCE OF TRIANGLES

🟦 Activity 5(A)

🟢 Answer

SSS
SAS
ASA
Hypotenuse-Side

🟡 Explanation

🟣 SSS

Side – Side – Side

If all three corresponding sides are equal, the triangles are congruent.

🟣 SAS

Side – Angle – Side

Two sides and the included angle are equal.

🟣 ASA

Angle – Side – Angle

Two angles and the included side are equal.

🟣 Hypotenuse-Side

This is used for suitable right-angled triangles when the hypotenuse and one corresponding side are equal.

🟦 Activity 5(B)

🟢 Answer

∠QPR, 70°, 180°, 70°, 20°, 90°

🟡 Explanation

The angle sum property of a triangle is:

🟣 180°

For example, if two angles are 70° and 90°:

Third angle:

180° − 70° − 90°

= 20°

🟦 Activity 6(A)

🟢 Answer

seg CB, seg AD, Common side, SSS test

🟡 Explanation

The corresponding sides are identified and the SSS test is used to establish congruence.

🟦 Activity 6(B)

🟢 Answer

Vertically opposite angles, TR, SAS, ∠TSR, ∠TQP, seg SR

🟡 Explanation

The activity combines the property of vertically opposite angles with the SAS congruence test.

🔵 CHAPTER 4 – CONSTRUCTIONS

🟦 Activities 7(A), 7(B), 8(A), 8(B)

🟢 Answer

Students should complete the constructions.

🟡 Explanation

These activities are based on geometrical constructions.

The required construction must be completed using appropriate geometric tools and construction methods.

Since the answer book does not provide the complete original questions, the exact construction cannot be reconstructed from the answer page alone.

🔵 CHAPTER 5

🟦 Activity 9(A)

🟢 Answer

AB², BC², AC², 10 cm

🟡 Explanation

These expressions are related to triangle side calculations.

🟣 Pythagoras Theorem

For a right-angled triangle:

Hypotenuse² = Base² + Perpendicular²

This theorem is used when the length of one side of a right triangle has to be determined from the other two sides.

🟦 Activity 9(B)

🟢 Answer

∠FDE, 65, 5, ∠FDG, 35, 7

These are diagram-based angle and length calculations.

🟦 Activity 10(A)

🟢 Answer

180°, 40°, 220°, 110°

These values are obtained using the appropriate angle relationships.

🟦 Activity 10(B)

🟢 Answer

2/3, 2/3, 3/2, 9, 9, 3

These are the required numerical values from the activity.

🔵 CHAPTER 6 – CIRCLES

🟦 Activity 11(A)

🟢 Answer

BM, QM, BM, QM

🟦 Activity 11(B)

🟢 Answer

PQ, 24, 12, 13, OM, 5 cm

🟦 Activity 12(A)

🟢 Important Answers

Radii of the same circle

Hypotenuse-side test

Perpendicular drawn from the centre of the circle to the chord bisects the chord

🟡 Explanation

All radii of the same circle are equal.

If O is the centre of a circle:

OA = OB = OC

🟣 Important Circle Theorem

If a perpendicular is drawn from the centre of a circle to a chord, it bisects the chord.

If:

OM ⟂ AB

then:

AM = MB

Therefore, the chord is divided into two equal parts.

🟦 Activity 12(B)

🟢 Answer

AB, 16 cm, 8, 8², 289, 17 cm

These values are obtained from the corresponding circle/chord calculations.

🔵 CHAPTER 7 – COORDINATE GEOMETRY

🟦 Activity 13(A)

🟢 Answer

(0, 4), y = 3, 3

🟡 Explanation

A point in coordinate geometry is written as:

(x, y)

For:

(0, 4)

we have:

x = 0

y = 4

When x = 0, the point lies on the y-axis.

🟦 Activity 13(B)

🟢 Answer

−1, (0, −1), 0, 1, 0, 3, 3, 2

🟡 Explanation

These values involve positive and negative coordinates.

Remember:

Positive x → right
Negative x → left
Positive y → upward
Negative y → downward

🟦 Activity 14(A)

🟢 Answer

3, 3, y = 3, No

🟡 Explanation

The equation:

y = 3

represents a horizontal line.

Every point on this line has the same y-coordinate:

For example:

(−2, 3), (0, 3), (4, 3)

all lie on the line:

y = 3

🔵 CHAPTER 8

🟦 Activity 15(A)

🟢 Answer

AB, x, 2x, 1/2

🟡 Explanation

The activity involves line segments and their relationships.

🟦 Activity 15(B)

🟢 Answer

70, 60, 50, 45, 80, 63

These are the required values from the activity.

🟦 Activity 16(A)

🟢 Answer

1, 1/√2, 1/2, 1

🟡 Explanation

These values represent ratios or relationships between lengths in the corresponding geometric activity.

🟦 Activity 16(B)

🟢 Answer

LM/LN, LM/LM, MN/LM, LM/MN, MN/LN, MN/LN

🟡 Explanation

These are ratios between the specified line segments.

For example:

LM/LN

means:

Length of LM divided by length of LN.

Ratios are commonly used to compare corresponding lengths.

🔵 CHAPTER 9 – MENSURATION

🟦 Activity 17(A)

🟢 Answer

7.5 cm, l³, 7.5, 421.875

🟣 Formula

For a cube:

Volume = l³

If:

l = 7.5 cm

then:

7.5³

= 7.5 × 7.5 × 7.5

= 421.875 cm³

🟦 Activity 17(B)

🟢 Answer

1/3 πrh², 753.60, 12, 3, 3.14, 5

🟡 Explanation

The activity uses a formula involving π and the given dimensions.

The calculation uses:

π = 3.14

as specified in the answer material.

🟦 Activity 18(A)

🟢 Answer

4πr², 4 × 3.14, 225, 15

🟣 Formula

Surface area of a sphere:

4πr²

If:

r = 15

then:

r² = 225

Therefore:

4 × 3.14 × 225

is the required calculation.

🟦 Activity 18(B)

🟢 Answer

4l², 4.5, 81, 6l², 4.5, 121.50

These values are obtained from the corresponding mensuration calculations.

🟣 SECTION 2 — MULTIPLE CHOICE QUESTION TESTS

This section contains the answer key.

🔵 Mathematics Part-I

🟢 Test 1

1-D | 2-D | 3-A | 4-B | 5-A | 6-D | 7-C | 8-B | 9-A | 10-D

🟢 Test 2

1-B | 2-A | 3-C | 4-A | 5-A | 6-C | 7-C | 8-D | 9-D | 10-C

🟢 Test 3

1-A | 2-D | 3-B | 4-C | 5-C | 6-D | 7-A | 8-C | 9-A | 10-B

🔵 Mathematics Part-II

🟢 Test 1

1-C | 2-C | 3-B | 4-A | 5-D | 6-D | 7-B | 8-A | 9-A | 10-A

🟢 Test 2

1-A | 2-B | 3-B | 4-A | 5-B | 6-B | 7-B | 8-C | 9-B | 10-C

🟢 Test 3

1-B | 2-C | 3-A | 4-C | 5-A | 6-C | 7-A | 8-A | 9-A | 10-C

🟡 Important

The uploaded answer book provides the A/B/C/D answer key, but it does not contain the complete MCQ questions and their four options. Therefore, individual MCQs cannot be explained exactly from this PDF alone.

🟣 SECTION 3 — PRACTICALS

🔵 MATHEMATICS PART-I

🟦 Practical 1 – Sets

🟢 Answer

All four given sets are subsets of U.

🟡 Explanation

A set A is called a subset of U if every element of A is also present in U.

We write:

A ⊆ U

Example

U = {1, 2, 3, 4, 5}

A = {1, 2, 3}

Therefore:

A ⊆ U

because every element of A belongs to U.

🟦 Practical 2 – Number Line

🟢 Answer 1

√3 is to the right side of −√3.

🟡 Explanation

We know:

√3 ≈ 1.732

and:

−√3 ≈ −1.732

Positive numbers are located to the right of zero, while negative numbers are located to the left.

Therefore:

−√3 < √3

🟢 Answer 2

Two points

One point is to the right of the origin and the other is to the left of the origin.

🟣 Number Line Rule

Positive numbers → Right of zero
Negative numbers → Left of zero
Zero → Origin

🟦 Practical 3 – Polynomial

🟢 Answer

p(x), (x − a), p(a)

🟡 Explanation

p(x) represents a polynomial in x.

If x is replaced by a particular value a, the resulting expression is written as:

p(a)

The expression:

x − a

is also important in polynomial factorisation and division.

🟦 Practical 5 – Income Tax

🟢 Answer 1

Miss Vishakha will not have to pay income tax.

🟡 Reason

Her income falls within the exemption amount shown in the relevant table.

🟢 Answer 2

Mr Girish will have to pay income tax.

🟡 Reason

His income is greater than the exemption amount.

🟢 Answer 3

Mr Kher will not have to pay income tax.

The answers are based on the tables referred to in the practical.

🟣 MATHEMATICS PART-II

🔵 Practical 1 – Coordinates

🟢 Answer 1

Coordinate

🟡 Explanation

A coordinate tells us the position of a point.

A point on a coordinate plane is generally represented as:

(x, y)

🟢 Answer 2

The distance between two points on a number line is:

🟣 Formula

Distance = Greater coordinate − Smaller coordinate

Example

Coordinates:

3 and 9

Distance:

9 − 3

= 6 units

🔵 Practical 2 – Parallel Lines and Transversal

🟢 Answer 1

When two parallel lines are intersected by a transversal, four pairs of corresponding angles are formed.

🟢 Answer 2

The measures of corresponding angles are equal.

Example

If one corresponding angle is:

70°

the other corresponding angle is also:

70°

🟢 Answer 3

The relevant pair of interior angles is supplementary.

🟣 Meaning of Supplementary

Two angles are supplementary when their sum is:

180°

For example:

110° + 70°

= 180°

🟢 Answer 4

100°

🔵 Practical 3 – Parallel Lines

🟢 Answer 1

When two parallel lines are intersected by a transversal:

Two pairs of alternate interior angles are formed.
Two pairs of alternate exterior angles are formed.

🟢 Answer 2

Those coplanar lines are not parallel.

🟡 Explanation

Parallel lines must satisfy the appropriate angle relationships when intersected by a transversal.

If those conditions are not satisfied, the lines cannot be considered parallel.

🔵 Practical 4 – Triangles

🟢 Answer 1

Equilateral Triangle

🟡 Explanation

An equilateral triangle has three equal sides.

Its three angles are also equal:

60°, 60°, 60°

🟢 Answer 2

Isosceles Triangle

🟡 Explanation

An isosceles triangle has two equal sides.

The angles opposite the equal sides are also equal.

🟢 Answer 3

If two sides of a triangle are congruent, the angles opposite those sides are also congruent.

🟣 Important Rule

Equal sides → Equal opposite angles

🟢 Answer 4

Yes, applicable.

🟢 Answer 5

A scalene triangle has all three sides of different lengths.

Therefore:

🟣 Important Rule

Greater side → Greater opposite angle

Smaller side → Smaller opposite angle

🔵 Practical 5 – Median of a Triangle

🟢 Answer 1 – Definition of Median

The segment joining a vertex of a triangle to the midpoint of its opposite side is called a median.

Example

In triangle ABC, if D is the midpoint of BC:

BD = DC

Then:

is a median.

🟢 Answer 2

A triangle can have:

3 medians

Each vertex can be connected to the midpoint of its opposite side.

🟢 Answer 3

In a right-angled triangle:

🟣 Important Rule

Median to the hypotenuse = Half of the hypotenuse

🟢 Answer 4

The circumcentre of a right-angled triangle lies at the midpoint of the hypotenuse.

🟢 Answer 5

If the hypotenuse is:

11 cm

then:

Median = 1/2 × 11

= 5.5 cm

🔵 Practical 6 – Similar Figures

🟢 Answer 1

Figures having the same shape but possibly different sizes are called similar figures.

🟡 Explanation

Two figures are similar when their corresponding sides are proportional and their corresponding angles have the appropriate equality.

Example

Suppose:

2/4 = 3/6

Both ratios equal:

1/2

Therefore, the corresponding lengths are proportional.

🟢 Answer 2

Proportionality of corresponding sides is an important aspect of similarity.

🟢 Answer 3

Data can help us in:

studying information,
analysing information,
working with information,
understanding useful patterns.

A room map made on graph paper is an example of representing information systematically.

🔵 Practical 7 – Circle

🟢 Answer 1 – Area

Area is a quantity that determines the size of a region.

🟢 Answer 2 – Circumference

🟣 Formula

C = 2πr

or:

C = πd

where:

C = circumference
r = radius
d = diameter

🟢 Answer 3 – Area of Circle

🟣 Formula

A = πr²

where:

A = area
r = radius

🟢 Answer 4 – Value of π

Common values used in calculations are:

π = 22/7

or:

π = 3.14

🔵 Practical 8 – Volume

🟢 Answer 1 – Volume

Volume is the space occupied by an object.

For example, the amount of space inside a box is its volume.

🟢 Answer 2 – Volume of a Cylinder

🟣 Formula

V = πr²h

where:

V = Volume

r = Radius

h = Height

🟡 Example

Suppose:

r = 5 cm

h = 10 cm

Then:

V = π × 5² × 10

V = π × 25 × 10

V = 250π cm³

If π = 3.14:

V = 250 × 3.14

= 785 cm³

🟣 QUICK FORMULA REVISION

🔵 Sets

n(A ∪ B) = n(A) + n(B) − n(A ∩ B)

🔵 Exponents

xᵃ × xᵇ = xᵃ⁺ᵇ

🔵 Square Root

(√a)² = a

🔵 Triangle

Sum of angles = 180°

🔵 Linear Pair

Sum = 180°

🔵 Vertically Opposite Angles

They are equal.

🔵 Pythagoras Theorem

Hypotenuse² = Base² + Perpendicular²

🔵 Circle Circumference

C = 2πr = πd

🔵 Circle Area

A = πr²

🔵 Cube Volume

V = l³

🔵 Cylinder Volume

V = πr²h

🔵 Sphere Surface Area

A = 4πr²

🔵 Number Line Distance

Distance = Greater coordinate − Smaller coordinate

🔵 Similar Figures

Corresponding sides are proportional.

🟢 COMPLETE TOPIC SUMMARY

The book covers the following major Class 9 Mathematics concepts:

🟦 Mathematics Part-I

Sets → Numbers → Algebra → Polynomials → Equations → Statistics → Data

🟪 Mathematics Part-II

Angles → Parallel Lines → Congruent Triangles → Constructions → Geometry → Circles → Coordinate Geometry → Similarity → Mensuration

🟨 Practicals

Sets → Number Line → Polynomial → Income Tax → Coordinates → Parallel Lines → Triangles → Median → Similar Figures → Data → Circle → Volume

The six-page uploaded answer book contains Home Assignment answers, MCQ answer keys, and Practical “Test Your Knowledge” answers across these sections.