Are these practice questions for I’m Up and Down, and Round and Round based on the CBSE pattern?

Yes. Every practice question is modeled on the CBSE Class 9 Mathematics exam pattern — including MCQs, assertion-reason questions, and short-answer formats that frequently appear in CBSE papers.

Are the practice questions for I’m Up and Down, and Round and Round free?

Yes. Every chapter includes free practice questions for Class 9 students to get you started.

What types of questions are included?

The practice set for I’m Up and Down, and Round and Round mainly includes MCQs and CBSE-style short-answer questions, with instant feedback on each answer. For full-length textbook practice, use the NCERT Solutions page.

Are the practice questions suitable for board exam preparation?

Yes. The questions test the same concepts and depth that CBSE asks in board exams. After finishing, also solve the NCERT and NCERT Exemplar exercises for I’m Up and Down, and Round and Round for full coverage.

How many practice questions are there for I’m Up and Down, and Round and Round?

The number scales with chapter length and concept density. Each chapter typically has 15-50 practice questions across MCQ and short-answer formats.

I’m Up and Down, and Round and Round Class 9 Mathematics Practice Questions with Answers

easy

List the two main types of symmetry a circle possesses.

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easy

In a cyclic quadrilateral

PQRS

, if

\angle Q = 95^\circ

, calculate the measure of

\angle S

.

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easy

What is a cyclic quadrilateral?

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easy

A student claims that if two chords in two different congruent circles are equal, they must subtend equal angles at their respective centres. Justify this claim.

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easy

A circle has a radius of

14.5

cm. Calculate the length of its longest chord.

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easy

An arc of a circle subtends an angle of

88^\circ

at the centre. Calculate the angle subtended by it at any point on the remaining part of the circle.

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easy

Justify why a regular pentagon inscribed in a circle must have all its sides equidistant from the centre of the circle.

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easy

Define a circle using the concept of a locus.

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easy

Describe the location of the circumcentre for an acute-angled, an obtuse-angled, and a right-angled triangle.

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easy

Design a method using only a compass and a straightedge to find the centre of a given circle. Justify the steps of your construction.

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easy

Formulate a rule to determine if a parallelogram is cyclic, and justify your reasoning.

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easy

What is the name of the longest chord in a circle?

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medium

State the theorem concerning equal chords of a circle and the angles they subtend at the centre. Also, state its converse.

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medium

The radius of a circle is

20

cm. Calculate the length of a chord that is at a distance of

12

cm from the centre.

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medium

PQRS

is a cyclic quadrilateral where

\angle P = (x+15)^\circ

and

\angle R = (4x+15)^\circ

. Solve for

x

and determine the measures of

\angle P

and

\angle R

.

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medium

Explain the relationship between a line drawn from the centre of a circle to the midpoint of a chord. Also, state the converse of this theorem.

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medium

Critique the statement: "Any quadrilateral where the perpendicular bisectors of all four sides are concurrent must be a cyclic quadrilateral."

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medium

Prove that of all chords that can be drawn through a given point P inside a circle, the one that is shortest is the chord that is perpendicular to the diameter passing through P.

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medium

Describe the locus of the centres of all circles that can be drawn through two given points A and B. Explain this concept and identify the circle with the smallest possible radius.

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medium

AB

is a diameter of a circle and

C

is a point on the circumference. If

\angle CAB = 35^\circ

, calculate the measure of

\angle ABC

.

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medium

Explain why the angle in a semicircle is always

90^\circ

. Use the theorem about the angle subtended by an arc at the centre.

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medium

Analyze the given statement: A quadrilateral

ABCD

has angles

\angle A = 70^\circ

,

\angle B = 100^\circ

,

\angle C = 110^\circ

, and

\angle D = 80^\circ

. Determine if this quadrilateral can be a cyclic quadrilateral.

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medium

Prove that if two circles intersect at two distinct points, the line joining their centres is the perpendicular bisector of their common chord.

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medium

In a circle with centre

O

, points

A

,

B

, and

C

are on the circle such that

\angle BOC = 110^\circ

and

\angle AOB = 90^\circ

. Determine the measure of

\angle BAC

.

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medium

Justify that a trapezium is cyclic if and only if it is an isosceles trapezium.

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medium

State the relationship between the angle subtended by an arc at the centre and at a point on the remaining part of the circle.

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medium

A chord of a circle is equal to its radius. Formulate and prove a theorem about the angle subtended by this chord at any point on the major arc.

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medium

Summarize the property that connects the lengths of two unequal chords to their distances from the centre of the circle.

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medium

A chord of length

30

cm is drawn in a circle at a distance of

8

cm from the centre. Calculate the radius of the circle.

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medium

Two parallel chords are drawn in a circle of radius

13

cm. If the chords have lengths

10

cm and

24

cm, and lie on opposite sides of the centre, calculate the distance between them.

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medium

Evaluate if it is possible to draw a circle passing through the four vertices of a kite that is not a rhombus. Justify your answer.

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medium

Summarize the properties of a cyclic quadrilateral. State the main theorem regarding its opposite angles and the converse of this theorem.

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medium

Explain why there is only one unique circle that can pass through three non-collinear points.

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medium

A, B, and C are three points on a circle with centre O. The angles subtended by the chords AB and AC at the centre O are

\angle AOB = 90^\circ

and

\angle AOC = 110^\circ

respectively. Formulate a method to find

\angle BAC

and evaluate the two possible values.

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hard

State the theorem that provides the condition for four points to be concyclic, based on the angles subtended by a line segment.

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hard

Explain the relationship between the length of a chord and its distance from the centre. Your explanation should cover both equal and unequal chords.

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hard

Two parallel chords of lengths

12

cm and

16

cm are drawn in a circle of radius

10

cm. If the chords are on the same side of the centre, analyze the geometry and calculate the distance between the two chords.

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hard

In a circle with centre O, chord AB is produced to a point P such that the length of the segment BP is equal to the radius of the circle. The line from P passes through the centre O and intersects the circle at C and D. Prove that

\angle AOD = 3 \times \angle APC

.

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hard

In a circle with centre O, if

\angle OAB = 40^\circ

and

\angle OCB = 30^\circ

, calculate the measure of the reflex angle

\angle AOC

. (A, B, C are points on the circle).

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hard

Two circles with centres O1 and O2 touch each other externally at point P. A direct common tangent is drawn touching the circles at points A and B respectively. Propose and prove a theorem about the measure of angle

\angle APB

.

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hard

A regular hexagon with side length

6

cm is inscribed in a circle. Analyze the properties of the hexagon and calculate the radius of the circle and the distance of each side from the centre.

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hard

Two equal chords AB and CD of a circle with centre O intersect at a point P inside the circle. Prove that the line segment OP bisects the angle formed by the chords,

\angle APD

.

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hard

In a circle with centre O, chord

AB

is equal to chord

AC

. If

\angle BAC = 80^\circ

, analyze the triangles formed and calculate

\angle OBC

.

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hard

Design and justify a method to construct a triangle ABC, given the length of its base BC, the vertical angle

\angle A = \alpha

, and the length of the altitude from vertex A to the base BC, say

h

.

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hard

Points A, B, C, and D are on a circle. AC and BD are chords intersecting at point E. If

\angle DAC = 30^\circ

and

\angle AEB = 85^\circ

, analyze the angles and calculate

\angle ABC

.

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I’m Up and Down, and Round and RoundClass 9 Mathematics Practice Questions