# ICSE Important Questions For Class 9 Maths

## ICSE Important Questions for Class 9 Mathematics

Extramarks Subject Matter Experts have created the Extramarks content, ICSE Important Questions for Class 9 Mathematics, to aid students in their test preparation. The questions were developed using the most recent syllabus for Class 9. Students become familiar with the key concepts in each Mathematics chapter. By practising the ICSE Important Questions for Class 9 Mathematics exam, they can assess their progress and preparation. Additionally, it aids in boosting their self-confidence.

To help students strengthen their conceptual learning, all the crucial ideas and concepts from Class 9 Mathematics are covered by Extramarks when formulating these important problems. Students can strengthen their concepts and be prepared to take on any type of question on the exam by completing these important Mathematics problems. All the formulas and important ideas that require greater concentration will be revised. It facilitates the students’ exam preparation.

Explore more resources for Important Questions for Class 9 Mathematics chapter-wise ICSE on the Extramarks website.All materials, such as NCERT book solutions, ICSE revision notes, and many more, are available to the students for free. Special tips and tricks have been included so that the students can grasp the concepts easily.

### What Chapters Are Covered in ICSE Important Questions for Class 9 Mathematics?

To quickly review the complete ICSE Class 9 Mathematics Syllabus, students should practise all of the ICSE Class 9 Mathematics Question Papers with Answers. The chapters from the NCERT Class 9 Mathematics textbook that are covered in the ICSE Important Questions for Class 9 Mathematics Solutions are listed below.

• Chapter 1: Pure Arithmetic
• Chapter 2: Commercial Mathematics
• Chapter 3: Algebra
• Chapter 4: Geometry
• Chapter 5: Statistics
• Chapter 6: Mensuration
• Chapter 7: Trigonometry
• Chapter 8: Co-ordinate Geometry

To do well on the ICSE Mathematics exam, students should study the ICSE Important Questions for Class 9 Mathematics. After finishing the full course, individuals should practise the key questions to help them analyse their performance and determine where they stand in terms of preparation. These ICSE Important Questions for Class 9 Mathematics are a useful tool to use in conjunction with other study tools when it comes to effectively cramming for the exam. As a result, this part of the crucial questions will be useful for reviewing vital ideas and grading the student in preparation for the tests.

## ICSE Important Questions for Class 9 Mathematics– Important Notes

Eight units covering the foundations make up the Class 9 Mathematics Syllabus. We will go through the units briefly here. Our important question bank has all ICSE Class 9 Mathematics Chapter Wise Questions  for the following chapters:

### Chapter 1: Pure Arithmetic

The topics covered in this unit are:

1. A) Rational Numbers

1)Rational and Irrational Numbers

Rational numbers, irrational numbers as real numbers, their place in the number system.

Surds and the rationalisation of surds. Simplifying an expression by rationalising the denominator. Representation of the rational and irrational numbers on the number line.

Proofs of irrationality of √2, √3, √5.

### Chapter 2: Commercial Mathematics

The topics covered in this unit are:

i)Compound Interest

(a) Compound interest as the repeated Simple Interest computation with a growing Principal. Use of this in computing the amount over a period of 2 or 3 years.

(b) Use of the formula A = P(1 + r/100)n. Finding the CI from the given relation CI = A – P.

• Interest compounded half-yearly included.
• Using the formula to find one quantity while given the different combinations of A, P, r, n, SI and CI; the difference between CI and SI type included. Rate of growth and depreciation.

### Chapter 3: Algebra

The topics covered in this unit are:

• Expansions
• Factorisation

Simultaneous Linear Equations in two variables. (With numerical coefficients only)

Solving different equations algebraically by:

• Elimination
• Substitution
• Cross Multiplication method

Solving the simple problems by framing the appropriate equations.

(iv) Indices/ Exponents

Handling the positive,  negative, fractional, and “zero” indices.

Simplification of the expressions involving various exponents; use of the laws of exponents.

(v) Logarithms

(a) Logarithmic form vis-à-vis the exponential form: interchanging.

(b) Laws of Logarithms and their uses.

Expansion of the expression with the help of laws of logarithms.

### Chapter 4: Geometry

The topics covered in this unit are:

(i) Triangles

(a) Congruency: four cases: SSS, SAS, AAS, RHS. Illustration through the cutouts. Simple applications.

(b) Problems based on:

• Angles that are opposed to equal sides have equal angles as well.
• The greater angle is opposite the greater side if the two sides of a triangle are not equal, and vice versa.
• Any two of the triangle’s sides added together exceed the sum of the third side.
• The perpendicular is the shortest of all the straight lines that may be drawn from a point outside of a given line.

No proof is required.

(c) Mid-Point Theorem and its converse, the equal intercept theorem

1. Proof and simple applications of the mid- point theorem and its converse.
2. Equal intercept theorem: its proof and simple application.

(d) Pythagoras Theorem

Area based proof and the simple applications of the Pythagoras Theorem and its converse.

(ii) Rectilinear Figures

(a) Proof and use of the theorems on parallelogram.

• Both pairs of the opposite sides are equal (without proof).
• Both pairs of opposite angles are equal.
• One pair of the opposite sides are equal and parallel (without proof).
• The parallelogram is divided into two halves by the intersection of two diagonals.
• As a unique parallelogram whose diagonals meet at right angles, a rhombus.
• The diagonals are equal in a rectangle and square and come together at right angles.

(b) Constructions of Polygons

Construction of the quadrilaterals (including parallelograms and rhombus) and the regular hexagon using ruler and compasses only.

(c) Proof and use of the area theorems on the parallelograms:

• The area of parallelograms with the same base and corresponding parallels is the same.
• A triangle’s area is half that of a parallelogram with the same base and parallel axes.
• Triangles with the same base and similar parallels have the same area (without proof).
• Triangles with identical bases and equal areas have identical corresponding heights.

(iii) Circle

(a) Chord properties

• A straight line that is not a diameter that is drawn from the centre of a circle to bisect the chord is at a right angle to the chord.
• The chord is divided in half by the perpendicular from the chord’s centre (without proof).
• Equal distances from the centre

separate equal chords.

• Equidistant chords from the centre are equal (without proof).
• The only circle that does not travel in a straight line across the three sites mentioned is the one and only circle.

(b) Arc and chord properties

• They are equal if the two arcs subtend the same angles at their centres, and vice versa.
• They cut off equal arcs if the
•  two chords are equal, and vice versa (without proof).
1. ICSE Mathematics Class 9 Syllabus

### Chapter 5: Statistics

The topics covered in this unit are:

Introduction, collection of the data, presentation of the data, Graphical representation of the data, Mean, Median of the ungrouped data.

Understanding and recognition of the raw, arrayed and the grouped data.

Tabulation of raw data using tally-marks.

Understanding and recognition of the discrete and continuous variables.

Mean, median of the ungrouped data

• Class intervals, class boundaries and the limits, frequency, frequency table, class size for the grouped data.
• Grouped frequency distributions: the need to and how to convert the discontinuous intervals to the continuous intervals.
• Drawing of frequency polygon.

### Chapter 6: Mensuration

The topics covered in this unit are:

Area and the perimeter of a triangle and a quadrilateral. Area and circumference of a circle. Surface area and the volume of Cube and Cuboids.

(a) Area and the perimeter of the triangle (including Heron’s formula), all types of Quadrilaterals.

(b) Circle: Area and the Circumference. Direct application problems including the Inner and Outer area.

Areas of the sectors of circles other than the quarter-circle and the semicircle are not included.

(c) Surface area and the volume of 3-D solids: the cube and cuboid including problems of type involving:

• Different internal and external dimensions of the solid.
• Cost.
• Concept of the volume being equal to the area of cross-section x height.
• Open / closed cubes / cuboids.

### Chapter 7: Trigonometry

The topics covered in this unit are:

• (a) Trigonometric Ratios: sine, cosine, tangent of an angle and their reciprocals.
• (b) Trigonometric ratios of the standard angles – 0, 30, 45, 60, 90 degrees. Evaluation of an expression involving these ratios.
• (c) Simple 2-D problems involving one right-angled triangle.
• (d) Concept of the trigonometric ratios of the complementary angles and their direct application.

### Chapter 8: Co-ordinate Geometry

The topics covered in this unit are:

• Cartesian System, the plotting of the points in the plane for given coordinates, solving simultaneous linear equations in the 2 variables graphically and finding the distance between the two points using distance formula.
• (a) Dependent and the independent variables.
• (b) Ordered pairs, the co-ordinates of the points and plotting them in the Cartesian Plane.
• (c) Solution of the Simultaneous Linear Equations graphically.
• (d) Distance formula.

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### ICSE Important Questions for Class 9 Mathematics – Chapter-Wise Questions

Mathematics for Class 9 has a vast syllabus, and a lot of preparation and practise are required.There are numerous topics to be covered, and the only way to keep them in mind is to practise regularly. It would be best if you practised the difficult questions regularly so that there was no scope for making any mistakes during your actual exams.

However, you no longer need to be concerned because Extramarks provides you with access to all of the ICSE Important Questions for Class 9 Mathematics for each chapter, as well as their solutions.

Click the chapter-wise questions and solutions below to check the ICSE Important Questions for Class 9 Mathematics.

• Important Questions Chapter 1: Pure Arithmetic
• Important Questions Chapter 2: Commercial Mathematics
• Important Questions Chapter 3: Algebra
• Important Questions Chapter 4: Geometry
• Important Questions Chapter 5: Statistics
• Important Questions Chapter 6: Mensuration
•  Important Questions Chapter 7: Trigonometry
• Important Questions Chapter 8: Co-ordinate Geometry

Make the best use of these solved questions covered in our ICSE Important Questions for Class 9 Mathematics. Be on board with Extramarks to get exclusive notifications and news about the upcoming examinations, along with study material, a syllabus, an exam pattern, and various other information.

Register today with Extramarks to practise more and explore in-depth knowledge of all the topics. Also, look at ICSE’s past years’ question papers, ICSE sample papers, and ICSE additional questions.

### Benefits of Solving ICSE Important Questions for Class 9 Mathematics

• The student’s confidence is increased, which helps them achieve high grades.
• They can evaluate their preparation and strengthen their weak themes as a result.
• It addresses all of the significant numerical issues that could come up in the final exam.
• For further practice, students should answer these important questions after finishing the required curriculum.

Extramarks’ ICSE Important Questions for Class 9 Mathematics is a meticulously curated collection of key questions drawn from each chapter.It will help you practise and improve your problem-solving skills.

### 1. How do I clear my doubts about ICSE Class 9 Mathematics?

It’s normal to have questions while studying. Clarifying any ambiguities right away is another crucial step. Fortunately, this is doable with Extramarks. So that there are no obstacles in the way of your learning, our topic specialists are prepared to address your questions right away.

### 2. How to plan a study schedule for Mathematics in Class 9?

To master and improve in the field of Mathematics, one must pay close attention to it. This does not imply that you must spend eight hours per day studying Mathematics. In reality, if you study Mathematics efficiently for just 30 minutes a day, you will be successful. Set aside time each day to work on Mathematics, and practise frequently. You are positioning yourself for success by developing the habit of finishing your assignment.

### 3. What is the importance of solving ICSE Class 9 Mathematics Important Questions?

The benefits of answering the crucial Mathematics Class 9 ICSE problems are numerous. Let’s examine its significance.
ICSE Mathematics key question resolution Students in the ninth grade will gain effective time management skills when they take their exams.
These ICSE Class 9 Mathematics sample exams were created in accordance with the prescribed curriculum. While completing the practise papers, students will have the opportunity to review the complete syllabus.
These Class 9 Mathematics ICE sample tests were created in accordance with the curriculum. While completing the practise papers, students will have the opportunity to review the complete syllabus.
The ICSE Class 9 Mathematics Important Questions help the students concentrate on the crucial subject and deepen their comprehension.
According to the perspective of the exam, students can evaluate their preparation plan.

### 4. Is ICSE Mathematics Class 9 syllabus helpful?

The ICSE course structure is designed to ensure that students don’t experience a lot of stress, and texts are created to be understandable and engaging so that students may participate in their investigations.In order to encourage students to study actively,  a tonne of entertaining tasks are inserted in between the sections. It makes the most popular method of educating children sound and effective. Due to the ICSE board’s extensive explanations of its courses, the ICSE syllabus is more difficult than the CBSE curriculum.