UK Board class 9 mathematics Syllabus

The curriculum at Secondary stage primarily aims at enhancing the capacity of students to employ Mathematics in solving day-to-day life problems and studying the subject as a separate discipline. It is expected that students should acquire the ability to solve problems using algebraic methods and apply the knowledge of simple trigonometry to solve problems of height and distances. Carrying out experiments with numbers and forms of geometry, framing a hypothesis and verifying these with further observations form an inherent part of Mathematics learning at this stage. The proposed curriculum includes the study of the number system, algebra, geometry, trigonometry, mensuration, statistics, graphs, and coordinate geometry, etc.
The teaching of Mathematics should be imparted through activities which may involve the use of concrete materials, models, patterns, charts, pictures, posters, games, puzzles, and experiments.

Objectives for UK Board class 09 mathematics Syllabus

The broad objectives of teaching of Mathematics at the secondary stage are to help the learners to:

• consolidate the Mathematical knowledge and skills acquired at the upper primary stage;
• acquire knowledge and understanding, particularly by way of motivation and visualization, of basic concepts, terms, principles and symbols, and underlying processes and skills;
• develop mastery of basic algebraic skills;
• develop drawing skills;
• feel the flow of reason while proving a result or solving a problem;
• apply the knowledge and skills acquired to solve problems and wherever possible, by more than one method;
• to develop an ability to think, analyze and articulate logically;
• Develop awareness of the need for national integration, protection of the environment, observance of small family norms, removal of social barriers, elimination of gender biases;
• to develop necessary skills to work with modern technological devices and mathematical softwares.
• Dvelop interest in mathematics as a problem-solving tool in various fields for its beautiful structures and patterns, etc.
• to develop reverence and respect towards great Mathematicians for their contributions to the field of Mathematics;
• Dvelop interest in the subject by participating in related competitions;
•  acquaint students with different aspects of Mathematics used in daily life;
•  develop an interest in students to study Mathematics as a discipline.

UK Board class 9 mathematics Syllabus

UNIT I: NUMBER SYSTEMS

REAL NUMBERS (18 Periods)

1. Review of representation of natural numbers, integers, rational numbers on the number line. Representation of terminating / non-terminating recurring decimals on the number line through successive magnification. Rational numbers as recurring/ terminating decimals. Operations on real numbers.
2. Examples of non-recurring/non-terminating decimals. The existence of non-rational numbers (irrational numbers) such as 2‾√,3‾√2,3 and their representation on the number line.
   Explaining that every real number is represented by a unique point on the number line and conversely, viz. every point on the number line represents a unique real number.
3. Definition of n^th root of a real number.
4. The existence of x√x for a given positive real number x and its representation on the number line with geometric proof.
5. Rationalization (with precise meaning) of real numbers of the type 1a+bx√1a+bx and 1x√+y√1x+y (and their combinations) where x and y are a natural number and a and b are integers.
6. Recall of laws of exponents with integral powers. Rational exponents with positive real bases (to be done by particular cases, allowing the learner to arrive at the general laws.)

UNIT II: ALGEBRA

1. POLYNOMIALS (23 Periods)
   Definition of a polynomial in one variable, with examples and counter examples. Coefficients of a polynomial, terms of a polynomial and zero polynomial. The degree of a polynomial. Constant, linear, quadratic and cubic polynomials, monomials, binomials, trinomials. Factors and multiples. Zeros of a polynomial. Motivate and State the Remainder Theorem with examples. Statement and proof of the Factor Theorem.
   Factorization of ax² + bx + c, a≠0a≠0 where a, b and c are real numbers, and of cubic polynomials using the Factor Theorem.
   Recall of algebraic expressions and identities. verification of identities:
   (x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx
   (x±y)3=x3±y3±3xy(x±y)(x±y)3=x3±y3±3xy(x±y)
   x3±y3=(x±y)(x2∓xy+y2)x3±y3=(x±y)(x2∓xy+y2)
   x³ + y³ + z³ – 3xyz = (x + y + z) (x² + y² + z² – xy +yz – zx)
   and their use in factorization of polynomials.
2. LINEAR EQUATIONS IN TWO VARIABLES (14) Periods
   Recall of linear equations in one variable. Introduction to the equation in two variables.
   Focus on linear equations of the type ax+by+c=0. Prove that a linear equation in two variables has infinitely many solutions and justify their being written as ordered pairs of real numbers, plotting them and showing that they lie on a line. Graph of linear equations in two variables. Examples, problems from real life, including problems on Ratio and Proportion and with algebraic and graphical solutions being done simultaneously.

UNIT III: COORDINATE GEOMETRY

1. COORDINATE GEOMETRY (6) Periods
   The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, notations, plotting points in the plane.

UNIT IV: GEOMETRY

INTRODUCTION TO EUCLID’S GEOMETRY (6) Periods

History – Geometry in India and Euclid’s geometry. Euclid’s method of formalizing observed phenomenon into rigorous mathematics with definitions, common/obvious notions, axioms/postulates, and theorems. The five postulates of Euclid. Equivalent versions of the fifth postulate. Showing the relationship between axiom and theorem, for example:
(Axiom) 1. Given two distinct points, there exists one and only one line through them.
(Theorem) 2. (Prove) Two distinct lines cannot have more than one point in common.

LINES AND ANGLES (13 Periods)

1. (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 180° and the converse.
2. (Prove) If two lines intersect, vertically opposite angles are equal.
3. (Motivate) Results on corresponding angles, alternate angles, interior angles when a transversal intersects two parallel lines.
4. (Motivate) Lines which are parallel to a given line are parallel.
5. (Prove) The sum of the angles of a triangle is 180°.
6. (Motivate) If a side of a triangle is produced, the exterior angle so formed is equal to the sum of the two interior opposite angles.

TRIANGLES UK Board class 9 mathematics Syllabus (20 Periods)

1. (Motivate) Two triangles are congruent if any two sides and the included angle of one triangle is equal to any two sides and the included angle of the other triangle (SAS Congruence).
2. (Prove) Two triangles are congruent if any two angles and the included side of one triangle is equal to any two angles and the included side of the other triangle (ASA Congruence).
3. (Motivate) Two triangles are congruent if the three sides of one triangle are equal to three sides of the other triangle (SSS Congruence).
4. (Motivate) Two right triangles are congruent if the hypotenuse and a side of one triangle are equal (respectively) to the hypotenuse and a side of the other triangle.
5. (Prove) The angles opposite to equal sides of a triangle are equal.
6. (Motivate) The sides opposite to equal angles of a triangle are equal.
7. (Motivate) Triangle inequalities and relation between ‘angle and facing side’ inequalities in triangles.

QUADRILATERALS (10 Periods)

1. (Prove) The diagonal divides a parallelogram into two congruent triangles.
2. (Motivate) In a parallelogram opposite sides are equal, and conversely.
3. (Motivate) In a parallelogram opposite angles are equal, and conversely.
4. (Motivate) A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and equal.
5. (Motivate) In a parallelogram, the diagonals bisect each other and conversely.
6. (Motivate) In a triangle, the line segment joining the midpoints of any two sides is parallel to the third side and in half of it and (motivate) its converse.

AREA UK Board class 9 mathematics Syllabus (7 Periods)
Review concept of area, recall area of a rectangle.

1. (Prove) Parallelograms on the same base and between the same parallels have the same area.
2. (Motivate) Triangles on the same (or equal base) base and between the same parallels are equal in area.

CIRCLES (15 Periods)

Through examples, arrive at the definition of a circle and related concepts-radius, circumference, diameter, chord, arc, secant, sector, segment, subtended angle.

1. (Prove) Equal chords of a circle subtend equal angles at the center and (motivate) its converse.
2. (Motivate) The perpendicular from the center of a circle to a chord bisects the chord and conversely, the line is drawn through the center of a circle to bisect a chord is perpendicular to the chord.
3. (Motivate) There is one and only one circle passing through three given non-collinear points.
4. (Motivate) Equal chords of a circle (or of congruent circles) are equidistant from the center (or their respective centers) and conversely.
5. (Prove) The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.
6. (Motivate) Angles in the same segment of a circle are equal.
7. (Motivate) If a line segment joining two points subtends an equal angle at two other points lying on the same side of the line containing the segment, the four points lie on a circle.
8. (Motivate) The sum of either of the pair of the opposite angles of a cyclic quadrilateral is 180° and its converse.

UNIT V: MENSURATION

1. AREAS (4 Periods)
   Area of a triangle using Heron’s formula (without proof) and its application in finding the area of a quadrilateral.
2. SURFACE AREAS AND VOLUMES (12 Periods)
   Surface areas and volumes of cubes, cuboids, spheres (including hemispheres) and right circular cylinders/cones.

UNIT VI: STATISTICS & PROBABILITY(13 Periods)

1. STATISTICS (13) Periods

   Introduction to Statistics: Collection of data, presentation of data – tabular form, ungrouped /grouped, bar graphs, histograms (with varying base lengths), frequency polygons. Mean, median and mode of ungrouped data.

2. PROBABILITY UK Board class 9 mathematics Syllabus

   History, Repeated experiments and observed frequency approach to probability.
   The focus is on empirical probability. (A large amount of time to be devoted to group and to individual activities to motivate the concept; the experiments to be drawn from real – life situations, and from examples used in the chapter on statistics).

QUESTIONS PAPER DESIGNS 2018-2019
UK Board class 9 mathematics Syllabus

Remembering

1. (Knowledge-based- Simple recall questions, to know specific facts, terms, concepts, principles, or theories; Identity, define or recite information)
   VSA Question (1 mark) = 2
   SA Question I (2 marks) = 2
   SA Question II (3 marks) = 2
   LA Question (4 marks) = 2
   Total Marks = 20
   Weightage = 25%

Understanding

1. (Comprehension- to be familiar with the meaning and to understand conceptually, interpret, compare, contrast, explain, paraphrase, or interpret information)
   VSA Question (1 mark) = 2
   SA Question I (2 mark) = 1
   SA Question II (3 marks) = 1
   LA Question (4 mark) = 4
   Total Marks = 23
   Weightage = 29%

Application

1. (Use abstract information in the concrete situation, to apply knowledge to new situations; Use given content to interpret a situation, provide an example, or solve a problem)
   VSA Question (1 mark) = 2
   SA Question I (2 mark) = 2
   SA Question II (3 mark) = 3
   LA Question (4 mark) = 1
   Total Marks = 19
   Weightage = 24%
2. Higher Order Thinking Skills (Analysis & Synthesis- Classify, compare, contrast, or differentiate between different pieces of information; Organize and/or  integrate unique pieces of information from a variety of sources)
   VSA Question (1 mark) = 0
   SA Question I (2 mark) = 1
   SA Question II (3 mark) = 4
   LA Question (4 mark) = 0
   Total Marks = 14
   Weightage = 17%
3. Evaluation (Judge, and/or justify the value or worth of a decision or outcome, or to predict outcomes based on values)
   VSA Question (1 mark) =0
   SA Question I (2 mark) = 0
   SA Question II (3 mark) = 0
   LA Question (4 mark) = 1
   Total Marks = 4
   Weightage = 5%

• TOTAL:
  VSA Question (1 mark) =6×1=6
  SA Question I (2 mark) = 6×2=12
  SA Question II (3 mark) = 10×3=30
  LA Question (4 mark) = 8×4=32
  Total Marks = 80
  Weightage = 100%

INTERNAL ASSESSMENT (20 Marks)

• Periodical Test (10 Marks)
• NoteBook Submission (05 Marks)
• Lab Practical (Lab activities to be done from the prescribed books) (05 Marks)

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