Mathematics Syllabus

💁TEXTBOOK

MATHEMATICS SYLLABUS FOR CLASS X

Course Content

 

UNIT 1     MATRICES AND NETWORK

• Meaning, and uses of matrix;   description of a matrix in terms of the number of rows by columns; special matrices such as square matrix, column matrix, row matrix; describing the elements of a matrix by their positions within the matrix;  using a matrix to display information; using a matrix to describe a shape on a grid.
• Addition and subtraction of matrices; applications and problems involving them
• Multiplying a matrix by a scalar; applications and problems involving it
• Multiplication of matrices; the compatibility of two matrices for multiplication; applications and problems involving multiplication of matrices
• Network: it meaning; describing a network with a matrix; applications and problems involving network and matrices

UNIT 2     NUMBER AND OPERATION  

• Consumer math:  profit, loss, discount, commission as actual amounts and percentages; their meanings, formulas and problems involving their applications
• Compound Interest:  its meaning and its comparison with simple interest; the formula for the calculation of compound interest and its derivation; calculating compound interests compounded annually, semi-annually, and quarterly; problems involving calculation of compound interest, and other related information given the other necessary information;  
• The Rule of 72 and its connection with compound interest; why the Rule of 72 works may be explored
• Using consumer math to make decisions in purchasing and investment
• Radicals: their meaning; representing radicals in the form of powers with fractional exponents; simplifying radicals; representing radicals geometrically
• Operations with radicals:  addition, subtraction, multiplication and division

UNIT 3     LINEAR FUNCTIONS AND RELATIONS

• Patterns:  using patterns to predict
• Functions and relations:  meanings and basic definitions of relations and functions; representing relations that are functions in function notation; ways of representing functions; determining if a given relation is a function either in the form of a table, a graph or an algebraic expression; recognizing different types of functions namely, linear, quadratic and exponential; using functions to describe some real life situations
• Linear Functions:  Given a linear relationship in its standards form, determining which variable could be expressed as a function of the other (in other words which variable could be made the dependent variable and which could be made the independent variable); Transforming standard form of a linear relation to slope and y-intercept form; 
• Application of Linear Functions:  Using a Linear Function to solve a Financial Problem; Using Linear functions to represent a Line of Best Fit
• Linear Inequalities:  meaning and algebraic expression of Linear Inequalities; Graphing
• Linear Inequalities; writing or determining Linear Inequality algebraically from its Graph
• Transforming Graphs of Linear Functions:  express transformations either algebraically or with a mapping rule when given an image of a known graph  
• Systems of Linear Equations: Solving Systems of Linear Equations using various algebraic methods, namely The Comparison Strategy, The Substitution Strategy, The Elimination Strategy, and Using Matrices;  Determining the solution of a system of Linear Equation from their graphs; realizing that the graphing method will not always give exact solutions easily; Translating real life problem situations into a system of Linear Equations and solving it to solve the real life problems, for example in determining the break even point in businesses.

UNIT 4     MEASUREMENT 

• Review from earlier classes:  area, perimeter, volume etc of various shapes
• Precision and Accuracy:  meaning of precision in connection with the measuring units and instruments used to measure; meaning of accuracy of measurement.
• Significant digits:  determining the number of significant digits in given number; Rules for determining the number of significant digits in calculations and the rationale for the rules 
• 2-D Efficiency:  Knowing which 2-D shape has the maximum area for the same perimeter or minimum perimeter for same area; application of this knowledge in problem situations
• 3-D Efficiency:  the relationship between the surface area and the volume of a 3-D shape; determining which would have the maximum volume or capacity for a constant surface area or minimum surface area for a given volume; application of this knowledge in real life situations; 
• Exploring occurrence of geometric principles in the nature’s design of the animals shapes  

UNIT 5     QUADRATIC AND ABSOLUTE VALUE FUNCTIONS 

• Quadratic Functions:  definition of quadratic function; various forms of quadratic function, namely the Standard Form, the Factored Form, and the Vertex Form; the shape or nature of the graph of any quadratic function, i.e, the parabola; means to check if a given quadratic function is equivalent to another one using table of values, graphs, or using algebra; using quadratic functions to solve problems
• Graphs of Quadratic Functions:  Sketching the graph of quadratic function in factored form;  constructing graphs from table of values; analyzing graphs to determine mathematics characteristics 
• Transforming and Relating Graphs of Quadratic Function:  realizing that the graph of any quadratic function is a parabola; and that its size, direction of opening and position are one or more transformation to the graph of the function f(x) = x², affected by the coefficients of the x², x, and the constant; describing these transformations algebraically or with a mapping notation when given an image of a known graph
• The Absolute value Function:  meaning of absolute value of a number and its notation; geometrical representation of absolute value; the nature and shape of the graph of the absolute function f(x) =  x
• Graphs of other forms of absolute value functions; realizing that the graph of any absolute value function has the shape of two rays meeting to form a “V”above the x-axis; and that it size is one or more transformation of the graph of the absolute value function f(x) =  x
• Describing these transformations using mapping notation.
• Factoring Quadratic Expressions:  Exposure to various method of factoring quadratic expressions including Using Algebra Tiles, Using an Area Model, and using Algebraic methods.  The Algebraic methods include: Assuming that the factors are two binomials, (ax + b) and (cx + d), and equating the product of these two binomial factors with the original polynomial to get information about the coefficients and the constants; using common factors; and using the Sum and Product Rule.
• Solving Quadratic Equations:  solving the quadratic equation by equating a quadratic function to 0; the meaning of the solution as finding the value of x; relating to its geometrical meaning should be clear
• Solving Absolute Value Equations:  solving simple given Absolute Value Equation using algebraic methods, as well as by graphing the corresponding Absolute Value Functions

UNIT 6     DATA MANAGEMENT, STATISTCS AND PROBABILITY 

• Review of mean, median, mode, the quartiles, range etc of a given set of data
• Data display and data analysis: comparing various methods of displaying data which are grouped in intervals and evaluate their effectiveness depending on the situations;  Stem and Leaf plots, Box and Whisker plots, and Histograms.
• Correlation and Lines of best fit:  meaning of correlation; examining the correlations between the variables; understand that a correlation coefficient is a description of how well a data fits a linear pattern 
• Non-Linear data and Curves of Best fit:  various types of curves like the quadratic curve, exponential curve, cubic curve, and periodic curves should be used to model the nonlinear relationship for appropriate examples of data 
• Data distribution and Normal Curve:  understanding that a frequency polygon is created by joining the mid points of the top of each bar in a histogram; identifying situations that give rise to common distributions (e.g., U-shaped, skewed, and normal)ndemonstrating an understanding of the properties of the normal distribution (e.g., the mean, median, and mode are equal; the curve (and data) is symmetric about the mean); understand that a normal curve is based upon a certain type of histogram with infinitely small bins

• Probability:  distinguish between two events that are dependent and independent using reasoning and calculations

UNIT 7     TRIGONOMETRY 

• Similar Triangles:  Observing relationships in similar triangles; using similarity properties of proportionality to solve problems; 
• Trigonometric Ratios:  Definition of the three trig ratios (Sine, Cosine, and Tangent) as the ratios of the sides of a right triangle; the reciprocals of the three primary trig ratios; understand that the primary trig ratios are equivalent for the equal angles in similar right triangles
• Trigonometric ratio Values of special angles:  Use Pythagorean Theorem and analytical proofs to determine the exact values for the sine, cosine, and tangent of 0^o, 30 ^o, 45 ^o, 60 ^o, and 90 ^o; use calculators to determine the values of trig ratios; 
• Trigonometric Identities:  Basic Trigonometric Identities like:  sin² x+cos² x=1; sin x= cos(90−x); tan x= ^{sin x} ; understand what identities are; test statements to see cos x if they are identities; and understand why each ones of these identities are identities
• Application of trigonometric ratios:  Calculating the side lengths and angles of triangles; their use in the determination of lengths, distances and height, angles of elevations (measured from the horizontal up) and angles of depressions (measured from the horizontal down); their use in the calculation of areas of polygons; In all of these, calculators may be used as appropriate, in fact its use is encouraged where appropriate
• Vectors and Bearing:  meaning of vectors and bearing; use of Pythagorean theorem and trigonometric ratios in solving vector and bearing problems  

UNIT 8     GEOMETRY 

• Reflectional or Mirror Symmetry: compare 2-D and 3-D mirror symmetry; lines of symmetry in a 2-D shape; planes of symmetry in a 3-D shape; properties of reflectional or mirror symmetry; 
• Rotational or Turn Symmetry:  compare 2-D and 3-D rotational symmetry; the centre of rotation; the order of turn symmetry; the axis of rotation for 3-D shapes;  
• Reasoning:  distinguish between inductive and deductive reasoning using both mathematical and non-mathematical reasoning; use inductive and deductive reasoning such as generalizing relationships, proving theorems and proving or disproving conjectures.
• Constructions:  construction of perpendicular bisector of a line; construction of angle bisector; meaning of construction
• Construct circumcirlces and incircles of a triangle using perpendicular and angle bisector constructions; location of cirmcumcentr and incentres; 
• Construct the Centre of Gravity or Centroid of a triangle using median and altitudes constructions; explore the relationship among the medians; explore relationships among the altitudes
• Use paper folding:  as a way to construct bisector of a line, bisector of an angle, altitude of a triangle; as a way to locate centre of gravity of a triangle, centre of a circle, etc

WEIGHTING OF MARKS FOR THE END OF THE YEAR EXAMINATION

	UNITS	PERCENTAGE MARK
1	Matrices and Network	11
2	Number and Operation	12
3	Linear Functions and Relations	13
4	Measurement	11
5	Quadratic and Absolute Value Functions	15
6	Data management and Statistics	14
7	Trigonometry	14
8	Geometry	10
	Total	100

MODE OF ASSESSMENT

There are two types of assessment, depending on what you do with them:  Formative Assessment and Summative Assessment.  Formative Assessment is observation to guide further instruction; and the observation is normally not measured, or its measurement is not recorded to grade the students.  Summative Assessment is used to determine a mark or a grade.  There are various ways provided to accomplish formative and summative assessments (Please see the “Teacher’s Guide to Understanding Mathematics, Textbook for class X”).  The mode of assessment given here is for summative assessment of students in class X.  However, observations and analysis made on students’ performance in these summative assessments could very well be used for further instructions.  

In class X, students’ mathematical assessment will be done by two agencies:  The School (or the subject teacher) and the Bhutan Board of Examinations Division (BBED).  The overall weight the school has for the final assessment of the students is 20%, and the rest 80% is determined by the BBED.  The school based assessment is called Internal Assessment, and the BBED carried out assessment is referred to as External Assessment.

Internal Assessment – 20%

The subject teacher will carry out the summative of the students, from the start of the academic session up to the Trail examinations, which lead to the final examinations in December, which is conducted by the BBED.  The mode of the internal assessment will be as per the following break-downs:

 Year beginning to mid-year

Unit Tests:  At the end of each unit, a unit test should be conducted.  It should normally be carried out during one of the class periods.  The unit tests can be directly used or adapted from the ones provided in the Teacher’s Guide, including the marking schemes.  The teacher should keep proper record of the students’ achievement in the series of unit tests.  A minimum of two unit tests should be conducted before the mid-term exams, and the average of the total should be worked out to be worth 5%, and entered onto student’s progress report card.  Please get more information on unit test from the Teacher’s Guide.

Home Works:  Reasonable amounts of home works should be assigned quite regularly. More importantly, they should be checked, and prompt feedback provided to the students on their works. The teacher will check at least two times each student’s home works during the first half term of the year; they can devise their own marking scheme.  The average mark from the total should be worked out to be worth 5% for entering onto the students’ progress report card.  

Performance Tasks and Assessment Interviews:  Performance Tasks require students to perform some mathematical tasks usually requiring problem solving and communication:  they are often hands on activities.  It is not appropriate to give marks or numerical grades to assess students on performance task.  So, a rubric is used to guide the assessment.  Assessment Interviews mean interacting and interviewing students on the concepts learned; asking questions; asking for reasoning; and explanations; and evening demonstrations of their understanding.  Both these two methods of assessments are excellent alternatives to the traditional paper and pencil test assessments.  They can cater to assessing other important aspects of mathematics like problem solving, communication, and reasoning in a better and in-depth manner.  Teachers should carry out at least one performance task and one assessment interview during the first half term of the year.  The average from using these two methods of assessment should then be worked out to be worth 5% for entering in the student’s progress report card.  

Please get more information on Performance Task and Assessment Interviews from the Teacher’s guide and the samples provided with some of the units.

Mid-term examination:  The mid-term examination may be modeled on the Trial Examinations model provided below.  The mark obtained in it should be brought down to 25% for entering into the progress report card.

Mid-year to Year-end:

Unit tests:  To be done similarly as during the first half term of the year, but with the units covered after the mid term examination.

Home works:  To be done similarly as during the first half term of the year.

Performance Tasks and Assessment Interviews:  To be done similarly as during the first half term of the year, but with the units covered after the midterm examination.

Trial Examination (November):  The Trial examinations paper will be set for 100 marks, with the writing time of 3 hours.  The paper will consist of three sections:  Sections A, B and C.   

Section A will be composed of 10 multiple choice questions, and will carry a total of 20 marks.  

Section B will be composed of about 10 to 12 questions requiring short answers, and will carry a total of 32 marks.  

Section C will be composed of 8 pairs of questions, each pair set from one of the 8 units.  Candidates are required to attempt only one question from each of the pairs provided.  The questions making up the pairs should be of equivalent level of difficulty.   Each single question will be worth 6 marks, which then gives a total of 48 marks to this section.  The questions should be composed of inter-related sub questions, designed to test in-depth knowledge and understanding on a particular concept.

Care should be taken to reflect the marks accorded for each unit as per the weighting given below:

	UNITS	PERCENTAGE MARK
1	Matrices and Network	11
2	Number and Operation	12
3	Linear Functions and Relations	13
4	Measurement	11
5	Quadratic and Absolute Value Functions	15
6	Data management and Statistics	14
7	Trigonometry	14
8	Geometry	10
	Total	100

Care should also be taken in the preparation of questions having a balance of them requiring conceptual understanding, problem solving, communication, reasoning, and applications of procedural knowledge and skills.  Some questions should cross strands or units.  Along with these, test blue print based on Blooms Taxonomy would also need to be used in the preparation of the paper.

Candidates are permitted to use scientific calculators in the examinations.

The marks obtained out of 100 in this examination should be worked out to be worth 45% for entering in to the students’ progress report card.

The assessments done up to the trial examinations, as would then be reflected or recorded onto the students progress report cards will be out of 100 %.  This over all student achievement will then need to be brought down to be out of 20, and sent to the Bhutan Board of Examinations when asked by BBED in its specified format.

External Assessment – 80%

As already explained, the external assessment consists of the final examination conducted by the Bhutan Board of Examinations Division in December.  This examination carries a weight of 80% of the overall student assessment in class X.  It is therefore clear that this examination is high stake for the students.  But, if done correctly and consistently during the course of the year with the series of internal assessments, the external examination will not be any strange, for it will be based purely on the syllabus.  In fact, the paper will be the exact model of the Trial Examinations outlined above.  For this reason it is not elaborated here. 

TEXTBOOKS AND REFERENCES 

Understanding Mathematics Textbook for class X – published by CAPSD 2007

Teacher’s Guide to Understanding Mathematics Textbook for class X – published by CAPSD 2007, for teachers as reference