Math+Syllabus

=**MATHEMATICS SYLLABUS FOR YEAR 10**:=

**Rationale**
Most pupils studying at these levels aim to pursue higher studies. For some, mathematics will become core to what they study later, while for others it will be a support in another area of study. The topics in classes IX and X not only go deeper than what the students have studied in earlier classes but also introduce them to abstract topics. This level of mathematics will adequately equip the students in functional numeracy as well as give them a good foundation for pursuing mathematics further.

**Aims**
Teachers should guide the pupils to develop their:
 * Understanding of mathematical concepts and their applications for further studies in mathematics
 * Logical reasoning skills
 * Communication skills in mathematics
 * Skills of accuracy and clear logical thinking for effective communication of mathematics ideas and understanding
 * Confidence and skills in using mathematical procedures and solving problems
 * Learning Experiences

Students should be able to:

 * Explore, discover, describe and record mathematical patterns and relationships
 * Solve problems individually and in groups
 * Share ideas and take risks in doing it
 * Relate mathematics to the situations relevant to their daily lives

**Learning Outcomes**
These experiences will help the students to:
 * Become alert to the reasonableness of results
 * Read mathematical information and interpret formulae in problem solving
 * Apply logical thinking pattern to draw conclusions
 * Use reasoning to interpret the mathematical procedures and arguments used
 * Gain adequate knowledge in mathematics to serve as a foundation to pursue it at higher levels and other subjects of specialization needing mathematics

=** SYLLABUS 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 52
 * 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 xaxis; 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 53 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 non-linear 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) demonstrating 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 0o, 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 sin cos x x x= ; understand what identities are; test statements to see 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 54 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

Australian Syllabus:
1. New South Wales: 2. Western Australia 3. New South Wales