ADDITIONAL MATHEMATICS SYLLABUS
FOR FORM I---IV.
2010
FORM ONE TOPICS/SUBTOPICS/SPECIFIC OBJECTIVES
{1}.NUMBERS.
--- Number Patterns.+generate different number patterns.+apply number patterns.
---Rules for Divisibility. +state the rules for divisibility. +apply the rules of divisibility on natural numbers.
{2}.SYMMETRY.
---Symmetrical Figures. +Identify different symmetrical figures/shapes/ objects in the surroundings.+draw different symmetrical shapes.
--- Lines Of Symmetry. +draw lines of symmetry.+describe rotational symmetry.
----Patterns with Shapes. +create patterns with shapes. +draw different simple patterns.
{3}. ALGEBRA.
----Simplifying Expressions. +Collect like terms in an algebraic expression. +Simplify algebraic expressions.
----Solving Equations. +Solve equations involving absolute values. +Solve word problems involving linear simultaneous equations.
----Transposition of Formulae . + rearrange a given formula to make one variable the subject. +solve problems given some of the variables.
----Inequalities. +Solve linear inequalities. + Locate the solution of linear inequality on the number line.
{4}. GEOMETRICAL CONSTRUCTIONS.
---Proportional Division Of a Line Segment. +Divide a given line segment into equal parts by constructions.
----Angles Of a Polygon. +derive the formula for sum of interior angles and exterior angles of any polygon. +apply the formula to compute sum of angles in degrees for any polygon.
----Construction Of Polygons. +Construct different regular polygons with more than four sides.
{5}. COORDINATE GEOMETRY.
---Graphs Of Linear Equations. + draw a graph of a linear equation. +form an equation given a linear graph. +solve linear simultaneous equations by graphical method.
---Collinear Points. +describe collinear points.
+identify collinear points.
----Parallel and Perpendicular Lines.+identify parallel Lines. + Identify perpendicular Lines. +Solve problems involving parallel and perpendicular lines in the coordinate plane.
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FORM TWO.
TOPICS/SUB-TOPICS/SPECIFIC OBJECTIVES
{1}.ALGEBRA
---Simultaneous Equations. +solve algebraically simultaeous equations {one linear and one quadratic }. + solve graphically simultaneous equations {one linear and one quadratic }.+ form simultaneous equations from word problems.
{2}.VARIATIONS.
----Direct Variations. +interpret direct variations. + solve problems on direct variations. + draw graphs of direct variations.
---Inverse Variations. + interpret inverse variations. +solve problems on inverse variations. + draw graphs of inverse variations.
----Joint Variations. + interpret joint variations. +solve problems on joint variations.
{3}.LOGIC.
---Statements/ propositions. +define a mathematical statement. +distinguish between simple and compound statements. +identify symbols used for logical connectives.
----Truth Tables. +construct truth tables. +identify tautologies and contradictions using truth tables. + apply truth table in simple electrical circuits.
---Arguments. +state logical arguments. + identify the basic propositiob in an argument. +determine the validity of an argument using truth tables.
{4}.LOCUS.
---Locus on a Fixed Point .
+describe the locus of a point moving at equal distances from a fixed point in a plane. +trace the locus of a point moving at equal distances from a fixed point in a plane.
----Locus on Two Fixed Points.
+ describe the locus of a point equidistant from two fixed points. +trace the locus of a point equidistant from two fixed points in a plane.
----Locus on a Line. +describe the locus of a point moving at a fixed distance from a fixed line in a plane. +trace the locus of a point moving at equal distances from a fixed line in a plane.
-----Locus On Intersecting Lines. +describe the locus of a point moving at equal distances from two intersecting lines. +trace the locus of a point moving at equal distances from two intersecting lines in a plane.
{5}. SETS.
---Operations On Sets. +find the union of three given sets. +find the intersection of three given sets.
----Number Of Members in a Set. + find the number of elements in the union and intersection of three sets. + solve problems invoving three sets.
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FORM THREE.
TOPICS/SUBTOPICS/SPECIFIC OBJECTIVES.
{1}.SETS.
--- Set Properties. +state commutative ,associative ,distributive and identify properties of sets. +apply set properties in simplifying set expressions. +use venn diagrams to verify distributive , associative and commutative properties.
----De Morgan"s Laws. +state De Morgan"s laws for two sets. +apply De Morgan"s Laws in simplifying set expressions.
{2}.EQUATIONS AND REMAINDER THEOREM.
--- Roots Of Quadratic Equations. +write the general form of a quadratic equation. +calculate the sum and product of the roots of a quadratic equation. +use sums and products of roots to form and solve equations.
+ use sums and products of quadratic equations to solve equation.
----The Remainder Theorem. +divide a polynomial of degree up to three by another polynomial of lower degree. +find the remainder using the remainder theorem.
{3}. FUNCTIONS.
----Rational Functions. +identify rational functions. +find the domain and range of rational functions. +perform basic operations on rational functions. +draw graphs of rational functions.
{4}.STATISTICS.
---Measures Of Central Tendency + find quartiles of data.
+Calculate a mean of data by estimated mean.
-----Measures Of Dispesion .
+ Calculate the variance of given data.
+Calculate the standard deviation of given data.
{5}.TRIGONOMETRY.
----Trigonometrical identinties.+derive the trigonometric identities. +state the compound angle formulae. +simplify expressions involving compound angles. +deduce the double angle formulae from the compound angle formulae.+ Use the double angle formulae in solving trigonometric problems.
-----Trigonometric Equations.+ solve simple trigonometric equations up to second degree.+ Simplify trigonometric expressions.
{6}.DIFFERENTIAION.
---- The Derivative Of a Function. +explain the concept of derivative. +write down derivative notations.
----Techniques Of Differentiation. + differentiate a polynomial function from first principles. +differentiate polynomials term by term , products and quontients. +find the derivatives of simple trigonometric functions.
-----Applications Of Differentiation. + solve problems involving rates of change. +deduce relative maximum and minimum of a function. +find turning points and points of inflexion of curves. +sketch a curve without using a table of values. +find the equation of a tangent to a curve at a given point. + find the equation of a line normal to a curve at a given point.
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FORM FOUR.
TOPICS/SUBTOPICS/SPECIFIC OBJECTIVES.
{1}. INTEGRATION.
----The Integral. +interpret an integral expression.+ write down integral expressions using the integral notation. +explain the concept of definite and indefinite integrals.
----Integration of Functions. +find the indefinite integral of a polynomial expression and of simple trigonometric functions.+
evaluate definite integrals of a polynomial expression and simple trigonometric functions.
---Applications Of Integration. + find the area under a curve. + find volume of revolution of simple curves about the axes.
{2}. COORDINATE GEOMETRY.
-----Division Of a Line Segment In a given Ratio. + determine the coordinates of a point dividing a line segment in a given ratio.
---- distance of a Point From a Line. +calculate the perpendicular distance from a point to a line.
----The Angle Between Two Intersecting Lines. +determine the angle between two interesting lines.
----The Equation Of a Circle . +Derive the general equation of a circle. +Apply the equation of a circle in solving mathematical problems.
{3}. PLAN AND ELEVATIONS.
----Orthogonal Projection. +draw orthogonal projections of plane figures onto a line and of three dimensional figures onto plane.
----Scale Drawing. +construct simple plans using scales.
----Plan , Front and Side Elevations. +draw plans and elevations. +interpret simple technical drawings.
{4}.PERMUTATIONS AND COMBINATIONS.
----Permutations. +explain the concept of fundamental Principle of Counting {FPC}. + apply the Fundamental Principle Of Counting{FPC}. + explain the concept of permutation. +apply permutations in solving problems.
----Combinations. +show practically a combination of things. +explain the concept combinations. +apply combinations in solving problems.
{5}. PROBABILITY.
-----Mutually Exclusive Events. +
explain the concept of mutually exclusive events. +
determine the probability of mutually exclusive events.
----Independent Events. +explain the concept of independent events. + find the probablity of independent events.
{6}.CONDITIONAL PROBABILITY.+ explain the concept of conditional probability of combined events. +calculate the conditional probability of combined events. +apply conditional probability in solving problems from real life situations.
{6}.VECTORS.
---Components of a vector. +represent a vector in a plane.
+write components of a plane vector.
---Dot Product. +explain the concept of dot product of two vectors in a plane. +calculate the dot product of two vectors in a plane. +apply dot product in solving problems.
---Cross Product. +explain the concept of cross product of two vectors. +find cross product of two vectors in a plane. +apply cross product of vectors in solving problems.
{7}. MATRICES AND LINEAR TRANSFORMATION .
--- Matrices. +add 3x3 matrices. + subtract 3x3 matrices. +multiply a 3x 3 matrix by a scalar. +calculate the determinant of a 3 x 3 matrix. +multiply two matrices of the order up to 3 x3. +find the inverse of 3x3 matrix. + use 3 x 3 matrices in solving systems of linear simultaneous equations in three unknowns.
----Linear Transformations. +define a linear transformation. + use matrix method to reflect a point P( x, y ) in the line y=mx. + use matrix method to rotate a point ( x ,y ) about the origin.
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REFERENCE.
© Ministry of Education and Vocational Training. First Edition 2005 . First Education 2010.
Designed and prepared by :
Tanzania Institute of Education. P.O BOX 3504, Dar es Salaam, Tanzania.
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