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NABTEB MATHEMATICS SYLLABUS
This course is designed to provide trainees with a sound knowledge of mathematical concepts as aids in the conceptualization, interpretation, and application of the technical soft wares and hard wares as well as to enhance their mathematical problems – solving ability in their various trades. It is also to form a basis for post secondary technical education.
Recommended: Nabteb syllabus for all subjects
All candidates are expected to answer questions from General Mathematics while those in Secretarial Studies and BookKeeping are in addition to answer questions from Commercial Mathematics.
Examination Scheme:
The examination consists of Two Papers:
 0021 – Paper I (112 Hrs)
 0022 – Paper II (212 Hrs)
The total mark for both papers is 150.
Paper I: is made up of 50 multiplechoice items for 50 marks. All candidates are expected to attempt this paper.
Paper II: Consists of three sessions namely A, B and C.
Section A consists of five questions from General Mathematics. All candidates are expected to attempt all questions. This section carries 40 marks.
Section B consists of six questions. All candidates are to attempt any four of the six questions except Secretarial and Business candidates who are to attempt only two questions. Each question carries 15 Marks.
Section C consists of four questions from Commercial Mathematics for Secretarial and Business candidates only. Candidates are expected to attempt any two out of the four questions. Each question carries 15 marks.
Candidates should be familiar with unitslength, area, cubic capacity, mass – and their abbreviations. Any currency unit used will be defined.
Examination Materials: www.flashlearners.com
Candidates are allowed to use the recommended mathematical statistical tables in the examination hall for the papers. It is strongly recommended that schools/candidates obtain copies of these tables for use through the course.
Candidates should bring rules and complete mathematical instrument set for all papers. Borrowing of instruments from other candidates in the examination hall will not be allowed. The use of noiseless, cordless and nonprogrammable calculators is allowed.
If required, the following will be provided for any paper.
 (i) Graph paper ruled in 2mm squares
 (ii) Plain drawing sheets for construction work.
General Mathematics Nabteb
Topic/objectives  Contents  Activities/Remarks 
1. Number Bases. Count and
perform 
(i) Number bases – counting in different bases: Converting from one base to another; addition, subtraction, multiplication and division in different bases.
(ii)_Modules arithmetic 
Arithmetic operation in different bases should exclude fractions. Comparison between place value system and additive system should be stressed e.g. 4520 means 4 thousands, 5 hundreds, 2 tens and 0 unit: 26 in base eight means 2 eight and 6 unit etc.
Relate to market days etc. Truth sets (solution sets) for various open sentences e.g. 3 x 2 a(mod)48+y=4(mod)9 
2. System Internationale
Unit. Solve problems involving S.I. and imperial units. 
Difference between S.I. and Imperial units of linear measures: conversion of S.I. units and vice versa: mm to m; m to km and vice versa; exercises involving time – hours, minutes and seconds  The basic units of S.I. units must be emphasized e.g the basic units of mass, length, time, area, volume are gramme, metre, second, square metre, cubic metre respectively. The advantages of S.I. units over the imperial units should be deduced by students; the use of S.I. units in science, social sciences should be brought out and exercise should be related to practical use. 
3. Fractions
Solve 
The law of equivalence of decimals and vulgar/common fractions. Vulgar fractions to decimal fractions and vice versa. Basic processes – addition, subtraction, multiplication and division – applied to decimals and fractions (vulgar/common fractions.)  Decimal fraction should be confined to two places e.g. 0.13 x 2.14 etc. Interrelationship between the different fractional systems e.g. 0.5 x 0.2 = 12 x 1/5 and 2/5 = 0.4 – 40% etc should be stressed. 
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4. Standard Forms.
Express numbers in standard forms and to the required number of significant figures decimal places. 
Standard forms, decimal places and significant figure. Rounding off number and give answer in the required number of decimal places ad significant figures; express number in standard forms; A x 10n where 1<A<10 and n is either – ve or + ve integer  
5. Ratio and Proportion .
Solve problems on ratio and proportion. 
Ratio and proportion. Relationship between ratio and proportion representative fraction Examples and exercises on direct and inverse ratios and proportions including representative fraction. 
Relate these to the students’ work in science and technical subjects. 
6. Variation  Direct, inverse and partial variations. Joint variations.  Applications to simple practical problems. 
7. Percentages, Profit and Loss. Apply the principles of percentages to fractions and decimals.  Percentages, profit and loss calculation. Conversion of fraction and decimal to percentages and vice versa; percentage change, commercial arithmetic including profit and loss, small decimal fractions. Application of profit and loss to commerce generally.  The means of transactions e.g. money, cheques, money orders, postal orders etc. should be mentioned. 
8. Simple Interest
Solve problems involving simple interest. 
Simple Interest – Calculation of Principal (P), Interest (I), Rate (R) and Time (T) using I = PRT
100 
Transformation of the formula for P.R and T should be clear. 
9. Logarithms
Apply logarithms, square And square root tables in calculations. 
Based 10 logarithms tables and anti logarithm tables, calculation involving multiplication, division, powers and roots using logarithm tables. Examples and exercise from simple to complex combination of multiplication, division, powers and roots of numbers e.g.
ˆš172.7 x 15.42 

10. Indices
Apply the laws of indices in simplification and calculation. 
Indices as a shorthand notation. Laws of indices: (a) ax x ay=ax+y (b) ax ¸ ay=axy.(c) (ax)y = axy 
The use of indices in science and technical subjects should be emphasized and exercises should be related to practical use.
Trainers should be encouraged to discover 
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the laws and deduce the meaning of ao, ax, a1
x By considering ax ¸ ax,ao¸ax 

11. Relationship Indices and Logarithms
Explain the relationship between indices and logarithms. 
Indices and logarithms as inverse operations e.g. Y = 10x x = log 10y graphsof Y = 10x (0< x < 1) Use of graph for multiplication and division. 
Students should ONLY be familiar with the graph of Y = 10x 
12. Rules of Logarithms.
Identify and apply the basic rules of Logarithms. 
Rules of Logarithms (a) Log 10 (xy) = Log 10 X + Log 10y (b) Log 10 (x) = Log 10x – Log 10yy (c ) Log 10xp = plog10xslketches and comparison with indices to be made. 

13. Arithmetic and Geometric
Progressions. (a) Identify and calculate the nth term of a given sequence in AP and GP. sum of AP and GP 
Sequences and series. Difference between AP and GP. Nth terms of AP and GP. Sum of AP and GP  Scope and depth of treatment of these topics should be limited to ordinary level mathematics. 
14. Sets
solve problems involving sets using Venn 
Meaning of set, universal set, finite and infinite sets, empty set and subsets. Idea and Notation for Union (U) intersection (Ã‡), empty (Ã†), 
Introduce set as a tool and not as a topic. Do not use set to solve exercise that can be 
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diagrams  complement of A, say (A’), disjoint sets. Venn Diagrams. Use Venn diagrams as a diagrammatic representation of sets e.g.
Blue Problem solving involving sets and classification using Venn diagrams. Classification of objects based on students experiences both in school and in the home. Compare alternative methods of solving the same exercise(s) white Red 
quickly and easily solved by other methods except for the sake of comparison.
Treatment this topic briefly. Do not use more than three sets for illustration. Include the interpretation of terms like union, intersection etc. Consider alternative methods advantage and appropriateness of solving the same exercises particularly with brighter students. 
15. Logical reasoning  Simple statements . True and false statements. Negation of 5 statements. Implication, equivalence and valid argument.  Use of symbols: ~, Ãž, ÃœÃ›
Use of Venn diagrams preferable. 
16. Surds  Simplification and Rationalization of simple surds.  Surds of the form a and Ã–b
aÃ–b whee a is rational and b is a positive integer. 
17. Algebraic Processes
Solve basic arithmetic operations with algebraic symbols. 
Like and unlike terms. Ilustrate this with objects around the students’ environments e.g. grainsrice and beans etc.
Addition, subtraction, multiplication and division of simple algebraic expression. Insertion and removal of brackets. Use of letters to represent numbers. Solution of exercises in symbolic forms e.g. if 2 pencils cost 50 kobo, hoe much would 3 pencils of the same type cost? How much will Y pencils of the same type cost? If Bayo who has 3 mangoes has 2 less than Joy, how many mangoes 
Exercise should include operations such as 4x + 7x, 8y2y; 3 x 2m; 4f + 3m – 4f + 2m etc. Emphasize the use of operations – collection of like terms removal and use of brackets.The importance of defining precisely what the symbol represents should be emphasized. Simple cases only should be treated. Substitution of values 
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has Joy? Construction and evaluation of formulae Change of subject of formulae e.g. if V = 14 Ã•d2h express d in terms of V and h etc. 
into the formulae should be included.  
18. Simple Equations
Solve problems involving simple equations. 
Simple equations, illustrate the meaning of equality with reference to simple equations by using the idea of simple balance.
Bring out the meaning of equality sign by adding or subtracting quantities to each side or by multiplying and dividing each side by a common factor (excuding each side by a common factor (excluding zero). Solving of simple equations e.g. 2y+6=4y+2 etc. Simple equations in one variable. Substitute different values for unknown in literal statements of the form k + 7 = 13. It may also be expressed in words to find the correct value e.g. to what can I add 7 to obtain a result of 13?. 
The expression “cancel out” should be avoided. 
19. Algebraic Process;
Linear simultaneous Equation. Solve linear simultaneous equations in two variables. 
Simultaneous linear equations. Solution of simultaneous linear equation of the form.
x + y = 8; 
Check the accuracy of answer by substitution. This should be encouraged. 
20. Algebraic Expressions.
(a) Solve simple equations involving fractions. (b) Factorise 
HCF and LCM. Exercises on HCF and LCM of given algebraic expression.
Simplification of algebraic fractions (with monomial denominators). Simple equations involving fractions i.e. 1 =4 x+3 x4 
Application of expression and factorization of algebraic terms to the simplification of expression such as:
1+1=5 1 +1=y+x x y xy 
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practical applications to word problems.
Factorable and nonfactorable expressions. Nonquadratic expressions. Introduction of brackets and Removing common factors in non quadratic expressions. Application of perfect squares and difference of two squares. Factorisation of expressions of the form; and their application. Factorisation of simple quadratic expressions. Exercises on factorization of simple quadratic expressions e.g. a2 + 7a + 12 = (a+3) (a+4) etc. 
Note: It is used for rapid calculation.
Use appropriate method(s) 

21. Graphs of Algebraic
Expression Solve 
Coordinates, meaning of Cartesian plane. Linear equations in two variables. Tables of values, Linear graphs, Quadratic graphs Examples on coordinates of points. Compile table of values to draw: (a) Linear Graphs (b) Two linear graphs (c) Quadratic graphs, using the same axes. Consider cost situations leading to graphs of the form: y = ax; y = ax + b etc. 
The intersection of the two lines is the solution of the two linear equations. When the two lines do not meet (i.e. parallel), there is no solution. Also where the graph of a quadratic intersect with the x, axis, the points of the intersection are the solutions of the quadratic equation. 
22. Quadratic Equations.
(a) Solve quadratic equations using appropriate method. (b) Construct quadratic equations with given roots. (c) Solve word problems 
Definition of quadratic equations. Solution of quadratic equation by factorization. Solution of quadratic equation by completing the square. Expansion of expressions like (a+b)2Given an expression of the form y = x2 + ax, and trainers should be able to find a constant term, k which can be added to make the expression a perfect square e.g. (x2 + 8x)+16=(x+k)2 etc Deduce the formula of quadratic 
The use of the ”˜scissors methods’ can also be introduced.
Compare this method with the factorization method and emphasize the advantage of one over the other. Compare this method with the previous 
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involving quadratic equations.
(d) Graphs of Linear and Quadratic function. (e) Linear Inequalities 
equation (ax2 + bx + c) from completing the square.
Solution of quadratic equation by formula method e.g. 2a Construction of quadratic equation with given roots e.g. Given the roots x = 2; x=3 Ãž (x2) (x3)= 0 Given x = 2 and x = 3 Ãž (x+2) (x3) = 0 Ãž x2 x6 = 0 (a) Coordinate plane axes ordered pairs.
quadratic functions.
y=mx+k and ax2 +bx+c=y.
gradient.
(c) Graphical solution of linear inequalities in two variables. 
methods.
Difference between an equation and expression should be emphasized. (a) the coordinate of the maximum and Obtaining minimum points from the graphs. (b) Intercepts on the axes. (c) Identifying axis of smelly recognizing sketched graphs Recognising sketched graphs. Use of quadratic graph to solve a related equation e.g. Graph of y = x2 – 5x+6 to solve x2 5x+4=0 (a) By drawing relevant tangent to determine the gradient. (b) The gradient M1 of the line joining points M1 = y2y1 X2x1 include word problems. 
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23 Plane figures
Identify plane figures by their properties 
Properties of plane figure e.g. rectangle, triangle, rhombus parallelogram, square, kite, trapezium. Quadilateral, polygon and circles. Relate the shape to solid and lead the students to draw them.  Students should be encouraged to discover the properties for themselves and faces of shapes. 
24. Perimeters and Areas of Plane Figures Circulate the perimeter and areas of simple geometric plane figures.  Meaning of perimeter and area of plane figure. Calculation of perimeters of plane figures, squares, rectangles etc. Use string to measure round the boundaries of plane figures.  Lead the students to develop the formulae for the perimeter of square, rectangle, and a circle. The use of the units cm and m should be used in the activities. 
25. Areas of Regular and
Irregular Shapes Calculate the areas of regular and irregular shapes 
Areas of regular and irregular shapes: (a) Triangle = 12 base x height (b) Rectangle = length x breadth (c) Rhombus = one side x height(d) Parallelogram = one parallel side x height(e) Square = side x side (f) Kite (g) Trapezium = 12 height x sum of parallel sides of sides) 
Lead the students to discover that there is no direct relationship between perimeter, area of shapes e.g. shapes with the same perimeters do not have the same area. 
26. Lines and Angles
Identify the different types of lines and angles. 
Definition of a point, line, parallel lines, straight lines, curve; and perpendicular lines.
Identification of different angles e.g.0 acute, obtuse, right angles, reflex, 30 , 600, 900, 1200, 1900 etc. Complimentary, and suplementary; adjacent angles, vertically opposite angles, alternate and corresponding angles. Angle measurement. 
It is pertinent that students discover these special properties of angles themselves. 
27. Polygons
(a) Identify the types of triangles and polygons. (b) Apply the sum of the angles of a triangle to 
Types of triangle and quadrilateral e.g. isosceles right angled, scalene, obtuse, equilateral triangles rhombus, parallelograms. Squares, kite etc. Types of polygon e.g. pentagon, hexagon, heptagon, octagon, decagon, practical illustration of types of polygon.  Students should discover the relationship between these plane figures e.g. rectangle, rhombus are special parallelogram, a square is a parallelogram but a parallelogram may not be a square etc. 
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calculate any interior or exterior angle of a triangle.
(c) Apply the sum of interior angles of a polygon of n sides to calculate any interior or exterior angle. 
Application of the sum of a triangle to calculate interior or exterior angles of a triangle.
Angle sum of a convex polygon. Application of sum of interior and exteriror angles of a polygon. Formulae of the sum of the interior and exterior angles of a convex polygon e.g. divide an n””sided polygon Into: (a) n – sided polygon (b) n triangles e.g. (n2) triangles n triangles formula for sum formula for sum interior angle of interior angles 
Illustrate this method with several examples before generalization is arrived at. The use of right angle(s) should also be emphasized. 
28. Constructions. Construct simple geometrical constructions  Measuring and drawing angles. Use protractors and rulers to measure and draw angles. Construction of parallel and perpendicular lines. Bisection of a line segment. Bisection of an angle.
Construction of angles equal to a given angle e.g. 300, 450 600 900, 1050, 1200 etc Construction of triangles and quadilaterals using setsquare, protractor and a pair of compasses. 
Parallel and perpendicular lines should be constructed using ruler and setsquare only. Line segment and angles bisection should be carried out using compasses and straight edge ruler. Division of a line segment into a given number of equal parts or into parts in a given ratio should be carried out. Checking the accuracy of constructions.
Neatness and accuracy should be emphasized. 
29. Loci.
Define and 
Definition of locus. Ilustrate locus based on geometric principles with a variety of  Limit the locus of points to two dimension. Locus 
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construct loci of moving points in two dimensions.  constructions and measurements on paper and also by considering practical situations e.g. sports tracks and fields, tethering goat etc. Loci of points that are: (a) at a given distance from a givenpoint.
straigth line.
points. (d) At a given segment of a straight line subtends a given angle (constant angle locus). 
of points should be shown to be directly related to parallel lines, perpendicular bisectors, angle bisectors etc. 
30. Midpoint and Intercept
Theorems. Apply the intercept and mid point theorems to solve exercises. 
Midpoint and intercept theorems. Application of the midpoint and intercept theorems to solve exercises related to the proportional division of lines.`  Note that the midpoint theorem is a special case of one of the intercept theorems. 
31. Similar Triangles
Apply the properties of similar triangles to solve exercises on plane geometrical figures and solids. 
Properties of similar triangles, Compare angles and sides of similar triangles by measurement, sliding, rotation or tracing. Application of the properties of similar triangles to solve simple problems on areas and volumes of similar plane geometrical shapes and solid respectively.  Note that in similar triangle: (a) corresponding angles are equal. (b) ratio of responding sides is a constant.Illustrate that the bisector angle on a triangle divides the opposite side in the ratio of the side containing the angles. 
32. Chord and Tangent of a Circle. (a) Illustrate with
examples the theorems associated with the chord and tangent of a circle. (b) Apply the theorem associated with Chord and tangent of a circle to 
Theorems associated with the chord and tangent of a circle; (a) equal chord substends equal angleat the circumference; (b) the angle which an arc subtends atthe circumference; (c) angles in the same segment are equal; su[pplementary in a cyclic quadrilatreral; 
Deductive proofs of these theorem are not required. Role learning of the theorem without understanding the principles should be discouraged 
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construction exercises. 
(h)a tangent is perpendicular to the radius of a circle; (i) If two circles touch, the point of contact is on the line of centre; (j) the tangents of circle from an extended point are equal; (k)the direct and transverse common tangents to two circles are equal. Application of the theorems associated with chord and tangent of a circle to construction of chains, belts, gears and sprockets, etc. 
Project work should be encouraged. 
33. Congruent Triangles.
Apply the conditions of congruency to solve exercises on triangles 
Meaning of congruent. Conditions of congruency e.g. (a) SideSideSide (SSS) (b) SideAngleSide (sas(c) SideAngleAngle (SAA) (d) Right AngleHypotenusSide (RHS) Application of conditions of congruency to solve related problems. 

34. Properties of Quadrilaterals. Solve problems involving the properties of parallelograms  Properties of: (a) Parallelogram (b) Rhombus (c ) Rectangle (d) Square Application of parallelogram properties to solve exercises. 
Practical illustration of this topic is important; trainers are encouraged to discover the relationships between and among these plane figures. 
35. CirclesArcs, Radius,
Diameter, Sector and Segment. Calculate lengths and areas related to the circle 
Parts of a circle – arc, radius diameter, sector and segment. Sector and segment. Length of arc of circles.Perimeter of sectors and segments. Draw circles, draw in various sectors and list in pairs the angle at the centre (Ã˜) and the arc (L) measured with string for 
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each circle. For each sector, compare the ratio Ã˜= L 3600 2ÐŸr Ã˜hence, deduce theformula L = 2ÐŸr Ã˜ 3600 Work ample examples on perimeters. Application of trigonometric ratios when required to determine lengths of chords. Areas of sectors and segments of a circle. 3600 ror Ã˜Ã˜ 2r sin Ã˜ Calculation of the area of a segment sector area minus triangle area. Deduce and use the formula: 

36. Mensuration Pythagoras
Theorem Apply the principles of 
Pythagors Rule. Calculation of lengths using the Pythagoras rule.  Use a square of a + b or any number you choose.
Use diagram to show that a2 + b2 = c2 
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Pythagoras’ to solve problems involving right angled triangles.  
37. Areas and Volumes of solids Calculate the surface area and volume of solid figures  Types of solid figures e.g. cuboids, cylinder, cone, pyramids, prisms, hemisphere ande frustum of cone and pyramid.
Surface areas of : Volumes of solid figure listed in (a) to (b) contents above. Fill hollow cubes and cuboids with unit cubes. Calculation of volumes of given containers, hollow solids, pipes and hollow bricks. 
It is pertinent that trainers are allowed to discover these solid figures with the aid of objects around them e.g. tins, sugar box, bowl, buckets etc.
Emphasise the formulae for the total surface area of solids e.g. cylinder = (2Ð»r2 + 2 Ð»rh) square units etc. Unit cubes can be got from sugar cubes, cubes made from local clay, wood, cubes by a local carpenter or students in a woodwork class. 
38. Longitude and Latitude
Calculate distances along lines of latitudes and longitudes. 
Definition of latitude and longitude as angles. Definition of latitude and longitude from the geographical point of view.
Relationship and comparison between the two definitions above. The earth as a sphere. 
Treat simple examples. 
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39. Irregular Geometric
Figures Solve exercises involving areas of irregular figures. 
(a) Regular and irregular plane figures. (b) Areas of irregular plane figures Use midordinate and trapezoidal rules to calculate the areas of irregular plane figures.  Trainers suggest examples. 
40. Everyday Statistics.
(a) Interpret graphs and charts. (b) Calculate statistical average with equal and unequal forms. 
Practical presentation of data using histogram, bar chart, linegraph and pie chart.
Interpretation of graphs and charts. Frequency distribution of equal and unequal forms. Identification of mode, and median in a set of data. Calculation of mean mode and median of grouped data. 
Students can work in groups and results discussed by the whole class.
Discuss which of the central measures i.e. mode, median and mean is most useful. Methods of determining median mode for grouped data, including equal class interval for grouped data. 
41. Probability.
(a) Define probability terms. (b) Solve problems on theoretical and experimental probabilities. 
Meaning of the terms: Probability, Events, Mutually exclusive events, independent events. Trials.Experimental probability. Throwing dice or tossing of coins. Number of boys and girls in different classes and corresponding probability of a girl.Theoretical probability. Theoretical consideration of short parents producing short Children. Consider also 1 short parent and 1 tall parent and probable offspring. Mutually exclusive events. Exercises on probability of mutually exclusive events. Addition and multiplication laws of probability. Illustrate the addition law in mutually exclusive events. Also illustrate the multiplication law in independent event. Interpretation of and or both/and; or either/or. 
Treat theoretical probability as a limiting value of experimental probability as a number of trials become large.
Use the addition law to solve exercises containing the word or or either/or. 
42. Trigonometry.
Apply 
Trigonometric Ratios Define the trigonometric ratios and their 
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trigonometric ratios to solve simple problems  inverse: Sinecosecant, tangent cotangent using rightangled triangle.
Trigonometric Ratios of angles greater than 900 Tables of trigonometric ratios. Use table to find value of trigonometric ratios and vice versa. elevation and depression; 12 ac Sin B and 

43. Trigonometry
Apply sine and cosine rules to solve problems 
Sine and Cosine Rules – Statement only. Application of sine and cosine rules to solve related problems e.g. problems in triangles, bearing etc.  Note when to apply each of the rules 
44. Vectors and transformation in a plane.
(i) Vectors in a plane. (ii) Transformations in the Cartesian coordinate plane. 
(i) Vector as a directed line, segment, magnitude, equal vectors, sums and differences of vectors. (ii) Parallel and equal vectors.(iii) Multiplication of a vector by a Scalar. (iv) Cartesian components of a vector (v) Reflection.(vi) Rotation. (vii) Translation. 
Column notation emphasis on graphical representation. Notation ÎŸ Vector ÎŸ ) for the zeroThe reflection of points and shapes in the x and y axes and in the lines x = k, and y = k where k is a rational number. Determination of the mirror lines of points. shapes and their images. Rotation about the origin. Use of the translation Vector. 
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COMMERCIAL MATHEMATICS
Topic/Objective  Contents  Activities/Remark 
1. Significant Figures
Identify the problems of significant digit as it relates to zero. 
Significant figures. Identification of significant digits as it relates to zero e.g. (a) a zero that falls betweensignificant digits e.g. 50502 (b)a zero that falls after a significantdigit especially when number contains decimal points e.g. 13,840 (c) a zero that falls after the last significant digits of a whole number e.g. 67000 

2. Statistical Computation
(a) State different kinds of averages and their uses. (b) Calculate statistical problems as related to basic business problems. 
Meaning of “Average” Use of an average as: (a) it provides for a summary (b) it provides for a common denominator(c) as a measure of typical size Kinds of average: (a) moving average; (b) median(c) mean; (d) weighted average (e) quartile and percentile, range, interpercentile and interquartile range. Mean of distribution and its calculations, range, variance and standard deviation. 

3. Ratios and Proportions.
Solve exercises on proportions and proportional parts. 
Ratios and proportion. Express two or more quantities as a ratio. Divide a given quantity in a given proportion. Sole problems in direct and indirect ratio and proportion. The concept of partnership in simple business operations. Solve exercises in simple business operations. Meaning of percentages.
Conversion between fractions decimals and percentage. 
Study of application such as speeds, productivity, consumption and reciprocal. 
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4. Percentages.
Solve exercises in percentages related to buying and selling 
(a) Calculation of percentage increase (b)Explain the concepts “buying
price” , “cost price” and “selling price” price, cost price, and selling price. (d) Explain “Makeup” and percentage “markdown percentage”. 
When treating fractions, decimals and percentages, buying and selling should be taken into account. 
5. Profit and Loss
Solve exercises involving profit and loss 
Meaning of “profit and Loss” and (a) Difference between (b) “Gross Profit” and “Net profit”,“Gross Loss” and “Net Loss” (c) Calculation of gross and netprofit as percentage of sales. (d)Calculation of probability ratios, gross profit and net profit as percentages of sales. 

6. Aliquot Parts Commission and Discount Solve problems involving Aliquot parts commission and discount 
Meaning of Aliquot parts (a) Exercises involving ratio e.g.dividing profit between A,B, andC in the ratio 4:2:1 or 4:2:3 (b)Commission where commissions are to be received or paid as a percentage of profit. commission. and quantity discount. (e) Solve problems involving discount and commission. 

7. Costing
Identify the various element by costs 
Costing (a) Elements of cost e.g. buyingprices, tax, commission transport and discount, labour, storage delivery charges.(b)Calculation of unit cost of a product taking into accounts the elements of cost. (c ) Solve problems involving cost. 
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8. Budgeting.
Applying the principle of simple budgeting. 
(a) Meaning of budgeting (b) Budgeting techniques (c) Elements of budgeting i.e.income, expenditure etc. (d) Preparation of simple budget fora family or small firms. (e) Comparison of actual with the budget. 

9. Cost and Selling Price
Solve problems involving cost and selling price. 
Cost and Selling Prices (a) Calculation of gross profit as apercentage on cost (b)Calculation of gross profit as apercentage of selling. (c) Calculation of gross price when profit on cost percentage and price are given. profit as a percentage and cost price is given. 

10. Simple and Compound Interest.
Solve simple problem involving simple and compound interest. 
Difference between simple and compound interest. Simple Interest – exercises on simple interest.Compound interest – exercises on compound interest. 
The formula and tabulation methods of calculating compound interest should be taught. 
11. Depreciation
Calculate depreciation. 
Meaning of depreciation. Difference between depreciation and present value. Methods of computing depreciation e.g. (a) straight – line method (b) reducing balance method, (c) sum of the digits method, Calculation of depreciation. 

12. Instalmental Payment and Hire Purchase Solve problems involving instalmental payments and Hire Purchase.  Difference between instalmental payment and hire purchases. Solve problems on hire purchases, instalmental payment and mortgages.  
13. Rates.
Convert one currency to another currency i.e. foreign exchange. 
Exchange rates. Rates and their uses. Conversion of one currency to another currency. 
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14. Rates, Income Tax, Insurance and
Freights. Solve problems involving income tax, rates on insurance and freights. 
Use of rates in relationship with various payments like taxes, insurance, freight rates etc. Calculation of various rates. Computation of income tax at various income levies.  
15. Payrolls
Prepare payment of wages 
Wages and payroll. Enumeration of elements involved in preparing wage e.g. salaries, allowances, overtime bonus, tax, rent and other rates, professional payments, pension etc. Preparation of payroll cards, wage sheet, pay slips etc. Preparation of cash analysis for wage payment. Preparation of wage packets for individuals  The merits and demerits of the use of computer in preparing payrolls and wages should be mentioned. 
16. Stock and Shares.
Solve simple problems in stock and shares 
Meaning of stock, shares, debentures and bonds. Enumeration of different kinds of stocks and shares e.g. preferential, ordinary, debenture shares. Solve simple exercises on stocks, shares, debentures and bonds.  
17. Bankruptcy
Solve problems involving bankruptcy. 
Definition of bankruptcy. Calculation of dividends in bankruptcy. Solve problems in bankruptcy. 
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