05-12-2017, 10:20 PM

TOPICS/CONTENTS/NOTES

OBJECTIVES

SECTION I: NUMBER AND NUMERATION

1. Number bases:

(a) operations in different number bases from 2 to 10;

(b) conversion from one base to another including fractional parts.

Candidates should be able to:

i. perform four basic operations (x,+,-,÷)

ii. convert one base to another.

2. Fractions, Decimals, Approximations and Percentages:

(a) fractions and decimals;

(b) significant figures;

© decimal places;

(d) percentage errors;

(e) simple interest;

(f) profit and loss percent;

(g) ratio, proportion and rate;

(h) shares and valued added tax (VAT).

Candidates should be able to:

i. perform basic operations

(x,+,-,÷) on fractions and decimals;

ii. express to specified number of significant figures and decimal places;

iii. calculate simple interest, profit and loss percent; ratio proportion and rate;

iv. Solve problems involving share and VAT.

3. Indices, Logarithms and Surds:

(a) laws of indices;

(b) standard form;

© laws of logarithm;

(d) logarithm of any positive number to a given base;

(e) change of bases in logarithm and application;

(f) relationship between indices and logarithm;

(g) surds.

Candidates should be able to:

i. apply the laws of indices in calculation;

ii. establish the relationship between indices and logarithms in solving problems;

iii. solve problems in different bases in logarithms;

iv. simplify and rationalize surds;

v. perform basic operations on surds.

4. Sets:

(a) types of sets

(b) algebra of sets

© venn diagrams and their applications.

Candidates should be able to:

i. identify types of sets, i.e empty, universal, complements, subsets, finite, infinite and disjoint sets;

ii. solve problems involving cardinality of sets;

iii. solve set problems using symbol;

iv. use venn diagrams to solve problems involving not more than 3 sets.

SECTION II: ALGEBRA.

1. Polynomials:

(a) change of subject of formula

(b) factor and remainder theorems

© factorization of polynomials of degree not exceeding 3.

(d) multiplication and division of polynomials

(e) roots of polynomials not exceeding degree 3

(f) simultaneous equations including one linear one quadratic;

(g) graphs of polynomials of degree not greater than 3.

Candidates should be able to:

i. find the subject of the formula of a given equation;

ii. apply factor and remainder theorem to factorize a given expression;

iii. multiply and divide polynomials of degree not more than 3;

iv. factorize by regrouping difference of two squares, perfect squares and cubic expressions; etc.

v. solve simultaneous equations - one linear, one quadratic;

vi. interpret graphs of polynomials including applications to maximum and minimum values.

2. Variation:

(a) direct

(b) inverse

© joint

(d) partial

(e) percentage increase and decrease.

Candidates should be able to:

i. solve problems involving direct, inverse, joint and partial variations;

ii. solve problems on percentage increase and decrease in variation.

3. Inequalities:

(a) analytical and graphical solutions of linear inequalities;

(b) quadratic inequalities with integral roots only.

Candidates should be able to:

i. solve problems on linear and quadratic

inequalities;

ii. interprete graphs of inequalities.

4. Progression:

(a) nth term of a progression

(b) sum of A. P. and G. P.

Candidates should be able to:

i. determine the nth term of a progression;

ii. compute the sum of A. P. and G.P;

iii. sum to infinity of a given G.P.

5. Binary Operations:

(a) properties of closure, commutativity, associativity and distributivity;

(b) identity and inverse elements (simple cases only).

Candidates should be able to:

i. solve problems involving closure, commutativity, associativity and distributivity;

ii. solve problems involving identity and inverse elements.

6. Matrices and Determinants:

(a) algebra of matrices not exceeding 3 x 3;

(b) determinants of matrices not exceeding 3 x 3;

© inverses of 2 x 2 matrices

[excluding quadratic and higher degree equations].

Candidates should be able to:

i. perform basic operations (x,+,-,÷) on matrices;

ii. calculate determinants;

iii. compute inverses of 2 x 2 matrices.

SECTION III: GEOMETRY AND TRIGONOMETRY

1. Euclidean Geometry:

(a) Properties of angles and lines

(b) Polygons: triangles, quadrilaterals and general polygons;

© Circles: angle properties, cyclic quadrilaterals and intersecting chords;

(d) construction.

Candidates should be able to:

i. identify various types of lines and angles;

ii. solve problems involving polygons;

iii. calculate angles using circle theorems;

iv. identify construction procedures of special angles, e.g. 30°, 45°, 60°, 75°, 90° etc.

2. Mensuration:

(a) lengths and areas of plane geometrical figures;

(b) lengths of arcs and chords of a circle;

© Perimeters and areas of sectors and segments of circles;

(d) surface areas and volumes of simple solids and composite figures;

(e) the earth as a sphere:- longitudes and latitudes.

Candidates should be able to:

i. calculate the perimeters and areas of triangles, quadrilaterals, circles and composite figures;

ii. find the length of an arc, a chord, perimeters and areas of sectors and segments of circles;

iii. calculate total surface areas and volumes of cuboids, cylinders. cones, pyramids, prisms, spheres and composite figures;

iv. determine the distance between two points on the earth's surface.

3. Loci:

locus in 2 dimensions based on geometric

principles relating to lines and curves.

Candidates should be able to:

identify and interpret loci relating to parallel lines, perpendicular bisectors, angle bisectors and circles.

4. Coordinate Geometry:

(a) midpoint and gradient of a line segment;

(b) distance between two points;

© parallel and perpendicular lines;

(d) equations of straight lines.

Candidates should be able to:

i. determine the midpoint and gradient of a line segment;

ii. find the distance between two points;

iii. identify conditions for parallelism and perpendicularity;

iv. find the equation of a line in the two-point form, point-slope form, slope intercept form and the general form.

5.Trigonometry:

(a) trigonometrical ratios of angels;

(b) angles of elevation and depression;

© bearings;

(d) areas and solutions of triangle;

(e) graphs of sine and cosine;

(f) sine and cosine formulae.

Candidates should be able to:

i. calculate the sine, cosine and tangent of angles between - 360° ≤ θ ≤ 360°;

ii. apply these special angles, e.g. 30°, 45°, 60°, 75°, 90°, 105°, 135° to solve simple problems in trigonometry;

iii. solve problems involving angles of elevation and depression;

iv. solve problems involving bearings;

v. apply trigonometric formulae to find areas of triangles;

vi. solve problems involving sine and cosine graphs.

SECTION IV: CALCULUS

I. Differentiation:

(a) limit of a function

(b) differentiation of explicit

algebraic and simple

trigonometrical functions -

sine, cosine and tangent.

Candidates should be able to:

i. find the limit of a function

ii. differentiate explicit algebraic and simple trigonometrical functions.

2. Application of differentiation:

(a) rate of change;

(b) maxima and minima.

Candidates should be able to:

solve problems involving applications of rate of change, maxima and minima.

3. Integration:

(a) integration of explicit

algebraic and simple

trigonometrical functions;

(b) area under the curve.

Candidates should be able to:

i. solve problems of integration involving algebraic and simple trigonometric functions;

ii. calculate area under the curve (simple cases only).

SECTION V: STATISTICS

1. Representation of data:

(a) frequency distribution;

(b) histogram, bar chart and pie chart.

Candidates should be able to:

i. identify and interpret frequency distribution tables;

ii. interpret information on histogram, bar chat and pie chart

2. Measures of Location:

(a) mean, mode and median of ungrouped and grouped data - (simple cases only);

(b) cumulative frequency.

Candidates should be able to:

i. calculate the mean, mode and median of ungrouped and grouped data (simple cases only);

ii. use ogive to find the median, quartiles and percentiles.

3. Measures of Dispersion:

range, mean deviation, variance and standard deviation.

Candidates should be able to:

calculate the range, mean deviation, variance and standard deviation of ungrouped and grouped data.

4. Permutation and Combination:

(a) Linear and circular arrangements;

(b) Arrangements involving repeated objects.

Candidates should be able to:

solve simple problems involving permutation and combination.

5. Probability:

(a) experimental probability (tossing of coin,

throwing of a dice etc);

(b) Addition and multiplication of probabilities

(mutual and independent cases).

Candidates should be able to:

solve simple problems in probability (including addition and multiplication).

OBJECTIVES

SECTION I: NUMBER AND NUMERATION

1. Number bases:

(a) operations in different number bases from 2 to 10;

(b) conversion from one base to another including fractional parts.

Candidates should be able to:

i. perform four basic operations (x,+,-,÷)

ii. convert one base to another.

2. Fractions, Decimals, Approximations and Percentages:

(a) fractions and decimals;

(b) significant figures;

© decimal places;

(d) percentage errors;

(e) simple interest;

(f) profit and loss percent;

(g) ratio, proportion and rate;

(h) shares and valued added tax (VAT).

Candidates should be able to:

i. perform basic operations

(x,+,-,÷) on fractions and decimals;

ii. express to specified number of significant figures and decimal places;

iii. calculate simple interest, profit and loss percent; ratio proportion and rate;

iv. Solve problems involving share and VAT.

3. Indices, Logarithms and Surds:

(a) laws of indices;

(b) standard form;

© laws of logarithm;

(d) logarithm of any positive number to a given base;

(e) change of bases in logarithm and application;

(f) relationship between indices and logarithm;

(g) surds.

Candidates should be able to:

i. apply the laws of indices in calculation;

ii. establish the relationship between indices and logarithms in solving problems;

iii. solve problems in different bases in logarithms;

iv. simplify and rationalize surds;

v. perform basic operations on surds.

4. Sets:

(a) types of sets

(b) algebra of sets

© venn diagrams and their applications.

Candidates should be able to:

i. identify types of sets, i.e empty, universal, complements, subsets, finite, infinite and disjoint sets;

ii. solve problems involving cardinality of sets;

iii. solve set problems using symbol;

iv. use venn diagrams to solve problems involving not more than 3 sets.

SECTION II: ALGEBRA.

1. Polynomials:

(a) change of subject of formula

(b) factor and remainder theorems

© factorization of polynomials of degree not exceeding 3.

(d) multiplication and division of polynomials

(e) roots of polynomials not exceeding degree 3

(f) simultaneous equations including one linear one quadratic;

(g) graphs of polynomials of degree not greater than 3.

Candidates should be able to:

i. find the subject of the formula of a given equation;

ii. apply factor and remainder theorem to factorize a given expression;

iii. multiply and divide polynomials of degree not more than 3;

iv. factorize by regrouping difference of two squares, perfect squares and cubic expressions; etc.

v. solve simultaneous equations - one linear, one quadratic;

vi. interpret graphs of polynomials including applications to maximum and minimum values.

2. Variation:

(a) direct

(b) inverse

© joint

(d) partial

(e) percentage increase and decrease.

Candidates should be able to:

i. solve problems involving direct, inverse, joint and partial variations;

ii. solve problems on percentage increase and decrease in variation.

3. Inequalities:

(a) analytical and graphical solutions of linear inequalities;

(b) quadratic inequalities with integral roots only.

Candidates should be able to:

i. solve problems on linear and quadratic

inequalities;

ii. interprete graphs of inequalities.

4. Progression:

(a) nth term of a progression

(b) sum of A. P. and G. P.

Candidates should be able to:

i. determine the nth term of a progression;

ii. compute the sum of A. P. and G.P;

iii. sum to infinity of a given G.P.

5. Binary Operations:

(a) properties of closure, commutativity, associativity and distributivity;

(b) identity and inverse elements (simple cases only).

Candidates should be able to:

i. solve problems involving closure, commutativity, associativity and distributivity;

ii. solve problems involving identity and inverse elements.

6. Matrices and Determinants:

(a) algebra of matrices not exceeding 3 x 3;

(b) determinants of matrices not exceeding 3 x 3;

© inverses of 2 x 2 matrices

[excluding quadratic and higher degree equations].

Candidates should be able to:

i. perform basic operations (x,+,-,÷) on matrices;

ii. calculate determinants;

iii. compute inverses of 2 x 2 matrices.

SECTION III: GEOMETRY AND TRIGONOMETRY

1. Euclidean Geometry:

(a) Properties of angles and lines

(b) Polygons: triangles, quadrilaterals and general polygons;

© Circles: angle properties, cyclic quadrilaterals and intersecting chords;

(d) construction.

Candidates should be able to:

i. identify various types of lines and angles;

ii. solve problems involving polygons;

iii. calculate angles using circle theorems;

iv. identify construction procedures of special angles, e.g. 30°, 45°, 60°, 75°, 90° etc.

2. Mensuration:

(a) lengths and areas of plane geometrical figures;

(b) lengths of arcs and chords of a circle;

© Perimeters and areas of sectors and segments of circles;

(d) surface areas and volumes of simple solids and composite figures;

(e) the earth as a sphere:- longitudes and latitudes.

Candidates should be able to:

i. calculate the perimeters and areas of triangles, quadrilaterals, circles and composite figures;

ii. find the length of an arc, a chord, perimeters and areas of sectors and segments of circles;

iii. calculate total surface areas and volumes of cuboids, cylinders. cones, pyramids, prisms, spheres and composite figures;

iv. determine the distance between two points on the earth's surface.

3. Loci:

locus in 2 dimensions based on geometric

principles relating to lines and curves.

Candidates should be able to:

identify and interpret loci relating to parallel lines, perpendicular bisectors, angle bisectors and circles.

4. Coordinate Geometry:

(a) midpoint and gradient of a line segment;

(b) distance between two points;

© parallel and perpendicular lines;

(d) equations of straight lines.

Candidates should be able to:

i. determine the midpoint and gradient of a line segment;

ii. find the distance between two points;

iii. identify conditions for parallelism and perpendicularity;

iv. find the equation of a line in the two-point form, point-slope form, slope intercept form and the general form.

5.Trigonometry:

(a) trigonometrical ratios of angels;

(b) angles of elevation and depression;

© bearings;

(d) areas and solutions of triangle;

(e) graphs of sine and cosine;

(f) sine and cosine formulae.

Candidates should be able to:

i. calculate the sine, cosine and tangent of angles between - 360° ≤ θ ≤ 360°;

ii. apply these special angles, e.g. 30°, 45°, 60°, 75°, 90°, 105°, 135° to solve simple problems in trigonometry;

iii. solve problems involving angles of elevation and depression;

iv. solve problems involving bearings;

v. apply trigonometric formulae to find areas of triangles;

vi. solve problems involving sine and cosine graphs.

SECTION IV: CALCULUS

I. Differentiation:

(a) limit of a function

(b) differentiation of explicit

algebraic and simple

trigonometrical functions -

sine, cosine and tangent.

Candidates should be able to:

i. find the limit of a function

ii. differentiate explicit algebraic and simple trigonometrical functions.

2. Application of differentiation:

(a) rate of change;

(b) maxima and minima.

Candidates should be able to:

solve problems involving applications of rate of change, maxima and minima.

3. Integration:

(a) integration of explicit

algebraic and simple

trigonometrical functions;

(b) area under the curve.

Candidates should be able to:

i. solve problems of integration involving algebraic and simple trigonometric functions;

ii. calculate area under the curve (simple cases only).

SECTION V: STATISTICS

1. Representation of data:

(a) frequency distribution;

(b) histogram, bar chart and pie chart.

Candidates should be able to:

i. identify and interpret frequency distribution tables;

ii. interpret information on histogram, bar chat and pie chart

2. Measures of Location:

(a) mean, mode and median of ungrouped and grouped data - (simple cases only);

(b) cumulative frequency.

Candidates should be able to:

i. calculate the mean, mode and median of ungrouped and grouped data (simple cases only);

ii. use ogive to find the median, quartiles and percentiles.

3. Measures of Dispersion:

range, mean deviation, variance and standard deviation.

Candidates should be able to:

calculate the range, mean deviation, variance and standard deviation of ungrouped and grouped data.

4. Permutation and Combination:

(a) Linear and circular arrangements;

(b) Arrangements involving repeated objects.

Candidates should be able to:

solve simple problems involving permutation and combination.

5. Probability:

(a) experimental probability (tossing of coin,

throwing of a dice etc);

(b) Addition and multiplication of probabilities

(mutual and independent cases).

Candidates should be able to:

solve simple problems in probability (including addition and multiplication).