SYLLABUS

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1. NUMBER AND NUMERATION
2. ALGEBRAIC PROCESSES
3. Fractions, Decimals, Approximations and Percentages
4. MENSURATION
5. Indices, Logarithms and Surds
6. PLANE GEOMETRY
7. TRIGONOMETRY
8. STATISTICS AND PROBABILITY
9. Calculus


1. NUMBERS AND NUMERATION
S/NO TOPICS CONTENTS
i. Positive and Negative integers. Rational numbers Relationships between integers and rational numbers.
ii. Fractions, decimals and approximations
(a) Basic operations on fractions and decimals.
(b) Decimal places and significant figures
(c) Accuracy of results correct to the nearest unit. E.g. cm, 1km, m3
iii Ratio, proportions and rate Household Arithmetic, Commercial Arithmetic.
iv Percentages Simple interest, compound interest, profit and loss discount, commission and hire purchase. Percentage error.
v. Number Bases Binary numbers
vi. Indices
(a) Laws of indices
(b) Numbers in standard form (indices as a shorthand notation).
vii. Logarithms (a) Relationships between indices and logarithms e.g. x=10y; y= logo10x
(b) Basic rules of logarithms
(c) Use of Base 10 logarithm tables and antilogarithm tables.
viii Sets (a) Idea of a set, universal, finite and infinite sets, empty sets and sub-sets. Idea of a notation for union, intersection, disjoint and
complements of sets.
(b) Venn diagrams as diagrammatic representation of sets.
(c) Uses of Venn diagrams to solve problems involving classification

ix Sequences (a) Pattern of sequences Determine the nth term of a given sequence.
(b) Arithmetic progression (A.P) and Geometric progression (G.P).

(i) ALGEBRAIC PROCESSES
Algebraic Expressions.
(a) Use of letters to represent numbers.
(b) Formulating algebraic expressions from given situations.
(c) Simplifying/solving algebraic expressions.
(ii) Simple operations on algebraic expressions (a) Expansion
(b) Factorization
(iii) Variations Direct, inverse, joint and partial variations.
(iv) Change of the subject of a formula (a) Change of the subject of a formula
(b) Substitutions
(v) Algebraic fractions Basic Operations applied to algebraic fractions with
(a) monomial denominator
(b) binomial denominators
(c) undefined fractions.
(vi) Solutions of linear equations (a) Linear equations in one variable
(b) Simultaneous linear equations in two Variables
(vii) Quadratic equations (a) Solution of quadratic equations
(b) Construction of quadratic equations with given roots.
(viii) Graphs of linear and quadratic functions (a) Coordinate plane axes, ordered pairs
(b) Computation of tables of values
(c) Drawing graphs of linear and quadratic functions.
(d) Interpretation of graphs
(e) Graphical solution of the form Y = mx + k and ax2 + bx + c = y
(f) Drawing of a tangent to a curve
(g) Use of tangent to determine gradient
(ix) Linear inequalities (a) Solution of linear inequalities in one variable
(b) Representation on the number line
(c) Graphical solution of linear inequalities in two variables

(i) MENSURATION lengths and perimeters
(a) Use of Pythagoras theorem, Pythagorean triple
(b) Use of the sine and cosine rules to determine lengths and distances.
(c) Lengths of an arc of circle perimeters of sectors and segments
(d) Latitudes and longitudes
(ii) Areas
(a) Triangles and special quadrilaterals: rectangles, parallelograms and trapezia
(b) Circles, sectors and segments, of circles
(c) Surface areas of cube, cuboid, cylinder, right triangular prisms, cones and spheres.
(iii) Volumes (a) Volumes of cubes, cuboids, cylinders, cones, right pyramids and spheres.
(b) Volumes of similar solids

PLANE GEOMETRY Types of Angles
(i) Definition and identification of special angles.
(ii) Angles and intercepts on parallel line
(a) Angles at a point add up to 360o
(b) Adjacent angles on a straight line are Supplementary
(c) Vertically opposite angles are equal
(d) Alternate angles are equal
(e) Corresponding angles are equal
(f) Interior opposite angles are supplementary
(g) Intercept theorem.
(iii) Triangles and polygons
(a) The sum of angles of a triangle is two right angles
(b) Areas of triangles on the same or equal base and between the same parallels are equal
(c) The exterior angle of a triangle is equal to the sum of the two interior opposite angles.
(d) Congruent triangles
(e) Properties of special triangles:- isosceles, equilateral, right angle.
(f) Properties of special quadrilaterals:- parallelogram, rhombus, rectangle, square, trapezium and kite
(g) Properties of similar triangles.
(h) The sum of the interior angle of a polygon of n sides is (2n-4) right angles.
The sum of exterior angles of a polygon is 4 right angles (360o).
(iv) Circles
(a) The angle, which an arc of a circle subtends at the center, is twice that which it subtends at any point on the remaining part of the
circumference
(b) Angles in the same segment are equal.
(c) Chords:- Angles subtended by chords in a circle, perpendicular bisectors of chords, angles in alternate segment.
(d) Any angle subtended at the circumference by a diameter is a right angle.
(e) Angles in opposite segment of a cyclic quadrilateral are supplementary.
(f) If a straight line touches a circle and from the point of contact a chord is drawn, each angle which this chord makes with the tangent is equal
to the angle in the alternate segment.

(vi) Constructions.

Loci.
(a) Bisectors of angles and line segment.
(b) Construction of angles of sizes 30o, 45o, 60o and 90o.
(c) Construction of lines perpendicular to each other and lines parallel to given lines.
(d) Construction of an angle equal to a given angle
(e) Construction of three and four-sided plane figures given certain conditions.

(a) A locus as a set of points which satisfies a given condition
(b) Knowledge of the following loci and their intersections on the Cartesian plane:-
(i) Points at a given distant from a given point.
(ii) Points equidistant from two given straight lines
(iii) Points equidistant from two given points.


TRIGONOMETRY
Sine, cosine and tangent ratios of acute angles

Sine, cosine and tangent ratios of any angle

Graphs of sine and cosine of angles
(a) Sine, cosine and tangent with respect to an acute angle.
(b) Use of tables.
(c) Trigonometry ratios of special angles 30o, 45o and 60o

Sine, cosine and tangent of angles from 0o to 360o

Graphs of sine and cosine for 0o < x > 360o
(iv) Angles of elevation and depression
(a) Calculation of angles of elevation and depression
(b) Application to heights and distances
(v) Bearings
(a) Bearing of one point from another
(b) Calculation of distances and angles


vi STATISTICS AND PROBABILITY

Measure of central tendency:-

Graphical representation of data

Cumulative frequency

Measures of dispersion

Experimental and Theoretical probabilities

Addition and multiplication of probabilities

Mean, median and mode of a set of data

Pie charts, bar charts and histogram

(a) Frequency distribution table and frequency polygons
(b) Cummulative frequency table:- percentiles, quartiles and semi-interquarter range

Range, interquartile range, mean deviation and standard deviation.

(a) Experimental probability
(b) Theoretical probability

(a) Addition of probabilities for mutually exclusive
events.
(b) Multiplication of probabilities for independent
events.