**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. **2. Fractions, Decimals, Approximations ** **and Percentages: **
(a) fractions and decimals; (b) significant figures; (c) 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). **3. Indices, Logarithms and Surds: ** (a) laws of
indices; (b) standard form; (c) 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. **4. Sets: ** (a) types of sets (b) algebra of sets (c) venn diagrams and their applications. **SECTION II: ALGEBRA. ** **1. Polynomials: **
(a) change of subject of formula (b) factor and remainder theorems (c)
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. **2. Variation: ** (a) direct (b) inverse (c) joint (d) partial (e) Percentage increase and decrease. **3. Inequalities: ** (a) analytical and graphical solutions of linear inequalities; (b) Quadratic inequalities with integral roots only. **4. Progression: ** (a) nth term of a progression (b) Sum of A. P. and G. P. **5. Binary Operations: **
(a)properties of closure, commutativity, associativity and
distributivity; (b)identity and inverse elements (simple cases only). **6. Matrices and Determinants: **
(a)algebra of matrices not exceeding 3 x 3; (b)determinants of matrices
not exceeding 3 x 3; (c)inverses of 2 x 2 matrices [excluding quadratic
and higher degree equations]. **SECTION III: GEOMETRY AND ** **TRIGONOMETRY. ** **1. Euclidean Geometry: **
(a) Properties of angles and lines (b) Polygons: triangles,
quadrilaterals and general polygons; (c) Circles: angle properties,
cyclic quadrilaterals and intersecting chords; (d) construction. **2. Mensuration: **
(a) lengths and areas of plane geometrical figures; (b) lengths of arcs
and chords of a circle; (c) 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.
**3. Loci: ** Locus in 2 dimensions based on geometric principles relating to lines and curves. **4. Coordinate Geometry: **
(a) midpoint and gradient of a line segment; (b) distance between two
points; (c) parallel and perpendicular lines; (d) equations of straight
lines. |
**5. Trigonometry: **
(a)trigonometrical ratios of angels; (b)angles of elevation and
depression; (c)bearings; (d)areas and solutions of triangle; (e)graphs
of sine and cosine; (f)Sine and cosine formulae. **SECTION IV: CALCULUS **
I. Differentiation: (a) limit of a function (b) Differentiation of
explicit algebraic and simple trigonometrical functions – sine, cosine
and tangent. **2. Application of differentiation: ** (a) rate of change; (b) Maxima and minima. **3. Integration: ** (a)integration of explicit algebraic and simple trigonometrical functions; (b)Area under the curve. **SECTION V: STATISTICS ** **1. Representation of data: ** (a) frequency distribution; (b) Histogram, bar chart and pie chart. **2. Measures of Location: ** (a)mean, mode and median of ungrouped and grouped data – (simple cases only); (b)Cumulative frequency. **3. Measures of Dispersion: ** Range, mean deviation, variance and standard deviation. **4. Permutation and Combination: ** (a)Linear and circular arrangements; (b)Arrangements involving repeated objects. **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: ** i.perform four basic operations (x,+,-,÷) ii.Convert one base to another. **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. **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. **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. **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. **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. **Candidates should be able to: ** i.solve problems on linear and quadratic inequalities; ii.interprete graphs of inequalities. **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. |
**Candidates should be able to: **
i.solve problems involving closure, commutativity, associativity and
distributivity; ii.Solve problems involving identity and inverse
elements. **Candidates should be able to: ** i.perform basic operations (x,+,-,÷) on matrices; ii.calculate determinants; iii.Compute inverses of 2 x 2 matrices. **Candidates should be able to: **
iii.identify various types of lines and angles; iv.solve problems
involving polygons; v.calculate angles using circle theorems;
vi.Identify construction procedures of special angles, e.g. 30º, 45º,
60º, 75º, 90º etc. **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. **Candidates should be able to: ** Identify and interpret loci relating to parallel lines, perpendicular bisectors, angle bisectors and circles. **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. **Candidates should be able to: **
i.calculate the sine, cosine and tangent of angles between - 360º ≤ Ɵ ≤
360º; ii.apply these special angles, e.g. 30º, 45º, 60º, 75º, 90º,
1050, 135º 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. **Candidates should be able to: ** i.find the limit of a function ii.Differentiate explicit algebraic and simple trigonometrical functions. **Candidates should be able to: ** Solve problems involving applications of rate of change, maxima and minima. **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). **Candidates should be able to: ** i.identify and interpret frequency distribution tables; ii.Interpret information on histogram, bar chat and pie chart. **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. **Candidates should be able to: ** Calculate the range, mean deviation, variance and standard deviation of ungrouped and grouped data. **Candidates should be able to: ** Solve simple problems involving permutation and combination. **Candidates should be able to: ** Solve simple problems in probability (including addition and multiplication). |

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