Mathematics Syllabus

Objectives — candidates should be able to:

• ✓perform four basic operations (x, +, −, ÷)
• ✓convert one base to another
• ✓perform operations in modulo arithmetic

Objectives — candidates should be able to:

• ✓perform basic operations (x, +, −, ÷) on fractions and decimals
• ✓express to specified number of significant figures and decimal places
• ✓calculate simple interest, profit and loss per cent; ratio proportion, rate and percentage error
• ✓solve problems involving share and VAT

Objectives — candidates should be able to:

• ✓apply the laws of indices in calculation
• ✓establish the relationship between indices and logarithms in solving problems
• ✓solve equations involving indices
• ✓solve problems in different bases in logarithms
• ✓simplify and rationalize surds
• ✓perform basic operations on surds

Objectives — candidates should be able to:

• ✓identify types of sets, i.e. empty, universal, complements, subsets, finite, infinite and disjoint sets
• ✓solve problems involving cardinality of sets
• ✓solve set problems using symbols
• ✓use Venn diagrams to solve problems involving not more than 3 sets

Objectives — candidates should be able to:

• ✓find the subject of the formula of a given equation
• ✓apply factor and remainder theorem to factorize a given expression
• ✓multiply, divide polynomials of degree not more than 3 and determine values of defined and undefined expression
• ✓factorize by regrouping difference of two squares, perfect squares and cubic expressions; etc.
• ✓solve simultaneous equations – one linear, one quadratic
• ✓interpret graphs of polynomials including applications to maximum and minimum values

Objectives — candidates should be able to:

• ✓solve problems involving direct, inverse, joint and partial variations
• ✓solve problems on percentage increase and decrease in variation

Objectives — candidates should be able to:

• ✓solve problems on linear and quadratic inequalities
• ✓interpret graphs of inequalities

Objectives — candidates should be able to:

• ✓determine the nth term of a progression
• ✓compute the sum of A. P. and G.P
• ✓sum to infinity of a given G.P.

Objectives — candidates should be able to:

• ✓solve problems involving closure, commutativity, associativity and distributivity
• ✓solve problems involving identity and inverse elements

Objectives — candidates should be able to:

• ✓perform basic operations (x, +, −, ÷) on matrices
• ✓calculate determinants
• ✓compute inverses of 2 x 2 matrices

Objectives — candidates should be able to:

• ✓identify various types of lines and angles
• ✓solve problems involving polygons
• ✓calculate angles using circle theorems
• ✓identify construction procedures of special angles, e.g. 30º, 45º, 60º, 75º, 90º etc.

Objectives — candidates should be able to:

• ✓calculate the perimeters and areas of triangles, quadrilaterals, circles and composite figures
• ✓find the length of an arc, a chord, perimeters and areas of sectors and segments of circles
• ✓calculate total surface areas and volumes of cuboids, cylinders, cones, pyramids, prisms, spheres and composite figures
• ✓determine the distance between two points on the earth’s surface

Objectives — candidates should be able to:

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

Objectives — candidates should be able to:

• ✓determine the midpoint and gradient of a line segment
• ✓find the distance between two points
• ✓identify conditions for parallelism and perpendicularity
• ✓find the equation of a line in the two-point form, point-slope form, slope intercept form and the general form

Objectives — candidates should be able to:

• ✓calculate the sine, cosine and tangent of angles between -360º ≤ Ɵ ≤ 360º
• ✓apply these special angles, e.g. 30º, 45º, 60º, 75º, 90º, 105º, 135º to solve simple problems in trigonometry
• ✓solve problems involving angles of elevation and depression
• ✓solve problems involving bearings
• ✓apply trigonometric formulae to find areas of triangles
• ✓solve problems involving sine and cosine graphs

Objectives — candidates should be able to:

• ✓find the limit of a function
• ✓differentiate explicit algebraic and simple trigonometrical functions

Objectives — candidates should be able to:

• ✓solve problems involving applications of rate of change, maxima and minima

Objectives — candidates should be able to:

• ✓solve problems of integration involving algebraic and simple trigonometric functions
• ✓calculate area under the curve (simple cases only)

Objectives — candidates should be able to:

• ✓identify and interpret frequency distribution tables
• ✓interpret information on histogram, bar chart and pie chart

Objectives — candidates should be able to:

• ✓calculate the mean, mode and median of ungrouped and grouped data (simple cases only)
• ✓use Ogive to find the median, quartiles and percentiles

Objectives — candidates should be able to:

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

Objectives — candidates should be able to:

• ✓solve simple problems involving permutation and combination

Objectives — candidates should be able to:

• ✓solve simple problems in probability (including addition and multiplication)