top of page  Target Students - Grade 12 students who did not achieve a satisfactory grade of C and above on their BGCSE Math examinations.

Course Objectives

Upon completion of this course, students should be able to:

1.         use the laws of indices in solution of related problems

2.         solve different kinds of algebraic equations by more than one method

3.         differentiate between ratio and proportion and solve related problems

4.         apply the correct formulae in calculating areas of plane geometric figures and  volumes of solids

5.         become familiar with the plotting of linear and quadratic graphs

6.         apply linear inequalities to simple linear programming

7.         use matrices to perform mathematics operations, including the solution of simultaneous equations

Course outline

1.         Indices and Standard form

1.1       Laws of indices (examples of integer power)

1.2       Square roots (what they are and how to simplify them)

1.3       General roots and fractional indices-

Apply laws of indices to fractional indices

1.4       Manipulation of numbers in standard form

2.         Algebra

2.1       Review solution of simple linear equations

2.2       Review solution of fractional linear equations with numerical  denominators

2.3       Solution of simultaneous linear equations by methods of elimination and

substitution

2.4       Factorization of quadratic expressions, perfect squares, and difference of

two squares

2.5       Solution of quadratic equations by factors and by formula

2.6       Solution of simultaneous equations where one is a quadratic equation

2.7       Transposition of and substitution into formulae

3.         Ratio and Proportion

3.1       Expressing the relationship between two quantities as a ratio

3.2       Proportions

3.3       Differentiate between ratio and rate

3.4       Solve a proportion for the missing item

3.5       Direct and inverse proportion

3.6       Direct and inverse variation

4.         Mensuration

4.1       Problem solving involving areas of plane figures: rectangles, triangles,

circles, trapezoids and parallelograms

4.2       Lengths of arcs and areas of sectors of circles

4.3       Volumes of solids of uniform cross-sectional area

4.4       Volumes of cuboids, spheres and cones

4.5       Problems involving volumes: eg. material in a box or a pipe

4.6       Surface areas of cuboids, spheres, cones and solids of uniform cross-sectional area

5.1       Solutions of simple linear equations and solution of simultaneous

equations, both linear, as well as one quadratic and one linear

5.2       Construction and solution of equations of quadratic graphs where roots are

given by intersections with the x-axis

6.         Linear inequalities

6.1       Review solution of linear inequalities with solution represented on a

number line

6.2       Cartesian plane: graphing the solution of a set of linear inequalities in two

variables

6.3       solving word problems involving linear inequalities

6.4       Simple linear programming where the polygon region is given

7.         Similarity and Enlargement, and Congruent triangles

7.1       Identification of similar figures

7.2       Problems using scale factors of dimensions, area and volume

7.3       Demonstrations of constructions

7.4       Identification of congruent triangles

8.         Matrices

8.1       Uses of matrices

8.2       Order

8.3       Matrix operations: addition, subtraction, and scalar and matrix

multiplication

8.4       Identity and inverse of 2x2 matrices

8.5       Solutions of simultaneous linear equations using matrices 