Mathematics

course outline

Topics

• Number Bases

  Count and perform basic arithmetic operations in different bases, including modular arithmetic.

• Standard Forms

  Express numbers in standard forms and to the required number of significant figures or decimal places.

• Percentages, Profit and Loss

  Apply the principles of percentages to fractions and decimals, and perform calculations related to profit and loss.

• Logarithms

  Apply logarithms and anti-logarithm tables in calculations involving multiplication, division, powers, and roots.

• Arithmetic and Geometric Progressions

  Identify sequence patterns and calculate the nth term and sum of arithmetic and geometric progressions.

• Sets

  Solve problems involving sets using Venn diagrams and understanding set notation.

• Logical reasoning

  Understand simple statements, truth values, negation, implication, equivalence, and valid arguments.

• Algebraic Processes

  Solve basic arithmetic operations with algebraic symbols, including simplifying expressions and changing the subject of formulae.

• Algebraic Process; Linear simultaneous Equation

  Solve linear simultaneous equations in two variables using elimination or substitution methods and apply to word problems.

• Algebraic Expressions

  Factorise simple quadratic and non-quadratic expressions, and solve equations involving fractions.

• Quadratic Equations

  Solve quadratic equations using factorization, completing the square, or the formula method, and construct quadratic equations with given roots.

• Graphs of Linear and Quadratic function

  Plot and interpret graphs of linear and quadratic functions, and solve equations graphically.

• Linear Inequalities

  Solve linear inequalities in one variable and represent them on a number line, and solve linear inequalities in two variables graphically.

• Plane figures

  Identify plane figures by their properties, including triangles, quadrilaterals, and polygons.

• Perimeters and Areas of Plane Figures

  Calculate the perimeters and areas of simple geometric plane figures like squares and rectangles.

• Areas of Regular and Irregular Shapes

  Calculate the areas of various regular and irregular shapes using specific formulae.

• Lines and Angles

  Identify the different types of lines and angles, and understand their properties and measurement.

• Polygons

  Identify types of triangles and polygons, and apply angle sum properties to calculate interior and exterior angles.

• Constructions

  Construct simple geometrical figures and angles using instruments like protractors and compasses.

• Loci

  Define and construct loci of moving points in two dimensions based on given conditions.

• Mid-point and Intercept Theorems

  Apply the intercept and mid-point theorems to solve exercises related to the proportional division of lines.

• Similar Triangles

  Apply the properties of similar triangles to solve exercises on plane geometrical figures and solids.

• Chord and Tangent of a Circle

  Illustrate and apply theorems associated with the chord and tangent of a circle.

• Congruent Triangles

  Apply the conditions of congruency (SSS, SAS, SAA, RHS) to solve exercises on triangles.

• Properties of Quadrilaterals

  Solve problems involving the properties of parallelograms, rhombuses, rectangles, and squares.

• Mensuration Pythagoras Theorem

  Apply the principles of Pythagoras' theorem to solve problems involving right-angled triangles.

• Areas and Volumes of solids

  Calculate the surface area and volume of various solid figures including cuboids, cylinders, cones, and pyramids.

• Longitude and Latitude

  Calculate distances along lines of latitude and longitude, treating the Earth as a sphere.

• Irregular Geometric Figures

  Solve exercises involving areas of irregular figures using methods like the mid-ordinate and trapezoidal rules.

• Everyday Statistics

  Interpret graphs and charts, and calculate statistical averages (mean, median, mode) for grouped data.

• Probability

  Define probability terms and solve problems on theoretical and experimental probabilities, including mutually exclusive and independent events.

• Trigonometry

  Apply trigonometric ratios to solve simple problems involving heights, distances, and areas.

• Vectors and transformation in a plane

  Understand vectors as directed line segments and perform transformations like reflection, rotation, and translation in the Cartesian plane.

• Significant Figures

  Identify the role and problems of significant figures, particularly concerning zeros.

• Statistical Computation

  State different kinds of averages and their uses, and calculate statistical problems related to basic business scenarios.

• Ratios and Proportions

  Solve exercises on proportions and proportional parts, including partnerships and percentages.

• Percentages

  Solve exercises in percentages related to buying and selling, including price calculations and mark-ups/downs.

• Profit and Loss

  Solve exercises involving profit and loss, including gross and net profit calculations as percentages of sales.

• Aliquot Parts Commission and Discount

  Solve problems involving aliquot parts, commission, and various types of discounts.

• Costing

  Identify the various elements of costs and calculate the unit cost of a product.

• Budgeting

  Apply the principles of simple budgeting, including income, expenditure, and comparison of actual results with the budget.

• Cost and Selling Price

  Solve problems involving cost and selling price, including calculating profit as a percentage of cost or selling price.

• Simple and Compound Interest

  Differentiate between and solve problems involving simple and compound interest.

• Depreciation

  Calculate depreciation using different methods like straight-line and reducing balance.