Maths

course outline

Topics

• Number Bases - Conversion

  Conversion from one base to base 10 and vice versa. Conversion from one base to another base.

• Modular Arithmetic - Concept

  Interpretation of modulo arithmetic e.g. 6 + 4 = k(mod7), 3 x 5 = b(mod6), m = 2(mod 3), etc.

• Approximations and Significant Figures

  Approximations should be realistic e.g. a road is not measured correct to the nearest cm.

• Indices - Laws of Indices

  e.g. aˣ aʸ = aˣ⁺ʸ, aˣ÷aʸ = aˣ⁻ʸ, (aˣ)ʸ = aˣʸ, etc where x, y are real numbers and a ≠0. Include simple examples of negative and fractional indices.

• Numbers in Standard Form (Scientific Notation)

  Expression of large and small numbers in standard form e.g. 375300000 = 3.753 x 10⁸, 0.00000035 = 3.5 x 10⁻⁷. Use of tables of squares, square roots and reciprocals is accepted.

• Logarithms - Basic Rules

  e.g. log₁₀(pq) = log₁₀p + log₁₀q, log₁₀(p/q) = log₁₀p – log₁₀q, log₁₀pⁿ = nlog₁₀p. Calculations involving multiplication, division, powers and roots.

• Sequence and Series - Patterns

  Determine any term of a given sequence. The notation Uⁿ = the nth term of a sequence may be used.

• Arithmetic Progression (A.P.) and Geometric Progression (G.P.)

  Simple cases only, including word problems. (Include sum for A.P. and exclude sum for G.P).

• Sets - Concepts and Notations

  Idea of sets, universal sets, finite and infinite sets, subsets, empty sets and disjoint sets. Idea of and notation for union, intersection and complement of sets. Notations: ∈, ⊂, ∪, ∩, { }, Ø, P'( the compliment of P). Properties e.g. commutative, associative and distributive.

• Logical Reasoning - Simple Statements

  Simple statements. True and false statements. Negation of statements, implications. Use of symbols: ⇒, ⇔, use of Venn diagrams.

• Rational Numbers - Operations

  The four basic operations on rational numbers. Match rational numbers with points on the number line.

• Surds (Radicals) - Simplification and Rationalization

  Notation: Natural numbers (N), Integers (Z), Rational numbers (Q). Surds of the form a/√b and a ±√bwhere a is a rational number and b is a positive integer. Basic operations on surds (exclude surd of the form a / (b+c√d)).

• Matrices and Determinants - Determinant of a Matrix

  Application to solving simultaneous linear equations in two variables. Restrict to 2 x 2 matrices.

• Ratio, Proportions and Rates - Concepts

  Ratio between two similar quantities. Proportion between two or more similar quantities. Relate to real life situations.

• Ratio, Proportions and Rates - Financial Applications

  Financial partnerships, rates of work, costs, taxes, foreign exchange, density (e.g. population), mass, distance, time and speed. Include average rates, taxes e.g. VAT, Withholding tax, etc.

• Percentages

  Simple interest, commission, discount, depreciation, profit and loss, compound interest, hire purchase and percentage error. Limit compound interest to a maximum of 3 years.

• Financial Arithmetic - Depreciation/Amortization

  Definition/meaning, calculation of depreciation on fixed assets, computation of amortization on capitalized assets.

• Financial Arithmetic - Capital Market Instruments

  Shares/stocks, debentures, bonds, simple problems on interest on bonds and debentures.

• Variation

  Direct, inverse, partial and joint variations. Expression of various types of variation in mathematical symbols e.g. direct (z ∝ n), inverse (z ∝ 1/n), etc. Application to simple practical problems.

• Algebraic Expressions - Formulating

  e.g. find an expression for the cost C Naira of 4 pens at x Naira each and 3 oranges at y naira each. Solution: C = 4x + 3y.

• Algebraic Expressions - Factorization

  Factorization of expressions of the form ax + ay, a(b + c) + d(b + c), a² – b², ax² + bx + c where a, b, c are integers. Application of difference of two squares e.g. 49² – 47² = (49 + 47)(49 – 47) = 96 x 2 = 192.

• Linear Equations - One Variable

  Solving/finding the truth set (solution set) for linear equations in one variable.

• Linear Equations - Simultaneous in Two Variables

  Solving/finding the truth set of simultaneous equations in two variables by elimination, substitution and graphical methods. Word problems involving one or two variables.

• Quadratic Equations - Solution

  Using factorization i.e. ab = 0 ⇒ either a = 0 or b = 0. By completing the square and use of formula.

• Quadratic Equations - Forming with Given Roots

  Simple rational roots only e.g. forming a quadratic equation whose roots are -3 and 5/2 ⇒ (x + 3)(x - 5/2) = 0.

• Graphs of Linear and Quadratic Functions - Interpretation and Drawing

  Finding: (i) the coordinates of maximum and minimum points on the graph. (ii) intercepts on the axes, identifying axis of symmetry, recognizing sketched graphs.

• Graphs - Graphical Solution of Equations

  Graphical solution of a pair of equations of the form: y = ax² + bx + c and y = mx + k. Use of quadratic graphs to solve related equations e.g. graph of y = x² + 5x + 6 to solve x² + 5x + 4 = 0.

• Linear Inequalities - Graphical Solution in Two Variables

  Maximum and minimum values. Application to real life situations e.g. minimum cost, maximum profit, linear programming, etc.

• Algebraic Fractions with Binomial Denominators

  Simple cases only e.g. 1/(x-a) + 1/(x-b) = (2x-a-b)/((x-a)(x-b)) where a and b are constants and x≠a or b. Values for which a fraction is undefined e.g. 1/(x+3) is not defined for x = -3.

• Functions and Relations - Types

  One-to-one, one-to-many, many-to-one, many-to-many. Functions as a mapping, determination of the rule of a given mapping/function.

• Areas - Triangles and Quadrilaterals

  Areas of similar figures. Include area of triangle = ½ base x height and ½absinC. Areas of compound shapes.

• Areas - Surface Areas of 3D Shapes

  Surface areas of cubes, cuboids, cylinder, pyramids, righttriangular prisms, cones andspheres.

• Triangles and Polygons - Sum of Angles in a Polygon

  Sum of interior angles = (n - 2)180° or (2n – 4)right angles, where n is the number of sides.

• Circles - Chords

  Angles subtended by chords in a circle and at the centre. Perpendicular bisectors of chords.

• Construction - Angles

  Angles e.g. 90°, 60°, 45°, 30°, and an angle equal to a given angle. Include combination of these angles e.g. 75°, 105°,135°, etc.

• Equation of a line

  In the form y = mx + c and y - y₁ = m(x – x₁), where m is the gradient (slope) and c is a constant.

• Differentiation of Algebraic Functions

  Concept/meaning of differentiation/derived function, dy/dx, relationship between gradient of a curve at a point and the differential coefficient of the equation of the curve at that point. Standard derivatives of some basic function e.g. if y = x², dy/dx = 2x. If s = 2t³ + 4, ds/dt = v = 6t², where s = distance, t = time and v = velocity. Application to real life situation such as maximum and minimum values, rates of change etc.

• Integration of Simple Algebraic Functions

  Meaning/ concept of integration, evaluation of simple definite algebraic equations.

• Vectors in a Plane - Properties and Operations

  Magnitude of a vector, equal vectors, addition and subtraction of vectors, zero vector, parallel vectors, multiplication of a vector by scalar. Knowledge of graphical representation is necessary.

• Transformation - Reflection

  Reflection of points and shapes in the Cartesian Plane. Restrict Plane to the x and y axes and in the lines x = k, y = x and y = kx, where k is an integer. Determination of mirror lines (symmetry).

• Transformation - Rotation

  Rotation of points and shapes in the Cartesian Plane. Rotation about the origin and a point other than the origin. Determination of the angle of rotation (restrict angles of rotation to -180° to 180°).

• Transformation - Translation

  Translation of points and shapes in the Cartesian Plane. Translation using a translation vector.

• Transformation - Enlargement

  Draw the images of plane figures under enlargement with a given centre for a given scale factor. Use given scales to enlarge or reduce plane figures.

• Length Conversions

  1000 millimetres (mm) = 100 centimetres (cm) = 1 metre(m). 1000 metres = 1 kilometre (km)

• Mass Conversions

  1000 milligrammes (mg) = 1 gramme (g). 1000 grammes (g) = 1 kilogramme( kg ). 1000 kilogrammes (kg) = 1 tonne.