Yakili | FORM 4 MATHEMATICS

Course / Course Details

FORM 4 MATHEMATICS

Form 4
Math

By - Secondary Mathematics Tutor
4 students
166 Hours 40 Min
(0)

Course Requirements

All what was done from points, lines, plane figures, angles, metric system form basic knowledge and skills necessary to continue this module on geometry. This module continues with some aspects of vectors and vector geometry. It goes further to simple transformation, the loci and geometrical construction, trigonometry then circle and circle theorems. It ends with then earth as a sphere. This module is within the families of situations: Representations and transformation of plane shapes within the environment. Three categories of actions are involved namely: Perception of the physical environment, production of plane shapes and transformation of the physical environment and determination of measures.

Course Description

This module will continue to improve upon learners’ understanding and appreciation of pattern, precision and beauty in natural and cultural forms. Learners will also develop the ability to visualize, measure, represent, describe and compare plane figures in the environment, use vector methods to solve problems and associate vectors to people and things in motion, use sine, cosine or tangent in right-angled triangles to determine distances. In addition, learners will develop the sense of order, rigour in working, ability to represent, accuracy and sense of precision and initiation to scientific method in handling life situations. The ability to construct will help learners to be able to represent and interpret the physical environment and also be able to investigate and model situations in the environment. As a result, they will be able to make sensible estimates, verify results, measure accurately, locate positions in real life as well as be alert to the reasonableness of measurements and calculation results.

Critical thinking, creativity and sense of initiative that learners will also develop are attitudes that will contribute to make a citizen autonomous and responsible in carrying out his social roles.

Course Outcomes

Plane geometry is one of the main parts of the Mathematics syllabus due to the expected learning outcome. Measuring in general relates directly to the scientific, technological and economic world of the learner. Accurate measuring and calculations involving lengths, angles and areas, representations and descriptions are an integral part of chemistry, Biology, Physics and other parts of Mathematics. Vectors and trigonometry are used in Physics while transformation, circle are applied in other science subjects. The earth as a sphere shows the application of mathematics to understand nature. Transformation is used by computer and video.

Course Curriculum

15 chapters
211 lectures
9 quizzes
166 Hours 40 Min total length

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1 Three Kinds of Numbers

2 Min

Three Kinds of Numbers

2 Number Line

2 Min

Number Line

3 Addition and Subtraction of Directed Numbers (addition on the number line)

3 Min

Addition and Subtraction of Directed Numbers (addition on the number line)

4 Addition and Subtraction of Directed Numbers (subtraction on the number line)

3 Min

Addition and Subtraction of Directed Numbers (subtraction on the number line)

5 Addition Without the Number Line

3 Min

Addition Without the Number Line

6 Subtraction without the number line

3 Min

Subtraction without the number line

7 Multiplication of directed numbers

3 Min

Multiplication of directed numbers

8 Division of directed numbers

3 Min

Division of directed numbers

9 Order of operations

3 Min

Order of operations

10 Vulgar fractions

2 Min

Vulgar fractions

11 Equivalent fractions

3 Min

Equivalent fractions

12 Adding fractions

3 Min

Adding fractions

13 Subtracting fractions

3 Min

Subtracting fractions

14 Multiplication of fractions

5 Min

Multiplication of fractions

15 Division of fractions

5 Min

Division of fractions

16 Converting fractions

5 Min

Converting fractions

17 Introduction to Circles and Parts of Circles

3 Min

Introduction to Circles and Parts of Circles

18 More practice with fractions

5 Min

More practice with fractions

19 Decimal fractions

5 Min

Decimal fractions

20 Adding and subtracting decimals

5 Min

Adding and subtracting decimals

21 Multiplication and division by powers of ten

5 Min

Multiplication and division by powers of ten

22 Multiplication of decimals

3 Min

Multiplication of decimals

23 Division of decimals

3 Min

Division of decimals

24 More practice with decimals

3 Min

More practice with decimals

25 Percentages and decimals

3 Min

Percentages and decimals

26 Percentage relations

3 Min

Percentage relations

27 Profit and loss

3 Min

Profit and loss

28 Calculating cost price

3 Min

Calculating cost price

29 Simple interest

3 Min

Simple interest

30 Finite and infinite sets; universal set, null set, singleton set

3 Min

Finite and infinite sets; universal set, null set, singleton set

31 Cardinality of finite sets

3 Min

Cardinality of finite sets

32 Subsets

3 Min

Subsets

33 Intersection and union of sets

3 Min

Intersection and union of sets

34 Subsets and Complement of a set

3 Min

Subsets and Complement of a set

35 Equal and Equivalent Sets

3 Min

Equal and Equivalent Sets

36 Power set with finite set of cardinality not more than 3

3 Min

Power set with finite set of cardinality not more than 3

37 Venn Diagrams

2 Min

Venn Diagrams

38 The Unit Vector In The Direction Of A Given Vector

4 Min

39 The Power Zero

3 Min

The Power Zero

40 Roots

3 Min

Roots

41 Negative Indices

3 Min

Negative Indices

42 Operations with Indices

3 Min

Operations with Indices

43 Fractional Indices

3 Min

Fractional Indices

44 Logarithms

3 Min

Logarithms

45 Degree of accuracy (rounding off, rounding down, and rounding up)

4 Min

Degree of accuracy (rounding off, rounding down, and rounding up)

46 Approximating to a specified number of significant figures

3 Min

Approximating to a specified number of significant figures

47 Approximating to a specified number of decimal places

3 Min

Approximating to a specified number of decimal places

48 Approximation error, absolute error and percentage error

4 Min

Approximation error, absolute error and percentage error

49 Maximum and minimum values from a given approximation

3 Min

Maximum and minimum values from a given approximation

50 Manipulation of numbers in standard form

4 Min

Manipulation of numbers in standard form

51 Indices

3 Min

Indices

52 Logarithms

3 Min

Logarithms

53 Changing the base of an logarithm

3 Min

Changing the base of an logarithm

54 Simple logarithmic equations

3 Min

Simple logarithmic equations

55 Surds and surds form

3 Min

Surds and surds form

56 Rules for simplifying surds

3 Min

Rules for simplifying surds

57 Calculations that involve surds

3 Min

Calculations that involve surds

58 Matrices

5 Min

Matrices

59 Matrices - Columns and rows

4 Min

Matrices - Columns and rows

60 Square and rectangular matrices

3 Min

Square and rectangular matrices

61 Null, diagonal, and unit matrices

3 Min

Null, diagonal, and unit matrices

62 Equality of matrices

3 Min

Equality of matrices

63 Addition and subtraction of matrices

3 Min

Addition and subtraction of matrices

64 Multiplication of matrices

3 Min

Multiplication of matrices

65 The identity matrix

3 Min

The identity matrix

66 The transpose of a matrix

3 Min

The transpose of a matrix

67 The determinant of a 2-by-2 matrix

4 Min

The determinant of a 2-by-2 matrix

68 The inverse of a 2-by-2 matrix

4 Min

The inverse of a 2-by-2 matrix

69 Using inverse matrices to solve equations

3 Min

Using inverse matrices to solve equations

70 Solving simultaneous equations using matrices

3 Min

Solving simultaneous equations using matrices

71 Route and incidence matrices

3 Min

Route and incidence matrices

72 Representing vectors using line segments

2 Min

Representing vectors using line segments

73 Coordination in two dimensions

3 Min

Coordination in two dimensions

74 Expressing vectors using base unit vectors i and j

3 Min

Expressing vectors using base unit vectors i and j

75 Free and position vectors in the x-y plane

3 Min

Free and position vectors in the x-y plane

76 Collinear and orthogonal vectors

3 Min

Collinear and orthogonal vectors

77 Inverse of a vector

2 Min

Inverse of a vector

78 Modulus (magnitude) of a vector

3 Min

Modulus (magnitude) of a vector

79 Direction of a vector

3 Min

Direction of a vector

80 Addition and subtraction of vectors

3 Min

Addition and subtraction of vectors

81 Multiplication of a vector by a scalar

3 Min

Multiplication of a vector by a scalar

82 Introduction To Circle Theorems

5 Min

83 The Circumference of a Circle

6 Min

84 The Area of Sector

5 Min

85 The Area Of A Segment

7 Min

86 Subtraction of Vectors

4 Min

87 The First Theorem Under Tangents

4 Min

88 The Second Theorem of Tangents

6 Min

89 Third Theorem Of Tangent

7 Min

90 Degree of accuracy (rounding off, rounding down, and rounding up)

4 Min

91 Approximating to a specified number of significant figures

3 Min

92 Approximating to a specified number of decimal places

3 Min

93 Approximation error, absolute error and percentage error

3 Min

94 Manipulation of numbers in standard form

4 Min

95 Indices

3 Min

96 Logarithms

3 Min

97 Changing the base of an logarithm

3 Min

98 Simple logarithmic equations

3 Min

99 Operations with Logarithms

3 Min

Operations with Logarithms

100 Percentage change

3 Min

Percentage change

1 The Circumference of a Circle

6 Min

2 Introduction to Circles and Parts of Circles

3 Min

3 Area of segment

7 Min

4 Area of sector

5 Min

5 Circle and associated vocabularies: radius, diameter, circumference, arc, chord, tangent, sector, segment, secant, Centre;

5 Min

6 Area of circle

5 Min

1 the unit vector in the direction of a given vector

4 Min

2 Subtraction of Vectors

4 Min

3 Multiplication of a vector by a matrix

5 Min

4 Coordinates in 2- dimension

5 Min

5 Collinear and orthogonal vectors

5 Min

6 Position vectors in the x-y plane

5 Min

7 Vectors expressed in terms of unit vectors i and j

5 Min

8 Dot or scalar product of two vectors;

5 Min

9 Angles between two vectors

5 Min

10 Vector geometry

5 Min

11 Mid point theorem

5 Min

12 Proportional division of a vector

5 Min

1 Introduction to circle theorems

5 Min

2 Angle properties;

5 Min

3 Tangent properties

5 Min

4 Cyclic quadrilateral

5 Min

5 -Intersecting chords theorem;

5 Min

6 Concentric circle. -Ring

5 Min

1 Transformation of a point

5 Min

2 Matrix operator

5 Min

3 Enlargement

5 Min

4 Isometrics transformations (translation, reflection, rotation).

5 Min

5 Shear and stretch in the x- axis and in the y- axis;

5 Min

6 Invariant point, invariant line

5 Min

7 Successive transformation,

5 Min

8 Transformation in real life

5 Min

1 Loci in 2- dimensional plane (description and construction)

5 Min

1 Drawing instruments

5 Min

2 Copy lengths and segments

5 Min

3 Triangles of given dimensions,

5 Min

4 Angle bisector

5 Min

5 Mediator or perpendicular bisector of a line segment

5 Min

6 Special angles (30o and 60o , 90o and 45o)

5 Min

7 Division of a line segment into a given number of congruent sides

5 Min

8 Circum-circle, in- circle

5 Min

9 Parallel lines

5 Min

10 Construct Concentric circles

5 Min

1 Trigonometric ratios for acute angles

5 Min

2 Radian measure

5 Min

3 Trig ratios for angles greater than 90º

5 Min

4 Trigonometric identities

5 Min

5 Trigonometric ratios for Secant, cosecant, cotangent

5 Min

6 Graphs of trigonometric functions: y = sinx, y = cosx, y = tanx, y = asinx, y = acosx, y = atanx where a is a constant and a ≠1,

5 Min

7 Sine and cosine rule

5 Min

8 Angle of elevation, angle of depression in 2 dimensions

5 Min

9 Height of an in accessible object

5 Min

10 Bearings in 2- dimension

5 Min

1 Great circle

5 Min

2 Equator

5 Min

3 Meridian

5 Min

4 parallel of latitude

5 Min

5 longitude and time

5 Min

6 GMT and local time

5 Min

7 Position of a place on the surface of the earth

5 Min

8 Shortest distance between two points on the earth

5 Min

9 Angular distance between two points on the earth

5 Min

1 Flow Diagrams

5 Min

2 Types of flow diagrams

5 Min

3 Related vocabularies: Line segment, arc, vertices, endpoints, odd and even vertex, traversable networks,

5 Min

1 -Graphs in real life

5 Min

2 Types of graphs (null graphs, complete graphs, directed graphs, mixed graphs, weighted graphs)

5 Min

3 Properties of graphs

5 Min

1 Expansion of expressions

5 Min

2 Factorisation of expressions

5 Min

3 Quadratic expressions

5 Min

4 Quadratic identities

5 Min

5 Perfect squares

5 Min

6 Completing the square

5 Min

7 Solution of quadratic equations by completing the squares

N/A

8 The quadratic formula

5 Min

9 Quadratic identities

5 Min

10 Word problems leading to quadratic equations and their solutions

5 Min

11 Polynomials -Factor and remainder theorem

5 Min

1 linear inequalities in one unknown

5 Min

2 Solution of an inequality on the real number line

5 Min

3 Interval notations (opened, closed interval)

5 Min

4 Absolute and conditional inequalities

5 Min

5 Inequalities of the form a ≤ mx ±c

5 Min

6 Quadratic in-equations

5 Min

7 Graphical representation of linear inequality in two unknown

5 Min

8 Graphical solution of linear simultaneous equations and inequalities

5 Min

9 Nature of roots

5 Min

10 Graphs of quadratic functions

5 Min

11 Graphical solution of quadratic equations;

5 Min

1 Simple number patterns

5 Min

2 Sequences

5 Min

3 Terms of a sequence, the nth term of a sequence and its notation;

5 Min

1 Arithmetic (sequence) progression (AP),

5 Min

N/A

3 Arithmetic mean

5 Min

N/A

5 Sum of the first n terms of an AP

5 Min

N/A

7 Geometric progression (GP)

5 Min

N/A

9 Geometric mean

5 Min

N/A

11 Finite series

5 Min

N/A

13 Sum of the first n terms of a GP

5 Min

N/A

15 Application of sequences to real life situations

5 Min

N/A

17 Application of sequences to solve real life problems.

5 Min

N/A

Instructor

Secondary Mathematics Tutor

our secondary mathematics tutor plays a crucial role in helping students grasp complex mathematical concepts, develop problem-solving skills, and build confidence in their abilities.

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