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Grade 10 Mathematics:
Learners’ Book
INNODEMS
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Front Matter
1
Numbers and Algebra
1.1
Real Numbers
1.1.1
Classifying whole numbers as odd, even, prime and composite in different situations
1.1.2
Classifying real numbers as rational and irrational in different situations
1.1.3
Finding reciprocals of real numbers using division
1.1.4
Finding reciprocals of real numbers using mathematical tables and calculators
1.1.4.1
Finding reciprocals of numbers using mathematical tables
1.1.4.2
Finding reciprocals using a calculator
1.1.5
Using reciprocals of real numbers in mathematical computations
1.1.6
Real-world applications of reciprocals of real numbers
1.2
Indices and Logarithms
1.2.1
Indices
1.2.1.1
Expressing Numbers in Index Form
1.2.1.2
Laws of Indices
1.2.1.2
Exercises
1.2.1.3
Zero and Negative Indices
1.2.1.3
Exercises
1.2.1.4
Applications of Indices in Real-Life situations
1.2.1.4
Exercises
1.2.2
Logarithms
1.2.2.1
Logarithms notation
1.2.2.1
Exercises
1.2.2.2
Using Logarithms with Standard Form
1.2.2.3
Determining Common Logarithms Using Mathematical Tables and Calculators
1.2.2.3
Exercises
1.2.2.3
Exercises
1.2.2.4
Multiplying and Dividing Logarithms
1.2.2.5
Applying Logarithms to Powers and Roots
1.2.2.5
Exercises
1.3
Quadratic Expressions and Equations 1
1.3.1
Quadratic Expressions
1.3.1.1
Multiplying a monomial by a binomial.
1.3.1.1
Exercises
1.3.1.2
Multipling Two Binomials.
1.3.1.2
Exercises
1.3.2
Quadratic Identities.
1.3.2.1
Difference of Squares.
1.3.2.2
Perfect Squares.
1.3.2.3
Factoring Quadratic.
1.3.2.4
Exercises
1.3.3
Factorisation Of Quadratic Expressions.
1.3.3.1
Factorisation When The Coefficient Of
\(x^2\)
Is One
1.3.3.1
Exercises
1.3.3.2
Factorisation When The Coefficient Of
\(x^2\)
Is Not One.
1.3.3.2
Exercises
1.3.4
Formation of Quadratic Equations by Factorisations.
1.3.4
Exercises
1.3.5
Solutions Of Quadratic Equations By Factorisations.
1.3.5
Exercises
1.3.6
Application Of Quadratic Equations To Real Life Situations.
1.3.6
Exercises
2
Measurements and Geometry
2.1
Similarity and Enlargement
2.1.1
Similarity
2.1.1
Exercises
2.1.2
Enlargement
2.1.2
Exercises
2.1.3
Scale Factors
2.1.3.1
Area Scale Factor
2.1.3.1
Exercises
2.1.3.2
Volume Scale Factor
2.1.3.2
Exercises
2.1.3.3
Further Exercise
2.2
Reflection and Congruence
2.2.1
Identifying Lines of Symmetry Given an Object
2.2.1
Exercises
2.2.2
Plane of Symmetry
2.2.2
Exercises
2.2.3
Properties of Reflection
2.2.3
Exercises
2.2.4
Reflection of Different Shapes on a Plane
2.2.4
Exercises
2.2.5
Determining the Equation of a Mirror Line ( Line of Reflection) Given an Object and its Image
2.2.5
Exercises
2.2.6
Congruence
2.2.6
Exercises
2.2.7
Congruence Tests for Triangles
2.2.7
Exercises
2.3
Rotation
2.3.1
Properties of Rotation
2.3.1.1
Centre and Angle of Rotation
2.3.1.1
Exercises
2.3.2
Rotation on Different Planes
2.3.2.1
Rotation in the Cartesian Plane
2.3.2.1
Exercises
2.3.3
Rotational Symmetry
2.3.3.1
Determining the Order of Rotational Symmetry of Plane Figures
2.3.3.1
Exercises
2.3.3.2
Determining the Axis of Rotation and Order of Rotational Symmetry in Solids
2.3.3.2
Exercises
2.3.4
Rotation and Congruence
2.3.4
Exercises
2.4
Trigonometry 1
2.4.1
Trigonometric Ratios of Acute Angles
2.4.1.1
Tangent of an Acute Angle
2.4.1.2
Sine and Cosine of an Acute Angle
2.4.2
Sines and Cosines of Complimentary Angles
2.4.3
Trigonometric ratios of Special Angles((30°, 45° and 60°))
2.4.3.1
Tangent, Cosine and Sine of 45°
2.4.3.2
Tangent, Cosins and Sine of 30° and 60°
2.4.4
Determining Trigonometric Ratios Using a Calculator
2.4.5
Application of Trigonometric Ratios
2.4.5.1
Trigonometric Ratios to Angles of Elevation and Depression
2.5
Area of Polygons
2.5.1
Area of Triangles.
2.5.1.1
Area of a Triangle using Heron’s Formula
2.5.1.2
Area of a triangle given two sides and an included angle
2.5.2
Area of Quadrilaterals.
2.5.2.1
Area of a Parallelogram
2.5.2.2
Area of a Rhombus
2.5.2.3
Area of a Trapezium
2.5.2.4
Area of a Kite
2.5.3
Area of Regular Polygons
2.5.3.1
Area of Heptagon
2.5.3.2
Area of a an Octagon
2.5.3.3
Area of a Nonagon
2.5.3.4
Area of a Decagon
2.5.4
Area of Irregular Polygons
2.6
Area of a Part of a Circle
2.6.1
Area of an Annulus
2.6.2
Area of a Sector of a Circle
2.6.3
Area of an Annular Sector
2.6.4
Area of a Segment of a Circle
2.6.5
Area of Common Region between two Intersecting Circles
2.7
Surface Area and Volume of Solids
2.7.1
Surface area of Prisms
2.7.2
Surface area of a cuboid
2.7.3
Surface Area of a pyramid
2.7.4
Surface Area of a Sphere
2.7.5
Surface Area of a Triangular Prism
2.7.6
Surface area of a Cone
2.7.7
Surface Area of Composite solids
2.7.8
Surface area of a Frustum
2.7.9
Volume of Solids.
2.7.10
Volume of a Cuboid
2.7.11
Volume of a Triangular Prism
2.7.12
Volume of a Pyramid
2.7.13
Volume of a Cylinder
2.7.14
Volume of a Sphere
2.7.15
Volume of a Cone
2.7.16
Volume of a Frustum
2.7.17
Volume of Composite solids
2.8
Vectors I
2.8.1
Vector and Scalar Quantities
2.8.2
Representation of Vectors and Vector Notation
2.8.3
Equivalent Vectors
2.8.3
Exercises
2.8.4
Addition of Vectors
2.8.4
Exercises
2.8.5
Multiplication of Vectors by a Scalar
2.8.5
Exercises
2.8.6
Column Vectors
2.8.6
Exercises
2.8.7
Position Vectors
2.8.7
Exercises
2.8.8
Magnitude of a Vector
2.8.8
Exercises
2.8.9
Midpoint of a Vector
2.8.9
Exercises
2.8.10
Translation Vector
2.8.10
Exercises
2.8.10
Further Exercises
2.9
Linear Motion
2.9.1
Speed
2.9.1
Exercises
2.9.2
Velocity and Acceleration in Different Situations
2.9.2
Exercises
2.9.3
Displacement Time Graph of Different Situations
2.9.3
Exercises
2.9.4
Interpretation of Displacement Time Graph
2.9.4
Exercises
2.9.5
Velocity Time Graph
2.9.5
Exercises
2.9.6
Relative Speed
2.9.6.1
When Objects Move in the Same Direction
2.9.6.1
Exercises
2.9.6.2
When Objects Move Toward Each Other (Opposite Directions).
2.9.6.2
Exercises
3
Statistics and Probability
3.1
Statistics 1
3.1.1
Collection of Data
3.1.1.1
Sources of Data
3.1.1.1
Exercises
3.1.1.2
Methods of Data Collection
3.1.1.2
Exercises
3.1.2
Representing Data using a Frequency Distribution Table
3.1.2
Exercises
3.1.3
Measures of Central Tendency
3.1.3.1
Ungrouped Data for Measures of Central Tendency
3.1.3.1
Exercises
3.1.3.2
Grouped Data for Measures of Central Tendency
3.1.3.2
Exercises
3.1.4
Representation of Data
3.1.4.1
Drawing Histograms and Frequency Polygons of Data
3.1.4.1
Exercises
3.1.5
Interpretation of data
3.1.5.1
Interpreting Histograms and Frequency Polygons of Data
3.1.5.1
Exercises
3.2
Probability 1
3.2.1
Introduction to Probability
3.2.2
Probability Experiment and Sample Space
3.2.2
Exercises
3.2.3
Probability of Simple Events
3.2.3
Exercises
3.2.4
Mutually Exclusive and Independent Events
3.2.4.1
Mutually Exclusive
3.2.4.1
Exercises
3.2.4.2
Independent Events
3.2.4.2
Exercises
3.2.5
Law of Probability
3.2.5.1
Addition Law of Probability
3.2.5.1
Exercises
3.2.5.2
multiplication rule
3.2.5.2
Exercises
3.2.6
Tree Diagrams and Independent Events
3.2.6
Exercises
Backmatter
Colophon
Colophon
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