### Course Description

Cambridge IGCSE Mathematics for G-9 & 10 has been developed by subject experts of KVERSITY. We are well aware that mathematics is the foundation of all creations, without which no proof of an established law can be given. Everybody uses mathematics in their lives directly or indirectly, knowingly or unknowingly. Obviously, mathematicians and scientists rely on mathematical principles to do the most basic aspects of their work, such as test hypotheses. While scientific careers famously involve math, they are not the only careers to do so. Even operating a cash register requires that one understands basic arithmetic. People working in a factory must be able to do mental arithmetic to keep track of the parts on the assembly line and must, in some cases, manipulate fabrication software utilizing geometric properties (such as the dimensions of a part) in order to build their products. Really, any job requires math because you must know how to interpret your paycheck and balance your budget. Mathematics is involved in our every movement and helps us to understand the world better. To live in a mathematically-driven world and not know math is like walking through an art museum with your eyes closed. Learning and appreciating math can help you appreciate things that you would not otherwise notice about the world. In reality, mathematics is everywhere! Bees, masters of geometry, use hexagons to build their honeycombs. The Fibonacci sequence, a famous sequence of numbers in mathematics, is found throughout nature: in pinecones, seashells, trees, flowers, and leaves.

#### Contents,

CHAPTER 1: REVIEWING NUMBER CONCEPTS
1.1 Different types of numbers
1.2 Multiples and factors
1.3 Prime numbers
1.4 Powers and roots
1.5 Working with directed numbers
1.6 Order of operations
1.7 Rounding numbers
CHAPTER 2: MAKING SENSE OF ALGEBRA
2.1 Using letters to represent
unknown values
2.2 Substitution
2.3 Simplifying expressions
2.4 Working with brackets
2.5 Indices
CHAPTER 3: LINES, ANGLES AND SHAPES
3.1 Lines and angles
3.2 Triangles
3.3 Quadrilaterals
3.4 Polygons
3.5 Circles
3.6 Construction
CHAPTER 4: COLLECTING, ORGANISING AND
DISPLAYING DATA
4.1 Collecting and classifying data
4.2 Organising data
4.3 Using charts to display data.

CHAPTER 5: FRACTIONS
5.1 Equivalent fractions
5.2 Operations on fractions
5.3 Percentages
5.4 Standard form
5.5 Your calculator and standard form
5.6 Estimation
CHAPTER 6: EQUATIONS AND TRANSFORMING FORMULAE
6.1 Further expansions of brackets
6.2 Solving linear equations
6.3 Factorising algebraic expressions
6.4 Transformation of a formula
CHAPTER 7: PERIMETER, AREA AND VOLUME
7.1 Perimeter and area in two dimensions
7.2 Three-dimensional objects
7.3 Surface areas and volumes of solids
CHAPTER 8: INTRODUCTION TO PROBABILITY
8.1 Basic probability
8.2 Theoretical probability
8.3 The probability that an event does not
happen
8.4 Possibility diagrams
8.5 Combining independent and mutually
exclusive events.

CHAPTER 9: SEQUENCES AND SETS
9.1 Sequences
9.2 Rational and irrational numbers
9.3 Sets
CHAPTER 10: STRAIGHT LINES AND QUADRATIC EQUATIONS
10.1 Straight lines
10.2 Quadratic expressions
CHAPTER 11: PYTHAGORAS’ THEOREM AND
SIMILAR SHAPES
11.1 Pythagoras’ theorem
11.2 Understanding similar triangles
11.3 Understanding similar shapes
11.4 Understanding congruence
CHAPTER 12: AVERAGES AND MEASURES OF SPREAD
12.1 Different types of average
12.2 Making comparisons using averages
and ranges
12.3 Calculating averages and ranges for
frequency data
12.4 Calculating averages and ranges for grouped
continuous data
12.5 Percentiles and quartiles.

CHAPTER 13: UNDERSTANDING MEASUREMENT
13.1 Understanding units
13.2 Time
13.3 Upper and lower bounds
13.4 Conversion graphs
13.5 More money
CHAPTER 14: FURTHER SOLVING OF EQUATIONS AND
INEQUALITIES
14.1 Simultaneous linear equations
14.2 Linear inequalities
14.3 Regions in a plane
14.4 Linear programming
14.5 Completing the square
14.6 Quadratic formula
14.7 Factorising quadratics where the coefficient
of x2 is not 1
14.8 Algebraic fractions
CHAPTER 15: SCALE DRAWINGS, BEARINGS AND
TRIGONOMETRY
15.1 Scale drawings
15.2 Bearings
15.3 Understanding the tangent, cosine
and sine ratios
15.4 Solving problems using
trigonometry
15.5 Angles between 90° and 180°
15.6 The sine and cosine rules
15.7 Area of a triangle
15.8 Trigonometry in three dimensions
CHAPTER 16: SCATTER DIAGRAMS
AND CORRELATION
16.1 Introduction to bivariate data.

CHAPTER 17: MANAGING MONEY
17.1 Earning money
17.2 Borrowing and investing money
17.3 Buying and selling.
CHAPTER 18: CURVED GRAPHS
18.1 Plotting quadratic graphs (the parabola)
18.2 Plotting reciprocal graphs (the hyperbola)
18.3 Using graphs to solve quadratic equations
18.4 Using graphs to solve simultaneous linear
and non-linear equations
18.5 Other non-linear graphs
18.6 Finding the gradient of a curve
CHAPTER 19: SYMMETRY AND LOCI
19.1 Symmetry in two dimensions
19.2 Symmetry in three dimensions
19.3 Symmetry properties of circles
19.4 Angle relationships in circles
19.5 Locus
CHAPTER 20: HISTOGRAMS AND FREQUENCY DISTRIBUTION
DIAGRAMS
20.1 Histograms
20.2 Cumulative frequency.

CHAPTER 21: RATIO, RATE AND PROPORTION
21.1 Working with ratio
21.2 Ratio and scale
21.3 Rates
21.4 Kinematic graphs
21.5 Proportion
21.6 Direct and inverse proportion in
algebraic terms
21.7 Increasing and decreasing amounts
by a given ratio
CHAPTER 22: MORE EQUATIONS, FORMULAE AND
FUNCTIONS
22.1 Setting up equations to solve problems
22.2 Using and transforming formulae
22.3 Functions and function notation
CHAPTER 23: TRANSFORMATIONS AND MATRICES
23.1 Simple plane transformations
23.2 Vectors
23.3 Further transformations
23.4 Matrices and matrix transformation
23.5 Matrices and transformations
CHAPTER 24: PROBABILITY USING TREE DIAGRAMS
24.1 Using tree diagrams to show outcomes
24.2 Calculating probability from tree diagrams.

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