# Mathematics for CSEC

By Chandler, Smith, Mothersill, Bishop, Chan Tack-Jones

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Book Description

Written specifically for the needs of the Caribbean by an unsurpassed author team, this comprehensive text covers the latest CSEC mathematics syllabus, examinable from 2018. Mathematics for CSEC is a clear and challenging text with extensive practice and worked examples to strengthen and consolidate student knowledge as well as build confidence ahead of the examination. Carefully structured skills development also facilitates smooth progression through the course.

This title now also includes a chapter online to provide support for the SBA.

Table of Contents

- Front Cover
- Title Page
- Contents
- INTRODUCTION
- PREFACE
- 1 Number theory and computation
- Whole numbers
- Number bases and place value
- Negative numbers
- Order of operations
- Properties of operations
- Fractions
- Powers and roots
- Irrational numbers
- Indices
- Decimals
- Approximations
- Scientific notation
- Converting fractions to decimals
- Converting decimals to fractions
- Percentages
- Ratio
- Division in a given ratio

- 2 Sets
- Describing a set
- Definitions and notation
- Union and intersection
- Venn diagrams
- Harder problems

- 3 Algebra 1
- Algebra
- Definitions and conventions
- Simplifying expressions
- Factorising
- Simplifying fractions
- Substituting values into algebraic expressions
- Linear equations in one unknown
- Forming expressions and equations
- Simultaneous linear equations in two unknowns
- Linear inequalities

- 4 Measurement
- Measurements
- units of measurement
- units of length
- units of mass
- units of time
- Converting between units of measure
- temperature
- Currencies
- speed
- Imperial units
- units of length
- units of mass
- Conversions between metric and imperial units
- Polygons
- Circles
- Perimeter
- units of area
- areas of polygons and circles
- areas of irregularly shaped plane figures
- Volume
- Capacity
- Prisms
- sources of error

- 5 Consumer Arithmetic
- Percentage increase and decrease
- Compound percentage change
- Reverse percentage problems
- Profit and loss
- sales tax
- invoices and shopping bills
- utility bills and property tax
- hire purchase and mortgages
- salaries, wages and commission
- income tax
- investments and insurance
- Review test 1

- 6 Relations, Functions and Graphs
- Relations
- Diagrams representing relations
- Types of relation
- Functions
- linear functions
- straight line graphs
- the standard equation of a straight line
- parallel lines and perpendicular lines
- the intercept form of the equation of a straight line

- 7 Geometry and Trigonometry
- Symmetry
- Transformations
- Describing a transformation
- Parallel lines
- Triangles
- Quadrilaterals
- Polygons
- Necessary and sufficient conditions to prove that aquadrilateral is a parallelogram
- Similar shapes
- Congruent triangles
- Pythagoras’ theorem
- Bearings
- Angles of elevation and depression
- Trigonometry
- Coordinate geometry

- 8 Statistics
- Categorical and numerical data
- Measures of central tendency
- Frequency tables
- Bar charts
- Line graphs
- Pie charts
- Probability
- Independent events
- Mutually exclusive events
- Contingency tables

- 9 Algebra 2
- Binary operations
- The product of two brackets
- Factorising by grouping
- Factorising quadratic expressions
- Quadratic equations
- Solution by factorisation
- Solution by completing the square
- Solution by the formula
- Changing the subject of a formula

- 10 Circle Theorems
- Definitions
- Angles in circles
- Cyclic quadrilaterals
- Tangents to circles
- Alternate segment theorem
- Review test 2

- 11 Matrices
- Definitions
- Matrix multiplication
- Determinants
- The inverse of a matrix
- Applications of matrices
- Simultaneous equations
- Numerical applications

- 12 Sequences
- Sequences

- 13 Quadratic Functions
- The graph of a quadratic function
- Estimation of the gradient at a point
- Graphical solution of quadratice quations
- Graphical solution of quadratic inequalities
- Finding the maximum or minimum value of a quadratic function algebraically
- sketching the graphs of quadratic functions
- simultaneous equations – one linear and the other quadratic

- 14 More Functions
- Cubic functions
- The shape of a cubic curve
- Reciprocal functions
- Reciprocal curves
- Recognising curves
- Trigonometric functions
- The graph of f(x) = sin x°
- The graph of f(x) = cos x°
- The sine and cosine functions
- The tangent function
- Growth curves
- Decay curves
- Exponential growth and decay
- Vertical line test for a function
- Inverse functions
- The graph of a function and its inverse
- Compound functions
- Function of a function

- 15 Travel Graphs
- Straight line distance–time graphs
- Rates of change
- Tangents to curves
- Travel graphs
- Curved distance–time graphs
- Velocity
- Finding velocity from adistance–time graph
- Velocity at an instant
- Acceleration
- Velocity–time graphs
- Finding the distance from avelocity–time graph
- Review test 3

- 16 Inequalities
- Linear inequalities
- Inequalities involving two variables
- Shading the required region
- Coordinates of points in a region
- Greatest and least values
- Linear programming

- 17 Variation
- Formulae
- Relationships
- Direct variation
- Dependent and independent variables
- inverse variation
- Equations for inverse variation

- 18 Vectors in Geometry
- Definition of a vector
- Representation of a vector
- The magnitude of a vector
- Equal vectors
- Negative vectors
- Multiplication of a vector by a scalar
- Equivalent displacements
- Addition of vectors
- Subtraction of vectors
- Position vectors
- Vectors and geometry
- Using vectors to model practical situations
- Further problems

- 19 Transformations and Matrices
- The position vector of a point
- The image of a position vector
- Transformation matrix
- Finding the image
- Identifying a transformation
- Reflections
- Rotations
- Enlargements
- Transformations that cannot be described simply
- Mixed transformations
- The identity transformation
- Transformations and images
- Inverse transformations
- Inverse matrix transformations
- Inverse matrices and inverse transformations
- An invariant point
- Transformations not using matrices

- 20 Compound Transformations
- Compound transformations
- Equivalent single transformations
- The identity transformation
- Common transformation matrices
- Area scale factor
- Unit vectors and the unit square
- Finding a transformation matrix
- Compound transformations
- Defining transformations as matrix equations
- Compound transformations and matrices
- Review Test 4

- 21 Sine and Cosine Formulae
- Sines of obtuse angles
- Cosines of obtuse angles
- Trigonometric ratios as fractions
- Trigonometric ratios of 30°, 45°and 60°
- Triangle notation
- The sine rule
- Using the sine rule to find an angle
- The cosine rule
- Mixed questions
- The area of a triangle
- Sine formula for area of a triangle
- Heron’s formula
- The area of a segment of a circle

- 22 Constructions and transformations
- Constructions using ruler andcompasses
- accuracy
- scales
- transformations
- finding the mirror line
- finding the centre of rotation
- Circles and tangents
- Parallel lines

- 23 Grouped Data
- Collecting information
- Frequency tables
- Class intervals
- Measures of central tendency of a grouped frequency distribution
- the modal group
- the group containing the median
- the mean
- Histograms
- Frequency polygons
- Using the area under a histogram

- 24 Measures of Spreads
- Range
- Cumulative frequency tables
- Cumulative frequency curves
- Drawing a cumulative frequency curve
- Quartiles
- Statistical investigations
- Deciding which statistical measure to use

- 25 areas and volumes
- Pyramids
- volume of a pyramid
- surface area of a pyramid
- volume of a cylinder
- Curved surface area of a cylinder
- volume of a cone
- surface area of a cone
- volume of a sphere
- surface area of a sphere
- Review Test 5

- Model exam 1
- Sample Paper with Solutions
- Answers
- INDEX
- Back Cover
- Multiple Choice Tests

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