Oxford International AQA Examinations: International AS Level Mathematics
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Description
Contents
Reviews
Language
English
ISBN
9780198411260
Contents
About this book
1 Expanding Brackets, Surds and Indices
1.1 Algebraic expressions
1.2 Expansion of Two Brackets
1.3 Square roots and other roots
1.4 Surds
1.5 Indices
Summary
Review
Assessment
2 Quadratic Polynomials and Equations
2.1 Quadratic polynomials
2.2 Quadratic equations
2.3 Solution by completing the square
2.4 The formula for solving a quadratic equation
2.5 Properties of the roots of a quadratic equation
2.6 Simultaneous equations
Summary
Review
Assessment
3 Algebraic Division
3.1 Division of a polynomial by x − a
3.2 The remainder theorem and thefactor theorem
3.3 The factors of a3 − b3 and a3 + b3
Review
Assessment
4 Functions and Graphs
4.1 Functions
4.2 Graphical interpretation of equations
4.3 Inequalities
4.4 Transformations of graphs
Summary
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Assessment
5 Coordinate Geometry
5.1 Lines joining two points
5.2 Gradient
5.3 The equation of a straight line
5.4 Intersection
Summary
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Assessment
6 Differentiation
6.1 Chords, tangents, normals and gradients
6.2 Differentiation
6.3 Gradients of tangents and normals
6.4 Increasing and decreasing functions
6.5 Stationary points
6.6 Maximum and minimum points
Summary
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7 Integration
7.1 Indefinite integration
7.2 Using integration to find an area
7.3 The trapezium rule
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8 Sequences and Series
8.1 Defining a sequence
8.2 Series
8.3 Arithmetic series
8.4 Geometric series
8.5 The Binomial theorem
Summary
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Assessment
9 Coordinate Geometry and Circles
9.1 The equation of a circle
9.2 Geometric properties of circles
9.3 Tangents to circles
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10 Trigonometry
10.1 Trigonometric ratios of acute angles
10.2 The sine rule and cosine rule
10.3 The area of a triangle
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11 Trigonometric Functions and Equations
11.1 Angle units
11.2 The length of an arc
11.3 The area of a sector
11.4 The trigonometric functions
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12 Exponentials and Logarithms
12.1 Exponential functions
12.2 Logarithms
12.3 The laws of logarithms
12.4 Equations containing logarithmsor x as a power
Summary
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Assessment
13 Probability
13.1 Introduction to probability
13.2 Combined events
13.3 Conditional events
13.4 Tree diagrams
13.5 Further applications
Summary
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Assessment
14 Discrete Random Variables
14.1 Discrete variables
14.2 Discrete random variables
14.3 E(X), the expectation of X
14.4 The variance and standard deviation of X
14.5 Sum or difference of two independent random variables
14.6 Further applications
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15 Bernoulli and Binomial Distributions
15.1 The Bernoulli distribution
15.2 The binomial distribution
15.3 The cumulative binomial distribution function
15.4 Mean, variance and standard deviation of a binomial distribution
15.5 Further applications
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16 Displacement, Speed, Velocity and Acceleration
16.1 Displacement, speed, velocity and acceleration
16.2 Displacement-time and velocity-time graphs
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17 Motion in a Straight Line
17.1 Equations of motion with constant acceleration
17.2 Free fall motion under gravity
17.3 Motion in a straight line with variable acceleration
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18 Forces and Newton’s Laws
18.1 Types of force
18.2 Newton’s first law of motion
18.3 Connected particles
18.4 Dynamic friction
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19 Momentum and Impulse
19.1 Momentum and impulse
19.2 Conservation of linear momentum
Summary
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Glossary
Answers
Index
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