Maths is focus : year 11 mathematics extension 1

Title
Contents
1. ALGEBRAIC TECHNIQUES
	1.01 Index laws
	1.02 Zero and negative indices
	1.03 Fractional indices
	1.04 Simplifying algebraic expressions
	1.05 Expansion
	1.06 Binomial products
	1.07 Special products
	1.08 Factorisation
	1.09 Factorisation by grouping in pairs
	1.10 Factorising trinomials
	1.11 Further trinomials
	1.12 Perfect squares
	1.13 Difference of two squares
	1.14 Mixed factorisation
	1.15 Simplifying algebraic fractions
	1.16 Operations with algebraic fractions
	1.17 Substitution
	1.18 Simplifying surds
	1.19 Operations with surds
	1.20 Rationalising the denominator
	Test yourself 1
	Challenge exercise 1
2. EQUATIONS AND INEQUALITIES
	2.01 Equations
	2.02 Inequalities
	2.03 Absolute value
	2.04 Equations involving absolute values
	2.05 Exponential equations
	2.06 Solving quadratic equations by factorisation
	2.07 Solving quadratic equations by completing the square
	2.08 Solving quadratic equations by quadratic formula
	2.09 Formulas and equations
	2.10 Linear simultaneous equations
	2.11 Non-linear simultaneous equations
	2.12 Simultaneous equations with three unknown variables
	2.13 EXT1 Quadratic inequalities
	2.14 EXT1 Inequalities involving the unknown in the denominator
	2.15 EXT1 Inequalities involving absolute values
	Test yourself 2
	Challenge exercise 2
3. PERMUTATIONS AND COMBINATIONS
	3.01 EXT1 Counting techniques
	3.02 EXT1 The pigeonhole principle
	3.03 EXT1 Factorial notation
	3.04 EXT1 Permutations
	3.05 EXT1 Combinations
	3.06 EXT1 Pascal’s triangle and binomial coefficients
	Test yourself 3
	Challenge exercise 3
PRACTICE SET 1
4. FUNCTIONS
	4.01 Functions
	4.02 Function notation
	4.03 Properties of functions
	4.04 Linear functions
	4.05 The gradient of a straight line
	4.06 Finding a linear equation
	4.07 Parallel and perpendicular lines
	4.08 Quadratic functions
	4.09 Axis of symmetry
	4.10 EXT1 Quadratic inequalities
	4.11 The discriminant
	4.12 Finding a quadratic equation
	4.13 Cubic functions
	4.14 Polynomial functions
	4.15 Intersection of graphs
	Test yourself 4
	Challenge exercise 4
5. TRIGONOMETRY
	5.01 Trigonometric ratios
	5.02 Finding a side of a right-angled triangle
	5.03 Finding an angle in a right-angled triangle
	5.04 Applications of trigonometry
	5.05 The sine rule
	5.06 The cosine rule
	5.07 Area of a triangle
	5.08 Mixed problems
	5.09 Radians
	5.10 Length of an arc
	5.11 Area of a sector
	Test yourself 5
	Challenge exercise 5
6. POLYNOMIALS AND INVERSE FUNCTIONS
	6.01 EXT1 Division of polynomials
	6.02 EXT1 Remainder and factor theorems
	6.03 EXT1 Polynomial equations
	6.04 EXT1 Roots and coefficients of polynomial equations
	6.05 EXT1 Graphing polynomial functions
	6.06 EXT1 Multiple roots
	6.07 EXT1 The inverse of a function
	6.08 EXT1 Graphing the inverse of a function
	6.09 EXT1 Inverse functions
	Test yourself 6
	Challenge exercise 6
PRACTICE SET 2
7. FURTHER FUNCTIONS
	7.01 The hyperbola
	7.02 Absolute value functions
	7.03 Circles and semicircles
	7.04 Reflections of functions
	7.05 Combined and composite functions
	7.06 EXT1 Sums and products of functions
	7.07 EXT1 Reciprocal functions
	7.08 EXT1 Square root relations
	7.09 EXT1 Further absolute value functions
	7.10 EXT1 Parametric equations of a function
	Test yourself 7
	Challenge exercise 7
8. INTRODUCTION TO CALCULUS
	8.01 Gradient of a curve
	8.02 Differentiability
	8.03 Differentiation from first principles
	8.04 Short methods of differentiation
	8.05 Derivatives and indices
	8.06 Tangents and normals
	8.07 Chain rule
	8.08 Product rule
	8.09 Quotient rule
	8.10 Rates of change
	8.11 EXT1 Related rates of change
	8.12 EXT1 Motion in a straight line
	8.13 EXT1 Multiple roots of polynomial equations
	Test yourself 8
	Challenge exercise 8
9. PROBABILITY
	9.01 Set notation and Venn diagrams
	9.02 Relative frequency
	9.03 Theoretical probability
	9.04 Addition rule of probability
	9.05 Product rule of probability
	9.06 Probability trees
	9.07 Conditional probability
	Test yourself 9
	Challenge exercise 9
PRACTICE SET 3
10. EXPONENTIAL AND LOGARITHMIC FUNCTIONS
	10.01 Exponential functions
	10.02 Euler\'s number, e
	10.03 Differentiation of exponential functions
	10.04 Logarithms
	10.05 Logarithm laws
	10.06 Logarithmic functions
	10.07 Exponential equations
	10.08 EXT1 Exponential growth and decay
	10.09 EXT1 Further exponential growth and decay
	Test yourself 10
	Challenge exercise 10
11. TRIGONOMETRIC FUNCTIONS
	11.01 Angles of any magnitude
	11.02 Trigonometric identities
	11.03 EXT1 Further trigonometric identities
	11.04 Radians
	11.05 Trigonometric functions
	11.06 Trigonometric equations
	11.07 Applications of trigonometric functions
	11.08 EXT1 Inverse trigonometric functions
	11.09 EXT1 Properties of inverse trigonometric functions
	Test yourself 11
	Challenge exercise 11
12. DISCRETE PROBABILITY DISTRIBUTIONS
	12.01 Random variables
	12.02 Discrete probability distributions
	12.03 Mean or expected value
	12.04 Variance and standard deviation
	Test yourself 12
	Challenge exercise 12
PRACTICE SET 4
ANSWERS
	Chapter 1
	Chapter 2
	Chapter 3
	Chapter 4
	Chapter 5
	Chapter 6
	Chapter 7
	Chapter 8
	Chapter 9
	Chapter 10
	Chapter 11
	Chapter 12
INDEX