# Additional Maths 360 Solutions

/The solutions are for the exercises in the Additional Maths 360 textbook.

Not all the exercises are covered and the missing ones will be added in due time.

Navigation links:

- Chapter 1: Equations and Inequalities
- Chapter 2: Surds and Indices
- Chapter 3: Polynomials and Partial Fractions
- Chapter 4: The Modulus and Power Functions
- Chapter 5: Binomial Theorem
- Chapter 6: Points, Lines and Shapes
- Chapter 7: Logarithms
- Chapter 8: Applications of Straight Line Graphs
- Chapter 9: Parabolas and Circles
- Chapter 10: Plane Geometry
- Chapter 11: Trigonometric Functions
- Chapter 12: Simple Trigonometric Identities and Equations
- Chapter 13: Further Trigonometric Identities
- Chapter 14: Differentiation
- Chapter 15: Tangents, Normals and Rate of Change
- Chapter 16: Maxima and Minima
- Chapter 17: Further Differentiation
- Chapter 18: Integration
- Chapter 19: Application of Integration - Area of a Region
- Chapter 20: Application of Integration - Kinematics

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**Chapter 1: Equations and Inequalities**

Exercise 1.1: Simultaneous Equations

Exercise 1.2: Sum and Product of Roots

- Basic Questions 1 to 7
- Intermediate Questions 8 to 14
- Advanced Questions 15 to 19
- Advanced Questions 20 to 23

Exercise 1.3: Discriminants, Roots and *x*-intercepts

- Basic Questions 1 to 6
- Intermediate Questions 7 to 11
- Intermediate Questions 12 to 15
- Advanced Questions 16 to 20

Exercise 1.4: Quadratic Inequalities

Revision Exercise 1

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**Chapter 2: Surds and Indices**

Exercise 2.1: Surds

- Basic Questions 1 to 8
- Intermediate Questions 9 to 14
- Intermediate Questions 15 to 19
- Advanced Questions 20 to 22

Exercise 2.2: Indices

Exercise 2.3: Equations involving Indices

Exercise 2.4: Exponential Functions

Revision Exercise 2

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**Chapter 3: Polynomials and Partial Fractions**

Exercise 3.1: Polynomials and Identities

Exercise 3.2: Division of Polynomials

Exercise 3.3: The Remainder Theorem

Exercise 3.4: The Factor Theorem

Exercise 3.5: Cubic Polynomials and Equations

Exercise 3.6: Partial Fractions

Revision Exercise 3

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**Chapter 4: The Modulus and Power Functions**

Exercise 4.1: Modulus Functions and their Graphs

- Basic Questions 1 to 8
- Intermediate Questions 9 to 14
- Intermediate Questions 15 to 20
- Advanced Questions 21 & 22

Exercise 4.2: Graphs of Power Functions

Revision Exercise 4

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**Chapter 5: Binomial Theorem**

Exercise 5.1: The Binomial Expansion of $(1 + b)^n$

Exercise 5.2: The Binomial Expansion of $(a + b)^n$

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**Chapter 6: Points, Lines and Shapes**

Exercise 6.1: Mid-point of a Line Segment

Exercise 6.2: Parallel Lines

Exercise 6.3: Perpendicular Lines

Exercise 6.4: Areas of Triangles and Quadrilaterals

Revision Exercise 6

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**Chapter 7: Logarithms**

Exercise 7.1: Introduction to Logarithms

- Basic Questions 1 to 8
- Intermediate Questions 9 to 13
- Intermediate Questions 14 to 16
- Advanced Questions 17 to 21

Exercise 7.2: Laws of Logarithms

- Basic Questions 1 to 4
- Intermediate Questions 5 to 9
- Intermediate Questions 10 to 14
- Advanced Questions 15 to 18

Exercise 7.3: Logarithmic Equations

Exercise 7.4: Logarithms and Equations of the Form $ a^x = b $

Exercise 7.5: Graphs and Applications of Logarithmic Functions

Revision Exercise 7

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**Chapter 8: Applications of Straight Line Graphs**

Exercise 8.1: Reducing Equations to Linear Form

Exercise 8.2: Linear Law

Revision Exercise 8

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**Chapter 9: Parabolas and Circles**

Exercise 9.1: Graphs of Parabolas of the Form $y^2 = kx$

Exercise 9.2: Coordinate Geometry of Circles

- Basic Questions 1 to 7
- Intermediate Questions 8 to 11
- Intermediate Questions 12 to 17
- Advanced Questions 18 to 20

Revision Exercise 9

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**Chapter 10: Plane Geometry**

Exercise 10.1: Triangle Theorems

Exercise 10.2: Quadrilateral Theorems

- Basic Questions 1 to 3
- Intermediate Questions 4 to 8
- Advanced Questions 10 to 14
- Note: Question 9 is skipped as I think there's a problem with the question. Let me know if you have a solution!

Exercise 10.3: Circle Theorems

- Basic Questions 1 to 5
- Intermediate Questions 6 to 10
- Intermediate Questions 11 to 15
- Advanced Question 16
- Note: Question 17 is skipped as it is no longer in the syllabus.

Revision Exercise 10

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**Chapter 11: Trigonometric Functions**

Exercise 11.1: Trigonometric Ratios of Acute Angles

Exercise 11.2: Trigonometric Functions of Any Angle

Exercise 11.3: Graphs of Trigonometric Functions

- Basic Questions 1 to 4
- Basic Questions 5 to 9
- Intermediate Questions 10 to 14
- Intermediate Questions 15 to 20

Revision Exercise 11

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**Chapter 12: Simple Trigonometric Identities and Equations**

Exercise 12.1: Simple Identities

Exercise 12.2: Further Trigonometric Equations

- Basic Questions 1 to 4
- Basic Questions 5 to 7
- Intermediate Questions 8 to 10
- Intermediate Questions 11 to 14
- Advanced Questions 15 to 18

Revision Exercise 12

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**Chapter 13: Further Trigonometric Identities**

Exercise 13.1: The Addition Formulae

Exercise 13.2: The Double Angle Formulae

Exercise 13.3: The *R*-Formula

Revision Exercise 13

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**Chapter 14: Differentiation**

Exercise 14.1: The Derivative and its Basic Rules

Exercise 14.2: The Chain Rule

Exercise 14.3: The Product Rule

Exercise 14.4: The Quotient Rule

Revision Exercise 14

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**Chapter 15: Tangents, Normals and Rates of Change**

Exercise 15.1: Equations of Tangents and Normals

Exercise 15.2: Increasing and Decreasing Functions

Exercise 15.3: Rates of Change

Exercise 15.4: Connected Rates of Change

Revision Exercise 15

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**Chapter 16: Maxima and Minima**

Exercise 16.1: Nature of Stationary Points

Exercise 16.2: Maxima and Minima Problems

Revision Exercise 16

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**Chapter 17: Further Differentiation**

Exercise 17.1: Derivatives of Trigonometric Functions

Exercise 17.2: Derivatives of Exponential Functions

- Basic Questions 1 to 5
- Basic Questions 6 to 10
- Intermediate Questions 11 to 14
- Intermediate Questions 15 to 17
- Advanced Questions 18 to 20

Exercise 17.3: Derivatives of Logarithmic Functions

Revision Exercise 17

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**Chapter 18: Integration**

Exercise 18.1: Integration

- Basic Questions 1 to 6
- Basic Questions 7 to 10
- Intermediate Questions 11 to 14
- Intermediate Questions 15 to 18

Exercise 18.2: Definite Integrals

Exercise 18.3: Integration of Trigonometric Functions

Exercise 18.4: Integration of Exponential Functions and ${1 \over x}$

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**Chapter 19: Application of Integration - Area of a Region**

Exercise 19.1: Area between a Curve and an Axis

- Basic Questions 1 to 8
- Intermediate Questions 9 to 12
- Intermediate Questions 13 to 16
- Advanced Questions 17 to 21

Exercise 19.2: Area between a Curve and a Line

Revision Exercise 19

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**Chapter 20: Applications of Integration - Kinematics**

Exercise 20.1: Displacement, Velocity and Acceleration

- Basic Questions 1 to 7
- Intermediate Questions 8 to 11
- Intermediate Questions 12 to 16
- Advanced Questions 17 to 20

Revision Exercise 20