Extended Math

Dive into a comprehensive exploration of advanced mathematical concepts that bridge numerical and abstract reasoning. This enlightening guide covers the intricacies of number system notation, irrational numbers, and the conversion of recurring decimals to rational numbers. You'll master surds, roots, and radicals, including techniques for simplifying expressions and rationalizing the denominator.

Delve into the laws of exponents, including fractional and rational exponents, and unlock the practical applications of logarithms through the laws of logarithms and technology for value determination. Gain a solid understanding of absolute values, solutions of absolute equations, and the significance of different types of error, along with upper and lower bounds.

Revisit standard form (scientific notation) and delve into the world of sets and Venn diagrams, exploring their applications. Engage with variation and power modeling, factorizing quadratic expressions, and solving quadratic equations both graphically and algebraically using the null factor law and the quadratic formula. Learn to represent and solve linear inequalities, including compound and double inequalities, and master methods of differences in linear contexts.

Investigate patterns in quadratic, cubic, and geometric sequences, while enhancing your understanding of relations and functions, domain and range, and the representation of functions through mapping and graphs. Explore linear functions (y = mx + c) and simultaneous equations, as well as the applications of quadratic functions.

Expand your spatial reasoning skills by exploring triangle properties, including the Pythagorean theorem and measures of angles in degrees and radians. Delve into trigonometry ratios of right-angled triangles, bearings, and non-right-angled trigonometry through the sine and cosine rules. Discover the unit circle, tessellations, and the principles of rotation and enlargement, including finding the center of rotation and enlargement by a rational factor.

Finally, enhance your understanding of area and perimeter of 2D shapes, focusing on compound shapes, arc length, and the area of sector circles. Master coordinate geometry through midpoints, distance and gradient formulas, and the section formula, alongside essential circle geometry concepts.

This book is your ultimate resource for mastering these essential mathematical concepts, equipping you with the tools to excel in both academic and real-world applications.