You are not bad at maths. You have gaps. This book fills them.
This is not a dusty reference manual. It is a memoir‑textbook hybrid that walks you from the foundations of arithmetic through the precalculus concepts required to skip remedial courses. Written in clear, conversational UK English, each chapter delivers roughly 2,000 words of instruction followed by solved problems with written rationales that explain every move.
Diagnose your hidden gaps first. Chapter One opens with a 20‑question diagnostic quiz that maps exactly where your weaknesses live. The scoring guide directs you to the chapters you actually need – no wasted time on topics you already know.
Build number sense you were never taught. Chapter Two covers negative numbers as debt and temperature, fractions as unfinished division, decimals as fractions in disguise, and ratios that make sense. The debt model for subtracting negatives alone will change how you see signed numbers.
Learn algebra’s secret grammar. Chapter Three explains variables, expressions versus equations, like terms, the distributive law, solving linear equations, inequalities, and the special cases of no solution or infinite solutions – all treated as a language with rules.
Master word problems without weeping. Chapter Four introduces the Freedom Translation Grid – a dictionary that turns English phrases into algebra. You will work through number problems, age problems, rate problems (distance, work, speed), mixture problems, and a step‑by‑step translation process that eliminates guessing.
Conquer exponents, roots, and scientific notation. Chapter Five teaches the five laws of exponents, zero and negative exponents, square roots and higher roots, simplifying radicals, and scientific notation – all derived from the simple truth that exponents are repeated multiplication.
Achieve quadratic and polynomial mastery. Chapter Six covers adding, subtracting, and multiplying polynomials, factoring (GCF, difference of squares, perfect square trinomials, quadratics with a=1 and a≠1), solving quadratics by four methods, the discriminant, and graphing parabolas.
Understand functions and graphs that talk. Chapter Seven defines functions as machines, covers function notation, domain and range, evaluating functions, composite functions, linear functions, quadratic functions, exponential functions, and reading graphs left to right.
Work with exponentials and logarithms without fear. Chapter Nine explains exponential growth and decay, the definition of a logarithm as the same statement written backwards, the three log laws (product, quotient, power), evaluating logarithms without a calculator, solving exponential equations, and solving logarithmic equations – all for placement‑test level, not calculus.
Take the final simulated test. Chapter Ten provides a 40‑question cumulative exam covering arithmetic, negative numbers, fractions, decimals, ratios, algebra, exponents, radicals, polynomials, quadratics, functions, exponentials, logs, and word problems – with a complete answer key and step‑by‑step rationales.
1,000+ problems solved step‑by‑step – every rationale explains why we do each move, not just what the answer is. This is deliberate overlearning designed to build an organised mental filing system for mathematics.
