Further Modelling with Functions How do I solve modelling problems? There will be no one-size-fits-all step-by-step guide to solving modelling questions A combination of skills and problem-solving ...
Quadratic Denominators What is meant by partial fractions with quadratic denominators? How do I find partial fractions involving quadratic denominators? STEP 1 Factorise the denominator a...
Squared Linear Denominators Partial fractions In partial fractions the common denominator is split into parts (factors) This is the reverse process to adding (or subtracting) fractions In harder qu...
Linear Denominators What are partial fractions? This is the reverse process to adding (or subtracting) fractions When adding fractions a common denominator is required In partial fractions the comm...
Improper Algebraic Fractions What are top-heavy (improper) rational expressions (or algrbraic fractions)? The degree of the numerator is greater than or equal to the degree of the denominator How d...
Rational Expressions (Algebraic Fractions) What are rational expressions? Rational numbers are numbers that can be written as a fraction (quotient)Rational comes from ratio – a number is rational i...
Polynomial Factorisation What is polynomial factorisation? Factorising a polynomial combines the factor theorem with the method of polynomial division The goal is to break down a polynomial as far ...
Factor Theorem What is the factor theorem? The factor theorem is a very useful result about polynomials A polynomial is an algebraic expression consisting of a finite number of terms, with non-nega...
Polynomial Division What is a polynomial? A polynomial is an algebraic expression consisting of a finite number of terms, with non-negative integer indices only What is polynomial division? Polynom...
Modulus Functions - Solving Equations Modulus graphs and equations Two non-parallel straight-line graphs would intersect once If modulus involved there could be more than one intersection Deducing ...
Modulus Functions - Sketching Graphs Modulus functions The modulus function makes any ‘input’ positive |x| = x if x ≥ 0 |f(x)| = f(x) if f(x) ≥ 0 |x| = -x if x < 0 |f(x)| = -f(x) if f(...
Modelling with Volumes of Revolution What is meant by modelling with volumes of revolution? Many every day objects such as buckets, beakers, vases and lamp shades can be modelled as a solid of rev...
