CIE A Level Maths: Pure 3复习笔记1.2.3 Factorisation
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 ...
CIE A Level Maths: Pure 3复习笔记1.2.2 Factor & Remainder Theorem
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...
CIE A Level Maths: Pure 3复习笔记1.2.1 Polynomial Division
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...
CIE A Level Maths: Pure 3复习笔记1.1.2 Modulus Functions - Solving Equations
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 ...
CIE A Level Maths: Pure 3复习笔记1.1.1 Modulus Functions - Sketching Graphs
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(...
CIE A Level Maths: Pure 1复习笔记6.2.6 Modelling with Volumes of Revolution
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...
CIE A Level Maths: Pure 1复习笔记6.2.5 Adding and Subtracting Volumes
Adding and Subtracting Volumes Why might I need to add or subtract volumes of revolution? As with the area between a curve and a line or the area between 2 curves, a required volume may be created...
CIE A Level Maths: Pure 1复习笔记6.2.4 Volumes of Revolution
Volumes of revolution around the x-axis What is a volume of revolution around the x-axis? A volume of revolution is the volume of this solid formed How do I find the volume of revolution around the...
CIE A Level Maths: Pure 1复习笔记6.2.3 Area between 2 curves
Area between 2 curves What is the area between two curves? Ensure you are familiar with … Area under a curve Area between a line and a curve In general find the definite integral of “upper curve” –...
CIE A Level Maths: Pure 1复习笔记6.2.2 Area between a curve and a line
Area between a curve and a line What is the area between a curve and a straight line? This is the area enclosed by a curve and a line between their intersections The intersections may need to be fo...
CIE A Level Maths: Pure 1复习笔记6.2.1 Area Under a Curve
Area Under a Curve What does area under a curve mean? The phrase “area under a curve” refers to the area bounded by … ... the x-axis … the graph of y = f(x) … the vertical line x = a … the vertical...
CIE A Level Maths: Pure 1复习笔记6.1.5 Improper Integrals
Improper Integrals What are improper integrals? An improper integral is a definite integral where one or both of the limits is either: Positive or minus infinity A point where the function is undef...
