A-Level Maths Polynomials
Everything you need to know about polynomials for A-Level Maths. Save countless hours of time!
Polynomials Topics for A-Level Maths
This module will teach you the following:
- Polynomial expressions
- Arithmetic operations on polynomials
- Graphs of polynomials
- Simplifying algebraic fractions
We’ve created 52 modules covering every Maths topic needed for A level, and each module contains:
- An editable PowerPoint lesson presentation
- Editable revision handouts
- A glossary which covers the key terminologies of the module
- Topical mind maps for visualising the key concepts
- Printable flashcards to help students engage active recall and confidence-based repetition
- A quiz with accompanying answer key to test knowledge and understanding of the module
As a premium member, once rolled out you get access to the entire library of A-Level Maths resources. For now, we have made the first five topics completely free of charge for you to get a taste of what’s to come.
A Level Maths Resources Mapped by Exam Board
Once completed our modules can be used with both UK and international A Level examination board specifications.
We will put together comprehensive mapping documents which will show you exactly which modules align to the specification you are teaching or learning.
What Are Polynomials?
Quadratic expression consists of a coefficient of x2. It is in the form of ax2+bx+c=0 where a is a non-zero number, b and c can be any real number.
Cubic expression consists of coefficient of x3. It is in the form of ax3 + bx2 + cx + d = 0 where a is a non-zero number, b, c and d can be any real number. For example: 3x3 – 2x2 + x – 1, p3 – 1 and z3 – 2z2 + 1.
The above described expressions are called polynomials. The order of a polynomial is equal to the highest power of variable it contains. For example, order of a quartic expression is 4.
- A n-order polynomial has a maximum of n-1 turning points.
- At repeated roots, the curve touches the x-axis at those points
Arithmetic operations of polynomials:
- Addition or subtraction: like terms
- Multiplication: term by term
- Division: long division method
Finding nature of curves:
- To find the nature of curves:
- x→∞, substitute a large positive value for x.
- x→ -∞, substitute a large negative value for x.
Graphs of polynomials:
- Shape of curve varies with respect to:
- Order of the polynomial
- Sign of the highest power of the variable.
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