A-Level Maths Polynomials

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Polynomials Topics for A-Level Maths

This module will teach you the following:

Year 1

  • Polynomial expressions
  • Arithmetic operations on polynomials
  • Graphs of polynomials

Year 2

  • Simplifying algebraic fractions

What’s Included?

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?

Polynomial expressions

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.

Turning points:

  • 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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