Algebraic Techniques Flashcards

Questions and Answers

What does the index law state for multiplication of exponents?

m^a x m^b = m^(a-b)

m^a x m^b = m^(a+b) (correct)

m^a x m^b = 1

m^a x m^b = a + b

What is the value of m^0?

What does m^-1 equal?

1/m

The expression 2/(8x-y)^5 can be written as 2(8x-y)^5.

False Signup and view all the answers

What is the relationship expressed in fractional indices?

m^(1/2) x m^(1/2) = m Signup and view all the answers

Write in surd form: m^2/3.

3√m^2 Signup and view all the answers

Write √2m in index form.

2m^(1/2) Signup and view all the answers

The formula for the difference of two squares is a^2 - b^2 = ______

(a+b)(a-b) Signup and view all the answers

What is factorisation (HCF)?

A method to rewrite an expression as a product of its highest common factor. Signup and view all the answers

What does 'trinomials' refer to?

Turning three terms into a bracketed equation. Signup and view all the answers

What is meant by 'rationalising the denominator'?

To eliminate any radicals in the denominator of a fraction. Signup and view all the answers

Study Notes

Index Laws

m^a x m^b results in m^(a+b)
m^a ÷ m^b results in m^(a-b)

Zero Indices

Any base raised to the power of zero equals one: m^0 = 1

Negative Indices

m^-1 is equivalent to 1/m
To express a negative exponent in a fraction, flip the fraction to make it positive, e.g., (2/3)^-1 = 3/2

Expressions with Negative Indices

An expression like 2/(8x - y)^5 can be rewritten as 2(8x - y)^-5

Fractional Indices

The expression √m multiplied by itself equals m
m^(1/2) multiplied by m^(1/2) also equals m, establishing that √m = m^(1/2)
The cube root of m, 3√m, multiplied by itself three times also equals m; therefore, 3√m = m

Writing in Surd Form

The expression m^(2/3) can be expressed as the cube root of m squared: 3√(m^2)

Writing in Index Form

The square root of 2m can be denoted as 2m^(1/2)

Factorisation (HCF)

Revisiting factorisation methods is essential; concepts are usually straightforward.

Grouping in Pairs

Practice problems related to grouping in pairs to enhance understanding.

Trinomials

Trinomials can be transformed into bracketed equations, facilitating easier factorisation.

Perfect Squares

Review perfect squares to strengthen algebraic manipulation skills.

Difference of Two Squares

The formula a^2 - b^2 factors into (a+b)(a-b), a crucial algebraic identity to remember.

Algebraic Fractions

Go through related questions to gain a better grasp of simplifying and manipulating algebraic fractions.

Simplifying Surds

Practice examples focused on simplifying surds, reinforcing techniques learned.

Rationalising the Denominator

It's crucial to fully revise methods of rationalising denominators to eliminate roots from the bottom of fractions.

Description

This quiz consists of flashcards covering essential algebraic techniques, specifically index laws, zero, negative, and fractional indices. Each card provides a definition and examples to help reinforce your understanding of these concepts. Test your knowledge and master the fundamentals of algebra.