Understanding Standard Form and Algebra Basics

Standard Form

A way to express large or small numbers.

A

The front number in standard form, 1 < A < 10.

n

The power of 10 indicating decimal movement.

Positive n

Indicates a big number in standard form.

Negative n

Indicates a small number in standard form.

Decimal Point Movement

Determines the value of n in standard form.

Expressing Big Numbers

Convert to standard form by adjusting decimal.

Expressing Small Numbers

Convert to standard form with negative power.

Calculating in Standard Form

Add, subtract, multiply, or divide without a calculator.

Multiplying in Standard Form

Multiply front numbers and add powers of 10.

Dividing in Standard Form

Divide front numbers and subtract powers of 10.

Adding in Standard Form

Ensure powers of 10 are equal before adding.

Subtracting in Standard Form

Align powers of 10 before subtracting front numbers.

Negative Numbers

Follow specific rules for multiplication and division.

Terms in Algebra

Collections of numbers, letters, and brackets multiplied.

Like Terms

Terms with the same variable combinations.

Simplifying Expressions

Combine like terms to simplify algebraic expressions.

Powers

Indicate repeated multiplication of a number.

Roots

Inverse operation of raising to a power.

Collecting Like Terms

Reorganize and combine similar terms in expressions.

Perimeter Expression

Sum of all sides of a rectangle.

Invisible Sign

Indicates a positive sign when absent.

Squaring Negative Numbers

Results in a positive value.

Cubing Negative Numbers

Results in a negative value.

Standard Form Conversion

Transform numbers into A x 10^n format.

Exam Practice Questions

Exercises to reinforce understanding of concepts.

Power

A number multiplied by itself a specified number of times.

Multiplying Powers Rule

Add the exponents when multiplying like bases.

Dividing Powers Rule

Subtract the exponents when dividing like bases.

Raising Powers Rule

Multiply the exponents when raising a power to another power.

Power of One

Any number to the power of one equals itself.

Power of Zero

Any number to the power of zero equals one.

Power of One Rule

One raised to any power remains one.

Negative Power Rule

A negative exponent indicates a reciprocal.

Fractional Powers

Represent roots; e.g., 1/2 is square root.

Two-Stage Fractional Powers

Evaluate roots before applying powers.

Algebraic Fraction Simplification

Use power rules to simplify algebraic fractions.

Single Brackets Expansion

Multiply outside term by each inside term.

Double Brackets Expansion

Multiply each term in the first bracket by each in the second.

FOIL Method

First, Outside, Inside, Last for double brackets.

Cubed Brackets Expansion

Expand by writing as three brackets.

Difference of Squares

Factoring form: a² - b² = (a-b)(a+b).

Height of Tower Expression

Sum of heights from stacked pieces of tubing.

Simplifying Surds

Express square roots in simplest form.

Evaluating Without Calculator

Solve expressions using known powers and roots.

Algebraic Factorisation

Rewriting expressions as products of factors.

Combining Like Terms

Add or subtract terms with the same variable.

Negative Fraction Powers

Turn upside down and make positive.

Roots and Powers Relationship

Roots are fractional powers; e.g., √x = x^(1/2).

Simplifying Algebraic Expressions

Use rules to combine and reduce expressions.

Height Calculation Example

Find total height using f, g, h variables.

Expanding Triple Brackets

Multiply two brackets, then multiply by the third.

Brackets in Algebra

Use brackets to denote multiplication and order.

Evaluating Powers

Calculate powers and roots for simplification.

Simplicity in Algebra

Aim for the simplest form of expressions.