GCSE Maths

ultimate gcse maths flashcard set

Product Rule for Counting

Multiply outcomes of each event together.

Estimate Powers and Roots

Approximate square roots without a calculator.

Square Root Calculation

Find number that multiplies by itself to form given number.

Higher Powers Calculation

Multiply number by itself n times.

Negative Roots

Use reciprocal for negative roots.

Fractional Indices Calculation

Use n√x then raise to power m.

Natural Numbers

Positive whole numbers, sometimes including zero.

Integers

Whole numbers including negatives and zero.

Rational Numbers

Expressible as a ratio of two integers.

Square Root of 25

5 is the square root of 25.

Estimate √109

Between 10 and 11 based on nearby squares.

Notation for Powers

Powers represent repeated multiplication.

Example of 3^5

3 multiplied by itself five times equals 243.

Negative Fractional Indices

Take reciprocal of the result.

Definition of Rational Numbers

Can be expressed as a fraction.

Natural Numbers Representation

Represented by letter N.

Integers Representation

Represented by letter Z.

Subset Relationship

All natural numbers are integers (N ⊂ Z).

Exclusion of Zero

Natural numbers sometimes exclude zero.

Rational Number Examples

Examples include 1/2, -1, 2/3.

Whole Number Definition

A number that is not a fraction.

Reciprocal of a Number

1 divided by that number.

Natural Numbers

All positive integers, sometimes including zero.

Integers

Whole numbers including negatives, zero, and positives.

Rational Numbers

Numbers expressible as a ratio of two integers.

Irrational Numbers

Numbers with non-repeating, non-terminating decimals.

Real Numbers

All numbers without imaginary components.

Pi (π)

Ratio of circumference to diameter of a circle.

Surds

Square roots expressed without decimal approximation.

Repeating Decimals

Decimals that have a digit or group repeating.

Non-Repeating Decimals

Decimals that do not have repeating digits.

Rational Representation

Expressed as a fraction a/b, b≠0.

Rational Set

All rational numbers represented by Q.

Irrational Set

All irrational numbers represented by I.

Real Set

All real numbers represented by R.

Square Root

A value that, when multiplied by itself, gives the original number.

Simplifying Surds

Reducing surds to eliminate square factors.

Multiplication Rule for Surds

Multiply inside square roots for final answer.

Division Rule for Surds

Divide integers and surds separately for final answer.

Area of Circle

Calculated as A = πr².

Decimal Approximation of π

π is approximately equal to 3.14.

Set Inclusion

N ⊂ Z means natural numbers are in integers.

Negative Ratio

A rational number can be negative.

Confusion in Natural Numbers

Natural numbers may or may not include zero.

Rationalising Denominators

Removing surds from fraction denominators.

Surd

An irrational root, typically represented as √.

Difference of Two Squares

Formula: a² - b² = (a-b)(a+b).

Recurring Decimal

A decimal with digits that repeat indefinitely.

Error Interval

Range specifying possible values of a rounded number.

Upper Bound

Maximum possible value of a rounded number.

Lower Bound

Minimum possible value of a rounded number.

Truncation

Cutting off digits after a certain decimal place.

Rounding

Adjusting a number to a specified decimal place.

Conversion of Recurring Decimals

Process of turning decimals into fractions.

Fraction Representation

Expressing numbers as a ratio of integers.

Multiplying by Surd

Used to eliminate surds from denominators.

Inequality Notation

Mathematical symbols representing ranges of values.

Decimal to Fraction Formula

x = a/9 for single recurring digit.

Error in Data Output

Potential inaccuracies due to rounding or truncation.

Numerical Example

Using specific numbers to illustrate mathematical concepts.

Mathematical Notation

Symbols used to represent mathematical ideas.

Simplifying Expressions

Making mathematical expressions easier to work with.

Calculating Upper Limits

Finding the highest value within a range.

Calculating Lower Limits

Finding the lowest value within a range.

Surd Multiplication Example

4/√5 multiplied by √5 equals 4√5.

Decimal Conversion Steps

Multiply, subtract, and solve for x.

Rounding Rules

Guidelines for determining upper and lower bounds.

Upper Bound

Maximum limit of a variable's value.

Lower Bound

Minimum limit of a variable's value.

Overall Sum Upper Bound

Sum of individual upper bounds.

Overall Sum Lower Bound

Sum of individual lower bounds.

Subtracting Bounds

Finding new bounds by subtraction.

Multiplying Bounds

Product of individual bounds' limits.

Overall Product Upper Bound

Product of individual upper bounds.

Overall Product Lower Bound

Product of individual lower bounds.

Dividing Bounds

Finding new bounds by division.

Variables

Symbols representing unknown or changeable values.

Coefficients

Numerical factors multiplying variables in terms.

Terms

Single mathematical entities in expressions.

Expressions

Mathematical phrases without equality signs.

Equations

Statements showing two expressions are equal.

Identities

Equations true for all variable values.

Simplifying Expressions

Reducing expressions to simpler forms.

Evaluating Expressions

Calculating values by substituting variables.

Solving Equations

Finding variable values that satisfy equality.

Mathematical Operations

Addition, subtraction, multiplication, division actions.

Generalization in Mathematics

Representing a range of numbers with variables.

Building Blocks of Expressions

Terms combined to form expressions.

Implied Coefficient

Coefficient of 1 not explicitly written.

Disappearing Term

Term with a coefficient of 0.

Terms

Basic components of expressions in mathematics.

Coefficients

Numerical factors multiplying variables in a term.

Expressions

Mathematical phrases combining terms without equality.

Equations

Statements asserting equality of two expressions.

Solving Equations

Process of finding variable values satisfying equations.

Quadratic Equations

Equations in the form ax² + bx + c = 0.

Factorising

Breaking down a quadratic into binomial products.

Quadratic Formula

x = (-b ± √(b² - 4ac)) / 2a.

Completing the Square

Method to solve quadratics by forming a perfect square.

Binomials

Algebraic expressions with two terms.