Studied by 2 people
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.
