Gr10 Math Lit: June test easy P(1)

Number Formats and Conventions

• Convention: A standard way of doing something.
• Format: The way something appears or is set out.
• In South Africa, the convention is to use a decimal comma to separate whole numbers from decimal fractions and spaces to separate groups of three digits.
• Other formats include using decimal points and commas in different contexts, like in bank statements.

Numbers in Different Situations

• Measurements: Used for lengths and masses.
• Counting Numbers: Represent exact counts.
• Order Numbers: Indicate positions.
• Money Amounts: Represent financial values.
• Percentages: Represent rates.
• Codes: Used for identification.

Whole Numbers in Words

• Separate numbers into groups of three digits from right to left.
• Read and write each group individually.

Place Value of Large Numbers

• Use place value to understand the size of numbers.
• Use a place value table to compare numbers.

Arranging Numbers in Order

• Create a place value table.
• Write the numbers in the table.
• Compare the numbers column by column from left to right.
• Arrange the numbers accordingly.

Operations Using Numbers and Calculator Skills

Estimating

• Helps to think about a problem before working it out.
• Assists in checking the accuracy of answers.

Using a Calculator

• Basic keys: On/Off, Memory Functions, Basic Operations, and Other Functions.
• Memory keys allow storing and recalling numbers during calculations.

Order of Operations and Brackets (BODMAS)

• B: Brackets first.
• O: Orders (powers, roots).
• DM: Division and Multiplication (from left to right).
• AS: Addition and Subtraction (from left to right).

Addition and Multiplication Shortcuts

• Breaking Down and Multiplying: Break numbers into parts, multiply each part, and add results.
• Grouping: Rearrange numbers to make calculations easier.

Multiplying by 10, 100, and 1000

• Shift each digit to the left by the number of zeros in the multiplier.

Common Fractions

Definitions

• Proper Fractions: Numerator is smaller than the denominator.
• Improper Fractions: Numerator is larger than the denominator.
• Mixed Numbers: A combination of a whole number and a fraction.

Operations with Fractions

• Adding and Subtracting Fractions: Convert fractions to have a common denominator.
• Multiplying Fractions: Multiply the numerators together and the denominators together.
• Dividing Fractions: Multiply by the reciprocal of the divisor.

Decimal Fractions

Definitions

• Decimal fractions represent parts of a whole.

Converting Between Fractions and Decimal Fractions

• Use division to convert common fractions to decimal fractions.
• Convert decimal fractions to common fractions with denominators of 10, 100, etc.

Positive and Negative Numbers

Definitions

• Positive Numbers: Greater than zero.
• Negative Numbers: Less than zero.
• Opposite numbers are equal distances from zero but on opposite sides.

Using Positive and Negative Numbers

• Represent values below zero, such as debts or temperatures.

Rounding

Rules for Rounding

• Nearest 10: Numbers with units digits 1-4 round down, 5-9 round up.
• Contextual Rounding: Consider the practical implications of rounding in real-life situations.

Ratio, Rate, and Proportion

Definitions

• Ratio: Comparison of two or more numbers of the same type.
• Rate: Comparison of two numbers with different units.
• Proportion: Relationship indicating that two ratios are equal.

Calculations

• Simplify ratios by dividing both terms by their greatest common divisor.
• Calculate unit rates by dividing the given quantities.
• Find missing values by setting up equivalent ratios or using cross-multiplication.

Percentages

Calculating Percentages

• Convert the percentage to a fraction.
• Multiply the fraction by the given amount to find the percentage value.

Percentage Discounts and Increases

• Discount: Decrease from the original price.
• Increase: Additional amount added to the original price.

Financial Documents

Introduction and Key Concepts

• Understanding financial documents and tariff systems is crucial for managing personal and household finances.

Household Bills

• Bill: A document detailing purchased items or services, the amount paid, or the amount due.
• Credit: Money paid into an account.
• Debit: Money paid from an account.
• Debt: Money owed.

Municipal Bills

• Municipal bills in South Africa often include charges for electricity, water, and waste disposal.
• These bills provide detailed information about the property, the services used, and the amounts due.

Components of a Municipal Bill

• Property owner and address.
• Property size and valuation details.
• Invoice number.
• Account number.
• Municipality contact details.
• VAT numbers of municipal departments.
• Invoice issue date.
• Easy Pay payment number.
• Municipality banking details.
• Total amount due and payment due date.
• Code for accessing the account online.

Additional Terms

• Value Added Tax (VAT): A fixed extra cost added to the cost of most items and services in South Africa, calculated at 15%.
• Opening Balance: The amount due on the account before the current month's expenses.
• Closing Balance: The total amount due after adding the current month's expenses.

Telephone Bills

• Telephone bills detail charges for landline or cell phone usage.
• These bills can include fixed charges for line rental and variable charges for calls made.

Key Concepts

• Financial documents include household bills, telephone bills, and tariff systems.

• Understanding these documents is crucial for managing personal and household finances.### Shopping Documents

• Till slips provide details of purchased items, including prices, total amount paid, and VAT charged.

• Key components of till slips include shop name and address, shop's VAT number, invoice number, date and time of sale, description of items or services, VAT charged, and total amount payable.

Account Statements

• Store accounts allow purchases on credit with monthly payments made against the outstanding balance.
• Account statements detail purchases, payments made, and amounts owed.
• Key terms include credit available, which is the amount of credit still available for use, and credit limit, which is the maximum amount of credit allowed.

Tariff Systems

• Tariff systems determine the cost of services like electricity, water, and transport based on usage.
• Types of tariff systems include municipal tariffs, telephone tariffs, and transport tariffs.
• A tariff is a pre-determined schedule of prices for services, typically including a unit of payment paired with a unit of measurement.

Municipal Tariffs

• Municipal tariffs cover services such as electricity, water, and refuse removal.
• The cost per unit typically increases with higher usage levels.
• Formula for calculating municipal costs: Total Cost = ∑ (Usage in Category × Tariff for Category)

Telephone Tariffs

• Telephone service providers charge based on call duration and distance.
• Costs can vary based on time of day and call destination.
• Formula for calculating telephone costs: Total Cost = Basic Fixed Charge + (Rate per Second × Duration in Seconds)

Transport Tariffs

• Transport tariffs are charged per unit distance and can vary based on the mode of transport.
• The further the distance, the higher the tariff and thus the more expensive the ticket.

Probability

• A probability scale is a continuous line used to describe the likelihood of an event occurring, ranging from 0 (impossible) to 1 (certain).
• Probabilities can be expressed as fractions, decimals, or percentages.
• Events can be categorized as very unlikely, unlikely, even chance, likely, or very likely based on their probability.

Prediction

• Games of chance involve frequency, random trials, and fair or unfair outcomes.
• Theoretical probability is the calculated probability of an event, not necessarily the actual result.
• Relative frequency is the actual result of an experiment.

Fair and Unfair Games

• A fair game has an equal chance of winning or losing.
• An unfair game is weighted to favor one player over another.
• Changing the rules can make a game less fair.

Single and Combined Outcomes

• Tree diagrams are used to show all possible outcomes of an event.
• Combined outcomes involve using more than one object or repeating an experiment.
• Tree diagrams and two-way tables can be used to show all possible outcomes of combined events.

Weather Predictions

• Weather predictions are made by analyzing past weather data.
• The probability of rain, for instance, is based on how often it has rained on days with similar weather conditions in the past.
• Formula for calculating probability: P(E) = (Number of favorable outcomes) / (Total number of possible outcomes)

Key Concepts and Formulas

• Probability of an event (E): P(E) = (Number of favorable outcomes) / (Total number of possible outcomes)
• Complement of an event: P(not E) = 1 - P(E)
• Tree diagrams are visual representations of all possible outcomes of an event or series of events.
• Two-way tables are used to show the outcomes of two events, making it easier to calculate combined probabilities.
• Relative frequency: (Number of times an event occurs) / (Total number of trials)

Number Formats and Conventions

• Convention: A standard way of doing something.
• Format: The way something appears or is set out.
• In South Africa, the convention is to use a decimal comma to separate whole numbers from decimal fractions and spaces to separate groups of three digits.
• Other formats include using decimal points and commas in different contexts, like in bank statements.

Numbers in Different Situations

• Measurements: Used for lengths and masses.
• Counting Numbers: Represent exact counts.
• Order Numbers: Indicate positions.
• Money Amounts: Represent financial values.
• Percentages: Represent rates.
• Codes: Used for identification.

Whole Numbers in Words

• Separate numbers into groups of three digits from right to left.
• Read and write each group individually.

Place Value of Large Numbers

• Use place value to understand the size of numbers.
• Use a place value table to compare numbers.

Arranging Numbers in Order

• Create a place value table.
• Write the numbers in the table.
• Compare the numbers column by column from left to right.
• Arrange the numbers accordingly.

Operations Using Numbers and Calculator Skills

Estimating

• Helps to think about a problem before working it out.
• Assists in checking the accuracy of answers.

Using a Calculator

• Basic keys: On/Off, Memory Functions, Basic Operations, and Other Functions.
• Memory keys allow storing and recalling numbers during calculations.

Order of Operations and Brackets (BODMAS)

• B: Brackets first.
• O: Orders (powers, roots).
• DM: Division and Multiplication (from left to right).
• AS: Addition and Subtraction (from left to right).

Addition and Multiplication Shortcuts

• Breaking Down and Multiplying: Break numbers into parts, multiply each part, and add results.
• Grouping: Rearrange numbers to make calculations easier.

Multiplying by 10, 100, and 1000

• Shift each digit to the left by the number of zeros in the multiplier.

Common Fractions

Definitions

• Proper Fractions: Numerator is smaller than the denominator.
• Improper Fractions: Numerator is larger than the denominator.
• Mixed Numbers: A combination of a whole number and a fraction.

Operations with Fractions

• Adding and Subtracting Fractions: Convert fractions to have a common denominator.
• Multiplying Fractions: Multiply the numerators together and the denominators together.
• Dividing Fractions: Multiply by the reciprocal of the divisor.

Decimal Fractions

Definitions

• Decimal fractions represent parts of a whole.

Converting Between Fractions and Decimal Fractions

• Use division to convert common fractions to decimal fractions.
• Convert decimal fractions to common fractions with denominators of 10, 100, etc.

Positive and Negative Numbers

Definitions

• Positive Numbers: Greater than zero.
• Negative Numbers: Less than zero.
• Opposite numbers are equal distances from zero but on opposite sides.

Using Positive and Negative Numbers

• Represent values below zero, such as debts or temperatures.

Rounding

Rules for Rounding

• Nearest 10: Numbers with units digits 1-4 round down, 5-9 round up.
• Contextual Rounding: Consider the practical implications of rounding in real-life situations.

Ratio, Rate, and Proportion

Definitions

• Ratio: Comparison of two or more numbers of the same type.
• Rate: Comparison of two numbers with different units.
• Proportion: Relationship indicating that two ratios are equal.

Calculations

• Simplify ratios by dividing both terms by their greatest common divisor.
• Calculate unit rates by dividing the given quantities.
• Find missing values by setting up equivalent ratios or using cross-multiplication.

Percentages

Calculating Percentages

• Convert the percentage to a fraction.
• Multiply the fraction by the given amount to find the percentage value.

Percentage Discounts and Increases

• Discount: Decrease from the original price.
• Increase: Additional amount added to the original price.

Financial Documents

Introduction and Key Concepts

• Understanding financial documents and tariff systems is crucial for managing personal and household finances.

Household Bills

• Bill: A document detailing purchased items or services, the amount paid, or the amount due.
• Credit: Money paid into an account.
• Debit: Money paid from an account.
• Debt: Money owed.

Municipal Bills

• Municipal bills in South Africa often include charges for electricity, water, and waste disposal.
• These bills provide detailed information about the property, the services used, and the amounts due.

Components of a Municipal Bill

• Property owner and address.
• Property size and valuation details.
• Invoice number.
• Account number.
• Municipality contact details.
• VAT numbers of municipal departments.
• Invoice issue date.
• Easy Pay payment number.
• Municipality banking details.
• Total amount due and payment due date.
• Code for accessing the account online.

Additional Terms

• Value Added Tax (VAT): A fixed extra cost added to the cost of most items and services in South Africa, calculated at 15%.
• Opening Balance: The amount due on the account before the current month's expenses.
• Closing Balance: The total amount due after adding the current month's expenses.

Telephone Bills

• Telephone bills detail charges for landline or cell phone usage.
• These bills can include fixed charges for line rental and variable charges for calls made.

Key Concepts

• Financial documents include household bills, telephone bills, and tariff systems.

• Understanding these documents is crucial for managing personal and household finances.### Shopping Documents

• Till slips provide details of purchased items, including prices, total amount paid, and VAT charged.

• Key components of till slips include shop name and address, shop's VAT number, invoice number, date and time of sale, description of items or services, VAT charged, and total amount payable.

Account Statements

• Store accounts allow purchases on credit with monthly payments made against the outstanding balance.
• Account statements detail purchases, payments made, and amounts owed.
• Key terms include credit available, which is the amount of credit still available for use, and credit limit, which is the maximum amount of credit allowed.

Tariff Systems

• Tariff systems determine the cost of services like electricity, water, and transport based on usage.
• Types of tariff systems include municipal tariffs, telephone tariffs, and transport tariffs.
• A tariff is a pre-determined schedule of prices for services, typically including a unit of payment paired with a unit of measurement.

Municipal Tariffs

• Municipal tariffs cover services such as electricity, water, and refuse removal.
• The cost per unit typically increases with higher usage levels.
• Formula for calculating municipal costs: Total Cost = ∑ (Usage in Category × Tariff for Category)

Telephone Tariffs

• Telephone service providers charge based on call duration and distance.
• Costs can vary based on time of day and call destination.
• Formula for calculating telephone costs: Total Cost = Basic Fixed Charge + (Rate per Second × Duration in Seconds)

Transport Tariffs

• Transport tariffs are charged per unit distance and can vary based on the mode of transport.
• The further the distance, the higher the tariff and thus the more expensive the ticket.

Probability

• A probability scale is a continuous line used to describe the likelihood of an event occurring, ranging from 0 (impossible) to 1 (certain).
• Probabilities can be expressed as fractions, decimals, or percentages.
• Events can be categorized as very unlikely, unlikely, even chance, likely, or very likely based on their probability.

Prediction

• Games of chance involve frequency, random trials, and fair or unfair outcomes.
• Theoretical probability is the calculated probability of an event, not necessarily the actual result.
• Relative frequency is the actual result of an experiment.

Fair and Unfair Games

• A fair game has an equal chance of winning or losing.
• An unfair game is weighted to favor one player over another.
• Changing the rules can make a game less fair.

Single and Combined Outcomes

• Tree diagrams are used to show all possible outcomes of an event.
• Combined outcomes involve using more than one object or repeating an experiment.
• Tree diagrams and two-way tables can be used to show all possible outcomes of combined events.

Weather Predictions

• Weather predictions are made by analyzing past weather data.
• The probability of rain, for instance, is based on how often it has rained on days with similar weather conditions in the past.
• Formula for calculating probability: P(E) = (Number of favorable outcomes) / (Total number of possible outcomes)

Key Concepts and Formulas

• Probability of an event (E): P(E) = (Number of favorable outcomes) / (Total number of possible outcomes)
• Complement of an event: P(not E) = 1 - P(E)
• Tree diagrams are visual representations of all possible outcomes of an event or series of events.
• Two-way tables are used to show the outcomes of two events, making it easier to calculate combined probabilities.
• Relative frequency: (Number of times an event occurs) / (Total number of trials)

Number Formats and Conventions

• A convention is a standard way of doing something.
• A format is the way something appears or is set out.
• In South Africa, the convention is to use a decimal comma to separate whole numbers from decimal fractions and spaces to separate groups of three digits.

Ways of Representing Numbers

• Different types of numbers are used in various contexts, including:
  • Measurements: used for lengths and masses.
  • Counting numbers: used for exact counts.
  • Order numbers: indicate positions.
  • Money amounts: represent financial values.
  • Percentages: represent rates.
  • Codes: used for identification.

Whole Numbers in Words

• To write numbers in words:
  • Separate the number into groups of three digits from right to left.
  • Read and write each group individually.

Place Value of Large Numbers

• Use a place value table to identify the value of each digit.
• Large numbers are easier to read in symbol form due to place value.

Arranging Numbers in Order

• To order numbers:
  • Create a place value table.
  • Write the numbers in the table.
  • Compare the numbers column by column from left to right.
  • Arrange the numbers accordingly.

Operations Using Numbers and Calculator Skills

• Estimating helps to:
  • Think about a problem before working it out.
  • Check answers for accuracy.
• Basic calculator keys include:
  • On/Off
  • Memory Functions (M+, M-, MRC)
  • Basic Operations (+, -, *, /)
  • Other Functions (Square root, Percentage, Change sign, etc.)

Order of Operations and Brackets

• Calculations must follow the order of operations, often remembered by the acronym BODMAS:
  • B: Brackets
  • O: Orders (powers, roots)
  • DM: Division and Multiplication (from left to right)
  • AS: Addition and Subtraction (from left to right)

Addition and Multiplication Shortcuts

• Breaking down and multiplying: break large numbers into smaller parts, multiply each part, and then add the results.
• Grouping: rearrange numbers to make multiplication and addition easier.

Multiplying by 10, 100, and 1000

• Multiply by 10: shift each digit one place to the left.
• Multiply by 100: shift each digit two places to the left.
• Multiply by 1000: shift each digit three places to the left.

Common Fractions

• Proper fractions: numerator is smaller than the denominator.
• Improper fractions: numerator is larger than the denominator.
• Mixed numbers: a combination of a whole number and a fraction.

Operations with Fractions

• Adding and subtracting fractions: convert fractions to have a common denominator before performing the operation.
• Multiplying fractions: multiply the numerators together and the denominators together.
• Dividing fractions: multiply by the reciprocal of the divisor.

Decimal Fractions

• A decimal fraction is another way to write fractions whose denominators are powers of ten.

Converting Between Fractions and Decimal Fractions

• Common fractions to decimal fractions: use division to convert.
• Decimal fractions to common fractions: convert the decimal to a fraction with a denominator of 10, 100, 1000, etc.

Positive and Negative Numbers

• Positive numbers: greater than zero.
• Negative numbers: less than zero.
• Each positive number has an opposite negative number, which is the same distance from zero but on the opposite side.

Rounding

• Rules for rounding:
  • Nearest 10: numbers with units digits 1-4 round down, 5-9 round up.
  • Contextual rounding: consider the practical implications of rounding in real-life situations.

Ratio, Rate, and Proportion

• Ratio: a comparison of two or more numbers of the same type.
• Rate: a comparison of two numbers with different units.
• Proportion: a relationship indicating that two ratios are equal.

Percentages

• Calculating percentages:
  • Convert the percentage to a fraction.
  • Multiply the fraction by the given amount to find the percentage value.

Financial Documents

• Household bills:
  • Municipal bills for utilities like electricity and water.
  • Telephone bills.
  • Shopping documents such as till slips and account statements.

Financial Documents and Tariff Systems

• Key terms:
  • Bill: a document detailing purchased items or services, the amount paid, or the amount due.
  • Credit: money paid into an account.
  • Debit: money paid from an account.
  • Debt: money owed.

Municipal Bills

• Components of a municipal bill:
  1. Property owner and address.
  2. Property size and valuation details.
  3. Invoice number.
  4. Account number.
  5. Municipality contact details.
  6. VAT numbers of municipal departments.
  7. Invoice issue date.
  8. Easy Pay payment number.
  9. Municipality banking details.
  10. Total amount due and payment due date.
  11. Code for accessing the account online.

Telephone Bills

• Telephone bills detail charges for landline or cell phone usage.
• These bills can include fixed charges for line rental and variable charges for calls made.### Shopping Documents
• Till slips provide details of purchased items, including prices, total amount paid, and VAT charged.
• Key components of till slips: shop name and address, VAT number, invoice number, date and time of sale, description of items or services bought, VAT charged, and total amount payable.

Account Statements

• Store accounts allow purchases on credit, with monthly payments made against the outstanding balance.
• Account statements detail purchases, payments made, and amounts owed.
• Key terms: Credit Available (amount of credit still available for use), Credit Limit (maximum amount of credit allowed).

Tariff Systems

• Tariff systems determine the cost of services like electricity, water, and transport based on usage.
• Types of tariff systems: Municipal Tariffs (electricity, water, and sewage), Telephone Tariffs (landline and mobile phone usage), Transport Tariffs (buses, taxis, and trains).
• Tariff definition: a pre-determined schedule of prices for services, typically including a unit of payment paired with a unit of measurement.

Municipal Tariffs

• Municipal tariffs cover services like electricity, water, and refuse removal.
• Cost per unit typically increases with higher usage levels.
• Formula for calculating municipal costs: Total Cost = ∑ (Usage in Category × Tariff for Category).

Telephone Tariffs

• Telephone service providers charge based on call duration and distance.
• Costs can vary based on time of day and call destination.
• Formula for calculating telephone costs: Total Cost = Basic Fixed Charge + (Rate per Second × Duration in Seconds).

Transport Tariffs

• Transport tariffs are charged per unit distance and can vary based on mode of transport.
• Generally, the further the distance, the higher the tariff and thus the more expensive the ticket.

Probability

• Probability scale: a continuous line ranging from 0 (impossible) to 1 (certain).
• Events can be categorized as very unlikely, unlikely, even chance, likely, or very likely.
• Probabilities can be expressed as fractions, decimals, or percentages.

Prediction

• Games of chance: frequency (number of times something happens), random (occurs without being made to happen deliberately), trial (a test), and fair (equal chance without advantage or disadvantage).
• Theoretical probability: the calculated probability of an event, not necessarily the actual result.
• Relative frequency: the actual result of an experiment.

Event and Outcome

• Outcome: result of a single trial (e.g., rolling a 6).
• Event: collection of one or more outcomes (e.g., rolling an even number).

Fair and Unfair Games

• Fair game: equal chance of winning or losing.
• Unfair game: weighted to favor one player over another.

Single and Combined Outcomes

• Tree diagrams: used to show all possible outcomes of an event.
• Combined outcomes: using more than one object or repeating an experiment creates a compound event.

Weather Predictions

• Weather predictions are made by analyzing past weather data.
• Probability of rain, for instance, is based on how often it has rained on days with similar weather conditions in the past.
• Calculating probability: P(E) = (Number of favourable outcomes) / (Total number of possible outcomes).

Key Concepts and Formulas

• Probability of an event (E): P(E) = (Number of favourable outcomes) / (Total number of possible outcomes).
• Complement of an event: P(not E) = 1 - P(E).
• Tree diagram: visual representation of all possible outcomes of an event or series of events.
• Two-way table: a table that shows the outcomes of two events, making it easier to calculate combined probabilities.
• Relative frequency: (Number of times an event occurs) / (Total number of trials).

Learn about number formats and conventions, including the use of decimal commas and spaces to separate groups of digits in South Africa.