Paper 1:
QUESTION 1 (30 marks ± 5 marks) Short context – mixed questions, ONLY Level 1.
QUESTION 2 – Finance
QUESTION 3 – Measurement
QUESTION 4 – Maps and Plans
QUESTION 5 – Data Handling
Probability will be dispersed in all five questions, where it is appropriate. Paper 2:
Four or five questions will be set. All contexts have mixed questions. A concerted effort will be made to place the questions in order of level of difficulty, however, it must be noted that 'level of difficulty' is subjective.
Level 1: Knowing
* Read information directly from an electricity bill (e.g. date; name of account holder; electricity consumption for the month).
* Show how the 'Total Due' on the electricity bill has been calculated by adding together all items listed on the bill.
* Show how the VAT value listed on the electricity bill has been calculated when told that VAT is 14% of the value excluding VAT (that is, calculating a direct percentage of an amount).
Level 2: Applying routine procedures in familiar contexts* Use a given formula to show how the amount charged for electricity consumption shown on the bill has been determined.
* Complete a table of values to show the cost of various quantities of electricity consumption.
* Use the table of values to construct a graph to represent the cost of electricity consumption.
* Increasing/Decreasing by a given percentage
Level 3: Applying multi-step procedures in a variety of contexts* Replicate the calculations/values shown on the bill for a different electricity consumption value.
* Without any scaffolded or guiding questions, draw a graph to represent the cost of electricity on a particular electricity system.
Level 4: Reasoning and reflecting* Choose an appropriate strategy (e.g. tables of values, graphs, and interpreting points of intersection.) to compare the electricity costs of two different electricity systems and make a decision about which system is the most cost effective for a user with particular needs.
* Analyse a newspaper article describing proposed increases in electricity tariffs and make deductions about the implications of these increases for consumers.
* Rework the answer if the initial conditions change
Level 1: Knowing
* Classify items on an income and expenditure statement as fixed, variable and occasional income and expenditure.
* Show how total income, expenditure and profit/loss values on an income and expenditure statement or budget have been determined.
Level 2: Applying routine procedures in familiar contextsConstruct an income and expenditure statement for an individual or a household.
* Construct a budget for a small household project.
Level 3: Applying multi-step procedures in a variety of contextsConstruct an income and expenditure statement for a business that includes a comparison of income and expenditure values over a two-year period.
* Construct a budget for a large fundraising event.
* Revise a budget if conditions change
Level 4: Reasoning and reflecting* Analyse a budget for a household or business and make recommendation as to how the expenditure should be changed to improve the finances of the household/business.
* Compare income and expenditure values for a business or organisation over a two-year period and describe differences and/or trends.
* Analyse projected versus actual budget values and explain differences
Level 1: Knowing
* Determine the cost price of an item by adding together given cost values for the component parts of the item.
* Determine the income generated from the sale of an item based on a given sales price and given sales volumes.
Level 2: Applying routine procedures in familiar contexts* Compare the difference between the cost and selling price of an item by calculating the percentage mark-up in price of the selling price from the cost price.
* Construct a table of values to show how the cost price of an item changes depending on the number of items made.
* Draw a graph from a given table.
Level 3: Applying multi-step procedures in a variety of contexts* Draw graphs, without scaffolded or guiding questions, to show the costs involved in producing an item and money generated from the sale of the item.
* Investigate, through research, the various costs involved in manufacturing an item, and decide on an appropriate selling price for the item.
* Calculate profit if only one of income or expenses is given and the other still needs to be calculated.
Level 4: Reasoning and reflecting* Conduct market research on a group of people and use the results of the research to defend a particular selling price for a product.
* Interpret graphs showing the cost of production and income generated from the production and sale of an item, and use the graphs to make decisions about the business (e.g. how many items must be manufactured and sold to cover all production costs).
Level 1: Knowing
* Define 'break-even' in the context in which a problem is posed (e.g. in the context of a business, 'break- even' refers to the income that must be generated to cover all expenses).
Level 2: Applying routine procedures in familiar contexts* Determine the break-even point of a business from a given table of income and expenditure values.
* When given two graphs that intersect, read off the value of the independent and dependent variables at the breakeven point (point of intersection) of the graphs.
Level 3: Applying multi-step procedures in a variety of contexts* Draw two or more graphs and identify the point of intersection of those two graphs in order to compare different options (e.g. income vs. expenditure; cellphone contract options; electricity tariff system.)
Level 4: Reasoning and reflecting*Explain the relevance of the breakeven point of two graphs in relation to the problem or context for which the graphs have been drawn.
* Explain the meaning of different regions on a graph (that is, between different points of intersection) in relation to the problem or context for which graphs have been drawn.
* Rework the answer if the initial conditions change.
Level 1: Knowing
* Define 'interest' and the 'interest rate'.
* Identify interest rate values quoted on bank statements.
Level 2: Applying routine procedures in familiar contexts* Perform simple interest calculations manually (that is, without the use of a calculator) over multiple time periods.
* Read values off graphs showing simple and compound investment scenarios.
* Calculate compound interest compounded annually.
*Increase or decrease a given amount by a certain percentage.
Level 3: Applying multi-step procedures in a variety of contexts* Perform compound interest calculations manually (that is, without the use of a formula) over multiple time periods.
* Complete a table that models a loan scenario and include consideration of a monthly interest calculation, monthly repayment, and monthly amount outstanding on the loan.
* Draw graphs from given tables of values to represent loan scenarios.
* Calculate compound growth/decline
Level 4: Reasoning and reflecting* Construct a model of a loan or investment scenario without scaffolded or guiding questions.
* Investigate and describe the impact of increasing the monthly repayments on the total cost of the loan/investment.
* Investigate and describe the impact of making a lump sum payment into a loan/investment during the first half of the loan/investment period on the total cost of the loan/investment.
* Rework the answer if need be.
Level 1: Knowing
* Define the term 'inflation'.
Level 2: Applying routine procedures in familiar contexts* Show by calculation how the price of an item might change if affected by inflation (that is, increasing a value by a percentage).
Level 3: Applying multi-step procedures in a variety of contexts* Calculate compound growth/decline
Level 4: Reasoning and reflecting* Show by calculation how the price of an item might change if affected by inflation over multiple time periods
* Use knowledge of inflation rates to argue and justify a particular salary
* Rework the answer if the initial conditions change
Level 1: Knowing
* Identify the name of the employee listed on a pay slip and the month for which the pay slip has been issued.
* Identify the employee's monthly salary.
* State how the employees 'taxable income' has been determined by referring to the salary and deduction values shown on the payslip.
* Define the terms 'gross pay', 'net pay', 'deductions', and 'taxable income' shown on a payslip
Level 2: Applying routine procedures in familiar contexts* Read appropriate tax values from given income tax deduction tables.
* Identify the income tax bracket into which an individual falls based on a given monthly and/or annual income.
Level 3: Applying multi-step procedures in a variety of contexts* Use formulae provided on income tax bracket tables to calculate an individual's annual and monthly income tax.
* Investigate through calculation how the tax rebate value is determined.
* Calculate compound growth/decline
Level 4: Reasoning and reflecting* Compare income tax tables over different financial periods and explain how an individual's tax may have changed from one period to another.
* Investigate the effect that an increase in salary has on increased tax payments.
* Analyse graphs showing changes in income tax over different time periods and explain differences
Level 1: Knowing
Identify the exchange rate between two currencies from a given table or rate board.
Level 2: Applying routine procedures in familiar contexts* Use a given exchange rate to determine the value of one currency for a specific quantity of another currency.
Level 3: Applying multi-step procedures in a variety of contextsPerform currency conversion calculations, taking into account currency exchange fees charged by banks and other financial institutions
Level 4: Reasoning and reflecting* Explain how the Big Mac Index' provides a tool for determining the worth of one currency in relation to another currency;
* Explain why it is not necessarily accurate when a South African tourist in America exclaims that a can of cool drink that costs $2,00 (R14,00) is much cheaper in South Africa.
Level 1: Knowing
* Convert between mm, cm, m and km.
* Convert between g and kg.
* Convert between ml and litres
Level 2: Applying routine procedures in familiar contexts* Convert from °C to °F (and vice versa) using given formulae.
* Convert between different systems using given conversion factors (e.g. convert from m3 to litres using the fact that 1 m3 = 1 000 litres)
Level 3: Applying multi-step procedures in a variety of contexts* Convert between different systems using given conversion tables, where it is necessary to first identify and then use an appropriate conversion factor from the table.
Level 4: Reasoning and reflecting* Compare solutions to a problem expressed in different units and make a decision about what unit is the most appropriate or useful for the particular context in which the problem is posed.
Level 1: Knowing
* Measure accurately using appropriate measuring instruments (e.g. ruler; tape measure; kitchen scale; jug).
Level 2: Applying routine procedures in familiar contexts* Perform calculations involving measured values (e.g. working out how much longer one piece of wood is than another piece)
Level 3: Applying multi-step procedures in a variety of contexts* Use measured values in conjunction with other content or skills to complete a larger project (e.g. measure the dimensions of a bedroom to determine the running metres of carpet needed for the floor).
* Make adjustments to calculated values to accommodate measurement errors and inaccuracies due to rounding.
Level 4: Reasoning and reflecting* Make decisions about the need for accuracy when performing a measurement in a particular context.
* Interpret a measured value and make a decision based on the value (e.g. measure the temperature of a child and decide if the child should be taken to hospital)
Level 1: Knowing
* Define terms (e.g. 'area', 'perimeter', 'volume', 'radius'). * Identify from a list of given formulae which formulae relate to perimeter calculations, which relate to area calculations, etc.
* Determine the radius of a circle from a given diameter.
* Know that area is expressed in units2 (e.g. cm2 ) and volume in units3 (e.g. cm3 ).
* Know and use formulae for perimeter, area and volume.
Level 2: Applying routine procedures in familiar contexts* Calculate perimeter, area and volume by substituting given values into given formulae.
* Describe relationships between input and output values in a table of data concerning space, shape and measurement.
Level 3: Applying multi-step procedures in a variety of contextsPerform preliminary calculations to determine dimensions required in perimeter/area/volume calculations and then calculate perimeter/area/volume (e.g. when asked to determine the volume of concrete needed for the foundations of a house, interpret top view plans of the foundation trench of a house, use the plans to determine the dimensions of the trench, and then calculate the volume of the trench).
Level 4: Reasoning and reflecting* Use perimeter, area and/or volume calculations to complete a project, where it is not stated specifically what type of calculation is required (e.g. when asked to determine the amount of paint needed to paint a building, first interpret plans to determine dimensions of the walls, then calculate the surface area of the walls, then use the paint conversion ratio on the back of the paint tin to determine the required number of litres of paint required).
Level 1: Knowing
* Read time values on a clock or watch.
*Converting between seconds, minutes and hours
Level 2: Applying routine procedures in familiar contexts* Record time values and perform calculations with time.
Level 3: Applying multi-step procedures in a variety of contexts* Interpret time values on a bus timetable to determine departure, arrival and travelling times.
Level 4: Reasoning and reflecting* Perform time calculations in conjunction with maps and other travel resources in order to plan a trip (e.g. determine approximate travelling times, appropriate stopping points for refuelling, the time to start a journey in order to arrive at a destination at a particular time).
Level 1: Knowing
* Explain the meaning of a given scale (e.g. explain what the scale 1 : 100 means in terms of the measurements on a plan and actual dimensions).
Level 2: Applying routine procedures in familiar contexts* Use a given scale to determine actual measurements when given measured values, or measured values from given actual values.
Level 3: Applying multi-step procedures in a variety of contexts* Use a given scale in conjunction with measurement on a plan/map to determine length/dimensions.
* Determine the scale of a map or plan.
* Use a given scale in conjunction with other content or skills to complete a project (e.g. use a given scale to determine the dimensions in which to draw a 2-dimensional plan of an object, and then draw the plan).
Level 4: Reasoning and reflecting* Critique the scale in which an object has been drawn and offer an opinion as to a more appropriate scale.
* Decide on an appropriate scale to which to draw a picture or build a model, and then complete the project.
Level 1: Knowing
Identify the labels/namses of national roads (e.g. N3) that must be travelled on to travel between two locations.
* Identify the names of the towns on the route between two locations.
* Identify the scale of a map.
Level 2: Applying routine procedures in familiar contexts* Identify the position of two locations on a map and use given distance values on the map to determine the travelling distance between the two locations.
* Interpret a given set of directions and describe what location the directions lead to.
* Provide a set of directions to travel between two locations in a town using street names.
Level 3: Applying multi-step procedures in a variety of contextsUse a map in conjunction with a distance chart to determine the shortest route to travel between two locations.
* Identify a possible route between two locations on a map, measure the distance between the locations, and use a given scale to estimate the distance between the two locations.
* Estimate travelling times between two or more locations based on estimated travelling speed and known or calculated distances.
Level 4: Reasoning and reflecting* Critique a proposed travel route in relation to distance, estimated travelling times, etc. and suggest and justify possible alternative routes.
* Use maps in conjunction with other travel resources (e.g. exchange rate information; distance chart; bus timetable) and financial information (e.g. fare tables; petrol price) to plan and cost a trip).
* Make decisions regarding appropriate stopping points during a journey based on considerations of fatigue, petrol consumption travelling time, etc.
Level 1: Knowing
* Identify the scale of a plan.
* Define terms (e.g. floor plan; elevation plan; layout plan; etc.).
* Read off the value(s) of given dimensions on the plan (e.g. the length of the wall is 4 m)
Level 2: Applying routine procedures in familiar contexts* Use a given key to identify the number of windows/doors/rooms shown on a plan for a building.
* Identify on which plan a particular structure is shown (e.g. the door is shown on the North elevation plan).
Level 3: Applying multi-step procedures in a variety of contexts* Measure dimensions on a plan and use a given scale to determine actual dimensions.
* Use plans in conjunction with other content, skills or applications to complete a project (e.g. interpret plans to determine the dimensions of a room in order to establish the amount of carpet needed for the floor of the room)
Level 4: Reasoning and reflecting* Describe an item represented in a plan.
* Critique the design of a structure shown on a plan.
* Decide on an appropriate scale in which to draw a plan and then draw the plan.
* Make connections between plans showing different views of the same structure (e.g. explain which wall shown on a floor plan is represented on a particular side view plan).
Level 1: Knowing
* Measure the dimensions of a structure for which a model or 2D drawing will be constructed.
Level 2: Applying routine procedures in familiar contexts* Build a model using a given table of dimensions or a given net/cut-out.
Level 3: Applying multi-step procedures in a variety of contexts* Use a given scale to determine the dimensions in which to build a model or make a 2D drawing, and complete the project.
* Build a model and use the model in conjunction with other content, skills or applications to solve a problem (e.g. build a model of a container and use the model to investigate different types of packaging arrangements; or build a model of a container and determine the surface area and volume of the model to investigate the amount of storage space available in the container).
Level 4: Reasoning and reflecting* Decide on an appropriate scale in which to build a model or make a 2D drawing, use the scale to determine dimensions, and complete the project.
* Construct and compare two models in terms of storage space and materials used and make a decision about which model will the better choice for packaging an item.
* Analyse a model and critique the layout of the structure shown in the model.
Level 1: Knowing
* Read information directly from a given questionnaire/survey (e.g. the name of the organisation for which the questionnaire is being conducted).
* Complete a given questionnaire.
* Sort data from smallest to biggest.
* Count the number of values in a data set.
* State the difference between categorical data and numerical data; discrete and continuous data.
* Read information from frequency tables.
Level 2: Applying routine procedures in familiar contexts* Conduct a given questionnaire/survey with a group of people.
Sort data according to two categories (e.g. sort a set of data separately for females and males).
* Complete a given frequency table.
* Calculate percentage values to represent the relative sizes of different categories of data.
Level 3: Applying multi-step procedures in a variety of contexts* Decide on appropriate questions to include on a questionnaire/survey, construct and then conduct the questionnaire/survey.
* When given a raw set of data, sort the data, decide on appropriate intervals (if necessary), and construct a frequency table to organise the data. If necessary, use the frequency table to draw an appropriate graph to represent the data.
Level 4: Reasoning and reflecting* Critique the questions/layout of a questionnaire/survey.
* Make a deduction about whether collected information is biased or valid based on the structure of instrument used to collect the data and the way in which the data was collected.
* Explain with justification whether data is discrete or continuous.
* Analyse data organised in tables and make deductions about trends in the data.
Level 1: Knowing
* Identify the percentage chance of rain for a particular town from a weather report in a newspaper.
* State the meaning of terms associated with probability (e.g. event; outcome)
Level 2: Applying routine procedures in familiar contextsExpress the probability of an event using fraction, percentage and decimal notation.
* Identify all of the possible outcomes of a particular event (e.g. rolling a dice; gambling game).
* Explain whether or not a particular rainfall prediction indicates that it is more or less likely to rain.
Level 3: Applying multi-step procedures in a variety of contexts* Conduct an experiment to compare the experimental probability of an event to its theoretical probability.
* Identify appropriate values from a given table of data values (e.g. on motor vehicle fatalities in South Africa) and express the probability of certain events shown in the table.
* Develop a game involving probability and play the game with another learner in the class.
* Design simple contingency tables and use them to calculate probabilities.
* Draw tree diagrams and use them to calculate probabilities
Level 4: Reasoning and reflecting* Analyse a table of rainfall data for a town and make predictions about the chance of rain in that town during a particular month during the year.
* Explain whether the statement 'if I take the same lottery numbers every week then my chances of winning increase' makes sense.
* Critique the use of references to probability values in newspaper articles.
* Analyse a table showing risk assessment profiles of people in different age groups and explain why particular age groups are classified as higher risks than others.
* Analyse a game involving probability and make a deduction about the fairness of the game.