Formula Centre
Formula guides and key subject rules for every grade and subject, with worked examples and practice.
Area of a Rectangle
Mathematical Literacy • Measurement • Grade 12
When to use it
Use when calculating the surface area of a rectangular floor, wall, garden or any flat rectangular surface.
Worked example
A tiler in Durban needs to tile a rectangular bathroom floor that measures 3.2 m in length and 2.5 m in breadth. How many square metres of tiles does he need? A = l × b = 3.2 × 2.5 = 8 m². The tiler needs 8 m² of tiles.
Common mistakes
- Forgetting to square the unit (writing m instead of m²)
- Confusing area with perimeter by adding sides instead of multiplying
- Not converting units before calculating (e.g. mixing mm and cm)
Practice question
A classroom in a school in George measures 8.5 m in length and 6 m in breadth. Calculate the area of the classroom floor.
Area of a Triangle
Mathematical Literacy • Measurement • Grade 12
When to use it
Use when calculating the area of a triangular surface such as a triangular garden bed, roof section or piece of land.
Worked example
A triangular park in Stellenbosch has a base of 14 m and a perpendicular height of 9 m. Calculate the area of the park. A = (1/2) × b × h = 0.5 × 14 × 9 = 63 m². The park has an area of 63 m².
Common mistakes
- Using the slant side instead of the perpendicular height
- Forgetting to multiply by 1/2
- Mixing up base and height values
Practice question
A triangular flowerbed at a shopping centre in Sandton has a base of 5.4 m and a perpendicular height of 3.2 m. Calculate the area of the flowerbed.
Basic Probability
Mathematical Literacy • Probability • Grade 12
When to use it
Use when determining how likely an event is to occur in a situation where all outcomes are equally likely, such as drawing cards, rolling dice or selecting items randomly.
Worked example
A bag contains 5 red marbles, 3 blue marbles and 2 green marbles. A learner at a school in Alexandra randomly picks one marble. What is the probability of picking a blue marble? Total outcomes = 5 + 3 + 2 = 10. Favourable outcomes (blue) = 3. P(blue) = 3/10 = 0.3 or 30%. The probability of picking a blue marble is 3/10.
Common mistakes
- Adding the probability of all events and getting more than 1
- Confusing favourable outcomes with total outcomes
- Not simplifying the fraction when required
Practice question
A box contains 12 pens: 4 black, 5 blue and 3 red. A learner at a school in Soweto randomly selects one pen. What is the probability that the pen selected is red? Express your answer as a fraction and as a percentage.
Break-Even Analysis
Mathematical Literacy • Finance • Grade 12
When to use it
Use in business contexts when determining the minimum number of items to sell or minimum revenue needed to cover all costs before making a profit.
Worked example
A matric learner in Thohoyandou sells homemade biscuits. Her fixed costs (oven hire, packaging) are R350 per month. Each packet of biscuits costs R8 to make (variable cost) and she sells each packet for R15. How many packets must she sell to break even? Income per packet = R15. Variable cost per packet = R8. Contribution per packet = 15 − 8 = R7. Break-Even Quantity = Fixed Costs ÷ Contribution per unit = 350 ÷ 7 = 50 packets. She must sell 50 packets to break even.
Common mistakes
- Using total income instead of contribution per unit in the denominator
- Ignoring fixed costs and only considering variable costs
- Confusing profit with break-even point
Practice question
A small business owner in Witbank sells handmade candles. Fixed costs are R600 per month. Each candle costs R12 to make and is sold for R20. Calculate the number of candles she must sell each month to break even.
Compound Interest
Mathematics • Finance, Growth and Decay • Grade 12
When to use it
Use it for investments or loans where interest is earned on interest.
Worked example
R10 000 at 8% p.a. for 5 years → A = 10 000(1,08)⁵ = R14 693,28.
Common mistakes
- Using 8 instead of 0,08 for i
- Not converting to monthly periods when compounding monthly
Practice question
R25 000 is invested at 6% p.a. compounded monthly for 3 years. Calculate A.
Compound Interest
Mathematical Literacy • Finance • Grade 12
When to use it
Use when interest is calculated on the principal AND previously earned interest. Common for savings accounts, home loans and investments over multiple years.
Worked example
Lerato from Johannesburg invests R15 000 in a fixed-deposit account that earns 7% per annum compounded annually for 5 years. A = P(1 + i)^n = 15000(1 + 0.07)^5 = 15000 × (1.07)^5 = 15000 × 1.40255 = R21 038.27. Lerato will have approximately R21 038.27 after 5 years.
Common mistakes
- Using the simple interest formula instead of the compound formula
- Not adjusting i and n when compounding is monthly or quarterly
- Rounding intermediate answers, which causes inaccurate final answers
Practice question
Sipho from Durban invests R20 000 at 9% per annum compounded annually for 6 years. Calculate the total accumulated amount at the end of the investment period.
Converting Units of Measurement
Mathematical Literacy • Measurement • Grade 12
When to use it
Use whenever measurements are given in different units and need to be made consistent before performing calculations in area, volume, perimeter or any other context.
Worked example
A swimming pool in a resort near Sun City is 12 m long, 6 m wide and 150 cm deep. Calculate the volume in cubic metres. First convert depth: 150 cm ÷ 100 = 1.5 m. V = l × b × h = 12 × 6 × 1.5 = 108 m³. The volume of the pool is 108 m³.
Common mistakes
- Forgetting to convert all measurements to the same unit before calculating
- Multiplying instead of dividing when converting from smaller to larger units
- Using the wrong conversion factor (e.g. 1 m = 10 cm instead of 100 cm)
Practice question
A storage tank on a farm in the Free State has a length of 2.5 m, a breadth of 180 cm and a height of 1.2 m. Convert all measurements to metres and then calculate the volume of the tank in cubic metres.
Cosine Rule
Mathematics • Trigonometry • Grade 12
When to use it
Use it in a non-right-angled triangle when you know two sides and the included angle, or all three sides.
Worked example
b = 8, c = 6, A = 60° → a² = 64 + 36 − 48 = 52, so a ≈ 7,21 units.
Common mistakes
- Using it when the angle is not between the two known sides
- Calculator in radian mode
Practice question
In △PQR, q = 10, r = 7 and P = 45°. Calculate p.
Derivative of a Power
Mathematics • Calculus • Grade 12
When to use it
Use it to differentiate any polynomial term, then to find gradients, tangents and stationary points.
Worked example
f(x) = 4x³ ⇒ f′(x) = 12x².
Common mistakes
- Forgetting that the derivative of a constant is 0
- Subtracting 1 from the coefficient instead of the exponent
Practice question
Differentiate f(x) = 5x⁴ − 3x² + 7.
Exchange Rate Conversion
Mathematical Literacy • Finance • Grade 12
When to use it
Use when converting between South African Rands and a foreign currency for travel, imports, exports or international purchases.
Worked example
The exchange rate is R18.50 to 1 US Dollar (USD). Ayanda from Bloemfontein wants to buy a product priced at USD 120 online. How much will she pay in Rands? Rand Amount = Foreign Amount × Exchange Rate = 120 × 18.50 = R2 220. Ayanda will pay R2 220.
Common mistakes
- Dividing instead of multiplying (or vice versa) when converting
- Using an outdated exchange rate
- Confusing which currency is the base currency in the rate given
Practice question
The exchange rate is R19.20 to 1 USD. Thandeka from Port Elizabeth is travelling to the USA and wants to exchange R5 760 into US Dollars. How many US Dollars will she receive?
Grade 12 Accounting essentials
Accounting • Essential reference • Grade 12
When to use it
Use to check the accounting equation after transactions.
Worked example
If equity is R8 000 and liabilities R2 000, assets are R10 000.
Common mistakes
- Recording a transaction on only one side.
Practice question
Calculate assets when equity is R12 000 and liabilities R3 500.
Grade 12 Afrikaans essentials
Afrikaans • Essential reference • Grade 12
When to use it
Use as a foundation for building and checking complete sentences.
Worked example
The learner reads the book.
Common mistakes
- Writing a sentence without a complete verb.
Practice question
Write one clear sentence and label its subject, verb and object.
Grade 12 Agricultural Sciences essentials
Agricultural Sciences • Essential reference • Grade 12
When to use it
Use when comparing the financial performance of farm enterprises.
Worked example
R50 000 income − R32 000 variable costs = R18 000 gross margin.
Common mistakes
- Including fixed costs as variable costs.
Practice question
Calculate gross margin from R72 000 income and R49 500 variable costs.
Grade 12 Business Studies essentials
Business Studies • Essential reference • Grade 12
When to use it
Use to assess whether a business earned a profit or loss.
Worked example
R10 000 revenue − R7 500 expenses = R2 500 profit.
Common mistakes
- Treating revenue as profit.
Practice question
Find profit on R18 000 revenue and R11 200 expenses.
Grade 12 Computer Applications Technology essentials
Computer Applications Technology • Essential reference • Grade 12
When to use it
Use to explain how digital systems handle information.
Worked example
A spreadsheet receives figures, calculates totals, displays results and saves the file.
Common mistakes
- Confusing raw data with processed information.
Practice question
Describe the information cycle for an online form.
Grade 12 Economics essentials
Economics • Essential reference • Grade 12
When to use it
Use for a simple comparison of average output between economies.
Worked example
Divide total GDP by the population for the period.
Common mistakes
- Assuming GDP per capita measures income distribution.
Practice question
Explain what happens if GDP rises faster than population.
Grade 12 Engineering Graphics and Design essentials
Engineering Graphics and Design • Essential reference • Grade 12
When to use it
Use to create or interpret scaled technical drawings.
Worked example
50 mm / 500 mm = 1:10 scale.
Common mistakes
- Using different units for the two lengths.
Practice question
Convert 2 m to a 1:20 drawing length.
Grade 12 English essentials
English • Essential reference • Grade 12
When to use it
Use as a foundation for building and checking complete sentences.
Worked example
The learner reads the book.
Common mistakes
- Writing a sentence without a complete verb.
Practice question
Write one clear sentence and label its subject, verb and object.
Grade 12 Geography essentials
Geography • Essential reference • Grade 12
When to use it
Use when comparing how densely places are populated.
Worked example
20 000 people / 100 km² = 200 people per km².
Common mistakes
- Forgetting the per-square-kilometre unit.
Practice question
Calculate density for 45 000 people in 150 km².
Grade 12 History essentials
History • Essential reference • Grade 12
When to use it
Use when evaluating usefulness, reliability and bias in a source.
Worked example
Identify the creator, intended audience, evidence and historical setting.
Common mistakes
- Calling a source unreliable only because it is biased.
Practice question
Apply the four-part rule to one historical source.
Grade 12 Information Technology essentials
Information Technology • Essential reference • Grade 12
When to use it
Use when planning algorithms and tracing programs.
Worked example
Read two numbers, add them, then display the sum.
Common mistakes
- Processing a value before it has been initialised.
Practice question
Write pseudocode that calculates an average.
Grade 12 IsiNdebele essentials
IsiNdebele • Essential reference • Grade 12
When to use it
Use as a foundation for building and checking complete sentences.
Worked example
The learner reads the book.
Common mistakes
- Writing a sentence without a complete verb.
Practice question
Write one clear sentence and label its subject, verb and object.
Grade 12 IsiXhosa essentials
IsiXhosa • Essential reference • Grade 12
When to use it
Use as a foundation for building and checking complete sentences.
Worked example
The learner reads the book.
Common mistakes
- Writing a sentence without a complete verb.
Practice question
Write one clear sentence and label its subject, verb and object.
Grade 12 IsiZulu essentials
IsiZulu • Essential reference • Grade 12
When to use it
Use as a foundation for building and checking complete sentences.
Worked example
The learner reads the book.
Common mistakes
- Writing a sentence without a complete verb.
Practice question
Write one clear sentence and label its subject, verb and object.
Grade 12 Life Orientation essentials
Life Orientation • Essential reference • Grade 12
When to use it
Use when planning study, career, health or personal goals.
Worked example
Improve my test mark from 60% to 70% by the end of term.
Common mistakes
- Setting a goal with no measure or deadline.
Practice question
Rewrite one personal goal using SMART.
Grade 12 Life Sciences essentials
Life Sciences • Essential reference • Grade 12
When to use it
Use when comparing microscope images with actual specimens.
Worked example
A 20 mm image of a 2 mm object has magnification 10×.
Common mistakes
- Mixing measurement units.
Practice question
Find the magnification of a 30 mm image of a 3 mm object.
Grade 12 Sepedi essentials
Sepedi • Essential reference • Grade 12
When to use it
Use as a foundation for building and checking complete sentences.
Worked example
The learner reads the book.
Common mistakes
- Writing a sentence without a complete verb.
Practice question
Write one clear sentence and label its subject, verb and object.
Grade 12 Sesotho essentials
Sesotho • Essential reference • Grade 12
When to use it
Use as a foundation for building and checking complete sentences.
Worked example
The learner reads the book.
Common mistakes
- Writing a sentence without a complete verb.
Practice question
Write one clear sentence and label its subject, verb and object.
Grade 12 Setswana essentials
Setswana • Essential reference • Grade 12
When to use it
Use as a foundation for building and checking complete sentences.
Worked example
The learner reads the book.
Common mistakes
- Writing a sentence without a complete verb.
Practice question
Write one clear sentence and label its subject, verb and object.
Grade 12 SiSwati essentials
SiSwati • Essential reference • Grade 12
When to use it
Use as a foundation for building and checking complete sentences.
Worked example
The learner reads the book.
Common mistakes
- Writing a sentence without a complete verb.
Practice question
Write one clear sentence and label its subject, verb and object.
Grade 12 Tourism essentials
Tourism • Essential reference • Grade 12
When to use it
Use when building a tour quotation or itinerary budget.
Worked example
R2 000 fixed + R500 variable = R2 500 total.
Common mistakes
- Leaving out taxes, commissions or exchange-rate effects.
Practice question
Calculate the cost of a tour from a supplied budget.
Grade 12 Tshivenda essentials
Tshivenda • Essential reference • Grade 12
When to use it
Use as a foundation for building and checking complete sentences.
Worked example
The learner reads the book.
Common mistakes
- Writing a sentence without a complete verb.
Practice question
Write one clear sentence and label its subject, verb and object.
Grade 12 Xitsonga essentials
Xitsonga • Essential reference • Grade 12
When to use it
Use as a foundation for building and checking complete sentences.
Worked example
The learner reads the book.
Common mistakes
- Writing a sentence without a complete verb.
Practice question
Write one clear sentence and label its subject, verb and object.
Hire Purchase (HP) Total Cost
Mathematical Literacy • Finance • Grade 12
When to use it
Use when a consumer buys goods on credit through a hire purchase agreement and you need to find the total amount paid over the repayment period.
Worked example
Zanele from Cape Town buys a refrigerator priced at R6 500 on hire purchase. She pays a 10% deposit and then 24 monthly instalments of R295. Calculate the total cost. Deposit = 10% × 6500 = R650. Total Cost = 650 + (295 × 24) = 650 + 7080 = R7 730. Zanele pays R7 730 in total, which is R1 230 more than the cash price.
Common mistakes
- Forgetting to include the deposit in the total cost calculation
- Calculating the deposit on the wrong base amount
- Not multiplying the instalment by the correct number of months
Practice question
Mandla from Pretoria buys a television set priced at R4 800 on hire purchase. He pays a 15% deposit and 18 monthly instalments of R260. Calculate the total cost of the television on hire purchase.
Impulse-Momentum Theorem
Physical Sciences • Momentum and Impulse • Grade 12
When to use it
Use it for collisions and impacts where a force acts for a short time.
Worked example
0,5 kg ball stopped from 4 m·s⁻¹ in 0,2 s → F = (0,5 × −4)/0,2 = −10 N.
Common mistakes
- Ignoring the direction of Δv
- Using speed instead of change in velocity
Practice question
A 0,15 kg cricket ball is struck from 30 m·s⁻¹ to −40 m·s⁻¹ in 0,05 s. Find the average force.
Inflation Adjustment
Mathematical Literacy • Finance • Grade 12
When to use it
Use when estimating how much an item or service will cost in the future, given a constant annual inflation rate.
Worked example
A bag of groceries in Kimberley currently costs R850. If inflation is 5.5% per annum, how much will the same basket of groceries cost in 3 years? Future Value = 850 × (1 + 0.055)^3 = 850 × (1.055)^3 = 850 × 1.17424 = R997.60. The groceries will cost approximately R997.60 in 3 years.
Common mistakes
- Confusing inflation with simple interest (inflation uses compound growth)
- Forgetting to convert the percentage to a decimal
- Rounding the inflation factor too early
Practice question
School fees at a school in Nelspruit are currently R12 000 per year. If the annual inflation rate is 6% per annum, what will the school fees be in 4 years?
Kinetic Energy
Physical Sciences • Work, Energy and Power • Grade 12
When to use it
Use it for the energy of a moving object and in the work-energy theorem.
Worked example
m = 2 kg, v = 3 m·s⁻¹ → E_k = ½(2)(9) = 9 J.
Common mistakes
- Squaring the mass instead of the speed
- Forgetting the ½
Practice question
Calculate the kinetic energy of a 60 kg athlete running at 8 m·s⁻¹.
Map Scale (Finding Actual Distance)
Mathematical Literacy • Maps and Scale • Grade 12
When to use it
Use when reading a map and converting the distance measured on the map to the actual real-world distance using the given scale.
Worked example
On a map of the Garden Route, the scale is 1:200 000. The distance between George and Knysna on the map measures 3.5 cm. Calculate the actual distance in km. Actual Distance = 3.5 cm × 200 000 = 700 000 cm. Convert to km: 700 000 ÷ 100 000 = 7 km. The actual distance between George and Knysna is 7 km.
Common mistakes
- Forgetting to convert cm to km after multiplying
- Dividing instead of multiplying the map distance by the scale denominator
- Misreading the scale ratio from the map
Practice question
On a street map of Pretoria, the scale is 1:50 000. The distance between two shopping centres on the map measures 4.6 cm. Calculate the actual distance in kilometres.
Mean (Arithmetic Average)
Mathematical Literacy • Data Handling • Grade 12
When to use it
Use when you want to find the average of a set of numerical data values, such as average test scores, average monthly expenses or average rainfall.
Worked example
Seven Grade 12 learners at Tshwane High School scored the following marks in a Mathematical Literacy test: 56, 63, 72, 45, 80, 67, 71. Calculate the mean mark. Sum = 56 + 63 + 72 + 45 + 80 + 67 + 71 = 454. Mean = 454 ÷ 7 = 64.86. The mean mark is approximately 64.86%.
Common mistakes
- Dividing by the wrong number of values (e.g. counting incorrectly)
- Including a value twice or omitting a value when summing
- Confusing the mean with the median or mode
Practice question
The monthly electricity bills (in Rands) for a household in Mamelodi over 6 months were: R780, R950, R1 020, R870, R1 100, R930. Calculate the mean monthly electricity bill.
Median
Mathematical Literacy • Data Handling • Grade 12
When to use it
Use when finding the central value of a data set, especially when the data has extreme values (outliers) that could skew the mean.
Worked example
The weekly wages (in Rands) of 7 workers at a construction site in Rustenburg are: R1 200, R3 500, R1 400, R1 300, R1 250, R1 450, R1 350. Step 1: Arrange in ascending order: R1 200, R1 250, R1 300, R1 350, R1 400, R1 450, R3 500. Step 2: n = 7 (odd), so the median is the 4th value = R1 350. The median wage is R1 350.
Common mistakes
- Forgetting to arrange data in ascending order before finding the median
- Selecting the wrong position when n is even (must average the two middle values)
- Confusing median with mean
Practice question
The ages of 8 employees at a clothing factory in Newcastle are: 28, 34, 41, 23, 55, 36, 29, 42. Calculate the median age of the employees.
Newton's Second Law
Physical Sciences • Mechanics: Motion and Forces • Grade 12
When to use it
Use it whenever a resultant force acts on an object and you need its acceleration (or vice versa).
Worked example
F_net = 20 N on a 5 kg box → a = 20/5 = 4 m·s⁻² in the direction of the force.
Common mistakes
- Using weight (N) where mass (kg) is required
- Adding forces without regard to direction
Practice question
A 1 200 kg car accelerates at 2,5 m·s⁻². Calculate the resultant force.
Percentage Discount
Mathematical Literacy • Finance • Grade 12
When to use it
Use when calculating the sale price of an item after a percentage discount has been applied, such as during sales at South African retail stores.
Worked example
A jacket at a store in Canal Walk, Cape Town is originally priced at R1 200. The store offers a 25% discount. What is the discounted price? Discounted Price = 1200 × (1 − 0.25) = 1200 × 0.75 = R900. The jacket will cost R900 after the 25% discount.
Common mistakes
- Calculating the discount amount but forgetting to subtract it from the original price
- Dividing the discount percentage instead of multiplying
- Incorrectly converting the percentage to a decimal (e.g. using 25 instead of 0.25)
Practice question
A pair of sneakers at a sports shop in Menlyn Park, Pretoria is priced at R1 850. During a sale, a 30% discount is offered. Calculate the sale price of the sneakers.
Perimeter of a Rectangle
Mathematical Literacy • Measurement • Grade 12
When to use it
Use when you need to find the total distance around the outside of a rectangular shape, such as fencing a garden or framing a picture.
Worked example
A rectangular vegetable garden in Limpopo measures 12 m in length and 7 m in breadth. Farmer Dlamini wants to fence the entire garden. Calculate the total length of fencing required. P = 2(l + b) = 2(12 + 7) = 2 × 19 = 38 m. Farmer Dlamini needs 38 m of fencing.
Common mistakes
- Adding only two sides instead of all four
- Using P = l × b (confusing perimeter with area)
- Mixing units (e.g. cm and m in the same calculation)
Practice question
A rectangular soccer field in Soweto measures 90 m in length and 55 m in breadth. Calculate the total distance around the field.
Quadratic Formula
Mathematics • Algebra and Equations • Grade 12
When to use it
Use it to solve any quadratic equation ax² + bx + c = 0, especially when the expression does not factorise.
Worked example
Solve 2x² + 3x − 2 = 0. x = [−3 ± √(9 + 16)]/4 = (−3 ± 5)/4, so x = 0,5 or x = −2.
Common mistakes
- Forgetting the ± and losing a root
- Dividing only part of the numerator by 2a
Practice question
Solve 3x² − 5x − 2 = 0 using the quadratic formula.
Range
Mathematical Literacy • Data Handling • Grade 12
When to use it
Use when measuring the spread or variability of a data set. A large range indicates high variability; a small range indicates consistency.
Worked example
The daily temperatures (in °C) recorded in Upington over one week were: 34, 38, 29, 41, 36, 33, 40. Calculate the range of temperatures. Maximum = 41°C. Minimum = 29°C. Range = 41 − 29 = 12°C. The range of temperatures is 12°C.
Common mistakes
- Subtracting in the wrong order (Minimum − Maximum gives a negative answer)
- Not identifying the true maximum or minimum from an unordered list
- Confusing range with interquartile range
Practice question
The number of customers served per day at a fast-food outlet in Khayelitsha over 6 days were: 145, 210, 178, 98, 230, 162. Calculate the range of customers served.
Reading and Interpreting a Bar Graph or Pie Chart (Proportion/Percentage)
Mathematical Literacy • Data Handling • Grade 12
When to use it
Use when interpreting data from charts, tables or surveys and you need to express one category as a percentage of the total, or when verifying the accuracy of a pie chart sector.
Worked example
A survey of 200 learners at a school in Mpumalanga asked them to choose their favourite sport. 60 chose soccer, 50 chose netball, 40 chose athletics, and 50 chose cricket. What percentage of learners chose soccer? Percentage = (60 ÷ 200) × 100 = 30%. 30% of learners chose soccer as their favourite sport.
Common mistakes
- Dividing the whole by the part instead of the part by the whole
- Forgetting to multiply by 100 to convert the decimal to a percentage
- Using an incorrect total (e.g. omitting a category when calculating the whole)
Practice question
At a community health clinic in Katlehong, 350 patients were seen in one week. 84 patients were treated for flu, 105 for injuries, 70 for chronic conditions and 91 for other ailments. Calculate the percentage of patients treated for injuries.
Simple Interest
Mathematical Literacy • Finance • Grade 12
When to use it
Use when interest is calculated only on the original principal amount, typically for short-term loans or fixed-deposit accounts that use simple interest.
Worked example
Thabo from Polokwane invests R8 000 in a savings account at a simple interest rate of 6.5% per annum for 3 years. Calculate the total amount he will have after 3 years. A = P(1 + in) = 8000(1 + 0.065 × 3) = 8000(1 + 0.195) = 8000 × 1.195 = R9 560. Thabo will have R9 560 after 3 years.
Common mistakes
- Forgetting to convert the percentage to a decimal before substituting
- Multiplying i × n incorrectly by adding instead of multiplying
- Confusing Simple Interest (SI = Pin) with the accumulated amount formula A = P(1 + in)
Practice question
Nomsa from East London borrows R12 500 at a simple interest rate of 8% per annum for 4 years. Calculate the total amount she must repay at the end of the period.
VAT Calculation (Adding VAT)
Mathematical Literacy • Finance • Grade 12
When to use it
Use when calculating the price a consumer pays after 15% Value Added Tax (VAT) is added to the original price of a VAT-inclusive item in South Africa.
Worked example
A plumber in Johannesburg charges R2 400 (excluding VAT) for a repair job. How much will the client pay including 15% VAT? Price including VAT = 2400 × 1.15 = R2 760. The client will pay R2 760 including VAT.
Common mistakes
- Adding 15 to the price instead of 15% of the price
- Using the incorrect VAT rate (South African VAT is 15%, not 14%)
- Confusing VAT-inclusive and VAT-exclusive prices
Practice question
A contractor in Sandton charges R8 500 (excluding VAT) to install a ceiling. Calculate the total amount the customer must pay, including 15% VAT.
Volume of a Cylinder
Mathematical Literacy • Measurement • Grade 12
When to use it
Use when calculating the capacity of cylindrical containers such as water tanks, tin cans, pipes or silos.
Worked example
A water tank on a farm in the Karoo is cylindrical with a radius of 1.2 m and a height of 2 m. Calculate the volume of the tank. V = π × r² × h = 3.142 × (1.2)² × 2 = 3.142 × 1.44 × 2 = 9.05 m³. The tank holds approximately 9.05 m³ of water (which is 9 050 litres).
Common mistakes
- Using diameter instead of radius in the formula
- Forgetting to square the radius
- Using π = 3 instead of 3.142
Practice question
A cylindrical tin of paint sold at a hardware store in Pietermaritzburg has a radius of 8 cm and a height of 22 cm. Calculate the volume of paint the tin can hold, in cm³. (Use π = 3.142)
Volume of a Rectangular Prism (Box)
Mathematical Literacy • Measurement • Grade 12
When to use it
Use when finding the capacity or space inside a box-shaped container such as a storage box, room or fish tank.
Worked example
A storage container at a warehouse in Johannesburg measures 5 m in length, 3 m in breadth and 2.5 m in height. Calculate the volume of the container. V = l × b × h = 5 × 3 × 2.5 = 37.5 m³. The container has a volume of 37.5 m³.
Common mistakes
- Forgetting to cube the unit (writing m² instead of m³)
- Mixing up volume and area formulas
- Using inconsistent units for different dimensions
Practice question
A rectangular fish tank at a pet shop in Roodepoort measures 80 cm in length, 35 cm in breadth and 40 cm in height. Calculate the volume of the tank in cubic centimetres.
Wave Equation
Physical Sciences • Waves, Sound and Light • Grade 12
When to use it
Use it for any wave when two of speed, frequency and wavelength are known.
Worked example
f = 50 Hz, λ = 4 m → v = 200 m·s⁻¹.
Common mistakes
- Using wavelength in cm without converting
- Confusing frequency with period
Practice question
A sound wave travels at 340 m·s⁻¹ with a frequency of 425 Hz. Find its wavelength.