Formula Centre

When to use it

Use when calculating the surface area of a rectangular floor, wall, garden or any flat rectangular surface.

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)

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.

Common mistakes

• Using the slant side instead of the perpendicular height
• Forgetting to multiply by 1/2
• Mixing up base and height values

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.

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

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.

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

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.

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

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.

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)

When to use it

Use when converting between South African Rands and a foreign currency for travel, imports, exports or international purchases.

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• Using an outdated exchange rate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

When to use it

Use for discounts, increases, budgets, data and comparisons.

Common mistakes

• Dividing the whole by the part.

When to use it

Use for discounts, increases, budgets, data and comparisons.

Common mistakes

• Dividing the whole by the part.

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.

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

When to use it

Use when estimating how much an item or service will cost in the future, given a constant annual inflation rate.

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

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.

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

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.

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

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.

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

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.

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)

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.

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)

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.

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

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.

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)

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.

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)

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.

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

When to use it

Use when calculating the capacity of cylindrical containers such as water tanks, tin cans, pipes or silos.

Common mistakes

• Using diameter instead of radius in the formula
• Forgetting to square the radius
• Using π = 3 instead of 3.142

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.

Common mistakes

• Forgetting to cube the unit (writing m² instead of m³)
• Mixing up volume and area formulas
• Using inconsistent units for different dimensions