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Grade 12 Maths Literacy Formula Sheet

CAPS / NSC · Paper 1 & Paper 2 · Grades 10–12

⇄ Conversions

Length	Mass	Volume & capacity	Time
1 km = 1 000 m	1 t = 1 000 kg	1 kℓ = 1 000 ℓ	1 h = 60 min
1 m = 100 cm	1 kg = 1 000 g	1 ℓ = 1 000 mℓ	1 min = 60 s
1 cm = 10 mm	1 g = 1 000 mg	1 mℓ = 1 cm³	1 h = 3 600 s
1 m = 1 000 mm	1 t = 1 000 000 g	1 m³ = 1 000 ℓ = 1 kℓ	1 year = 12 months

Temperature $^\circ\text{C} = (^\circ\text{F} - 32) \div 1{,}8$

and back $^\circ\text{F} = (^\circ\text{C} \times 1{,}8) + 32$

Converting up the list (mm to m) divides; converting down multiplies. Decide which before you touch the calculator — a conversion done the wrong way round is the most common single error in Paper 1.

▭ Perimeter & Area

Square $P = 4s \qquad A = s^{2}$

Rectangle $P = 2(l + b) \qquad A = l \times b$

Triangle $A = \tfrac{1}{2} \times b \times h$

Circle — circumference $C = 2\pi r = \pi d$

Circle — area $A = \pi r^{2}$

use $\pi \approx 3{,}14$

Perimeter is a length (m, cm) and area is a square (m², cm²). If the units of your answer do not match the quantity, the answer is wrong no matter what the calculator said.

⬔ Surface Area & Volume

Cube — SA $6s^{2}$

Cube — volume $s^{3}$

Rectangular prism — SA $2(lb + lh + bh)$

Rectangular prism — V $l \times b \times h$

Cylinder — SA $2\pi r^{2} + 2\pi r h$

Cylinder — volume $\pi r^{2} h$

Triangular prism — V $\left(\tfrac{1}{2} \times b \times h\right) \times H$

An open tank, a pipe or a tin without a lid does not have all its faces — read the question and subtract the ones that are not there. $h$ is the height of the triangle; $H$ is the length of the prism.

R Interest & Growth

Simple interest $A = P(1 + i \cdot n)$

Compound interest $A = P(1 + i)^{n}$

$A$ final amount

$P$ principal — the amount at the start

$i$ interest rate as a decimal ($8\%\rightarrow 0{,}08$)

$n$ number of periods

Interest earned $A - P$

Percentage change $\dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

Interest "compounded monthly" at $12\%$ per year means $i = 0{,}01$ and $n$ counts months. Divide the rate and multiply the periods by the same number, every time.

% Money, VAT & Business

Profit $\text{income} - \text{expenses}$

Percentage profit $\dfrac{\text{profit}}{\text{cost price}} \times 100$

Break-even $\text{income} = \text{expenses}$

VAT (South Africa) $15\%$

Add VAT $\text{incl.} = \text{excl.} \times 1{,}15$

Remove VAT $\text{excl.} = \text{incl.} \div 1{,}15$

BMI $\dfrac{\text{mass in kg}}{(\text{height in m})^{2}}$

To take VAT off a price you divide by $1{,}15$ — you do not subtract $15\%$. Subtracting gives a different, wrong number, and the exam asks this on purpose.

⏱ Rates & Proportion

Speed $\dfrac{\text{distance}}{\text{time}}$

Distance $\text{speed} \times \text{time}$

Time $\dfrac{\text{distance}}{\text{speed}}$

Fuel consumption $\dfrac{\text{litres used}}{\text{distance in km}} \times 100$

gives litres per 100 km

Exchange rate $\text{rands} = \text{foreign amount} \times \text{rate}$

Actual length $\text{measured length} \times \text{scale factor}$

$2{,}5$ hours is not 2 hours 50 minutes. Convert the decimal part by multiplying by 60 before you do anything else with a time answer.

σ Data Handling & Probability

Mean $\dfrac{\text{sum of all values}}{\text{number of values}}$

Median middle value of the ordered data

Mode the value that appears most often

Range $\text{maximum} - \text{minimum}$

Interquartile range $Q_3 - Q_1$

Probability $\dfrac{\text{favourable outcomes}}{\text{total possible outcomes}}$

As a percentage $\text{probability} \times 100$

Order the data before finding a median or a quartile. Every mark lost on this topic is lost to an unsorted list.

✓ What the Exam Gives You, and What It Does Not

Given in the paper Income tax tables and rebates, UIF rates, tariff tables, timetables, plans, maps and any scale you need

Why it matters Tax brackets change every year, so there is nothing to memorise — the marks are in reading the table correctly and applying the right bracket

Expected from you Every conversion above, all the measurement formulae, both interest formulae, and the ability to read a plan, a graph and a statement

Worth the most marks Showing the substitution before the answer. A correct number with no working scores less than working with an arithmetic slip

Maths Literacy is examined on context, not on manipulation: almost every question is a real document — a payslip, a municipal bill, a floor plan — and the first mark is for finding the right number in it.

Maths Literacy is examined on reading the context, not on the formula.

The formula is rarely the hard part — finding the right number on a payslip or a municipal bill is. I tutor Maths Literacy one-to-one in Gqeberha, at your own table, in English or Afrikaans. The first consultation is free.

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An independent revision aid aligned to the CAPS/NSC Mathematical Literacy syllabus. Not an official Department of Basic Education document. The VAT rate shown is the South African rate at the time of writing.