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Lessons & topics

Algebra and Equations

Grade 12 • Mathematics

Solving and manipulating expressions and equations, including quadratics.

Calculus

Grade 12 • Mathematics

Differentiation and its applications to graphs and maximum/minimum problems.

Chemistry: Mole and Stoichiometry

Grade 12 • Physical Sciences

Quantitative chemistry: moles, concentration and reacting masses.

Electricity and Electric Circuits

Grade 12 • Physical Sciences

Current, potential difference, resistance and electrical power.

Finance, Growth and Decay

Grade 12 • Mathematics

Interest, investments, loans and depreciation calculations.

Functions and Graphs

Grade 12 • Mathematics

Sketching and interpreting graphs, intercepts, asymptotes and transformations.

Mechanics: Motion and Forces

Grade 12 • Physical Sciences

How forces cause objects to accelerate, and how to describe their motion.

Momentum and Impulse

Grade 12 • Physical Sciences

Momentum changes, impulse and collisions.

Statistics and Probability

Grade 12 • Mathematics

Analysing data and calculating probabilities.

Trigonometry

Grade 12 • Mathematics

Ratios, identities, equations and solving triangles.

Formulas

Addition Rule for Probability

Mathematics • Statistics and Probability • Grade 11

P(A or B) = P(A) + P(B) − P(A and B)

P(A)Probability of event A (—)

P(B)Probability of event B (—)

When to use it

Use it when two events can happen together and you must not double-count the overlap.

Worked example

P(A) = 0,5, P(B) = 0,4, P(A and B) = 0,2 → P(A or B) = 0,5 + 0,4 − 0,2 = 0,7.

Common mistakes

Leaving out the overlap term for non-mutually-exclusive events

Practice question

If P(A) = 0,45, P(B) = 0,3 and P(A and B) = 0,1, find P(A or B).

Area of a Rectangle

Mathematical Literacy • Measurement • Grade 12

A = l × b

AArea of the rectangle (Square metres (m²), square centimetres (cm²), etc.)

lLength of the rectangle (Metres (m) or centimetres (cm))

bBreadth (width) of the rectangle (Metres (m) or centimetres (cm))

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

A = (1/2) × b × h

AArea of the triangle (Square metres (m²) or square centimetres (cm²))

bBase of the triangle (Metres (m) or centimetres (cm))

hPerpendicular height of the triangle (Metres (m) or centimetres (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.

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

P(Event) = Number of favourable outcomes ÷ Total number of possible outcomes

P(Event)Probability of a specific event occurring (No unit (value between 0 and 1, or expressed as a percentage or fraction))

Number of favourable outcomesHow many outcomes result in the desired event (No unit (count))

Total number of possible outcomesAll possible outcomes in the sample space (No unit (count))

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.

Practice questions

Lerato invests R12 500 in a savings account at Capitec Bank. The account offers 8,5% per annum compound interest. How much will her investment be worth after 3 years? Round your answer to the nearest cent.

Grade 10

Mathematics

Simplify the following expression: 3x²(2x - 4) - 2x(x² - 5x + 1)

Grade 10

Mathematics

In triangle PQR, the interior angle at P is (3x + 10)°, the interior angle at Q is (2x - 5)° and the interior angle at R is (x + 15)°. Which one of the following statements about the value of x and angle Q is CORRECT?

Grade 10

Mathematics

A straight line passes through the points (-2; 1) and (4; 13). Determine the equation of this line in the form y = mx + c.

Grade 10

Mathematics

The monthly salaries (in rands) of seven employees at a small business in Durban are: R8 200; R9 500; R7 800; R12 000; R8 200; R10 300; R15 600. Calculate the mean, median and mode of the salaries. If the owner earns R45 000 per month and is added to the dataset, which measure of central tendency is MOST affected and why?

Grade 10

Mathematics