Starting Grade 8? A complete High School Prep guide: every CAPS foundation from Grade 7 to Grade 8, with worked examples, self-checks and a head start on…
Grade 8 is your first year of high school, and maths changes more this year than in any other. Letters start standing for numbers, negative numbers become normal, and you begin to give reasons for your answers in geometry. Everything you learn now is used again in Grades 9 to 12.
This page is your High School Prep path. It takes each CAPS Senior Phase topic in turn, reminds you what you already know from Grade 7, shows what Grade 8 adds and why it matters later, and gives you worked examples and a quick self-check. Work through it in order at the start of the year, or jump to the topic you're finding hard.
When you finish a step, try the self-check without looking at the examples. If you get it right, move on. If not, snap the question into Snap&Learn for a step-by-step explanation written for Grade 8 learners. Once the foundations feel solid, the Grade 9 section gives you a head start on next year's work.
From Grade 7: You can compare and order integers on a number line, and add and subtract them.
What Grade 8 adds: Grade 8 adds multiplying and dividing integers and using them in calculations with several operations. The sign rules are used in every algebra question you'll ever do.
Calculate: −8 + 3 × (−4)
Multiply first: 3 × (−4) = −12. Then −8 + (−12) = −20.
Calculate: (−24) ÷ (−6)
A negative divided by a negative is positive: 24 ÷ 6 = 4.
Check yourself: Calculate −5 × (−3) − 20. (Answer: 15 − 20 = −5.)
From Grade 7: You know squares and cubes of small numbers, and square and cube roots of perfect squares and cubes.
What Grade 8 adds: Grade 8 introduces the exponent laws for multiplying and dividing powers with the same base, and scientific notation for very large numbers. Grade 9 adds negative exponents.
Simplify: a⁴ × a³
Multiplying powers with the same base: add the exponents. a⁴ × a³ = a⁷.
Calculate: 2³ + √49
2³ = 8 and √49 = 7, so the answer is 15.
Check yourself: Simplify x⁸ ÷ x². (Answer: x⁶.)
From Grade 7: You can add, subtract, multiply and divide common fractions and decimals, and find percentages of amounts.
What Grade 8 adds: Grade 8 uses these with negative numbers and in money problems: percentage increase and decrease, profit and loss, discount, simple and compound interest, and hire purchase.
Calculate: 3/4 + 2/3
Common denominator 12: 9/12 + 8/12 = 17/12 = 1 5/12.
A R240 item is discounted by 15%. What is the new price?
15% of R240 = R36, so the new price is R240 − R36 = R204.
Check yourself: Write 3/8 as a decimal and a percentage. (Answer: 0.375 and 37.5%.)
From Grade 7: You can share amounts in a ratio and work with simple rates.
What Grade 8 adds: Grade 8 adds direct and indirect (inverse) proportion and harder rate problems such as speed, distance and time. These come back in graphs and in Grade 9 financial maths.
Share R120 in the ratio 3 : 5.
8 parts in total, so one part is R15. The shares are R45 and R75.
A car travels 180 km in 2 hours. What is its average speed?
Speed = distance ÷ time = 180 ÷ 2 = 90 km/h.
Check yourself: If 4 pens cost R30, what do 10 pens cost? (Answer: R7.50 each, so R75.)
From Grade 7: You can continue patterns and describe the rule in words.
What Grade 8 adds: Grade 8 writes the rule as an algebraic expression, such as Tₙ = 3n, so you can find any term without listing them all. Grade 9 extends this to rules like Tₙ = 3n + 1.
What is the next number: 5; 9; 13; 17; …?
The terms go up by 4, so the next term is 21.
The pattern 3; 6; 9; 12; … has rule Tₙ = 3n. Find T₂₀.
T₂₀ = 3 × 20 = 60.
Check yourself: Find the 10th term of 7; 14; 21; … (Answer: Tₙ = 7n, so T₁₀ = 70.)
From Grade 7: You've seen letters used for unknown numbers and simple expressions like 2x + 3.
What Grade 8 adds: Grade 8 adds collecting like terms, multiplying a monomial by a binomial or trinomial, and dividing by a monomial. Grade 9 adds multiplying two binomials and factorising.
Simplify: 3x + 5y − x + 2y
Collect like terms: 3x − x = 2x and 5y + 2y = 7y, so 2x + 7y.
Expand: 2(x − 4)
Multiply each term by 2: 2x − 8.
Check yourself: Expand and simplify 3(a + 2) − a. (Answer: 3a + 6 − a = 2a + 6.)
From Grade 7: You can solve simple equations by inspection, such as x + 5 = 12.
What Grade 8 adds: Grade 8 solves equations step by step with inverse operations, including equations with brackets and with the variable on both sides. This is the main skill of high school algebra.
Solve: 3x − 7 = 11
Add 7: 3x = 18. Divide by 3: x = 6.
Solve: x/4 + 2 = 5
Subtract 2: x/4 = 3. Multiply by 4: x = 12.
Check yourself: Solve 5x + 3 = 2x + 15. (Answer: 3x = 12, so x = 4.)
From Grade 7: You can read and draw bar graphs and simple line graphs.
What Grade 8 adds: Grade 8 plots points on the Cartesian plane to draw graphs of relationships, and reads 'global' graphs that describe a situation, such as speed changing over time. Grade 9 adds the gradient and intercepts of straight lines.
Which point lies on the line y = 2x + 1: (3; 7) or (2; 4)?
Substitute x = 3: y = 7, so (3; 7) is on the line. For x = 2, y = 5, so (2; 4) is not.
A distance–time graph is a horizontal line. What does it mean?
The distance isn't changing, so the object is standing still.
Check yourself: Complete a table for y = x + 2 with x = 0, 1 and 2. (Answer: y = 2, 3 and 4.)
From Grade 7: You can measure and classify angles and triangles, and know that the angles of a triangle add up to 180°.
What Grade 8 adds: Grade 8 adds angles formed by parallel lines (corresponding, alternate and co-interior), congruent triangles and the properties of quadrilaterals, and you start giving a reason for each statement, which is how geometry is marked up to Grade 12.
Two angles on a straight line are 3x and 60°. Find x.
Angles on a straight line add up to 180°: 3x + 60° = 180°, so x = 40°.
In △ABC, Â = 50° and B̂ = 70°. Find Ĉ.
Angles of a triangle add up to 180°: Ĉ = 60°.
Check yourself: Two parallel lines are cut by a transversal; one alternate angle is 72°. What is the other? (Answer: 72°, alternate angles are equal.)
From Grade 7: You can recognise translations, reflections and rotations of shapes.
What Grade 8 adds: Grade 8 describes these on the Cartesian plane with coordinates, and adds enlargement. The coordinate rules prepare you for shifting graphs in Grades 10 and 11.
P(2; 5) is reflected in the x-axis. Find the image.
Keep x and change the sign of y: P′(2; −5).
A(1; −3) moves 4 units right and 2 units up. Where does it end up?
(1 + 4; −3 + 2) = (5; −1).
Check yourself: Reflect (−3; 4) in the y-axis. (Answer: (3; 4).)
From Grade 7: You can find the perimeter and area of squares, rectangles and triangles, and the volume of cubes and rectangular prisms.
What Grade 8 adds: Grade 8 adds the circumference and area of circles, surface area from nets, and the volume of triangular prisms. Grade 9 adds cylinders.
Find the area of a rectangle 8 cm by 5 cm.
Area = 8 × 5 = 40 cm².
Find the area of a circle with radius 10 cm (π ≈ 3.14).
A = πr² = 3.14 × 100 = 314 cm².
Check yourself: Find the volume of a cube with sides of 3 cm. (Answer: 27 cm³.)
From Grade 7: You know right angles and can identify right-angled triangles.
What Grade 8 adds: Pythagoras is new in Grade 8: in a right-angled triangle, hypotenuse² = sum of the squares of the other two sides. It is one of the most used results in high school maths.
The shorter sides of a right-angled triangle are 6 cm and 8 cm. Find the hypotenuse.
c² = 36 + 64 = 100, so c = 10 cm.
Is a triangle with sides 5, 12 and 13 right-angled?
5² + 12² = 169 = 13², so yes.
Check yourself: Find the hypotenuse when the other sides are 9 cm and 12 cm. (Answer: 15 cm.)
From Grade 7: You can collect data, draw bar graphs and pie charts, and find the mean, median and mode.
What Grade 8 adds: Grade 8 adds the range, grouping data, histograms, and comparing relative frequency from experiments with theoretical probability.
Find the median of 4; 9; 2; 7; 5.
Sort: 2; 4; 5; 7; 9. The middle value is 5.
A bag has 3 red and 5 blue marbles. Find P(red).
3 red out of 8 marbles: P(red) = 3/8.
Check yourself: Find the range of 12; 7; 19; 3; 15. (Answer: 19 − 3 = 16.)
Algebra. In Grade 8 letters stand for numbers in almost every topic, and you solve equations step by step. Getting comfortable with integers and algebraic expressions early makes the rest of the year much easier.
It's a step up, but every new idea builds on Grade 7. Work through the High School Prep path in order, practise a little every day, and ask for help as soon as something doesn't make sense.
Yes. Once these foundations feel solid, the Grade 9 section covers factorising, linear graphs, financial maths and more.
Yes. Set your grade to Grade 8 · High School Prep and every explanation uses short steps, everyday words and only the methods you've been taught.
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