Senior Phase · Grade 8

Mathematics

patterns and logic 🌱
Grade 8 CAPS Aligned Free Papers + Memos
Overview
What to expect in Grade 8

Grade 8 Mathematics extends the algebraic and geometric foundations of Grade 7. Learners develop fluency with linear equations, algebraic expressions and functions, and geometry is formalised with proofs about triangles and quadrilaterals. The number system expands to include irrational numbers and the concept of real numbers. Grade 8 Maths is critical — the algebraic and geometric thinking built here is directly required in Grade 10 Maths.

Weekly time
4.5 hours per week
Number system
Real numbers: rational + irrational
Assessment
Formal: 75% · Informal: 25%
Key concepts
Linear equations · functions · congruency · theorem of Pythagoras
CAPS curriculum
Term-by-term breakdown
Term 1
Real numbers and algebraic expressions
  • Real numbers: rational and irrational numbers — classify, order, represent on number line
  • Surds: simplify square roots and cube roots — rational vs irrational
  • Exponential laws: aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ, a⁰ = 1
  • Scientific notation: write large and small numbers, multiply and divide
  • Algebraic expressions: expand brackets — distributive law
  • Factorise: common factor, difference of two squares, trinomials (basic)
  • Add, subtract and multiply algebraic expressions
  • Simplify fractions with monomial denominators
Term 2
Linear equations, inequalities and functions
  • Solve linear equations: one variable, with brackets, fractions
  • Solve linear inequalities: represent solution on number line
  • Simultaneous equations: solve by substitution
  • Functions: input-output, tables of values, Cartesian plane
  • Graph y = mx + c: gradient and y-intercept
  • Interpret gradient: positive, negative, zero, undefined
  • Graph y = ax²: shape, turning point, axis of symmetry
  • Direct and inverse proportion: graphs and equations
Term 3
Geometry: triangles and quadrilaterals
  • Angle sum of a triangle: proof and application
  • Types of triangles: equilateral, isosceles, scalene — properties
  • Congruent triangles: four conditions — SSS, SAS, AAS, RHS
  • Similar triangles: AA condition — scale factor, proportional sides
  • Properties of quadrilaterals: parallelogram, rectangle, rhombus, square, trapezium, kite
  • Midpoint theorem: statement, proof and application
  • The Theorem of Pythagoras: proof, application, converse
  • Trigonometry introduction: sin, cos, tan ratios in right-angled triangles
Term 4
Measurement, data and revision
  • Area and perimeter of composite shapes including circles
  • Volume and surface area of cylinders, triangular prisms, rectangular prisms
  • Circles: area, circumference, arc length, area of sector
  • Data: frequency tables, grouped data
  • Histograms and frequency polygons
  • Cumulative frequency: ogive (cumulative frequency curve)
  • Measures of central tendency: mean, median, mode from grouped data
  • Scatter plots: draw, identify trend, line of best fit
Assessment
How marks are split
Numbers, Operations & Relationships
25%
Space & Shape / Measurement
30%
Patterns, Functions & Algebra
30%
Data Handling
15%
Key skills
What a strong Grade 8 student can do
Classify and work with real and irrational numbers Apply exponential laws Write numbers in scientific notation Factorise algebraic expressions Solve linear equations and inequalities Solve simultaneous equations by substitution Draw and interpret y = mx + c graphs Prove and apply triangle congruency conditions Apply the Theorem of Pythagoras Calculate sin, cos, tan ratios Calculate volume and surface area of prisms and cylinders Draw and interpret ogives and scatter plots
Practice materials
Grade 8 papers & memos
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Study smarter
Tips for Grade 8
📐

Factorise before you simplify. Always look for a common factor first. Then check for difference of two squares. Then trinomial.

✏️

Show every step when solving equations. Method marks are allocated at every step. Even a wrong answer can score marks with correct working.

📝

For geometry: state the reason. Every statement in a geometry proof needs a reason in brackets. 'angles of a triangle = 180°' is a reason.

🔢

Pythagoras: square, add/subtract, root. c² = a² + b². Write the formula, substitute, calculate, take the square root. Every time.

🌱

Functions need a table of values first. Before drawing any graph, calculate at least 3 points. Sketch then refine.