What we cover
Grade 11 maths, unit by unit through the year
Learners in the scientific and technological tracks use the same student book each semester: four units in semester 1, five in semester 2. General Mathematics, taught in the arts and humanities track, has a separate book.
- Semester 1, Unit 1
Sequences and series
Arithmetic and geometric sequences, recursive formulas, sigma notation and the sum of an infinite geometric series. Marks slip when learners confuse the nth term with the sum, or count one term too few.
- Arithmetic and geometric sequences
- Sigma notation
- Infinite geometric series
- Semester 1, Unit 2
Functions and operations on them
Domain and range, continuity, increasing and decreasing intervals, symmetry and asymptotes, then composition, inverse functions and graph transformations. Common losses: composing in the wrong order and shifting a graph the wrong way.
- Domain and range
- Composition and inverses
- Graph transformations
- Semester 1, Unit 3
Polynomial functions
Long and synthetic division, end behaviour, zeros and their multiplicity, and the remainder, factor and rational zeros theorems. A missing zero coefficient in synthetic division quietly spoils the whole answer.
- Synthetic division
- End behaviour
- Remainder and factor theorems
- Semester 1, Unit 4
Square root, absolute value, piecewise and rational functions
Square root and absolute value equations and graphs, absolute value inequalities, step and piecewise functions, inverse proportion and rational functions. Marks go when an extraneous root survives after squaring both sides.
- Radical equations
- Absolute value inequalities
- Rational functions
- Semester 2, Unit 5
Exponential and logarithmic functions
Growth and decay, the natural base e, common and natural logarithms, the laws of logarithms, and solving exponential and logarithmic equations. Splitting the logarithm of a sum into two logarithms is the classic slip.
- Growth and decay
- Laws of logarithms
- Natural logarithm
- Semester 2, Unit 6
Circular functions
Trigonometric ratios of any angle, reference angles, the unit circle, the graphs of sine, cosine and tangent, and phase shift. Signs by quadrant and a calculator left in degree mode cause many wrong answers.
- Unit circle
- Reference angles
- Phase shift
- Semester 2, Unit 7
Trigonometric identities and equations
Pythagorean and even-odd identities, sum and difference formulas, double and half angle formulas, proofs of identities and trigonometric equations. Learners often find one solution and miss the others inside the given interval.
- Proving identities
- Double angle formulas
- Trigonometric equations
- Semester 2, Units 8 and 9
Counting, probability and statistics
Permutations, combinations and the binomial theorem; mutually exclusive, independent and conditional probability; then the correlation coefficient and regression line. Choosing between permutation and combination is where marks usually go.
- Permutations and combinations
- Conditional probability
- Regression line
- Arts and humanities track
General Mathematics in the arts and humanities track
This track's semester 2 book covers absolute value, piecewise, square root and cube root functions, transformations and operations on functions, and statistics with standard deviation and two-way frequency tables.
- Functions and their graphs
- Standard deviation
- Two-way frequency tables
Unit numbers follow the MOEHE books for the scientific and technological tracks. Schools set their own weekly pace, so the tutor checks the class plan first.