Grade 11 math practice

A. Functions

1. Functions: notation, domain, range and the vertical line test
2. Inverse functions
3. Composite functions f(g(x))
4. Parent functions and their key features
5. Transformations: y = a f(k(x − d)) + c
6. Odd and even functions
7. Multiply, divide, add and subtract rational expressions
8. Simplify polynomial and radical expressions
9. Absolute value equations and inequalities

B. Quadratic Functions

1. Maximum or minimum of a quadratic function
2. Roots, zeros and x-intercepts
3. Quadratic inequalities
4. Where a line meets a parabola
5. Write a quadratic from its zeros, vertex or a family
6. Quadratic models in real life

C. Polynomial and Rational Functions

1. Polynomial functions: degree and end behaviour
2. Zeros and multiplicity
3. The remainder theorem
4. The factor theorem: factor cubics
5. Sum and product of the roots
6. Rational functions: asymptotes and holes
7. Rational functions: zeros, intercepts and end behaviour
8. Average rate of change
9. Choose a model: linear, quadratic or exponential

D. Exponential and Logarithmic Functions

1. Rational exponents
2. Simplify with the exponent laws
3. Exponential functions: graphs and transformations
4. Exponential growth and decay models
5. Logarithmic functions and their graphs
6. Log laws and change of base
7. Solve exponential and logarithmic equations
8. Exponential and logarithmic inequalities
9. Semi-log plots and linearizing exponential data

E. Sequences and Series

1. Recursive sequences
2. Arithmetic sequences: general term
3. Geometric sequences: general term
4. Arithmetic series
5. Geometric series
6. Infinite geometric series
7. Pascal's triangle and the binomial theorem

F. Financial Mathematics

1. Compound interest
2. Present value
3. Annuities: future value and present value
4. Loans, mortgages and the cost of owning a car
5. Rounding, significant figures and percentage error

G. Trigonometry

1. Angles in standard position and the CAST rule
2. Exact values for special angles up to 360°
3. Find all angles from 0° to 360° with a given ratio
4. Reciprocal ratios: csc, sec and cot
5. Radians and the unit circle
6. Trigonometric identities
7. Double-angle and compound-angle formulas
8. Solve trigonometric equations
9. The sine law: the ambiguous case (SSA)
10. Trigonometry in 3D and with bearings
11. Inverse trigonometric functions

H. Periodic and Sinusoidal Functions

1. Periodic functions: period, amplitude and axis
2. Graphs of y = sin x and y = cos x
3. Transformations: amplitude, period, phase shift and axis
4. Write the equation of a sinusoidal function
5. Sinusoidal models: Ferris wheels, tides and daylight
6. The tangent function and its graph
7. Polar coordinates

I. Complex Numbers, Counting and Proof

1. Complex numbers: add, subtract, multiply and divide
2. Quadratics with complex roots
3. Complex numbers in polar form and De Moivre's theorem
4. Permutations: arrangements where order matters
5. Combinations: selections where order doesn't matter
6. Systems of equations in three unknowns
7. Proof: deductive proof and induction
8. Partial fractions

J. Vectors, Matrices and Conics

1. Vectors: magnitude, addition and scalar multiples
2. The dot product and the angle between vectors
3. Vector and parametric equations of lines
4. Matrices: add, multiply and use in context
5. Determinant and inverse of a 2 × 2 matrix
6. Matrices as transformations
7. Eigenvalues of a 2 × 2 matrix
8. Parametric equations and planar motion
9. Conic sections: circles and parabolas
10. Conic sections: ellipses and hyperbolas

K. 3D Geometry, Voronoi Diagrams and Graphs

1. Distance and midpoint in 3D
2. 3D solids: volume, surface area and angles
3. Voronoi diagrams and nearest neighbours
4. Graph theory: degrees, Euler paths and minimum spanning trees

L. Statistics

1. Sampling methods, bias and study design
2. Summary statistics, IQR and outliers
3. Regression lines, residuals and r²
4. Spearman's rank correlation
5. Sampling distributions and the central limit theorem
6. Confidence intervals
7. Hypothesis tests, p-values and errors
8. Chi-squared tests

M. Probability

1. Probability rules: complements, or, and independence
2. Conditional probability and Bayes' theorem
3. Discrete random variables and expected value
4. The binomial distribution
5. The normal distribution and z-scores
6. The Poisson distribution
7. Markov chains and steady states

N. Introduction to Calculus

1. Limits
2. The derivative from first principles
3. Derivatives with the power rule
4. Tangent and normal lines
5. Increasing, decreasing and stationary points
6. Chain, product and quotient rules; eˣ, ln x, sin x, cos x
7. Optimization problems
8. Motion: displacement, velocity and acceleration
9. Introduction to integration and area
10. Differential equations: slope fields and Euler's method