Mathematical literacy is a primary goal of the school curriculum. Competence in mathematics underpins the successful study of many academic disciplines at Brentwood. Becoming numerate involves developing the ability to explore, conjecture, reason logically, and use a variety of mathematical methods to solve problems. It also involves the development of self-confidence and the ability to use quantitative and spatial information in problem solving and decision making. As students develop their numeracy skills and concepts, they generally grow more confident and motivated in their mathematical explorations. This growth occurs as they learn to enjoy and value mathematics, to think analytically, and to understand and appreciate the role of mathematics in everyday life.

The Brentwood mathematics curriculum emphasizes the development of numeracy skills and concepts and their practical application in higher education and the workplace. The curriculum places emphasis on probability and statistics, reasoning and communication, measurement, and problem solving. As far as possible, students are encouraged to apply mathematics to real world problems and to seek out the relationships between mathematics and the world around them. Students use technology to collect and analyse data from their surroundings and to bring a context to their explorations. At the same time, the curriculum investigates the creative and aesthetic aspects of mathematics by exploring the connections between mathematics, art, and design.

In 2009-2010 the curriculum in grade 9-12 will begin transition to a new model with the introduction of the new Mathematics 9 syllabus. The following year Mathematics 10 will be revised and so on.

Mathematics 9

Mathematics 9 begins with a study of exponents and the laws governing order of operations with respect to rational numbers, bases and their exponents. A problem solving context is used to derive patterns and relationships to introduce and explore linear equations and the algebra that is used to solve them. Polynomials are also explored with students, concretely, pictorially and symbolically. Students model, record and explain their approach to solving problems involving addition and subtraction of polynomial expressions. Graphing of linear relationships and extrapolating and interpolating from a graph introduces students to some of the concepts involved in critically analyzing and intelligently displaying data. Later in the course, students conduct a project that engages them in a study of statistics within a social context and brings them to an understanding of statistical bias in the collection, analysis and display of data. A study of 2D and 3D shapes requires students to solve problems and justify solution strategies involving circles, tangents, polygons and the surface area of objects. A unit on transformations involves students in drawing scale diagrams of 2D shapes and gaining an appreciation of line and rotational symmetry. Technology is incorporated into the curriculum through such means as data collection and GPS devices which provide information students can discuss, display and analyze within the classroom.

Mathematics 10

In Mathematics 10 students explain and illustrate the structure and the interrelationships of the sets of numbers within the real number system. They use basic arithmetic operations on real numbers and also use exact values together with algebraic expressions to solve problems. Generating and analyzing numerical patterns leads to a consideration of variables and equations which extends to generalized operations on polynomials, including rational expressions. In relations and functions students represent data using linear function models and use a real world context to interpret and explain the data they are examining. The measurement unit involves the geometry of triangles, including those found in 2D and 3D applications. The sine and cosine laws are derived and applied to solve problems. Coordinate geometry problems involving points, line and line segments supplement this topic.

Mathematics 11

Students begin by representing and analyzing situations that involve expressions, equations and inequalities. Quadratic, polynomial and rational functions are represented and analyzed. Students solve coordinate geometry problems involving points, lines and line segments and apply the geometric properties of circles to solve problems.

Mathematics 12

Students generate and analyze exponential patterns. They solve exponential, logarithmic and trigonometric equations and identities. Graphing calculators are used to represent and analyze exponential and logarithmic functions. In the transformations unit students perform, analyze and create transformations of functions and relations that are described by equations or graphs. The topics of chance and uncertainty are introduced in the statistics unit where students ultimately solve problems using probability theory including permutations and combinations.

Calculus 12 AP

All students must possess a graphing calculator for use in this course, a course recommended for all students who will be required to take a calculus course (first year mathematics) at university. This is essentially a first year university course.

Functions and Historical perspective: A review of functions (this will be complemented by the Math 12 curriculum). Historical perspective. Origins of the calculus approach. Contributions by famous mathematicians.

Continuity and Limit Theory: Secants and tangents. Limiting position/limiting value/instantaneous value. Limit notation. One-sided and two sided limits. Continuous functions, discontinuities. Horizontal and vertical asymptotes, limits at infinity. Computation of limits.

The Derivative: Differentiation from first principles. Derivative notation: Techniques of differentiation: Power Rule, Product Rule, Quotient Rule (plus Reciprocal Rule). Higher derivative. The Chain Rule. Implicit differentiation.

Curve Analysis: Conditions for increasing, decreasing, concave up, concave down functions. Definition of point of inflection, critical point. Relative and absolute maxima/minima. First derivative test and second derivative test for classification of maxima/minima. Analysis of the properties of functions through: symmetry, intercepts, intervals of increase/decrease, infinite tendencies, asymptotes (horizontal, vertical, and oblique), concavity, points of inflection, periodicity. Applications of the Derivative: Applied maximum and minimum problems. Related rates. Kinematics — motion along a line. Rolle's Theorem. Mean Value Theorem.

Specific Functions: Inverse functions. Continuity/differentiability of inverse functions. Logarithmic and exponential functions (review of log laws). Derivatives of exponential and logarithmic functions. Derivatives of trigonometric functions. Derivatives of inverse trigonometric functions. L'Hopital's rule for indeterminate forms.

Integration: Analysis of the area problem. The indefinite integral. Integration formulae. Integral curves. Differential equations. Integration by substitution. The definite integral. The Fundamental Theorem of Calculus. Average value of a function. Slope fields.

Areas & Volumes: Area under a curve. Area between two curves. Reversal of variables/axes. Volumes of rotation computed by slicing (disks and washers) and cylindrical shells.

Techniques for Integration: Integration by parts, trigonometric integrals, cyclic integrals, partial fractions. Enrichment: trigonometric substitution.