Maths 12 syllabus

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All Maths 12 learning outcomes

Understand functions, domains, and ranges
Find when three lines are concurrent
Recognize linear, quadratic, and square-root functions
Find triangle medians, altitudes, and perpendicular bisectors
Define and use inverse functions
Show triangle lines are concurrent
Sketch graphs of linear functions (e.g.,
Find a triangle’s area from its vertices
Plot the graph of the function
Recognize homogeneous equations
Plot graph of quadratic function of the form
Investigate that the 2nd degree homogeneous equation in two variables
Draw graphs using factors
Apply concepts of analytical geometry to real life world problems (such as aviation, to track stars, distance between planets and satellites, space science and engineering).
Predict functions from their graphs (use the factor form to predict the equation of a function of the type
Explain vector-valued functions
Find intersections on graphs
Construct vector-valued functions
Solve everyday problems graphically
Find domain and range of vector functions
Classify algebraic and transcendental functions
Distinguish scalar and vector functions
Describe common transcendental functions
Explain derivatives of vector functions
Understand logarithms
Find velocity and acceleration from position
Use logarithm product, quotient, and power laws
Apply vector functions to real life
Analyze exponential and logarithmic graphs
Find domains and ranges of trigonometric functions
Solve exponential and logarithmic equations
Graph inverse trigonometric functions
Find domains and ranges of transcendental functions
Use inverse trigonometric addition formulas
Graph the modulus function
Solve trigonometric equations of the type
Relate a function to its inverse graphically
Solve graphically the trigonometric equations of the type:
Transform function graphs
Use trigonometric periods in equations
Find limits of sequences and functions
Apply inverse trigonometry to real-world measurements
Apply limit laws
Recognize the four main conic sections
Test continuity and discontinuity
Use the standard equation of a circle
Apply continuity and limits to real-life models
Find a circle through given points and conditions
Calculate inflation over time
Test whether a line cuts or touches a circle
Calculate depreciation
Find circle tangents and normals
Understand a tangent to a curve
Find a tangent length from an external point
Find a curve’s gradient
Use the standard equation of a parabola
Understand the derivative as a limit
Sketch conics and identify their features
Calculate a derivative at a point
Find a parabola from its defining elements
Estimate derivatives as rates of change
Recognize and find a tangent to a parabola
Recognize the derivative function
Find a parabola’s tangent and normal
Differentiate a square-root function
Use the standard equation of an ellipse
Differentiate a quadratic function
Convert and graph an ellipse equation
Connect derivatives and continuity
Find where a line meets an ellipse
Use differentiation rules
Find an ellipse tangent in point-slope form
Use the power rule with negative exponents
Find an ellipse’s tangent and normal
Combine differentiation rules
Use the standard equation of a hyperbola
Relate rates of change to motion
Find a hyperbola from its defining data
Differentiate trigonometric functions
Find where a line meets a hyperbola
Differentiate exponential functions
Find a hyperbola tangent in point-slope form
Differentiate logarithmic functions
Find a hyperbola’s tangent and normal
Use derivatives to identify increasing and decreasing functions
Apply conics to real-world problems
Use differentiation to find tangents and normals
Apply differentiation to real-life problems
Find higher-order derivatives
Use local linear approximations
Use differentials to approximate change
Calculate approximation errors
Identify global and local extrema
Find extrema with the second-derivative test
Find critical points on a closed interval
Use critical points to find absolute extrema
Optimize functions with derivatives
Apply higher derivatives to real-life problems
Find a general antiderivative
Use antiderivative notation
Apply the power rule for integrals
Use indefinite-integral properties
Define the definite integral
Identify integral components
Use definite-integral properties
Apply the Fundamental Theorem of Calculus
Relate definite integrals to net area
Find areas between curves and lines
Find volumes of revolution
Use the trapezium rule
Apply integration to real-life problems
Distinguish scalar and vector motion quantities
Interpret displacement-time and velocity-time graphs
Use calculus to solve motion problems
Use constant-acceleration formulas
Apply mechanics to real-life motion
Use trigonometric relationships in integration
Integrate exponential and logarithmic functions
Choose integration by parts
Apply integration by parts
Use trigonometric substitution
Use partial fractions to integrate
Apply integration to motion and measurement problems
Form and solve first-order differential equations
Solve separable first-order equations
Apply differential equations to real life
Analyze the searching of roots of an equation by graphical means and/or searching for the sign change.
Explain the basic principles of solving a nonlinear equation in one variable.
Calculate real roots of a nonlinear equation in one variable by Bisection Method, Regula-Falsi Method, Newton Raphson Method.
Apply concepts of nonlinear equations to real life word problems (such as chemical reactions, regulation of heart beats, electronic circuits, and cryptography).