G2 Additional Mathematics
Lessons in g2 additional mathematics. This course is still being developed; independent practice and assessment coverage is incomplete.
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G2 Additional Mathematics
- Quadratics and algebraSuggested next · 8 core lessonsConnect quadratic models, discriminants and inequalities with surds, polynomial factors and partial fractions.
- Coordinate geometrySuggested next · 1 core lessonUse line directions, midpoints, areas and circle equations with their geometric conditions.
- TrigonometrySuggested next · 4 core lessonsBuild and connect the representations and methods in trigonometry.
- Differentiation and integrationSuggested next · 5 core lessonsBuild and connect the representations and methods in differentiation and integration.
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Normal (Academic) Additional Secondary 3–4 Mathematics 2020
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G2 Additional Mathematics 2027
Mixed practice
Practise a mix of topics from this course.
About 10 minutes
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This is for practice only and doesn’t count towards your course progress.
- Question count is checked before you start.
- Feedback appears after you finish and submit.
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Beyond the syllabus: optional enrichment that does not count towards your progress.
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Lessons in g2 additional mathematics. This course is still being developed; independent practice and assessment coverage is incomplete.
Learning goals
- Use quadratic structure and discriminants to reason about roots
- Interpret and draw graphs of functions
- Formulate, use and interpret a mathematical model
- Solve simultaneous equations by justified methods
- Solve inequalities and represent their solution sets
- Manipulate surds and rationalise denominators
- Divide and factor polynomials using remainder and factor theorems
- Decompose appropriate rational expressions into partial fractions
- Reason and calculate using coordinate geometry
- Interpret and graph trigonometric functions
- Transform and justify trigonometric identities
- Solve trigonometric equations within stated intervals
- Interpret a derivative as gradient or rate of change
- Differentiate within the permitted function scope
- Apply the chain rule to composite functions
- Apply product and quotient differentiation rules
- Classify stationary points using justified derivative tests
- Find and interpret a tangent to a curve
- Find and interpret a normal to a curve
- Relate connected rates of change
- Model and solve an optimisation problem
- Find antiderivatives within the permitted scope
- Evaluate definite integrals
- Relate a definite integral to area under a curve
Syllabus statements covered
- Finding the maximum or minimum value of a quadratic function using the method of completing the square • Conditions for y = ax^2 + bx + c to be always positive (or always negative) • Using quadratic functions as models
- Conditions for a quadratic equation to have: • two real roots • two equal roots • no real roots and related conditions for a given line to: • intersect a given curve • be a tangent to a given curve • not intersect a given curve • Solving simultaneous equations in two variables by substitution, with one of the equations being linear equation • Solving quadratic inequalities, and representing the solution on the number line
- Four operations on surds, including rationalising the denominator • Solving equations involving surds
- Multiplication and division of polynomials • Use of remainder and factor theorems, including factorising polynomials and solving cubic equations • Use of: a^3 + b^3 = (a + b)(a^2 − ab + b^2 ) a^3 − b^3 = (a − b)(a^2 + ab + b^2 ) • Partial fractions with cases where the denominator is no more complicated than: • (ax + b)(cx + d) • (ax + b)(cx + d)² • (ax + b)(x² + c² )
- Condition for two lines to be parallel or perpendicular • Midpoint of line segment • Area of rectilinear figure • Coordinate geometry of circles in the form: • (x − a)² + (y − b)² = r^2 • x^2 + y^2 + 2gx + 2 fy + c = 0 (excluding problems involving two circles)
- Six trigonometric functions for angles of any magnitude (in degrees or radians) • Principal values of sin⁻¹x, cos⁻¹x, tan⁻¹x • Exact values of the trigonometric functions for special angles (30°, 45°, 60°) or (π/6, π/4, π/3) • Amplitude, periodicity and symmetries related to sine and cosine functions • Graphs of y = a sin(bx) + c, y = a sin(x/b) + c, y = a cos(bx) + c, y = a cos(x/b) + c and y = a tan(bx), where a is real, b is a positive integer and c is an integer • Use of: sin A/cos A = tan A; cos A/sin A = cot A; sin² A + cos² A = 1; sec² A = 1 + tan² A; cosec² A = 1 + cot² A; expansions of sin(A ± B), cos(A ± B), tan(A ± B); formulae for sin 2A, cos 2A, tan 2A; a cos θ + b sin θ in the form R cos(θ ± α) or R sin(θ ± α) • Simplification of trigonometric expressions • Solution of simple trigonometric equations in a given interval (excluding general solution) • Proofs of simple trigonometric identities • Use of trigonometric functions as models
- Derivative of f (x) as the gradient of the tangent to the graph of y = f (x) at a point • Derivative as rate of change • Use of standard notations f′(x), f″(x), dy/dx, d²y/dx² = d/dx(dy/dx) • Derivatives of x^n , for any rational n, together with constant multiples, sums and differences • Derivatives of products and quotients of functions • Use of Chain Rule • Increasing and decreasing functions • Stationary points (maximum and minimum turning points and stationary points of inflexion) • Use of second derivative test to discriminate between maxima and minima • Apply differentiation to gradients, tangents and normals, connected rates of change and maxima and minima problems • Integration as the reverse of differentiation • Integration of x^n for any rational n, (excluding n = −1 ), together with constant multiples, sums and differences • Integration of (ax + b)n for any rational n, (excluding n = −1 ) • Definite integral as area under a curve • Evaluation of definite integrals • Finding the area of a region bounded by a curve and line(s) (excluding area of region between 2 curves)
- Finding the maximum or minimum value of a quadratic function using the method of completing the square
- Conditions for y = ax^2 + bx + c to be always positive (or always negative)
- Using quadratic functions as models
- Conditions for a quadratic equation to have: • two real roots • two equal roots • no real roots and related conditions for a given line to: • intersect a given curve • be a tangent to a given curve • not intersect a given curve
- Solving simultaneous equations in two variables by substitution, with one of the equations being linear equation
- Solving quadratic inequalities, and representing the solution on the number line
- Four operations on surds, including rationalising the denominator
- Solving equations involving surds
- Multiplication and division of polynomials
- Use of remainder and factor theorems, including factorising polynomials and solving cubic equations
- Use of: a^3 + b^3 = (a + b)(a^2 − ab + b^2 ) a^3 − b^3 = (a − b)(a^2 + ab + b^2 )
- Partial fractions with cases where the denominator is no more complicated than: • (ax + b)(cx + d) • (ax + b)(cx + d)² • (ax + b)(x² + c² )
- Condition for two lines to be parallel or perpendicular
- Midpoint of line segment
- Area of rectilinear figure
- Coordinate geometry of circles in the form: • (x − a)² + (y − b)² = r^2 • x^2 + y^2 + 2gx + 2 fy + c = 0 (excluding problems involving two circles)
- Six trigonometric functions for angles of any magnitude (in degrees or radians)
- Principal values of sin⁻¹x, cos⁻¹x, tan⁻¹x
- Exact values of the trigonometric functions for special angles (30°, 45°, 60°) or (π/6, π/4, π/3)
- Amplitude, periodicity and symmetries related to sine and cosine functions
- Graphs of y = a sin(bx) + c, y = a sin(x/b) + c, y = a cos(bx) + c, y = a cos(x/b) + c and y = a tan(bx), where a is real, b is a positive integer and c is an integer
- Use of: sin A/cos A = tan A; cos A/sin A = cot A; sin² A + cos² A = 1; sec² A = 1 + tan² A; cosec² A = 1 + cot² A; expansions of sin(A ± B), cos(A ± B), tan(A ± B); formulae for sin 2A, cos 2A, tan 2A; a cos θ + b sin θ in the form R cos(θ ± α) or R sin(θ ± α)
- Simplification of trigonometric expressions
- Solution of simple trigonometric equations in a given interval (excluding general solution)
- Proofs of simple trigonometric identities
- Use of trigonometric functions as models
- Derivative of f (x) as the gradient of the tangent to the graph of y = f (x) at a point
- Derivative as rate of change
- Use of standard notations f′(x), f″(x), dy/dx, d²y/dx² = d/dx(dy/dx)
- Derivatives of x^n , for any rational n, together with constant multiples, sums and differences
- Derivatives of products and quotients of functions
- Use of Chain Rule
- Increasing and decreasing functions
- Stationary points (maximum and minimum turning points and stationary points of inflexion)
- Use of second derivative test to discriminate between maxima and minima
- Apply differentiation to gradients, tangents and normals, connected rates of change and maxima and minima problems
- Integration as the reverse of differentiation
- Integration of x^n for any rational n, (excluding n = −1 ), together with constant multiples, sums and differences
- Integration of (ax + b)^n for any rational n, (excluding n = −1 )
- Definite integral as area under a curve
- Evaluation of definite integrals
- Finding the area of a region bounded by a curve and line(s) (excluding area of region between 2 curves)