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These are the statements describing what students need to learn:

[Higher Level only statements are in blue]

• the distance between two points in three-dimensional space, and their midpoint. Volume and surface area of three-dimensional solids including right-pyramid, right cone, sphere, hemisphere and combinations of these solids. The size of an angle between two intersecting lines or between a line and a plane
• use of sine, cosine and tangent ratios to find the sides and angles of right-angled triangles. use of the sine rule, cosine rule and the sine formula for finding the area of a triangle
• applications of right and non-right angled trigonometry, including Pythagoras’s theorem. Angles of elevation and depression. Construction of labelled diagrams from written statements
• the circle: radian measure of angles; length of an arc; area of a sector
• Definition of cosθ, sinθ in terms of the unit circle. Definition of tanθ as sinθ ÷ cosθ. Exact values of trigonometric ratios of θ, π/6, π/4, π/3, π/2 and their multiples. Extension of the sine rule to the ambiguous case.
• the Pythagorean identity cos²θ+sin²θ=1. Double angle identities for sine and cosine. The relationship between trigonometric ratios
• the circular functions sinx, cosx, and tanx; amplitude, their periodic nature, and their graphs. Composite functions of the form f(x)=asin(b(x+c))+d. Transformations. Real-life contexts
• solving trigonometric equations in a finite interval, both graphically and analytically. Equations leading to quadratic equations in sinx, cosx or tanx
• Definition of the reciprocal trigonometric ratios secθ, cosecθ and cotθ.
  Pythagorean identities:
  1+tan²θ=sec²θ
  1+cot²θ=cosec²θ
  The inverse functions f(x)=arcsinx,
  f(x)=arccosx,f(x)=arctanx; their domains and ranges; their graphs.
• Compound angle identities. Double angle identity for tan.
• Relationships between trigonometric functions and the symmetry properties of their graphs.
• Concept of a vector; position vectors; displacement vectors.
  Representation of vectors using directed line segments.
  Base vectors i, j, k.
  Components of a vector:
  v=v₁i+v₂j+v₃k.
  Algebraic and geometric approaches to the following:
  the sum and difference of two vectors
  the zero vector 0, the vector -v
  multiplication by a scalar, kv, parallel vectors
  magnitude of a vector, |v|; unit vectors, v÷|v|
  position vectors OA=a, OB=b
  displacement vector AB=b-a
  Proofs of geometrical properties using vectors.
  
• The definition of the scalar product of two vectors. The angle between two vectors. Perpendicular vectors; parallel vectors.
• Vector equation of a line in two and three dimensions:
  r=a+λb.
  The angle between two lines.
  Simple applications to kinematics.
• Coincident, parallel, intersecting and skew lines, distinguishing between these cases. Points of intersection.
• The definition of the vector product of two vectors.
  Properties of the vector product.
  Geometric interpretation of |v×w|
• Vector equations of a plane: r=a+λb+μc, where b and c are non-parallel vectors within the plane.
  r·n=a·n, where n is a normal to the plane and a is the position vector of a point on the plane.
  Cartesian equation of a plane ax+by+cz=d.
• Intersections of: a line with a plane; two planes; three planes.
  Angle between: a line and a plane; two planes.

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