Download Atlas - Maths Yr12 SL

Maths Yr12 SL
Standards/Objectives
DP Group 5:Mathematics SL (1st exam 2014)
DP - Age 16-18
Syllabus - Topic 3—Circular functions and trigonometry
The aims of this topic are to explore the circular functions and to solve problems using trigonometry. On examination
papers, radian measure should be assumed unless otherwise indicated.
3.1 The circle: radian measure of angles; length of an arc; area of a sector.
3.2 Definition of cosθ and sinθ in terms of the unit circle.
Definition of tanθ as sin θ / cosθ.
Exact values of trigonometric ratios of 0, π/6, π/4, π/3, π/2 and their multiples.
3.3 The Pythagorean identity cos²θ + sin²θ =1.
Double angle identities for sine and cosine.
Circular functions and
Relationship between trigonometric ratios.
trigonometry
3.4 The circular functions sin x , cos x and tan x : their domains and ranges; amplitude, their periodic nature; and their
graphs.
(8 Weeks)
Composite functions of the form f (x) = a sin (b(x + c)) + d .
Transformations.
Applications.
3.5 Solving trigonometric equations in a finite interval, both graphically and analytically.
Equations leading to quadratic equations in sin x, cos x or tan x .
3.6 Solution of triangles.
The cosine rule.
The sine rule, including the ambiguous case.
Area of a triangle, ½ ab sinC
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Standards/Objectives
Vectors
(4 Weeks)
DP Group 5:Mathematics SL (1st exam 2014)
DP - Age 16-18
Syllabus - Topic 4—Vectors
The aim of this topic is to provide an elementary introduction to vectors, including both algebraic and geometric
approaches. The use of dynamic geometry software is extremely helpful to visualize situations in three dimensions.
4.1 Vectors as displacements in the plane and in three dimensions.
Components of a vector; column representation; v= v1 v2 v3 = v1i + v2j + v3k.
Algebraic and geometric approaches to the following: the sum and difference of two vectors; the zero vector, the vector
−v ; multiplication by a scalar, kv ; parallel vectors; magnitude of a vector, │v│ ; unit vectors; base vectors; i, j and k;
position vectors OA = a ; AB = OB – OA = b − a .
4.2 The scalar product of two vectors.
Perpendicular vectors; parallel vectors.
The angle between two vectors.
4.3 Vector equation of a line in two and three dimensions: r = a + tb .
The angle between two lines.
4.4 Distinguishing between coincident and parallel lines.
Finding the point of intersection of two lines.
Determining whether two lines intersect.
© International Baccalaureate Organization
DP Group 5:Mathematics SL (1st exam 2014)
DP - Age 16-18
Internal assessment criteria
Internal Assessment - Internal assessment criteria
Exploration
Criterion A: Communication
Criterion B: Mathematical presentation
(5 Weeks)
Criterion C: Personal engagement
Criterion D: Reflection
Criterion E: Use of mathematics
Standards/Objectives
© International Baccalaureate Organization
Mock exam revision
(2 Weeks)
DP Group 5:Mathematics SL (1st exam 2014)
DP - Age 16-18
Syllabus - Topic 6—Calculus
The aim of this topic is to introduce students to the basic concepts and techniques of differential and integral calculus and
their applications.
6.4 Indefinite integration as anti-differentiation.
Indefinite integral of xⁿ (n∈Q) , sin x, cos x, (1/x) and e ͯ.
The composites of any of these with the linear function ax + b.
Calculus - Integration
Integration by inspection, or substitution of the form ∫ f (g(x))g '(x)dx .
6.5 Anti-differentiation with a boundary condition to determine the constant term.
(6 Weeks)
Definite integrals, both analytically and using technology.
Areas under curves (between the curve and the x-axis).
Areas between curves.
Volumes of revolution about the x-axis.
6.6 Kinematic problems involving displacement s, velocity v and acceleration a.
Total distance travelled.
© International Baccalaureate Organization
Atlas Version 8.1.1
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