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Calculus/IBSL Analysis and Approaches Y2
This Week During Calculus
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In this unit students will cover the following IBSL Analysis and Approaches Standards:
SL 1.6
Simple deductive proof, numerical and algebraic; how to lay out a left-hand side to right-hand side (LHS to RHS) proof.
The symbols and notation for equality and identity.
SL 1.9
The binomial theorem: expansion of (a + b)^n,
n ∈ N.
Use of Pascal’s triangle and nCr
SL 2.4
Finding the point of intersection of two curves or lines using technology.
SL 2.6
The form f(x) = a(x − p)(x − q), x-intercepts (p, 0) and (q, 0).
SL 2.7
Solution of quadratic equations and inequalities. The quadratic formula.
The discriminant Δ = b
2
− 4ac and the nature of the roots, that is, two distinct real roots, two equal real roots, no real roots.
SL 2.10
Solving equations, both graphically and analytically.
Applications of graphing skills and solving equations that relate to real-life situations.
SL 2.11
Transformations of graphs.
Translations: y = f(x) + b; y = f(x − a).
Reflections (in both axes): y = − f(x); y = f( − x).
Vertical stretch with scale factor p: y = p f(x).
Horizontal stretch with scale factor 1/q: y = f(qx).
Composite transformations.
SL 3.1
The size of an angle between two intersecting lines or between a line and a plane.
SL 3.2
Use of sine, cosine and tangent ratios to find the sides and angles of right-angled triangles.
The sine rule: a/sinA=b/sinB=c/sinC.
The cosine rule: c
2
= a
2
+ b
2
− 2abcosC; cosC =a
2
+ b
2
− c
2
/(2ab) .
Area of a triangle as ½ absinC.
SL 3.3
Applications of right and non-right angled trigonometry, including Pythagoras’s theorem.
Angles of elevation and depression.
Construction of labeled diagrams from written statements.
SL 3.5
Extension of the sine rule to the ambiguous case.
SL 3.6
The Pythagorean identity cos^2(θ) + sin^2(θ) = 1.
Double angle identities for sine and cosine.
SL 3.8
Solving trigonometric equations in a finite interval, both graphically and analytically.
Equations leading to quadratic equations in sinx, cosx or tanx.
-I
B Diploma Program Mathematics: Analysis & Approaches Guide
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IBSL Analysis and Approaches Y1
This Week During IBSL Analysis Y1
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Week 8
HL STUDENTS: Sequences and Series and Matrices
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Calculus/IBSL Analysis and Approaches Y2
This Week During Calculus
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