In this unit students will review the following IBSL Analysis and Approaches Standards:
SL 1.5
Laws of exponents with integer exponents.
Introduction to logarithms with base 10 and e.
Numerical evaluation of logarithms using technology.
SL 1.7
Laws of Logarithms
log(xy) = log x + log y
log(x/y) = log x - log y
log (x^m) = m log x
Change of base of a logarithm.
Solving exponential equations, including using logarithms.
SL 1.9
The binomial theorem: expansion of (a + b)^n, n ∈ N.
Use of Pascal’s triangle and nCr
SL 2.1
Different forms of the equation of a straight line. Gradient; intercepts. Lines with gradients m1 and m2. Parallel lines m1 = m2. Perpendicular lines m1 × m2 = − 1.
SL 2.2
Concept of a function, domain, range and graph. Function notation, for example f(x), v(t), C(n). The concept of a function as a mathematical model.
Informal concept that an inverse function reverses or undoes the effect of a function. Inverse function as a reflection in the line y = x, and the notation f −1(x).
SL 2.3
The graph of a function; its equation y = f(x).
Creating a sketch from information given or a
context, including transferring a graph from screen to paper.
Using technology to graph functions including their sums and differences.
SL 2.4
Determine key features of graphs.
Finding the point of intersection of two curves or lines using technology.
SL 2.5
Composite functions.
Identity function. Finding the inverse function f−1(x).
SL 2.6
The quadratic function f(x) = ax2 + bx + c: its graph, y -intercept (0, c). Axis of symmetry.
The form f(x) = a(x − p)(x − q), xintercepts (p, 0) and (q, 0).
The form f(x) = a (x − h)2 + k, vertex (h, k).
SL 2.7
Solution of quadratic equations and inequalities. The quadratic formula.
The discriminant Δ = b2 − 4ac and the nature of the roots, that is, two distinct real roots, two equal real roots, no real roots.
SL 2.8
The reciprocal function f(x) = 1/x, x ≠ 0: its graph and self-inverse nature.
Rational functions of the form f(x) = (ax + b)/(cx + d) and their graphs. Equations of vertical and horizontal asymptotes.
SL 2.9
Exponential functions and their graphs: f(x) = ax, a > 0, f(x) = ex
Logarithmic functions and their graphs: f(x) = logax, x > 0, f(x) = lnx, x > 0.
SL 2.10
Applications of graphing skills and solving equations that relate to real-life situations.
SL 3.5
Definition of cosθ, sinθ in terms of the unit circle.
Definition of tanθ as sinθ/cosθ
Exact values of trigonometric ratios of 0, π/6, π/4, π/3, π/2, and their multiples.
Extension of the sine rule to the ambiguous case.
SL 3.6
The relationship between trigonometric ratios.
SL 3.7
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.
-IB Diploma Program Mathematics: Analysis & Approaches Guide