International Baccalaureate Mathematics Analysis and Approaches SL
These are the statements describing what students need to learn:
- Different forms of the equation of a straight line. Gradient, intercepts, parallel lines and perpendicular lines
- 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)
- 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
- determine key features of graphs. Maximum and minimum values; intercepts; symmetry; vertex; zeros of functions or roots of equations; vertical and horizontal asymptotes using graphing technology. Finding the point of intersection of two curves or lines using technology.
- composite functions. Identity function. Finding the inverse function f-1(x)
- 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), x-intercepts (p,0) and (q,0). The form f(x)=a(x-h)2+k, vertex (h,k)
- solution of quadratic equations and inequalities. The quadratic formula. The discriminant ∆=b2-4ac and the nature of the roots, that is, two distinct real roots, two equal real roots, no real roots
- 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
- 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
- solving equations, both graphically and analytically. Use of technology to solve a variety of equations, including those where there is no appropriate analytic approach. Applications of graphing skills and solving equations that relate to real-life situations
- 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=pf(x). Horizontal stretch with scale factor 1/q: y=f(qx). Composite transformations.
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