International Baccalaureate Mathematics Analysis and Approaches SL
These are the statements describing what students need to learn:
- introduction to the concept of a limit. Derivative interpreted as gradient function and as rate of change
- increasing and decreasing functions. Graphical interpretation of f'(x)>0, f'(x)=0,f'(x)<0
- derivative of f(x)=axn is f'(x)=anxn-1, The derivative of functions of the form fx=axn+bxn-1+… where all exponents are integers
- tangents and normals at a given point, and their equations
- introduction to integration as anti-differentiation of functions of the form f(x)=axn+bxn-1+.... Anti-differentiation with a boundary condition to determine the constant term. Definite integrals using technology. Area of a region enclosed by a curve y=f(x) and the x-axis, where f(x)>0
- derivative of xn, sinx, cosx, ex and lnx. Differentiation of a sum and a multiple of these functions. The chain rule for composite functions. The product and quotient rules
- the second derivative. Graphical behaviour of functions, including the relationship between the graphs of f,f' and f"
- local maximum and minimum points. Testing for maximum and minimum. Optimization. Points of inflexion with zero and non-zero gradients
- Kinematic problems involving displacement s, velocity v, acceleration a and total distance travelled.
- indefinite integral of xn,sinx,cosx,1/x and ex. The composites of any of these with the linear function ax+b. Integration by inspection (reverse chain rule) or by substitution for expressions of the form: ∫kg'(x)f(g(x))dx
- definite integrals, including analytical approach. Areas of a region enclosed by a curve y=f(x) and the x-axis, where f(x) can be positive or negative, without the use of technology. Areas between curves
Click on a statement above for suggested resources and activities from Transum.