Friday, 3/16 - Friday, 3/23: Spring Interim Assessments

Post date: Mar 13, 2018 3:01:33 PM

Here are some problems you can use to review for your Interim Assessment, which will cover all of calculus.

Here are some problems from the past few months that you've seen before, but which you can use again to practice:

Here are the formulae for calculus (derivatives and integrals) from your formula book.
Basics of derivatives: here are practice problems to feel more confident in our skills with derivatives.
Using derivatives for sketching curves: here are the practice problems from class.
Optimization: here are the problems and solutions from class.
Fall Semester Interim Assessment review (derivatives): here are the review problems & solutions you received printed out in class, covering all we've learned about vectors and about differential calculus (but remember your Spring IA won't have vectors on it)
Indefinite and definite integrals: here are the practice problems including full worked solutions from class
Finding areas with integrals: here are the problems we worked on in class
Finding volumes with integrals: here are the questions from class and here are the solutions
Here is a summary of the notes from our study of linear motion and kinematics. Here are the problems from class

Here is the list of IB Assessment Statements for Calculus that applies to our Spring Interim Assessment:

6.1) Informal ideas of limit and convergence. Limit notation. Definition of derivative from first principles as f^' (x)=lim┬(h→0)⁡〖(f(x+h)-f(x))/h〗. Derivative as interpreted as gradient function and as rate of change. Tangents and normals, and their equations.
6.2) Derivative of x^n (n∈Q). Differentiation of a sum and a real multiple of these functions. The second derivative. Extension to higher derivatives. Derivative of sin⁡(x), cos(⁡x), tan⁡(x), e^x, ln(⁡x); chain rule for composite functions; product and quotient rules
6.3) Local maximum and minimum points. Testing for maximum or minimum. Points of inflexion with zero and non-zero gradients. Graphical behavior of functions including relationship among the graphs of f, f', and f''. Optimization, applications
6.4) Indefinite integration as anti-differentiation; Indefinite integral of x^n (n∈Q), sin⁡x, cos⁡x, 1/x, and e^x; the composites of any of these with the linear function ax+b 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; Definite integrals, both analytically and using technology; Areas under curves (between curve and 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 traveled

Here is your IA schedule: