IB Mathematics Applications & Interpretation Calculus

Question Type 1: Drawing graphs of specific functions to determine their limits at specific places

Question Type 2: Using tables of values of small increments to explore different functions

Question Type 1: Finding intervals where a function is increasing or decreasing

Question Type 1: Finding the derivative of a polynomial with different ranges of integers

Question Type 2: Finding where a polynomial is increasing or decreasing up to cubics

Question Type 1: Finding the tangent and normal to a polynomial at a specific value of x

Question Type 2: Calculating the normal to the curve at the point where tangent is known

Question Type 3: Finding the tangent and normal to more complex functions using the GDC at different points

Question Type 1: Integrating a polynomial without boundary conditions

Question Type 2: Integrating polynomials with boundary conditions to solve for C

Question Type 3: Calculating the area between a polynomial in the positive section and the x axis

Question Type 4: Calculating the area between any function in the positive section and the x axis (using technology)

Question Type 1: Finding the first order conditions for polynomials up to cubics

Question Type 2: Finding the FOC for functions using technology

Question Type 3: Determining whether certain points are minimum and maximum by inspection through technology

Question Type 1: Finding the optimal area or volume of specific 2D or 3D shapes

Question Type 2: Optimizing profit or cost functions under a given context

Question Type 1: Estimating area with equal width intervals using trapezoids

Question Type 1: Calculating derivatives of complicated functions

Question Type 2: Applying chain rule on composite functions

Question Type 3: Applying product rule on multiplying functions

Question Type 4: Deriving functions with a combination of product and chain rule

Question Type 5: Applying quotient rule on functions as a rational

Question Type 6: Deriving functions by applying product, quotient and chain rule

Question Type 7: Finding the related rates between variable given contextual information on their relation

Question Type 1: Calculating second derivatives of functions

Question Type 2: Determining whether points satisfying the first order condition are local optimals

Question Type 3: Determining the regions of concavity and its type for a function

Question Type 1: Applying integration through using the basis integrals

Question Type 2: Applying integration through using the basis integrals alongside their composite transformations in linear functions

Question Type 3: Integrals with an inside function and its derivative

Question Type 4: Evaluating integrals with an inside function and its derivative

Question Type 1: Evaluating definite integrals analytically

Question Type 2: Calculating the area between a function and the x-axis

Question Type 3: Calculating the area between a function and the y-axis

Question Type 4: Finding the volume of revolution of a region about the x-axis

Question Type 5: Finding the volume of revolution of a region about the y axis

Question Type 1: Deriving to find the rate of change of a kinematic variable

Question Type 2: Finding specific conditions on the rate of change of a kinematic variable

Question Type 3: Integrating kinematic variables

Question Type 4: Accounting for the difference between distance and displacement

Question Type 1: Formulating a model for differential equation given a contextual description

Question Type 2: Separating a differential equation into two variables

Question Type 3: Solving a separable differential equation to obtain the general solution

Question Type 4: Finding the particular solution for a separable differential equation using the general solution

Question Type 1: Completing or creating slope field diagrams for different differential equations

Question Type 2: Sketching a solution curve that passes through a specific point using a slope field diagram

Question Type 1: Approximating values for a given step length using Euler's method

Question Type 2: Approximating values for a given interation amount and step length using technology

Question Type 3: Approximating values for coupled system using Euler's method for a given step length

Question Type 4: Approximating values for coupled system using Euler's method with fixed iteration and step length using technology

Question Type 1: Finding the general solution to linear coupled differential equations with real and distinct eigenvalues

Question Type 2: Finding the particular solution to linear coupled differential equations with some initial condition and real and distinct eigenvalues

Question Type 3: Finding the general solution to linear coupled differential equations with any type of eigenvalues

Question Type 4: Sketching trajectories of general solution of linear coupled differential equations onto a phase portrait

Question Type 5: Interpreting key informative points using phase portraits

Question Type 6: Determining the type of eigenvalue given a phase portrait diagram

Question Type 1: Converting a second order differential equation into a system of first order differential equations

Question Type 2: Applying Euler's method to second order differential equations