IB Mathematics Analysis and Approaches 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 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 derivatives of more complex functions that involve trigonometric, exponential functions

Question Type 2: Learning to apply chain rule on simple composites

Question Type 3: Learning to apply chain rule on more complex composite function with possible multiple chains

Question Type 4: Learning to apply product rule on functions of x that are in multiple

Question Type 5: Applying both chain rule and product rule together on composite functions

Question Type 6: Learning to apply the quotient rule on all derivatives in fraction form

Question Type 7: Learning to apply all the rules, product, chain and quotient together for any derivatives of composite functions of x

Question Type 1: Calculating the second derivatives of functions involving less rules

Question Type 2: Calculating the second derivatives of much more complicated functions

Question Type 1: Finding the stationary points of specific functions by setting first derivatives to 0

Question Type 2: Checking whether the first order conditions constitute to a local minimum or maximum

Question Type 3: Working with shapes to find the largest (or smallest) area (or volume) of specific 2D (or 3D) shapes

Question Type 4: Working with more complex, 3D shapes that are harder to optimize

Question Type 5: Classifying whether specific functions have points of inflexions or not by checking the conditions on which they occur

Question Type 6: Finding the regions of the function in which it is concave up and concave down with technology

Question Type 7: Finding the regions of concavity without technology

Question Type 1: Given the displacement or velocity, finding the velocity or acceleration respectively

Question Type 2: Finding specific conditions on velocity and acceleration

Question Type 3: Going from acceleration and velocity, to velocity and displacement

Question Type 4: Difference between distance and displacement

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: Integrals for total area (using absolute value)

Question Type 3: Using technology to calculate indefinite integrals and area between curve and x-axis

Question Type 4: Finding the area between two curves intersection points by finding where the curves intersect and integrating over the region

Question Type 5: Area between two curves with changing dominance

Question Type 1: Simple limits: convergence, divergence, and function behavior

Question Type 2: Derivatives from first principles

Question Type 3: Higher-order derivatives of functions with repeating patterns

Question Type 4: Induction with n-th order derivatives

Question Type 1: Computing more complex limits with L’Hopitals rule

Question Type 2: Computing harder derivatives from first principles

Question Type 3: Applying L’Hôpital’s rule multiple times

Question Type 4: Finding parameter values so that a limit exists (using L’Hôpital)

Question Type 1: Implicit differentiation

Question Type 2: Tangents to implicitly defined curves

Question Type 3: Related rates with geometric constraints

Question Type 4: Finding maxima and minima of a function on a closed interval

Question Type 1: The derivatives of simple composite functions of the reciprocal trigonometric functions

Question Type 2: Integrals of derivatives of reciprocal trigonometric functions in composite forms

Question Type 3: The derivatives of simple composites of inverse trigonometric functions

Question Type 4: The integrals of the derivatives of the inverse trigonometric functions in composite functions of linear changes

Question Type 5: Integrating rational functions using partial fractions (linear factors)

Question Type 1: Solving harder integrals with u-substitution

Question Type 2: Trigonometric substitution in integrals

Question Type 3: Solving simple integrals with integration by parts

Question Type 4: Solving harder integrals with integration by parts

Question Type 5: Integration by parts in a cycle

Question Type 1: Area enclosed by the y-axis and a function

Question Type 2: Volumes of revolution

Question Type 1: Euler’s approximation method for differential equations

Question Type 2: Solving separable differential equations

Question Type 3: Homogeneous differential equations (substitution 𝑣 = 𝑦 / 𝑥 )

Question Type 4: Solving with the integrating factor (linear ODEs)

Question Type 1: Maclaurin series with substitution

Question Type 2: Maclaurin series by differentiating or integrating known series

Question Type 3: Maclaurin series using the formula

Question Type 4: Maclaurin product series via coefficient comparison