Xiaodan Leng

Polar form of a complex number.

Finding the stationary points of a cubic with two turning points

Finding the stationary points of a rational function with specific features.

Find the $x$ and $y$ components of a force which is applied at an angle to a particle. Resolve using $F \cos \theta$. The force acts in the positive $x$ and positive $y$ direction.

Antiderivatives

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Step by step solving for integration by substitution

Integration by susbtitution, no hint given

Power rule

Power rule

Turning points of a cubic function

Rate of change problem involving velocity & acceleration

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Determine the resultant of three random 2-D vectors.  

Indefinite Integrals

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Testing whether students know how to use multiple log laws.

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Find the tension in a rope necessary to prevent a bracket from rotating by applying $\Sigma M = 0$.

Given three vectors, arrange them in a tip to tail arrangement using geogebra, then estimate the magnitude and direction of their resultant.

Find the sum of two 2-dimensional vectors, graphically and exactly using the parallelogram rule.

Add three vectors by determining their scalar components, summing them and then resolving the rectangular components to find the magnitude and direction of the resultant

Given three vectors with integer components, find the corresponding magnitude and direction.

Add three vectors by determining their scalar components, summing them and then resolving the rectangular components to find the magnitude and direction of the resultant.

Replace two parallel forces with an equivalent single force

Indefinite Integrals

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Simple Indefinite Integrals

Find $\displaystyle \int \frac{a}{(bx+c)^n}\;dx$

Find $\displaystyle \int \frac{a}{(bx+c)^n}\;dx$

Simple Indefinite Integrals

Simple Indefinite Integrals

Using the reduction formulas for products of powers or sin and cosine