Introduction to using the product rule

An introduction to using the quotient rule

Identifying the correct rule to use

Using the chain rule with polynomials

Using the chain rule with polynomials

Find $\displaystyle\int \frac{ax+b}{(x+c)(x+d)}\;dx,\;a\neq 0,\;c \neq d $.

Using the chain rule within product rule problems

Identifying the correct rule to use

An introduction to using the quotient rule

Identifying the correct rule to use

Identifying the correct rule to use

Identifying the correct rule to use

Using the chain rule with polynomials and negative powers.

Introduction to using the product rule

Using the chain rule with polynomials and negative powers

Introduction to using the product rule

Using the chain rule within product rule problems

An introduction to using the quotient rule

An introduction to using the quotient rule

Identifying the correct rule to use

Using the chain rule with polynomials

Integrate $f(x) = ae ^ {bx} + c\sin(dx) + px^q$. Must input $C$ as the constant of integration.

This question asks students to find the distance from an aircraft to a given marker. Angle of depression of 2 markers from the aircraft are given and the distance between the markers on the ground (all randomised). Students need to use the sine rule to find the answer. The workding of the question makes googling the answer difficult.

Student is asked to find the distance from a given point, A, to a house, given the distance between A and another point B, and the angles at A and B. Requires use of the sine rule. Distance and angles are randomised.

Student is asked to find the distance from a given point, B, to a house, given the distance between B and another point A, and the angles at A and B. Requires use of the sine rule. Distance and angles are randomised.

Question requires students to determine if the smallest angle of a triangle is smaller than a given value. Answer is Yes/No but students need to use cosine rule to find the smallest angle and to know that smallest angle is oppositeshortest side (otherwise they will need to find all angles of the triangle). Designed for a test where students upload handwritten working for each question as a check against guessing. Also designed to make it difficult for students to google or use AI to find the answer.

Question requires students to determine if the largest angle of a triangle is smaller than a given value. Answer is Yes/No but students need to use cosine rule to find the largest angle and to know that largest angle is opposite longest side (otherwise they will need to find all angles of the triangle). Designed for a test where students upload handwritten working for each question as a check against guessing. Also designed to make it difficult for students to google or use AI to find the answer.

Students are given lengths of 3 sides of a triangle (all randomised) and asked to find one of the angles in degrees. Requires use of the cosine rule.

Students are given two angles and the length of the side between them, they are asked to find the length of the side opposite angle A. Can be completed with the ine rule.

Calculating the rate of change of the temperature during a chemical reaction using the chain rule in a function of the form $T=ate^{-t}$, and finding the maximum temperature of the reaction.