Xiaodan Leng

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Template question. The student is asked to perform a two factor ANOVA to test the null hypotheses that the measurement does not depend on each of the factors, and that there is no interaction between the factors.

Solve for $x$: $\displaystyle 2\log_{a}(x+b)- \log_{a}(x+c)=d$. 

Make sure that your choice is a solution by substituting back into the equation.

Solve for $x$:  $\log_{a}(x+b)- \log_{a}(x+c)=d$

How to input x^2 and x*y.

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.

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 is applied in the negative $x$ and negative $y$ direction.

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 is applied in the negative $x$ direction but the positive $y$. 

Another practical application of differentiation

Quotient and remainder, polynomial division.

Straightforward solving linear equations question

Find the $x$ and $y$ components of the resultant force on an object, when multiple forces are applied at different angles.

Another example of finding the $x$ and $y$ components when multiple forces are applied at different angles to a particle.

Finding the lengths and angles within a right-angled triangle using: pythagoras theorem, SOHCAHTOA and principle of angles adding up to 180 degrees.

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Using the chain rule within product rule problems.

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A credit card company charges compound interest at x% per month 
on unpaid balances.

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Find the mean, median and mode of a list of 10 test scores.

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Calculate the annual interest rate for a savings account where A, P and n are given.

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Using e to solve equations involving the natural log

Given the derivatives of a cubic function at a point, find the value of the function at another point.

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The student is asked to factorise a quadratic $x^2 + ax + b$. A custom marking script uses pattern matching to ensure that the student's answer is of the form $(x+a)(x+b)$, $(x+a)^2$, or $x(x+a)$.

To find the script, look in the Scripts tab of part a.

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