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Find the dot product and the angle between two vectors

A quadratic function $ax^2+bs+c$ is given. Six parabolas are sketched. Question is to select the correct parabola.  Need to consider the y-intercept, the coefficient of x^2, and the x-coordinate of the minimum/maximum point.

Finding the coordinates and determining the nature of the stationary points on a polynomial function

Elementary operations on vectors; sum, modulus, unit vector, scalar multiple. 

Student is asked to sketch $f(x)=2^x$, by plotting several points and selecting the correct graph.

Find $\displaystyle \frac{d}{dx}\left(\frac{m\sin(ax)+n\cos(ax)}{b\sin(ax)+c\cos(ax)}\right)$. Three part question.

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Choose Ferrous Metal

This question aims to test understanding and ability to use the laws of indices.

Rolling a pair of dice. Find probability that at least one die shows a given number.

Example showing how to calculate the probability of A or B using the law $p(A \;\textrm{or}\; B)=p(A)+p(B)-p(A\;\textrm{and}\;B)$. 

Easily adapted to other applications.

Five graphs are sketch. Task is to select those that look like parabolas/quadratics.

Thermoplastics

A second worked example about combinatorics. 

Uses an extension to embed SageMath cells into content areas.

Express $\log_a(x^{c}y^{d})$ in terms of $\log_a(x)$ and $\log_a(y)$. Find $q(x)$ such that $\frac{f}{g}\log_a(x)+\log_a(rx+s)-\log_a(x^{1/t})=\log_a(q(x))$

Several quadratics are given and students are asked to complete the square.

Use the rule $\log_a(n^b) = b\log_a(n)$ to rearrange some expressions.

Basic properties of atoms

This question aims to test understanding and ability to use the laws of indices involving an unkown parameter. 

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.

multiple choice question on this week's content