Week 2, Question 2

Week 2, Question 1

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.

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

Basic properties of atoms

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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

Factorise polynomials by identifying common factors. The first expression has a constant common factor; the rest have common factors involving variables.

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Quiz to assess matrix addition, subtraction, multiplication and multiplication by scalar, determinants and inverses, solving a system of simultaneous equations.

Choose from one of several pre-defined scenarios, and set variables to the corresponding values, defined in lists.

This question has three variables: city, population, and percent_like_chocolate. These differ for each city. We've defined a list for each variable, with the corresponding values. A variable called scenario picks a random position in the list, so the value of city, for example, is cities[scenario].

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Introductory exercise about power sets.

Translation to Dutch of 

"Given a description in words of the costs of some items in terms of an unknown cost, write down an expression for the total cost of a selection of items. Then simplify the expression, and finally evaluate it at a given point.

The word problem is about the costs of sweets in a sweet shop."

Cofactors Determinant and inverse of a 3x3 matrix.

Solve for $x$ and $y$:  \[ \begin{eqnarray} a_1x+b_1y&=&c_1\\   a_2x+b_2y&=&c_2 \end{eqnarray} \]

The included video describes a more direct method of solving when, for example, one of the equations gives a variable directly in terms of the other variable.