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This test checks that students understand the principles of double entry bookkeeping

Given an ODE solution: $y=  b x^n + cx$

Use a condition: $y(1)=a$ to find the particular solution and hence the value of $y(d)$.

Cálculo del módulo, argumento, multiplicación por conjugado complejo, dados dos números complejos.

Operaciones combinadas con números complejos.

Multiplicación y división de números complejos. 

Inverso y división de números complejos.

Multiplicación y suma de números complejos.

Ejemplos elementales de multiplicación y suma de números complejos. 

Questions on the construction $t+U$ where $K$ is a field, $t\in K^n$, $U\subseteq K^n$ (in parts a) - d), $K=\mathbb R$ and $n=2$ so that we can draw pictures). Part e) is a bit more abstract and probably more difficult.

Deduce some properties of elements of $\mathbb F_4$, given its multiplication table. (E.g., which element is the zero, the one element, ...)

Grichische Antike 1

Milesisches Zahlzeichensystem

Find angular speed of a swinging pendulum.

The derivative of $\displaystyle x ^ {m}(ax^2+b)^{n}$ is of the form $\displaystyle x^{m-1}(ax^2+b)^{n-1}g(x)$. Find $g(x)$.

Find the common ratio of a given geometric sequence, write down the formula for the nth term and use it to calculate a given term in the sequence.

Used for LANTITE preparation (Australia).SP = Statistics & Probability strand. Students are shown a divided bar chart and asked one of seven possible true/false questions.

Used for LANTITE preparation (Australia). SP = Statistics & Probability strand. NC = Non Calculator strand. Students are shown a table of lunch options, given a child's food preferences and asked how many combinations are possible. There are seven possible questions.

Used for LANTITE preparation (Australia). SP  Statistics & Probability strand. NC = Non Calculator strand. Students are shown a table and asked one of seven possible questions.

Used for LANTITE preparation (Australia). SP = Statistics & Probability strand. Students are shown an ngram and asked one of eight possible questions.

Used for LANTITE preparation (Australia). SP = Statistics & Probability strand. Students are shown a bar chart with error bars and asked one of five possible questions.

Used for LANTITE preparation (Australia). SP = Statistics & Probability strand. Students are shown an infographic and asked one of six possible questions.

Used for LANTITE preparation (Australia). SP  Statistics & Probability strand. Students are shown a BMI chart and asked one of seven possible questions.

Used for LANTITE preparation (Australia).  SP = Statistics & Probability strand. Students are shown an unuaual chart and asked one of seven possible questions. The Advice for this question is general in nature.

Used for LANTITE preparation (Australia). SP = Statistics & Probability strand. Students are shown a stacked bar chart and asked one of seven possible questions.

Multiple response question (3 correct out of 6) re properties of convergent and divergent sequences. Selection of questions from a pool.

Multiple response question (4 correct out of 8) covering properties of convergent and divergent sequences and boundedness of sets. Selection of questions from a pool.

Differentiate

\[ \sqrt{a x^m+b})\]