You are a professional question writer, mathematician, teacher, educator, and government official of the Queensland Government, working for the QCAA, tasked with creating simple familiar, complex familiar and complex unfamiliar questions for a grade 9 exam assessment for Queensland schools. 60% of the questions will be simple familiar. 20% will be complex familiar. 20% will be complex familiar. Before giving you the outline of the topics assessed, I will give you a definition of the terms: 

‘Simple familiar
Problems of this degree of difficulty require students to demonstrate knowledge and understanding of the subject matter and application of skills in a situation where:
*   relationships and interactions are obvious and have few elements; and
*   all of the information to solve the problem is identifiable; that is
-   the required procedure is clear from the way the problem is posed, or
-   in a context that has been a focus of prior learning.
Students are not required to interpret, clarify and analyse problems to develop responses. To put it simply, questions for this type mean ‘do the skill’.

Complex familiar
Problems of this degree of difficulty require students to demonstrate knowledge and understanding of the subject matter and application of skills in a situation where:
*   relationships and interactions have a number of elements, such that connections are made with subject matter within and/or across the domains of mathematics; and
*   all of the information to solve the problem is identifiable; that is
-   the required procedure is clear from the way the problem is posed, or
-   in a context that has been a focus of prior learning.
Some interpretation, clarification and analysis will be required to develop responses. To put it simply, questions of this type mean ‘do the skill in a multi-step, back to front or worded problem’

Complex unfamiliar
Problems of this degree of difficulty require students to demonstrate knowledge and understanding of the subject matter and application of skills in a situation where:
*   relationships and interactions have a number of elements, such that connections are made with subject matter within and/or across the domains of mathematics; and
*   all the information to solve the problem is not immediately identifiable; that is
-   the required procedure is not clear from the way the problem is posed, and
-   in a context in which students have had limited prior experience.
Students interpret, clarify and analyse problems to develop responses. To put it simply, questions of this type mean ‘unfamiliar worded or complex diagram they’ve never seen before that makes them problem solve.’’

With this expertise and knowledge, here are the topics that will be assessed: ‘- Construct and use a Venn diagram or two-way table to determine probabilities.
- Construct and use an array (table) for a two-step probability experiment to determine probabilities, both with and without replacement.
- Construct and use a tree diagram for two or more stage events to show all possible outcomes and determine probabilities, both with and without replacement.
- Expand binomial products.
- Expand perfect squares using the rules: 
- ((a + b)^2 = a^2 + 2ab + b^2)
- ((a - b)^2 = a^2 - 2ab + b^2)
- Expand using the difference of perfect squares rule: 
- ((a + b)(a - b) = a^2 - b^2)
- Factorise basic algebraic expressions.
- Factorise the difference of perfect squares.
- Factorise monic quadratics.
- Solve applications of quadratic equations.
- Simplify algebraic fractions using multiplication and division by factorising first.
- Simplify algebraic fractions using addition and subtraction.
- Solve algebraic equations involving fractions.’

With this knowledge, create 27 questions. Subquestions should be included as well.