Testing the understanding of the formal definition of $A\subseteq B$.

Example of a universal statement over the integers and its negation

Fourth part of the Core Foundation Maths pre-arrival self-assessment material:

Question 1:  Algebra IV: Properties of indices (1) - Multiplication/Division                                 

Question 2: Algebra IV: Properties of indices (2) - Fractions                                 

Question 3: Algebra IV - Properties of Indices (4) - Further

Question 4: Numbers V: standard index form (conversions and operations)                                 

Calculations are presented and students are asked to choose which angle/length the calculation corresponds to.

This question explores an understanding of an energy balance over a process stream.

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

Given a number evaluate simple power, negative power, to one half.

Simple Linear Equation.

$ \dfrac{n}{a} \pm b = c$

Testing addition, multiplication and division involving negative numbers.

Understanding order of operations on a calculator and using power and root keys.

Footballer expects to score in a/b matches.

Find a% of b using a calculator. Suggested method to use decimal equivalent.

Solve $p - t < \text{or}> q$

A box contains $m$ white balls and $n$ black balls. A ball is drawn out of the box at random. What is the probability that the ball is black/white?

Converting a length in m to mm, cm and km.

Addition, multiplication and division of fractions.

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A variety of worded fraction questions.

The simplest case. Divisor is single digit. There is no remainder. 

Solve a quadratic equation by completing the square. The roots are not pretty!

The simplest case. Divisor is single digit. There is no remainder. 

Simple Percentages

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 Basics, percentage of an amount, converting to fractions and decimals.

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6 questions which introduce the user to the Numbas system.

Practice with adding, subtracting and dividing basic algebraic fractions

Several problems involving dividing fractions, with increasingly difficult examples, including mixed numbers and complex fractions. 

Several problems involving the multiplication of fractions, with increasingly difficult examples, including a mixed fraction and a squared fraction. The final part is a word problem. 

One-way ANOVA example