Substitute values into formulae for the area or volume of various geometric objects.

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Two sample t-test to see if there is a difference between scores on questions between two groups when the questions are asked in a different order.

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Questions on integration using various methods such as parts, substitution, trig identities and partial fractions.

A collection of information and activities to introduce students to Numbas. There is some information on how Numbas works, information on how to write answers to mathematical expression and number entry parts, and a "test yourself" explore mode activity.

Note: This exam was written for students accessing Numbas exams through the Numbas LTI tool. Some of the information does not apply to exams accessed standalone or through a generic SCORM player.

Homework set.  Problems require finding centroid, then Moment of Inertia about a centroidal axis.

Given the moment of inertia of an area about an arbitrary axis, find the centroidal moment of inertia and the moment of inertia about a second axis.

Consider a binary tree with $2^n$ nodes.

We give generators for the isomorphisms of the tree: at each non-leaf vertex, swap the branches descending from that node.

• What is the action of a given word?
• Write a word which produces the required isomorphism
• Which generators commute?
• What is the order of each generator?
• Write one of the (non-root) generators in terms of the others.
• Which permutations of the leaves are possible?
• What is the order of the group of isomorphisms?
• What is the order of the quotient group obtained by identifying all the leaves of one branch?

Write expressions for the moment of inertia of simple shapes about various axes.

Simple % calculation to introduce and practice concept for students identified as weak in this area

In this question the student needs to calculate the Biochemical Oxygen Demand after 5 days. 

Assesses multiplying numbers

Given a random variable $X$  normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

Find the tension required to hold a pole at a specified angle.

Homework set.  Find 2-D moments or balance moments using Verignon's theorem:  $ M = \pm F_x d_y \pm F_y d_x$

Homework set.  Determine the moment of a force using the definition of the moment, $M = F d_\perp$.

Find the force required to balance a see-saw.

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Pulley supported by a cable, so the tension in the rope is constant.    Advice is a youtube video showing how to solve the problem.

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Write the expression $ax^2+bx+c$ in completed square form $a(x+p)^2+k$.

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