Homework set.  Calculate Moment of Inertia for I beams, channels, angles, etc.

Homework set.  Trusses solved using the method of sections

Find centroidal moments of inertia and radius of gyration for a beam composed of  two angle sections forming a box beam.

Find the centroid and the centroidal moments of inertia for a beam composed of a flat plate and two angle sections.

Determine expressions for internal shear and bending moment as a function of $x$ for a beam with two vertical loads.

Solve for the internal force in three members of a truss.

Solve for the internal force in three members of a truss.

Simple truss with a zero-force member

Find the inverse of three $2 \times 2$ invertible matrices.

$A,\;B$ $2 \times 2$ matrices. Find eigenvalues and eigenvectors of both. Hence or otherwise, find $B^n$ for largish $n$.

Calculate an intersection probability given a two way table.

Find the volume of a prism with a trapezium as a cross section from a diagram.

Calculation of bending resistance of wooden beams exposed to fire. The students have to calculate charring and effective cross sections ending in the bending resistance of the cross section.

This question assesses the learner's ability to compute a confidence interval for a difference of two means, given two samples.

Randomized variables: sample raw data and confidence level. 

Adapted from section 7.3.1 in OpenIntro Statistics (4th ed).

Given some random finite subsets of the natural numbers, perform set operations $\cap,\;\cup$ and complement.

A question to test understanding of set cardinality and intersections when limited information is known about the size of certain sets.

$A,\;B$ $2 \times 2$ matrices. Find eigenvalues and eigenvectors of both. Hence or otherwise, find $B^n$ for largish $n$.

The student is given the equations of a line and a circle, and has to find the coordinates of the points of intersection. They're always at integer coordinates.

Given cost of production and price of sale of a product; a percentage increase in cost of production; and unit sales before and after; work out the extra profit.

Based on question 6 from section 3 of the maths-aid workbook on numerical reasoning.

$I$ compact interval, $g:I\rightarrow I,\;g(x)=ax^3+bx^2+cx+d$. Find stationary points, local and global maxima and minima of $g$ on $I$

$I$ compact interval, $g:I\rightarrow I,\;g(x)=ax^3+bx^2+cx+d$. Find stationary points, local and global maxima and minima of $g$ on $I$

Given some random finite subsets of the natural numbers, perform set operations $\cap,\;\cup$ and complement.

The 7th task in HELM book 1.4 section 1.

The 6th task in HELM book 1.4 section 1.

The 5th task in HELM book 1.4 section 1.

The 4th task in HELM book 1.4 section 1.

The 3rd task in HELM book 1.4 section 1.

The 2nd task in HELM book 1.4 section 1.

The first task in HELM book 1.4 section 1.

Calculating the area enclosed between a linear function and a quadratic function by integration. The limits (points of intersection) are given in the question.