Homework set.  Find reactions for various 2-D rigid bodies in equilibrium.

Homework set.  Find reactions for various 2-D rigid bodies in equilibrium.

Homework set.  Identify student errors when drawing free body diagrams.

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

Homework set.  Problems involving two interacting particles.

Homework set.  Variations on problems involving single particle equilibrium.

Homework set.  Vector addition in two dimensions by summing scalar components.

This is a set of questions designed to help you practice adding, subtracting, multiplying and dividing fractions.

All of these can be done without a calculator.

Divisor is single digit. There is a remainder which we express as a decimal by continuing the long division process. Rounding is required to one decimal place. The working suggests determining the second decimal place so the student knows whether to round up or down.

A quadratic equation (equivalent to $(x+a)^2-b$) is given and sketched. Three equations are given that can be solved using the graph. There is a chance there will only be one solution.

Finding X-Y intercepts for quadratic and cubic equations.

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This is a set of questions designed to help you practice adding, subtracting, multiplying and dividing fractions.

All of these can be done without a calculator.

Divisor is single digit. There is a remainder which we express as a decimal by continuing the long division process. Rounding is required to one decimal place. The working suggests determining the second decimal place so the student knows whether to round up or down.

Two quadratic graphs are sketched with some area beneath them shaded. Question is to determine the area of shaded regions using integration. The first graph's area is all above the $x$-axis. The second graph has some area above and some below the $x$-axis.

Recovering original function given some information such as derivative and value at some point.

$x$ is given and (sin(x),cos(x)) is plotted on a unit circle.  Then the student is asked to determine sin(y) and cos(y), where y is closely related to x (e.g. y=-x, y=180+x, etc.) Also find values and sign of cos/tan/sin(x).

Use the parallel axis theorem to find the area moment of inertia of a triangle and a rectangle about various axes.

Use a table of properties to find the Area Moment of inertia for simple shapes: rectangle, triangle, circle, semicircle, and quarter circle.

 The parallel axis theorem is not required for any of these shapes.  One situation requires subtracting a triangle from a rectangle however.

Distinguish between centroidal and non-centroidal moments of inertia.

Find the reactions of a simply-supported beam with a trapazoidal distributed load.

Use integration to find the centroid of an area bounded by a parabola, a sloping line, and the y-axis.  

Find the area, first moment of area, and coordinates of a general spandrel.  The area may be above or below the function.

Find roots and the area under a parabola

Given a random spandrel, find the expressions for the differential elements of area and the coordinates of its centroid needed to determine the location of the centroid by integration. 

Find the centroid of a shape made up of a rectangle and two triangles.

Find the centroid of a shape made from a rectangle, triangle, and circle.

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

Calculate the moment of a force.  Must calculate perpendicular distance based on simple geometry, and recognize direction.

This question uses a Geogebra applet to solve a linear program with two variables using the graphical method. It contains three steps:

1. Construct the feasible area (polygon) by adding the constraints one by one. The students can see what happens when the constraints are added.
2. Add the objective function, and the level set of the objective value is shown, as well as its (normalised) gradient.
3. Compute the optimal solution by moving the level set of the objective around.

Solve linear equations with unkowns on both sides. Including brackets and fractions.

Identify the truth value of an inequality (T/F) between two numbers