Shear and bending moment diagram for a beam loaded with an arbitrary parabolic distributed load described with a loading function.  Integrate to find reactions and equations for shear and bending moment.

Questions to test if the student knows the inverse of an even power (and how to solve equations that contain a single power that is even). 

Questions to test if the student knows the inverse of an odd power (and how to solve equations that contain a single power that is odd). 

Differential equations.

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First- and second order recurrence equations, homogenous and nonhomogenous

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

Simple trig equations with radians

Apply the quadratic formula to find the roots of a given equation. The quadratic formula is given in the steps if the student requires it.

Students are given an exponential equation and asked to evaluate it at two points.

The constants in the exponential are randomised.

A variety of trigonometric equations which can be solved using inverse operations.

Given one point and the gradient determine the equation of the line.

Given the graph of the line determine the equation of the line.

An A-frame structure supporting a force and a moment. The feet are at the different vertical positions so the solution will require simultaneous equations, unless you rotate the coordinate system.

Find a regression equation.

Use two points on a line graph to calculate the gradient and $y$-intercept and hence the equation of the straight line running through both points.

The answer box for the third part plots the function which allows the student to check their answer against the graph before submitting.

This particular example has a positive gradient.

Implicit differentiation.

Given $x^2+y^2+dxy +ax+by=c$ find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$.

Also find two points on the curve where $x=0$ and find the equation of the tangent at those points.

Simple trig equations with radians

Based on Chapter 8, quite loosley.Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

This question tests the student's ability to solve simple linear equations by elimination. Part a) involves only having to manipulate one equation in order to solve, and part b) involves having to manipulate both equations in order to solve. 

Students are given an exponential equation and asked to evaluate it at two points.

The constants in the exponential are randomised.

Exercises in solving simultaneous equations with 2 variables.

Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

Résoudre des équations du second degré à une inconnue (cas d'un discriminant > 0, deux racines entières réelles et discrètes) à l'aide des formules.

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Identify co-efficients, then use quadratic formula to find roots.

All set to be distinct and real. Some can be non-integer (0.5 steps)

Solve quadratic equations (non-simple case, two real, discrete integer roots) using the formula.

Solve quadratic equations (non-simple case, two real, discrete roots) using the formula. Some, random, non integer roots.

Calculate discriminant of quadratic equations and use to determine number/nature of roots.

Calculation of quadratic discriminants.

State nature of roots.

Calculation of quadratic discriminants.

State nature of roots.