Factoring a quadratic equation

Basic solving of linear equations

Give the student three points lying on a quadratic, and ask them to find the roots.

Then ask them to find the equation of the quadratic, using their roots. Error in calculating the roots is carried forward.

Finally, ask them to find the midpoint of the roots (just for fun). Error is carried forward again.

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

Given the vector equations of two straight lines, find the coordinates of the point of intersection

Given the vector equations of two straight lines, find the angle between them

Questions on vector arithmetic and vector operations, including dot and cross product, as well as the vector equations of planes and lines.

Equations which can be written in the form

\[\dfrac{\mathrm{d}y}{\mathrm{d}x} = f(x),   \dfrac{\mathrm{d}y}{\mathrm{d}x} = f(y),   \dfrac{\mathrm{d}y}{\mathrm{d}x} = f(x)f(y)\]

can all be solved by integration.

In each case it is possible to separate the $x$'s to one side of the equation and the $y$'s to the other

Solving such equations is therefore known as solution by separation of variables

First- and second order recurrence equations, homogenous and nonhomogenous

Assessment questions for First Order Differential Equations (1)

Student is asked whether a quadratic equation can be factorised. If they say "yes", they're asked to give the factorisation.

Solve a system of linear equations using Gaussian elimination.

Two questions on solving systems of simultaneous equations.

Solve a pair of linear equations by writing an equivalent matrix equation.

Solve a pair of linear equations by writing an equivalent matrix equation.

Solve a first order algebraic equation

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Questions on vector arithmetic and vector operations, including dot and cross product, as well as the vector equations of planes and lines.

Solve a pair of linear equations by writing an equivalent matrix equation.

This question plots a general amplitude modulated carrier signal defined by $v_s(t) = (V_{DC} + V_m \cos(2\pi f_m t))\cos(2\pi f_c t)$, where $V_{DC}$ is a DC offset, $V_m$ is the message amplitude, $f_m$ is the message frequency and $f_c$ is the carrier frequency ($f_c = 20f_m$ in this question). The student must identify the values of $V_{DC}$ and $V_m$ and enter these values into the appropriate gaps in the equation of the AM signal.

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

Rearrange equations to make $x$ the subject.

Two questions on solving systems of simultaneous equations.

Given two numbers, find the gcd, then use Bézout's algorithm to find $s$ and $t$ such that $as+bt=\operatorname{gcd}(a,b)$.

Finally, find all solutions of an equation $\mod b$.

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