Search - Numbas at mathcentre.ac.uk

18 results.

Solve simulatenous equations. (Video)
Ready to use
Question in Core Foundation Maths by Jinhua Mathias

Solve for $x$ and $y$ : $\begin{eqnarray} a_1x+b_1y&=&c_1\\ a_2x+b_2y&=&c_2 \end{eqnarray}$

The included video describes a more direct method of solving when, for example, one of the equations gives a variable directly in terms of the other variable.
José's copy of Solve simulatenous equations. (Video)
Ready to use
Question in Jos's workspace by Jos Klenner

Solve for $x$ and $y$ : $\begin{eqnarray} a_1x+b_1y&=&c_1\\ a_2x+b_2y&=&c_2 \end{eqnarray}$

The included video describes a more direct method of solving when, for example, one of the equations gives a variable directly in terms of the other variable.
Numbas demo: video
Ready to use
Question in Demos by Christian Lawson-Perfect

Customised for the Numbas demo exam

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Video in Show steps.
Solving equations. (Video)
Draft
Question in Bill's workspace by Bill Foster

Solve $\displaystyle ax + b =\frac{f}{g}( cx + d)$ for $x$ .

A video is included in Show steps which goes through a similar example.
Quotient rule. (Video)
Draft
Question in Bill's workspace by Bill Foster

The derivative of $\displaystyle \frac{ax^2+b}{cx^2+d}$ is $\displaystyle \frac{g(x)}{(cx^2+d)^2}$ . Find $g(x)$ .

Contains a video solving a similar quotient rule example. Although does not explicitly find $g(x)$ as asked in the question, but this is obvious.
Simplify logarithms 1: (Video)
Draft
Question in Bill's workspace by Bill Foster

Express $\log_a(x^{c}y^{d})$ in terms of $\log_a(x)$ and $\log_a(y)$ . Find $q(x)$ such that $\frac{f}{g}\log_a(x)+\log_a(rx+s)-\log_a(x^{1/t})=\log_a(q(x))$ .

There is a video included explaining the rules of logarithms by going through simplification of logs of numbers rather than algebraic expressions.
Expansion of three brackets: (Video)
Draft
Question in Bill's workspace by Bill Foster

Expand $(ay+b)(cy+d)(py+q)$ .

Includes a video expanding three brackets, however uses the variable $x$ rather than $y$ .
Complete the square. (Video)
Draft
Question in Bill's workspace by Bill Foster

Find $p$ and $q$ such that $ax^2+bx+c = a(x+p)^2+q$ .

Hence, or otherwise, find roots of $ax^2+bx+c=0$ .

Includes a video which shows how to solve a quadratic by completing the square.
Chain rule. (Video).
Draft
Question in Bill's workspace by Bill Foster

Differentiate $\displaystyle \cos(e^{ax}+bx^2+c)$ .

Contains a video solving a similar example.
Solve a pair of simultaneous equations
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solve for $x$ and $y$ : $\begin{eqnarray} a_1x+b_1y&=&c_1\\ a_2x+b_2y&=&c_2 \end{eqnarray}$

The included video describes a more direct method of solving when, for example, one of the equations gives a variable directly in terms of the other variable.
Find the equation of a line with given gradient through a given point
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find the equation of a straight line which has a given slope or gradient $m$ and passes through the given point $(a,b)$ .

There is a video in Show steps which goes through a similar example.
Expand brackets and solve an equation
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solve $\displaystyle ax + b =\frac{f}{g}( cx + d)$ for $x$ .

A video is included in Show steps which goes through a similar example.
YJ's copy of Numbas demo: video
Ready to use
Question in YJ's workspace by YJ Kim

Customised for the Numbas demo exam

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Video in Show steps.
Solving equations. (Video)
Ready to use
Question in Bill's workspace by Bill Foster

Solve for $x$ and $y$ : $\begin{eqnarray} a_1x+b_1y&=&c_1\\ a_2x+b_2y&=&c_2 \end{eqnarray}$

The included video describes a more direct method of solving when, for example, one of the equations gives a variable directly in terms of the other variable.
Perdita's copy of Solving equations. (Video)
Ready to use
Question in Perdita's workspace by Perdita Harper

Solve for $x$ and $y$ : $\begin{eqnarray} a_1x+b_1y&=&c_1\\ a_2x+b_2y&=&c_2 \end{eqnarray}$

The included video describes a more direct method of solving when, for example, one of the equations gives a variable directly in terms of the other variable.
joshua's copy of Solve simulatenous equations. (Video)
Ready to use
Question in joshua's workspace by joshua boddy

Solve for $x$ and $y$ : $\begin{eqnarray} a_1x+b_1y&=&c_1\\ a_2x+b_2y&=&c_2 \end{eqnarray}$

The included video describes a more direct method of solving when, for example, one of the equations gives a variable directly in terms of the other variable.
Integration by partial fractions. (Video)
Ready to use
Question in Bill's workspace by Bill Foster

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Video in Show steps.
David's copy of Solving equations. (Video)
Ready to use
Question in David's workspace by David Rickard

Solve for $x$ and $y$ : $\begin{eqnarray} a_1x+b_1y&=&c_1\\ a_2x+b_2y&=&c_2 \end{eqnarray}$

The included video describes a more direct method of solving when, for example, one of the equations gives a variable directly in terms of the other variable.

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