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Solving equations
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solve for $x$ and $y$ :
$\begin{eqnarray} a_1x+b_1y&=&c_1\\ a_2x+b_2y&=&c_2 \end{eqnarray}$
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.
Solve a quadratic with the formula
Has some problems
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 2 others

Solve for $x$ : $\displaystyle ax ^ 2 + bx + c=0$ .

Entering the correct roots in any order is marked as correct. However, entering one correct and the other incorrect gives feedback stating that both are incorrect.
Solve an equation with a reciprocal
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solve for $x$ : $\displaystyle \frac{a} {bx+c} + d= s$
Complete the square
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Complete the square for a quadratic polynomial $q(x)$ by writing it in the form $a(x+b)^2+c$ . Find both roots of the equation $q(x)=0$ .
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.
Use the quadratic formula to solve an equation in terms of an unknown variable
Ready to use
Question in Transition to university by Hannah Aldous and 2 others

Factorise a quadratic expression of the form $x^2+akx+bk^2$ for $x$ , in terms of $k$ . $a$ and $b$ are constants.
Solve a linear equation $ax+b = c$
Ready to use
Question in Transition to university by Lauren Richards and 1 other

Solve a linear equation of the form $ax+b = c$ , where $a$ , $b$ and $c$ are integers.

The answer is always an integer.
Solving Quadratic Equations with $x^2$ Coefficients of 1 by Factorising
Should not be used
Question in Transition to university by Hannah Aldous

This question tests the students ability to factorise simple quadratic equations (where the coefficient of the x^2 term is 1) and use the factorised equation to solve the equation when it is equal to 0.
Solving linear simultaneous equations by elimination
Ready to use
Question in Transition to university by Lauren Richards and 1 other

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.
Factorising Quadratic Equations with $x^2$ Coefficients Greater than 1
Ready to use
Question in Transition to university by Hannah Aldous and 1 other

Factorise a quadratic equation where the coefficient of the $x^2$ term is greater than 1 and then write down the roots of the equation
Factorising Quadratic Equations with $x^2$ Coefficients of 1
Ready to use
Question in Transition to university by Hannah Aldous and 2 others

Factorise three quadratic equations of the form $x^2+bx+c$ .

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.
Extract common factors of polynomials
Has some problems
Question in Transition to university by Bradley Bush and 2 others

Factorise polynomials by identifying common factors. The first expression has a constant common factor; the rest have common factors involving variables.
Equations of parallel lines
Ready to use
Question in Transition to university by Bradley Bush and 1 other

Some conceptual questions about parallel lines - fill in the gaps in some statements.

Identify the lines corresponding to given equations, and the lines parallel to lines with given equations.
Solving log equations using exponentials
Ready to use
Question in Algebra by Ben Brawn

No description given
Interactive Newton-Raphson method
Ready to use
Question in Bill's workspace by Bill Foster

Write down the Newton-Raphson formula for finding a numerical solution to the equation $e^{mx}+bx-a=0$ . If $x_0=1$ find $x_1$ .

Included in the Advice of this question are:

6 iterations of the method.

Graph of the NR process using jsxgraph. Also user interaction allowing change of starting value and its effect on the process.
Solution curves and Vector fields 1 : dy/dx=sin(x-y)
Ready to use
Question in Bill's workspace by Bill Foster

Using Jsxgraph to draw the vector field for a differential equation of the form $\frac{dy}{dx}=f(x,y)=\sin(x-y)$ , and also by moving the point $(x_0,y_0)$ you can see the solution curves going through that point.

If you want to modify $f(x,y)$ simply change the definition of $f(x,y)$ and that of the variable str in the user defined function testfield in Extensions and scripts. You have to use javascript notation for functions and powers in the definition of $f(x,y)$ .
Solution curves and Vector fields 2 : $dy/dx=x^2-y^2$
Ready to use
Question in Bill's workspace by Bill Foster

Using Jsxgraph to draw the vector field for a differential equation of the form $\frac{dy}{dx}=f(x,y)=x^2-y^2$ , and also by moving the point $(x_0,y_0)$ you can see the solution curves going through that point.

If you want to modify $f(x,y)$ simply change the definition of $f(x,y)$ and that of the variable str in the user defined function testfield in Extensions and scripts. You have to use javascript notation for functions and powers in the definition of $f(x,y)$ .
Julie's copy of Second order differential equations 5
Draft
Question in Julie's workspace by Julie Crowley

Find the general solution of $y''+2py'+(p^2-q^2)y=x$ in the form $Ae^{ax}+Be^{bx}+y_{PI}(x),\;y_{PI}(x)$ a particular integral.

rebelmaths
Julie's copy of First order differential equations 5
Draft
Question in Julie's workspace by Julie Crowley

Find the solution of $\displaystyle x\frac{dy}{dx}+ay=bx^n,\;\;y(1)=c$

rebelmaths
Julie's copy of First order differential equations 4
Draft
Question in Julie's workspace by Julie Crowley

Find the solution of $\displaystyle \frac{dy}{dx}=\frac{1+y^2}{a+bx}$ which satisfies $y(1)=c$

rebelmaths
Julie's copy of First order differential equations 1
Draft
Question in Julie's workspace by Julie Crowley

Solve 4 first order differential equations of two types: $\displaystyle \frac{dy}{dx}=\frac{ax}{y},\;\;\frac{dy}{dx}=\frac{by}{x},\;y(2)=1$ for all 4.

rebelmaths
Rearrange equations
Ready to use
Question in Julie's workspace by Julie Crowley

rearranging the Michelas-Menten equation to make the substrate the subject.

rebelmaths
Rearranging equations by multiplying or dividing: One step
Ready to use
Question in Julie's workspace by Julie Crowley

Rearranging equations by multiplying or dividing: One step

rebelmaths
Q7 (simultaneous equations to solve forces in a system, and solve for x)
Ready to use
Question in David's workspace by TEAME CIT

Simultaneous Equations

rebelmaths
Q6 (Calculating cars/carparts using equations)
Draft
Question in David's workspace by TEAME CIT

Word Problems leading to simultaneous Linear Equations

rebelmaths
delete syntax checkinbg bryan's copy of MA4100 4.4 Gaussian Elimination
Ready to use
Question in bryan's workspace by bryan pearce

Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.
Lois's copy of Simultaneous linear equations (variables)
Ready to use
Question in Algebra by Lois Rollings

Shows how to define variables to stop degenerate examples.
Solving equations 2
Draft
Question in Algebra by Lois Rollings

Solve for $x$ : $\displaystyle \frac{a} {bx+c} + d= s$
Solving a quadratic equation
Draft
Question in Algebra by Lois Rollings

Solve for $x$ : $\displaystyle ax ^ 2 + bx + c=0$ .

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