Equating coefficients of a polynomial. Basic ones that don't require simultaneous equations.

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. 

Very good feedback and corresponds to instance of randomisation

A graph of a straight line $f$ is given. Questions include determining values of $f$, of $f$ inverse, and determining the equation of the line.

Solve a quadratic equation by completing the square. The roots are not pretty!

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. 

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. 

Equating coefficients of a polynomial. Basic ones that don't require simultaneous equations.

No description given

No description given

The student is asked to factorise a quadratic $x^2 + ax + b$. A custom marking script uses pattern matching to ensure that the student's answer is of the form $(x+a)(x+b)$, $(x+a)^2$, or $x(x+a)$.

To find the script, look in the Scripts tab of part a.

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.

Shows how to define variables to stop degenerate examples.

Shows how to define variables to stop degenerate examples.

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.

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

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

A parabolic graph is given. The question is to determine the equation of the graph. Non-calculator. Advice is given.

set up x- and y axises.

set linear equations and solve the simulatenous equations.

set up x- and y axises.

set linear equations and solve the simulatenous equations.

A few quadratic equations are given, to be solved by completing the square. The number of solutions is randomised.

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

Questions to test if the student knows the inverse of fractional power or root (and how to solve equations that contain them). 

Differential equations.

rebelmaths

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.

Questions involving various techniques for rearranging and solving quadratic expressions and equations

Solving two simultaneous linear equations

A graph of a straight line $f$ is given. Questions include determining values of $f$, of $f$ inverse, and determing the equation of the line.

Simple procedures are given and student is asked to carry them out or un-do them.

Version 1: i and ii have the same answer. iii and iv both have two answers.

Version 2: i and ii have different answers. iii has two answers,biv has one answer.

Version 3: i and ii have different answer. iii has one answer, iv has two answers.

Version 4: i and ii have the same answer. iii has one answer, iv has two answers.

Simple procedures are given and student is asked to carry them out or un-do them.

Version 1: i and ii have the same answer. iii and iv both have two answers.

Version 2: i and ii have different answers. iii has two answers,biv has one answer.

Version 3: i and ii have different answer. iii has one answer, iv has two answers.

Version 4: i and ii have the same answer. iii has one answer, iv has two answers.