This quiz contains questions on algebraic fractions, logarithmic equations, exponential equations, quadratic equations and simultaneous equations.

Students enter equation and turning point

Transposition of formulae. Changing the subject of an equation. 

rebel rebelmaths

Solving quadratic equations using a formula

Solving quadratic equations using a formula,

Solving quadratic equations using a formula,

Solve a logarithmic equation

Solve an exponential equation

This quiz contains questions on algebraic fractions, logarithmic equations, exponential equations, quadratic equations and simultaneous equations.

Solve simultaneous equations,

Need to know indices and logarithm

Solve quadratic equations using formula.

Selection of Quadratic Equations to Solve

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.

Shows how to define variables to stop degenerate examples.

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 $f(x,y)$.

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

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.

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.

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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.

Simplifying algebraic expressions

Students are given a graph of a cubic, and are asked to find the equation for it.

Students enter equation and turning point

Simplifying algebraic expressions

Several quadratics are given and students are asked to complete the square.

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

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.