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Ratio Questions

Graphing $y=ab^{\pm x+d}+c$

Graphing $y=ab^x+c$

Integration by susbtitution, no hint given

The easiest type of exponential to graph where the base is greater than 1 and no transformations take place.

Graphing $y=a\log_{b}(\pm x+d)+c$

Apply partial diffenetiation in a geology problem.

Graphing $y=a\log_{b}(x)+c$

The easiest type of exponential to graph where the base is greater than 1 and no transformations take place.

Solve simultaneous equations,

Need to know indices and logarithm

First test

A block of given mass is sliding down the plane with a given acceration. Find the normal reaction force, the parallel force and the missing value of a and mu.

The easiest type of exponential to graph where the base is greater than 1 and no transformations take place.

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Solve quadratic equations using formula.

Finding lengths of sides of triangles

Quiz covering basic arithmetic with complex numbers, solving a quadratic with complex solutions and converting to/from polar and rectangular forms.

Selection of Quadratic Equations to Solve

Eight expressions, of increasing complexity. The student must simplify them by expanding brackets and collecting like terms.

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.

Algebra:  Quadratic Factorisation.

              Coefficient of squared term is 1.

Shows how to define variables to stop degenerate examples.

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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 $f(x,y)$.

Factorising polynomials using the highest common factor.

Adapted from 'Factorisation' by Steve Kilgallon.

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