Question on drug calculations

Defines a CSS class in the preamble which styles the "Lemma" environment, used in the statement.

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.

Drug Calculations

Solve simultaneous equations,

Need to know indices and logarithm

Solve quadratic equations using formula.

This question assesses the knowledge of the formula to calculate the distance between a point and a plane in the 3D space.

Using Jsxgraph to draw the vector field for a differential equation of the form $\frac{dy}{dx}=f(x,y)=1-\sin(y)$, 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 $f(x,y)$.

This question provides practice at adding, subtracting, dividing and multiplying complex numbers in rectangular form.

A random heating question, that randomly picks a material, and then heats it through either one or two phase changes, provides an example graph of the heating with scaled temperature ranges (though not with scaled latent and specific heats), and a table with the suitable constants.

Using Jsxgraph to draw the vector field for a differential equation of the form $\frac{dy}{dx}=f(x,y)=\sin(x)-\sin(y)$, 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 $f(x,y)$.

A question to practise the following skills in the context of Earth Sciences:

• graph-reading skills
• using a graph to find the equation of a line
• used adpative marking

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 $f(x,y)$.

Use Sine rule and Cosine rule to solve a Geometry problem in geology.

Apply partial diffenetiation in a geology problem.

Calculating complex numbers raised to an natural number exponent

Calculating the square root of a complex number using De Moivre.

Newton-Raphson numerical method question to solve $g(x)=0$

Includes a graph of the function $g(x)$ in Advice using Jsxgraph.

Solving quadratic equations using a formula,

A student selects a card from a deck of 52 and rolls a dice once.

rebelmaths

Simple Definite Integrals

Simple Definite Integrals

Simple Definite Integrals

Simple Definite Integrals

Simple Definite Integrals

Ask for the square of each number from 0 to 15, in random order.

The shuffle function puts a list in random order.

Questions on integration using various methods such as parts, substitution, trig identities and partial fractions.

Calculate the cube roots of a complex number using De Moivre.

Calculating the square root of a complex number using De Moivre.

Calculating complex numbers raised to an natural number exponent