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

This question asks learners to use row operations to find the inverse of a 3x3 matrix.

This is a set of questions designed to help you practice adding, subtracting, multiplying and dividing fractions.

All of these can be done without a calculator.

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.

A selection of questions which use the "random person" extension to randomise the names of people in the question text.

Factorising polynomials using the highest common factor

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.

Obtain the equation of a straight line that passes through 2 points.

In this question the student will be asked to manipulate surds and rationalise the denominator of a fraction when it is a surd.

This exam covers 

• laws of indices
• using surds and rationalising the denominator
• expanding brackets
• simplifying expressions
• solving linear inequalities
• finding common factors
• dividing a polynomial with remainders, using algebraic division
• factor theorem
• remainder theorem
• inverse and composite functions

Solving quadratic equations using a formula,

This question tests the students ability to use the logarithm equivalence law to make x the subject of a given equation and to check which of a list of logarithmic expressions are equivalent to x.

Question assessing the students understanding of linear sequences.

Students are assessed on their ability to find the common difference and first term in a linear sequence and then find the nth term of the sequence using the arithmetic formula.

Solving quadratic equations using a formula,

This is a set of questions designed to help you practice adding, subtracting, multiplying and dividing fractions.

All of these can be done without a calculator.

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Questions testing understanding of the precedence of operators using BIDMAS, applied to integers. These questions only test DMAS. That is, only Division/Multiplcation and Addition/Subtraction.

An example of using the GeoGebra extension to ask the student to create a geometric construction, with marking and steps.

Given a graph of some function $f(x)$ (a cubic), the student is asked to write the coordinates of the maximum and minimum points. The student then finds the maximum and minimum points of a second cubic function without using a graph, by finding the derivative, solving the quadratic equation that results from setting the derivative equal to zero, and finally testing the value of the second derivative.

An example of using the GeoGebra extension to ask the student to create a geometric construction, with marking and steps.

Dosage questions using percentages

Solving quadratic equations using a formula,

Factorising polynomials using the highest common factor.

Adapted from 'Factorisation' by Steve Kilgallon.

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.

Solve quadratic equations using formula.

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 $f(x,y)$.

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

This exercise will help you solve questions based on subduction zones using  the Cosine rule.