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.

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.

This question shows how to ask for a number in scientific notation, by asking for the significand and exponent separately and using a custom marking algorithm in the gap-fill part to put the two pieces together.

Answers not in standard form, i.e. with a significand not in $[1,10)$, are accepted but given partial marks.

Information on inputting powers

Convert a variety of numbers from decimal to standard index form.

6 questions on standard statistical distributions.

Binomial, Poisson, Normal, Uniform, Exponential.

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.

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.

Given some random finite subsets of the natural numbers, perform set operations $\cap,\;\cup$ and complement.

Template question. The student is asked to perform a two factor ANOVA to test the null hypotheses that the measurement does not depend on each of the factors, and that there is no interaction between the factors.

Template question. The student is asked to perform a two factor ANOVA to test the null hypotheses that the measurement does not depend on each of the factors, and that there is no interaction between the factors.

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.

Given an equation or a worded formula determine if it is a function or not

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.

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

Given a geometric sequence, find the common ratio (negative in this question), write down the formula for the nth term and use it to calculate a given term.

Given the first four terms of a quadratic sequence, write down the formula for the $n^\text{th}$ term.

Given a formula for a sequence, calculate a given term.

Given the first three terms of a sequence, give a formula for the $n^\text{th}$ term.

In the first sequence, $d$ is positive. In the second sequence, $d$ is negative.

Given the first and last terms of a finite arithmetic sequence, calculate the number of elements and then the sum of the sequence.

Each part is broken into steps, with the formula given.

Factorise a quadratic expression of the form $x^2+akx+bk^2$ for $x$, in terms of $k$. $a$ and $b$ are constants.

Given the first few terms of an arithmetic sequence, write down its formula, then find a couple of particular terms.

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

Graphing exponentials with a base between 0 and 1 and no transformations take place.

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

Graphing $y=ab^x+c$

Graphing $y=ab^x+c$

A graph is drawn. A student is to identify the derivative of this graph from four other graphs. There are four version of this question: I: cubic, II: linear, III: quadratic, IV: sinusoisal.

A graph is drawn. A student is to identify the derivative of this graph from four other graphs. There are four version of this question: I: cubic, II: linear, III: quadratic, IV: sinusoisal.