A question testing the application of the Cosine Rule when given three side lengths. In this question, the triangle is always acute. A secondary application is finding the area of a triangle.

A question testing the application of the Cosine Rule when given three side lengths. In this question, the triangle is always obtuse. A secondary application is finding the area of a triangle.

Two questions testing the application of the Sine Rule when given two angles and a side. In this question the triangle is obtuse. In one question, the two given angles are both acute. In the second, one of the angles is obtuse.

Two questions testing the application of the Sine Rule when given two sides and an angle. In this question, the triangle is always acute and one of the given side lengths is opposite the given angle.

A question testing the application of the Sine Rule when given two sides and an angle.  In this question the triangle is obtuse and the first angle to be found is obtuse.

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+(a^2+b^2)y=0,\;y(0)=1$ and $y'(0)=c$. 

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+a^2y=0,\;y(0)=c$ and $y(1)=d$.  (Equal roots example).

Complete the square for a quadratic polynomial $q(x)$ by writing it in the form $a(x+b)^2+c$.  Find both roots of the equation $q(x)=0$.

Solve for $x$ and $y$:  \[ \begin{eqnarray} a_1x+b_1y&=&c_1\\   a_2x+b_2y&=&c_2 \end{eqnarray} \]

The included video describes a more direct method of solving when, for example, one of the equations gives a variable directly in terms of the other variable.

Solve for $x$: $\displaystyle ax ^ 2 + bx + c=0$.

Entering the correct roots in any order is marked as correct. However, entering one correct and the other incorrect gives feedback stating that both are incorrect.

Solve for $x$: $\displaystyle 2\log_{a}(x+b)- \log_{a}(x+c)=d$. 

Make sure that your choice is a solution by substituting back into the equation.

Solve for $x$: $\displaystyle \frac{a} {bx+c} + d= s$

Solve $\displaystyle ax + b = cx + d$ for $x$.

Solve for $x$: $\displaystyle ax ^ 2 + bx + c=0$.

Solve for $x$: $\displaystyle \frac{a} {bx+c} + d= s$

Solve for $x$ and $y$:  \[ \begin{eqnarray} a_1x+b_1y&=&c_1\\   a_2x+b_2y&=&c_2 \end{eqnarray} \]

Solve $\displaystyle ax + b =\frac{f}{g}( cx + d)$ for $x$.

A video is included in Show steps which goes through a similar example.

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

In the first three parts, rearrange linear inequalities to make $x$ the subject.

In the last four parts, correctly give the direction of the inequality sign after rearranging an inequality.

This question tests the student's ability to solve simple linear equations by elimination. Part a) involves only having to manipulate one equation in order to solve, and part b) involves having to manipulate both equations in order to solve. 

Solve a linear equation of the form $ax+b = c$, where $a$, $b$ and $c$ are integers.

The answer is always an integer.

This question tests the students ability to factorise simple quadratic equations (where the coefficient of the x^2 term is 1) and use the factorised equation to solve the equation when it is equal to 0.

No description given

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.

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

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

Find the general solution of $y''+2py'+(p^2-q^2)y=x$ in the form  $Ae^{ax}+Be^{bx}+y_{PI}(x),\;y_{PI}(x)$ a particular integral.

rebelmaths

Find the solution of $\displaystyle x\frac{dy}{dx}+ay=bx^n,\;\;y(1)=c$

rebelmaths

Find the solution of $\displaystyle \frac{dy}{dx}=\frac{1+y^2}{a+bx}$ which satisfies $y(1)=c$

rebelmaths

Solve 4 first order differential equations of two types:$\displaystyle \frac{dy}{dx}=\frac{ax}{y},\;\;\frac{dy}{dx}=\frac{by}{x},\;y(2)=1$ for all 4.

rebelmaths

Rearranging equations by multiplying or dividing: One step

rebelmaths