Solve a quadratic equation by completing the square. The roots are not pretty!

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. 

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. 

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

Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

set up x- and y axises.

set linear equations and solve the simulatenous equations.

set up x- and y axises.

set linear equations and solve the simulatenous equations.

A few quadratic equations are given, to be solved by completing the square. The number of solutions is randomised.

Some quadratics are to be solved by factorising

Questions to test if the student knows the inverse of fractional power or root (and how to solve equations that contain them). 

4 questions on using partial fractions to solve indefinite integrals.

Inverse and division of complex numbers.  Four parts.

Multiplication and addition of complex numbers. Four parts.

Multiplication and addition of complex numbers. Four parts.

Multiplication and addition of complex numbers. Four parts.

Solving three simultaneous congruences using the Chinese Remainder Theorem:

\[\begin{eqnarray*} x\;&\equiv&\;b_1\;&\mod&\;n_1\\ x\;&\equiv&\;b_2\;&\mod&\;n_2\\x\;&\equiv&\;b_3\;&\mod&\;n_3 \end{eqnarray*} \] where $\operatorname{gcd}(n_1,n_2,n_3)=1$

Differentiate $x^m\cos(ax+b)$

Differentiate the function $(a + b x)^m  e ^ {n x}$ using the product rule.

Solve an exponential equation for radioactivity

Solve an exponential equation

This exercise will help you solve equations of type ax-b = c.

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

Find the solution of a constant coefficient second order ordinary differential equation of the form $ay''+by'+cy=0$.

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.

Solve a simple linear equation algebraically. The unknown appears on both sides of the equation.

This question takes the student through variety of examples of quadratic inequalities by asking them for the range(s) for which $x$ meets the 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 for x and y on a given triangle and calculate the area

rebelmaths

Find the solution of a first order separable differential equation of the form $a\sin(x)y'=by\cos(x)$.