4 questions on using partial fractions to solve indefinite integrals.

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. 

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

Apply and combine logarithm laws in a given equation to find the value of $x$.

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 $x$:  $\log_{a}(x+b)- \log_{a}(x+c)=d$

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. 

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 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 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