Inputting algebraic expressions into Numbas.

Find the stationary points of the function: $f(x,y)=a x ^ 3 + b x ^ 2 y + c y ^ 2 x + dy$ by choosing from a list of points.

Inputting the values given into the partial derivatives to see if 0 is obtained is tedious! Could ask for the factorisation of equation 1 as the solution uses this. However there is a problem in asking for the input of the stationary points - order of input and also giving that there is two stationary points.

Find the stationary points of the function: $f(x,y)=a x ^ 3 + b x ^ 2 y + c y ^ 2 x + dy$ by choosing from a list of points.

Inputting the values given into the partial derivatives to see if 0 is obtained is tedious! Could ask for the factorisation of equation 1 as the solution uses this. However there is a problem in asking for the input of the stationary points - order of input and also giving that there is two stationary points.

What is the value of the expression given a choice of n?

Intorduction to using the defnition to prove simple stamtements.

Converting into a ratio

Converting into a ratio

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

Split $\displaystyle \frac{ax+b}{(cx + d)(px+q)}$ into partial fractions.

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

Convert a height given in feet and inches into cm and then metres.

Putting algebraic fractions into their simplest forms

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.

Split $\displaystyle \frac{ax+b}{(cx + d)(px+q)}$ into partial fractions.

Evaluate $\int_0^{\,m}e^{ax}\;dx$, $\int_0^{p}\frac{1}{bx+d}\;dx,\;\int_0^{\pi/2} \sin(qx) \;dx$. 

Evaluate $\int_0^{\,m}e^{ax}\;dx$, $\int_0^{p}\frac{1}{bx+d}\;dx,\;\int_0^{\pi/2} \sin(qx) \;dx$. 

Inputting algebraic expressions into Numbas.

Inputting algebraic expressions into Numbas.

Inputting algebraic expressions into Numbas.

Inputting algebraic expressions into Numbas.

Inputting algebraic expressions into Numbas.

Inputting algebraic expressions into Numbas.

Putting algebraic fractions into their simplest forms

Demonstrates that the marking algorithm for "match text pattern" parts doesn't put quotes around substituted strings any more.

Substitute given values into formulas.

Evaluate $\int_0^{\,m}e^{ax}\;dx$, $\int_0^{p}\frac{1}{bx+d}\;dx,\;\int_0^{\pi/2} \sin(qx) \;dx$. 

Substitute given values into formulas.

$f(X)$ and $g(X)$ are polynomials over $\mathbb{Z}_n$.

Find their greatest common divisor (GCD) and enter it as a monic polynomial.

Hence factorize $f(X)$ into irreducible factors.

Factorising 5 to 7 digit numbers into a product of prime powers.

Uses the marking algorithms from question 1 of this CBA