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

Evaluate $\int_1^{\,m}(ax ^ 2 + b x + c)^2\;dx$, $\int_0^{p}\frac{1}{x+d}\;dx,\;\int_0^\pi x \sin(qx) \;dx$, $\int_0^{r}x ^ {2}e^{t x}\;dx$

Factorising basic quadratics into linear expressions

Factorising further basic quadratics into linear expressions

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

In this assignment, try and find the roots of a randomly generated polynomial, using the quadratic equation.

A test assignment to see if it integrates properly into Canvas.

A simple question to find the roots of a quadratic. Using to test integration of NUmbas into Canvas.

Substitute values into formulae for the area or volume of various geometric objects.

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A table showing how to substitute raw LaTeX code into question text.

NOTE: You probably don't want to do this! There's usually a more robust way, where you get Numbas to make the expression for you.

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

Shows how to create a simplified JME subexpression, and substitute it into a string variable.

Convert a fraction into a percentage

Convert Index form into an Ordinary number

Inputting algebraic expressions into Numbas. (Translation to German)

Manipulate fractions in order to add and subtract them. The difficulty escalates through the inclusion of a whole integer and a decimal, which both need to be converted into a fraction before the addition/subtraction can take place.

https://numbas.mathcentre.ac.uk/question/22664/addition-and-subtraction-of-fractions/ by Lauren Richards

Translated to German and Part d) added.

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.

Intorduction to proof and existence statements.

Factorise $x^2+bx+c$ into 2 distinct linear factors and then find $\displaystyle \int \frac{a}{x^2+bx+c }\;dx$ using partial fractions or otherwise.

Customised for the Numbas demo exam

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Video in Show steps.

Demonstration of adaptive marking: the student must first add up the number of apples to buy, then work out how much that would cost. Adaptive marking carries an incorrect number of apples into the cost calculation.

Students are given a line equation (where the coefficient of y is 1) and asked to rearrange it into gradient-intercept form.

Students need to substitute a value into an equation and solve it. The equation constant (gravity) and the value (time) are both randomised.

Substitute values into formulae for the area or volume of various geometric objects.

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.

Exercise using a given uniform distribution $X$, calculating the expectation and variance. Also finding $P(X \le a)$ for a given value $a$.

Splitting an algebraic fraction into partial fractions

rebelmaths

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

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.