Simon Thomas

Maximising the volume of a rectangular box

Problem on a closed cylindrical tank having minimum surface area

Rate of change problem involving velocity & acceleration

Turning points of a cubic function

Problem on a closed cylindrical tank having minimum surface area

Harder implicit differentiation requiring both chain rule and product rule.

Implicit differentiation.

Given $x^2+y^2+dxy +ax+by=c$ find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$.

Also find two points on the curve where $x=0$ and find the equation of the tangent at those points.

Implicit differentiation.

Given $x^2+y^2+ax+by=c$ find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$.

Match the question with the correct formula.

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Laplace of constants and powers of t

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Laplace transform of e^{at}

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Intorduces students to the definition of a function $f:A\mapsto B$ as a subset of the Cartesian product $A\times B$.

Introductory exercise about subsets using custom grading code.

Slightly harder introductory exercises about the power set.

Introductory exercise about power sets.

Introductory exercise about subsets using custom grading code.

Introductory exercise about set equality

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Converting a decimal number to binary.

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Converting Binary to Decimal

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Converting a number from binary to decimal.

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

Rearrange expressions in the form $ax^2+bx+c$ to $a(x+b)^2+c$.

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

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.

Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

Factorise a quadratic equation where the coefficient of the $x^2$ term is greater than 1 and then write down the roots of the equation

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.

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.