Differentiate

\[ \sqrt{a x^m+b})\]

Differentiate $\displaystyle e^{ax^{m} +bx^2+c}$

Differentiate $\displaystyle \cos(e^{ax}+bx^2+c)$.

Contains a video solving a similar example.

The student must calculate the number of digits a given decimal number would have when written in a different base. Alternative answers catch some common mal-rules and give appropriate feedback.

Based on table 2 from "diagnosing student errors in e-assessment questions" by Philip Walker, D. Rhys Gwynllyw and Karen L. Henderson.

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Use the specific heat capacity of an object and the heat released to calculate the final temperature.

Custom marking used to allow for partial credit for common errors (mal rules)

Thermochemistry Revision Sheet Q7

Basic rules of derivatives

Use the specific heat capacity of an object and the change in temperature to calculate the heat added to that object.

Uses Custom marking to allow partial credit for common student errors (mal rules).

Thermochemistry Revision Sheet Q 5

Using BIDMAS rules to solve equations

Find the first 3 terms in the MacLaurin series for $f(x)=(a+bx)^{1/n}$ i.e. up to and including terms in $x^2$.

Find $\displaystyle \int \sin(x)(a+ b\cos(x))^{m}\;dx$

Integrate $f(x) = ae ^ {bx} + c\sin(dx) + px^q$. Must input $C$ as the constant of integration.

Find $\displaystyle \int (ax+b)\cos(cx+d)\; dx $ and hence find $\displaystyle \int (ax+b)^2\sin(cx+d)\; dx $ 

Find $\displaystyle \int x(a x ^ 2 + b)^{m}\;dx$

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.

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.

Find $\displaystyle\int \frac{ax+b}{(x+c)(x+d)}\;dx,\;a\neq 0,\;c \neq d $.

Integrating by parts.

Find $ \int ax\sin(bx+c)\;dx$ or $\int ax e^{bx+c}\;dx$ 

The derivative of $\displaystyle \frac{ax+b}{cx^2+d}$ is of the form $\displaystyle \frac{g(x)}{(cx^2+d)^2}$. Find $g(x)$.

The derivative of $\displaystyle \frac{a+be^{cx}}{b+ae^{cx}}$ is $\displaystyle \frac{pe^{cx}} {(b+ae^{cx})^2}$. Find $p$.

The derivative of  $\displaystyle \frac{ax+b}{\sqrt{cx+d}}$ is $\displaystyle \frac{g(x)}{2(cx+d)^{3/2}}$. Find $g(x)$.

The derivative of $\displaystyle \frac{ax^2+b}{cx^2+d}$ is $\displaystyle \frac{g(x)}{(cx^2+d)^2}$. Find $g(x)$.

Differentiate $\displaystyle e^{ax^{m} +bx^2+c}$

Find the first 3 terms in the Taylor series at $x=c$ for $f(x)=(a+bx)^{1/n}$ i.e. up to and including terms in $x^2$.

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

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

From mathcentre.ac.uk

Practice using the log rules to add and subtract logarithms