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• Question

Customised for the Numbas demo exam

Motion under gravity. Object is projected vertically with initial velocity $V\;m/s$. Find time to maximum height and the maximum height. Now includes an interactive plot.

• Question in STAT7008

Given a random variable $X$  normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

• Question in STAT7008

Given a random variable $X$  normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

• Question in STAT7008

Given a random variable $X$  normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

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Add, subtract, multiply and divide algebraic fractions.

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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.

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

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

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More work on differentiation with trigonometric functions

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Chain rule

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Given a description in words of the costs of some items in terms of an unknown cost, write down an expression for the total cost of a selection of items. Then simplify the expression, and finally evaluate it at a given point.

The word problem is about the costs of sweets in a sweet shop.

• Question

A few simple functions are provided of the form ax, x+b and cx+d. Values of the functions, inverses and compositions are asked for. Most are numerical but the last few questions are algebraic.

• Question
The reduced masses are pre-calculated for this question and included in a list. It would be more elegant to program Numbas to permute atoms together to generate diatomic molecules while constraining the permutations to those which are chemically/physically reasonable, so as to allow calculation of each reduced mass directly from the atomic masses- but organising this with high computational efficiency might be a significant programing task (add to "to do" list).
• Question
The reduced masses are pre-calculated for this question and included in a list. It would be more elegant to program Numbas to permute atoms together to generate diatomic molecules while constraining the permutations to those which are chemically/physically reasonable, so as to allow calculation of each reduced mass directly from the atomic masses- but organising this with high computational efficiency might be a significant programing task (add to "to do" list).
• Curl and divergence of a vector field.  Determine whether the vector field is irrotational or solenoidal.

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No description given

• Question in Demos

Contains some extremely basic code to do symbolic differentiation: it can give the derivative of terms of the form $x^n$, $sin(x)$ and $cos(x)$, and apply the chain rule.

• TEST
Needs to be tested
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a
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Differentiation I
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Differentiation II